Physics: concepts and connections [Pearson new international edition, Fifth edition] 1292039582, 1269374508, 9781292039589, 9781269374507, 9781292053615, 1292053615

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Physics: Concepts and Connections Hobson

9 781292 039589

5e

ISBN 978-1-29203-958-9

Physics: Concepts and Connections Art Hobson Fifth Edition

Pearson New International Edition Physics: Concepts and Connections Art Hobson Fifth Edition

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners.

ISBN 10: 1-292-03958-2 ISBN 10: 1-269-37450-8 ISBN 13: 978-1-292-03958-9 ISBN 13: 978-1-269-37450-7

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America

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Table of Contents Glossary Art Hobson

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1. The Way of Science: Experience and Reason Art Hobson

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Problem Set (5/e): The Way of Science: Experience and Reason Art Hobson

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2. Atoms: The Nature of Things Art Hobson

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Problem Set (5/e): Atoms: The Nature of Things Art Hobson

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3. How Things Move: Galileo Asks the Right Questions Art Hobson

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Problem Set (5/e): How Things Move: Galileo Asks the Right Questions Art Hobson

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4. Why Things Move as They Do Art Hobson Problem Set (5/e): Why Things Move as They Do Art Hobson

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5. Newton’s Universe Art Hobson

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Problem Set (5/e): Newton’s Universe Art Hobson

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6. Conservation of Energy: You Can’t Get Ahead Art Hobson

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Problem Set (5/e): Conservation of Energy: You Can’t Get Ahead Art Hobson

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7. Second Law of Thermodynamics Art Hobson

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Problem Set (5/e): Second Law of Thermodynamics Art Hobson

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8. Electromagnetism Art Hobson

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Problem Set (5/e): Electromagnetism Art Hobson

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9. Waves, Light, and Climate Change Art Hobson

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Problem Set (5/e): Waves, Light, and Climate Change Art Hobson

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10. The Special Theory of Relativity Art Hobson

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Problem Set (5/e): The Special Theory of Relativity Art Hobson

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11. Einstein’s Universe and the New Cosmology Art Hobson

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Problem Set (5/e): Einstein’s Universe and the New Cosmology Art Hobson

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12. The Quantum Idea Art Hobson

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Problem Set (5/e): The Quantum Idea Art Hobson

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13. The Quantum Universe Art Hobson

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Problem Set (5/e): The Quantum Universe Art Hobson

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14. The Nucleus and Radioactivity: A New Force Art Hobson

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Problem Set (5/e): The Nucleus and Radioactivity: A New Force Art Hobson

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15. The Energy Challenge

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Problem Set (5/e): The Energy Challenge Art Hobson

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16. Fusion and Fission—and a New Energy Art Hobson

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Problem Set (5/e): Fusion and Fission—and a New Energy Art Hobson

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17. Quantum Fields: Relativity Meets the Quantum Art Hobson

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Problem Set (5/e): Quantum Fields: Relativity Meets the Quantum Art Hobson

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18. Summing Up Art Hobson

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Periodic Table of the Elements Art Hobson

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Flow Chart of Topics Art Hobson

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Index

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GLOSSARY A-bomb See fission bomb. AC See alternating current. accelerating universe Observations of distant supernova explo-

sions show rather conclusively that the universe is not only expanding but is expanding at an ever-increasing speed. acceleration An accelerated object is one whose velocity is changing. Quantitatively, the acceleration is the change in velocity during a time interval divided by the duration of that time interval. It can be measured in (km/hr)/s, or in (m>s)>s = m>s2. acceleration due to gravity The acceleration of any freely falling object. On Earth this is about 10 m>s2 or, more precisely, 9.8 m>s2. action-reaction cycle A mutually reinforcing cycle of increased armaments by two or more hostile nations. active solar energy Energy provided by a solar-heated liquid or gas that is pumped to a location where it can be used for space or water heating. air A mixture of several chemical compounds: nitrogen (N2, about 80%), oxygen (O2, about 20%), argon (Ar, about 1%), and a smattering of trace gases. air resistance The resistive force that air molecules exert on an object moving through the air. alpha decay One type of radioactive decay. The spontaneous emission, by a nucleus, of an alpha particle (a helium nucleus that breaks off of a larger nucleus). alpha particle See alpha decay. alpha rays, beta rays, gamma rays The streams of particles that are emitted by a macroscopic sample of radioactive material. alternating current An electric current that reverses its direction of flow many times every second. amp or ampere The measurement unit for electric current. One amp is defined as a flow of 1 coulomb per second. amplitude The maximum disturbance in a wave; the maximum deviation from the undisturbed state of the medium. anthropic principle The idea that our universe must be organized in the way that it is because any other organization would not allow intelligent beings to be here to ask the question in the first place. antielectron See positron. antimatter Made of antiprotons, antineutrons, and positrons. Today’s universe consists overwhelmingly of matter, not antimatter. antineutron Antiparticle of the neutron. See also antiparticle. antiparticle The theory of special relativity requires that for every existing type of particle, there is an antiparticle carrying the opposite charge. Quantum uncertainties allow the creation and annihilation of particle–antiparticle pairs such as electron–positron pairs. antiproton Antiparticle of the proton. See also antiparticle. Aristarchus’s hypothesis A sun-centered theory that was rejected because it seemed to conflict with everyday observations. Aristotelian physics, difficulties Contrary to Aristotelian predictions, heavy and light objects often fall at the same acceleration, and horizontally moving objects would move forever if there were no external forces.

Aristotle’s physics

Plausible notions that have since been discarded by both Newtonian and modern physics. Aristotle believed that there were three kinds of motion: natural, violent, and celestial. artificial radiation Ionizing radiation from artificial sources such as medical sources. See also natural radiation. astrology The belief, rejected by science for over two centuries, that events on Earth are influenced by the positions and motions of the planets. astronomy The scientific study of the stars and other objects in space. atom See chemical element. atomic bomb See fission bomb. atomic number The number of protons in an atom. Also the number of electrons in a neutral atom. An atom’s atomic number determines its chemical properties and the element to which it belongs. atomic theory of matter All matter is made of tiny particles, too small to be seen. atomism The notion that nature can be reduced to the motion of tiny material particles. average speed An object’s average speed is its distance traveled during a time interval divided by the duration of that time interval. Measured in meters per second. See also instantaneous speed. beta decay

The other main type of radioactive decay. The spontaneous emission, by a nucleus, of a beta particle (an electron created in the nucleus). See also alpha decay. beta particle See beta decay. beta rays See alpha rays. big bang The event some 14 billion years ago that created time, space, matter, and the different forms of energy, and started the expansion of the universe. biofuel Biomass (organic substances) that has been processed to make transportation or other fuels. biology and the second law of thermodynamics The entropy of a growing plant decreases at the expense of a far greater entropy increase in the absorbed and reradiated solar energy that passes through the plant. A similar situation exists for all biological processes, including the evolution of species. biomass energy The chemical energy of organic substances. bit See quantum computer. black hole Any object whose matter (mass) has gravitationally collapsed into a single point. Nothing can escape from its vicinity. When very massive stars run out of fuel, they explode, and the remnant collapses to become a black hole. Giant black holes exist at the centers of most galaxies, including ours. breeder reactor A reactor that creates more than one 239Pu nucleus (from 238U) for each 235U nucleus it fissions and so creates more fuel than it uses. Brownian motion The erratic motion of a microscopic dust or pollen grain immersed in a liquid or gas, caused by numerous moving atoms or molecules colliding with the grain every second. bubble chamber See cloud chamber. burning This chemical reaction creates warmth by combining oxygen from air with a fuel such as carbon or hydrogen.

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GLOSSARY C See coulomb. Calorie The amount of work (or energy) needed to raise the

temperature of 1 kilogram of water by 1°C. cap and trade See carbon cap and trade. carbon cap and trade One suggested way to incorporate the cost of global warming into the cost of products and thus reduce CO2 emissions. An overall limit (cap) would be placed on total carbon emissions, and “tradable permits” to emit a certain amount of CO2 (adding up to the allowed cap) would be issued to carbon-emitting companies. Companies could buy and sell permits among themselves, so that less efficient companies would be able to buy additional permits from more efficient companies. carbon capture and storage The process of capturing CO2 from fossil-fuel-fired generating plants, compressing it, piping it to a storage facility, and permanently storing it underground. carbon dating A radioactive dating method in which radioactive 14C in a dead organism is measured as a fraction of the total carbon in order to determine how long the 14C has been decaying and when the organism died. carbon tax One suggested way of incorporating the cost of global warming into the cost of products and thus reducing CO2 emissions. Companies would be taxed a certain amount for each tonne of CO2 they emit. cellulosic biomass Biomass from non-edible organic materials such as grasses, paper products, wood, agricultural waste, and municipal solid waste. centimeter (cm) One-hundredth of a meter. centrifuge separation One way, widely used today, to enrich uranium. See also uranium enrichment. CFC See chlorofluorocarbons. chain reaction A series of neutron-induced fission reactions that proceed from one nucleus to the next by means of the neutrons released during each fission reaction. charge See electrically charged object. chemical compound A pure substance that can be chemically decomposed. Its smallest particle is a molecule, two or more atoms connected into a single unit. All of a compound’s molecules are identical. chemical decomposition Any process that changes a single substance into two or more other substances. chemical element One of the approximately 116 different substances that cannot be chemically decomposed. An atom whose nucleus has a specific atomic number (number of protons), regardless of how many neutrons it might have. The elements are listed in the periodic table. An atom is the smallest particle of an element. chemical energy Energy due to molecular structure. chemical origin of life See hypothesis of a chemical origin of life. chemical reaction A rearrangement of the atoms in molecules into new molecular forms. For examples, see burning, respiration, and photosynthesis. chemically inert Does not participate readily in chemical reactions. chemistry The study of the properties and transformations of substances (chemical compounds). Chernobyl Site of world’s worst nuclear power accident. The fuel melted down, the reactor suffered a “slow nuclear explosion,” and a large amount of radioactivity escaped. A few tens of people were killed from short-term effects, and about 4000 are expected to die of long-term cancers. See also meltdown.

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chlorofluorocarbons (CFCs)

Chemicals whose molecules are made of chlorine, fluorine, and carbon. Manufactured as coolants, spray propellants, foaming agents, and solvents. They destroy stratospheric ozone. climate model Computer calculations based on accepted principles of physics, chemistry, and other science that predict climatic conditions on Earth’s surface and throughout the atmosphere for many years into the future, at each point of a three-dimensional grid of points separated by several hundred kilometers. closed universe See geometry of the universe. cloud chamber A device that shows the path of a charged particle as a trail of droplets in water vapor. Its successor, the bubble chamber, shows a particle’s path as a trail of bubbles in a liquid. cogeneration The simultaneous production of electricity and useful thermal energy. collapse of a wave packet The instantaneous reduction in the size of a wave packet that occurs when a particle’s position is measured. See also wave packet. combined heat and power See cogeneration. compact fluorescent bulb See fluorescent bulb. conduction electrons The outermost one or two electrons in the atoms of any metal. These electrons move easily through the metal when subjected to even a small electric force. conductor See electrical conductor. conservation of charge See law of conservation of charge. conservation of energy See law of conservation of energy. conservation of matter The total amount of matter involved in any chemical reaction, or in any other physical process, is the same after the reaction as it was before. Although it is a useful principle, experiments have proved that it is only a useful approximation in chemical reactions, and entirely wrong in many other situations. conservation of momentum See law of conservation of momentum. constructive interference See interference. containment dome See nuclear power reactor. continuous spectrum A spectrum containing a continuous range of frequencies. See also spectrum. control rods See nuclear power reactor. coolant See nuclear power reactor. Copernican revolution The rejection of the idea that Earth is at the center of, and therefore basically different from, the rest of the universe. Copernican viewpoint The view that Earth is not a unique place in the universe, that the same principles of nature apply throughout the universe. For example, since intelligent life occurred here, this view argues that it also should have occurred elsewhere. Copernicus’s theory A sun-centered theory, similar to Aristarchus’s. The planets, including Earth, circle the sun, and Earth spins on its axis. cosmic inflation A widely respected hypothesis of the details of how the big bang occurred. According to this hypothesis, during a short period in the very early universe, the universe expanded enormously at a speed greater than lightspeed. This “inflation” stretched the universe to many times the size it had before the inflationary process began, flattening the geometry of the universe and creating the mass and energy observed today.

GLOSSARY cosmic microwave background

The faint microwave remnant of the high-energy radiation from the big bang that still fills the universe. cosmic rays High-energy particles that travel through outer space. cosmology The study of the origin, structure, and evolution of the large-scale universe. coulomb Abbreviated “C.” The metric measurement unit for electric charge. It’s the amount of charge that causes an electric force of 9 * 109 N on an identical charge at a distance of 1 m. It turns out to be the charge on 6.25 * 1018 electrons. Coulomb’s law of the electric force Between any two small charged objects there is a force that is repulsive if both objects have positive charge or if both have negative charge, and is attractive if one has positive and the other has negative charge. This force is proportional to the amount of charge on each object, and proportional to the inverse of the square of the distance between them. In symbols it is F r q1q2>d2. If charge is measured in coulombs and distance in meters, then the force in newtons is given by F = 9 * 109 q1q2>d2. creation and annihilation See antiparticle. creationism The belief that the Bible’s Old Testament can be read literally as scientific and historical truth and that Earth and the biological organisms, including humans, were created separately just a few thousand years ago. Scientists overwhelmingly reject creationism as pseudoscientific and false. critical mass The minimum amount of fissionable material that will sustain a chain reaction. curved space See gravity and warped space. dark energy

Observations show that the universe is filled with a nonmaterial form of energy that pushes outward on the fabric of space, causing it to accelerate in its outward expansion. The properties and the cause of this energy are not understood. It comprises 73% of the energy (and therefore 73% of the mass) of the universe. dark matter Also known as “exotic dark matter,” this is matter that does not interact with electromagnetic radiation and so does not emit, absorb, or reflect light. It is made of entirely new and unknown forms of matter. Dark matter comprises 23% of the universe’s mass (and therefore 23% of its energy), while other forms of matter (stars, planets, gas, black holes, neutrinos) comprise 4%. daughter nucleus The nucleus that remains after a radioactive decay has occurred. DC See direct current. decarbonization Replacement of high-carbon fossil fuels such as coal with lower-carbon fuels such as natural gas, and with zero-carbon fuels such as solar energy, nuclear power, and hydrogen gas generated from nonfossil energy. decay curve A graph of the amount of a radioactive material remaining, versus time. degrees Celsius See temperature. destructive interference See interference. difficulties with Aristotelian physics See Aristotelian physics, difficulties. direct current An electric current that maintains the same direction. dirty bomb A bomb powered with conventional explosions that does its damage primarily by the dispersal of radioactive materials. One of the possible forms of nuclear terrorism.

double-slit experiment with electrons When an electron beam passes through two narrow slits and strikes a viewing screen, an interference pattern is observed. This demonstrates that an electron beam is a wave. The same phenomenon occurs with a proton beam, neutron beam, and other beams of matter. double-slit experiment with light When single-frequency light from two synchronized sources such as two narrow slits strikes a viewing screen, an interference pattern is observed. This demonstrates that light is a wave. doubling time See exponential growth. d-quark See strong force. drift velocity The average forward speed of a typical electron along a wire in an electric current, typically less than 1 mm/s. dualism Descartes’ idea that there are two realities, physical and spiritual. In the physical realm, the real or primary qualities are objective, impersonal phenomena such as the motion of atoms. Human sense impressions are considered to be secondary qualities, caused by the primary qualities. E = mc2 See principle of mass-energy equivalence. efficiency See transportation efficiency, heat engine, and

energy efficiency. Energy due to the ability of a deformed system to snap back. electric circuit A closed loop around which electric current can flow. electric charge See electrically charged object. electric current A flow or motion of electrically charged particles. Electric currents in wires are due to electrons moving along the wire. electric discharge See excite. electric (or electromagnetic) energy The energy that an electrically charged object has due to its position in an electromagnetic field. electric field Exists wherever a charged object would feel an electric force if such an object were present. electric force The electric part of the electromagnetic force. See also electromagnetic force. electric force law Electrically charged objects exert forces on each other at a distance. Like charges repel each other, and unlike charges attract each other. electric force law (field version) An electric field surrounds every charged object. Charged objects feel electric forces whenever they are placed in an electric field. electric generator See steam-electric power plant. electric vehicle (EV) Vehicle powered by a storage battery that is recharged by plugging into a wall socket. Nonpolluting, provided that the electricity comes from an environmentally friendly source. electrical conductor A material (usually a metal) through which electric current can easily flow. The atoms of these materials have one or two outermost electrons that are only loosely attached. electrical insulator A material that doesn’t permit the easy flow of electric current. The atoms of these materials have firmly attached outermost electrons. electrical resistance See resistance. electrically charged (in quantum electrodynamics) See quantum electrodynamics. electrically charged object Any object that can exert or feel the electric force is said to “contain electric charge.” There are two elastic energy

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GLOSSARY

types of charge, positive and negative. Any process that causes an object to gain a net positive or negative charge is called charging. electromagnetic energy See electric energy. electromagnetic field The effect that electrically charged objects have on the surrounding space. An electromagnetic field fills the space around every electrically charged object and exists everywhere that a charged object would feel an electromagnetic force if such an object were present. Light is a wave in an electromagnetic field. electromagnetic force The total (electric and magnetic) force between charges. electromagnetic radiation Any electromagnetic wave. electromagnetic spectrum The complete range of electromagnetic waves. Divided into the radio, infrared, visible, ultraviolet, X-ray, and gamma-ray regions. electromagnetic wave See electromagnetic wave theory of light. All of the following are electromagnetic waves: radio, infrared, light, ultraviolet, X-rays, gamma rays. electromagnetic wave theory of light Every vibrating charged object creates a disturbance in its own electromagnetic field, which spreads outward through the field at 300,000 km/s. Light is just such an electromagnetic wave. electromagnetism The combined effects of electric and magnetic forces. electron One of the fundamental particles. A point particle (so far as we know today) having negative charge, about 2000 times less massive than a proton. electron field The quantized matter field for electrons and positrons. See also matter field. electron microscope Uses electron matter waves to form images of microscopic objects. See also wave theory of matter. electron–positron pair See antiparticle. electroweak force The combined EM and weak forces. The quanta (or exchange particles) of the electroweak force field are photons, W + , W - , and Z particles. The quanta of the electroweak matter field are electrons and electron-neutrinos. In addition, there are two more electroweak matter fields corresponding to a second and third generation of particles: the muon and its neutrino and the tau and its neutrino. Only the first generation is stable and contributes to ordinary matter. The other two generations are unstable and transmute quickly into other particles. electroweak force field See electroweak force. electroweak matter field See electroweak force. element See chemcial element. EM field See electromagnetic field. emission of radiation by an atom Atoms emit radiation when they quantum-jump to a lower energy level, creating and emitting a photon whose energy equals the difference between the two energy levels. energy The capacity to do work. The energy of a system is the amount of work the system can do. Units: joule (J), Calorie, kilowatt-hour (a power of 1000 watts operating for 1 hour). See also work. energy conservation Measures to reduce energy consumption, including both efficiency measures to save energy while providing the same services and switching to less energy-intensive lifestyles. See also energy efficiency. energy efficiency Useful energy output of a device divided by its total energy input. See also heat engine.

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energy flow diagram A diagram showing the energy transformations occurring during some process, with energy pictured as though it were a liquid flowing through pipes. energy fluctuations See vacuum. energy level The precise, predictable energy an atom has when it is in a particular quantum state. energy-level diagram A diagram showing the collection of possible energy levels for an atom. energy resource A natural resource containing useful energy. The major U.S. resources today are shown in Table 1. A resource is renewable if it can be replaced within a human lifetime; otherwise it is nonrenewable. enrichment See isotope separation. entropy A quantitative measure of a system’s microscopic disorganization. equivalence principle No experiment performed inside a closed room can tell you whether you are at rest in the presence of gravity or accelerating in the absence of gravity. ether See ether theory. ether theory The idea that a nonatomic, continuous, material medium, the ether, fills the entire universe and that light waves are waves traveling through this medium. This theory was rejected after 1905 because it contradicted Einstein’s theory. Philosophically, this amounts to a rejection of the idea that every physical thing is made of a material substance, because light waves are physical but not made of matter. exchange particle In quantum field theory, forces between two particles A and B are exerted by means of other particles, called exchange particles, that pass back and forth between A and B. For example, the electromagnetic force is exerted by exchanging photons. excite We excite one or more atoms whenever we cause them to go into an excited state; this generally causes the atom(s) to emit radiation. A gas can be excited by heating and by electric discharge—an electric current flowing through it. See also excited state and ground state. excited state Any quantum state of an atom having an energy higher than the lowest possible energy. See also ground state. exhaust See heat engine. exhaust temperature See heat engine. expansion of the universe The general theory of relativity predicts that the universe’s three-dimensional space must either expand or contract. Observations show that expansion is, in fact, occurring, as evidenced by the fact that distant galaxies are all moving away from us and from each other. experiment See observation. exponential growth Growth by a fixed percentage in each unit of time. It has a fixed doubling time, related to its fixed percentage growth rate by T L 70>P. external combustion engine See steam-electric power plant. Faraday’s law When a wire loop is placed in the vicinity of a magnet, and when either the loop or the magnet is moved, an electric current is created within the loop for as long as the motion continues. Stated in terms of fields, a changing magnetic field creates an electric field. feedback Any effect that further influences the phenomenon that caused it. Negative feedback diminishes its cause, and positive feedback enhances its cause. field A physical entity that is spread throughout a region of space. See also force field and matter field.

GLOSSARY field view of reality The view that the universe is made of fields, subject to the rules of relativity and quantum physics. fission bomb, or atomic bomb (A-bomb) A bomb that gets its energy from a fission chain reaction. The fuel can be either the uranium isotope 235U or plutonium. In the 235U bomb, the design can be as simple as bringing two subcritical masses together to equal or exceed a critical mass. If the bomb contains Pu, a subcritical mass is made critical by squeezing it to high density. fission fragment One of the two pieces that results from the fissioning of a nucleus. flat universe See geometry of the universe. fluorescent bulb In this device, an electric current flows through a gas that fills the bulb, exciting the gas to emit ultraviolet radiation, which is then absorbed by a phosphor coating inside the glass bulb causing the coating to emit light. New highfrequency compact fluorescent bulbs, in which the current oscillates much more frequently than the normal 60 Hz, have recently been developed for increased efficiency. force A body exerts a force on another body whenever the first body causes the second body to accelerate. A force is an action by one body on another; it is not a thing or a property of a body. Every force is similar to a push or a pull. force diagram A diagram that shows all of the individual forces acting on an object. Each force is shown as an arrow pointing in the direction of that force. force field The effect that the source of a force has on the surrounding space. Examples include gravitational fields and electromagnetic fields, which exist everywhere an object would feel, respectively, a gravitational or electromagnetic force if such an object were present. force of gravity The downward pull by Earth on objects in Earth’s vicinity; the pull that every material (i.e., having mass) object exerts on every other material object. See also Newton’s law of gravity. force pair The two forces that two bodies exert on each other. forms of energy See kinetic energy, gravitational energy, elastic energy, thermal energy, electromagnetic energy, radiant energy, chemical energy, and nuclear energy. fossil fuels Combustible fuels, including coal, oil, and natural gas, that store the chemical energy created by millions of years of accumulating layers of energy-rich plant and animal remains. four fundamental forces The gravitational, electromagnetic, strong, and weak forces. free fall Falling that is influenced only by gravity and not by air resistance or other influences. For an object that starts from rest and then falls freely to Earth, speed is proportional to the time, and distance is proportional to the square of the time. These proportionalities are also correct for any motion that starts from rest and maintains an unchanging acceleration in a straight line. See also weightlessness. frequency The number of vibrations that any part of a medium completes in each second as a wave passes through the medium. Also the number of complete wavelengths sent out by the wave source in each second. Higher-frequency waves have shorter wavelengths and (assuming equal amplitudes) higher energies. See also medium. friction The force that one surface exerts on another due to the roughness of the surfaces.

fuel cell See fuel cell vehicle. fuel cell vehicle Vehicle powered by hydrogen (or a hydrocar-

bon fuel such as methane) that is continuously injected into a “fuel cell,” a battery-like device that converts the chemical energy of the hydrogen directly into electricity that then runs the car. It is highly efficient and nonpolluting if the hydrogen is produced in an environmentally friendly way. fundamental forces See four fundamental forces. fusion bomb, or hydrogen bomb (H-bomb) A bomb that gets its energy from the fusion of hydrogen, triggered by a fission bomb. fusion reactor A nuclear power reactor that obtains its thermal energy from fusion rather than fission. Now under development, it might be commercially viable by the middle of the century. galaxy A large aggregation of stars. Most galaxies, such as our own Milky Way, have a disklike, pizza shape and revolve about their centers. Galilean relativity The intuitive theory of relativity, in which time and space are absolute (in other words, different observers measure the same time intervals and the same distances) and light has different speeds relative to different reference frames. See also reference frame. Galileo’s law of falling Neglecting air resistance, any two objects dropped together will fall together, regardless of their weights or shapes or substances of which they are made. gamma ray See alpha rays, beta rays, gamma rays. gamma-ray photon High-energy photons coming from nuclear and other processes. They often accompany alpha decay and beta decay. gas See three states of matter. gas pressure The outward push caused by gas molecules hitting the walls of a container. gasoline-electric hybrid vehicle Vehicle powered by a small gasoline engine that continuously runs an electric generator that energizes a small storage battery. The battery then runs the car, much as in an electric vehicle. It is highly efficient and thus creates little pollution. general theory of relativity Einstein’s theory based on the principle of equivalence. In this theory, gravity is a consequence of the warping of spacetime by masses. This theory applies to accelerated observers; the special theory of relativity applies only to nonaccelerated observers. generation See electroweak force. geological ages The major eras in Earth’s history, as determined by the differing layers of rock characterizing those eras. Some approximate ages, determined by several radioactive and other methods, are: Earth, 5 billion years; life, nearly 4 billion years; humans, 6 million years. geometry of the universe According to general relativity, the large-scale structure of the three-dimensional universe must have one of three possible shapes: A closed universe bends back on itself to form a three-dimensional space that is analogous to the two-dimensional surface of a sphere; it has a finite total volume. A flat universe has no overall large-scale curvature, and is analogous to a flat two-dimensional surface; it has infinite total volume. An open universe is analogous to a two-dimensional saddle-shaped surface; it has an infinite total volume. geothermal energy The thermal energy of hot underground steam, water, or rock.

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GLOSSARY global warming

The additional greenhouse-effect warming of Earth that is caused by fossil-fuel use, deforestation, and other human activities. gluon The exchange particle of the strong force. Gluons have zero mass and travel at lightspeed. See also exchange particle. grand unified theory A quantum field theory that would unify the standard model’s electroweak and strong forces into a single force, much as the EM force and weak force were unified into a single electroweak force. Although the parallels between the theories of the electroweak and strong forces suggest that such a theory should exist, there is as yet no agreed-on grand unified theory. gravitational collapse Dispersed matter drawing itself together because of gravity. gravitational energy Energy due to gravitational forces: GravE = weight * height. gravitational field The force field that surrounds every particle having mass and that is felt by every particle having mass. gravitational force See force of gravity. graviton The quantum of the quantized gravitational field, predicted but not yet observed. It is predicted to move at lightspeed and have zero mass. gravity See force of gravity. gravity and warped space Gravity bends light beams, so gravity must warp, or curve, spacetime. In the general theory of relativity, gravity is the warping of spacetime caused by masses. Greek atom See models of the atom. Greek model of the atom This model pictures the atom as a tiny indestructible object, like a small and rigid pea. greenhouse effect The warming created by Earth’s surrounding blanket of atmospheric gases. greenhouse gas The atmospheric gases, mostly water vapor and carbon dioxide, that cause the greenhouse effect. ground state The quantum state of the atom having the lowest possible energy. See also excited state. growth rate See exponential growth. half-life

The time during which half of a macroscopic amount of a radioactive isotope will decay. H-bomb See fusion bomb. heat engine Any cyclic device that uses thermal energy to do work. Its energy efficiency, the fraction of its input thermal energy that is converted to work, will be higher if the input temperature is higher and the exhaust temperature is lower. The portion of the input energy that is not converted to work is called the exhaust. heating The spontaneous flow of thermal energy from a highertemperature object to a lower-temperature object. Heisenberg uncertainty principle See uncertainty principle. hertz (Hz) The unit of frequency: 1 Hz = 1 vibration>second. See also frequency. Higgs field The standard model requires this field because without it all the particles of the standard model would need to have zero mass. However, there is as yet no direct evidence for this field. Its quanta, called Higgs particles, are currently sought in high-energy accelerators. The Higgs field is predicted to pervade the universe, interacting even with isolated particles. This interaction acts on accelerated particles in such a way as to resist their acceleration. Thus the Higgs field could be the reason that some of the fundamental particles have mass.

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high-level nuclear waste Used reactor fuel rods containing highly radioactive fission products. highly enriched uranium Uranium that has been enriched to about 90% 235U, which is suitable for nuclear weapons use. See also isotope separation. Hiroshima and Nagasaki The Japanese cities that were fissionbombed near the end of World War II. hybrid vehicle See gasoline-electric hybrid vehicle. hydroelectric energy The gravitational energy of raised water. hydrogen bomb See fusion bomb. hypothesis An educated suggestion or guess, a tentative theory. Hz See hertz. Industrial Revolution

The onset of the fossil-fueled industrial age, around 1750. inertia A body’s ability to stay at rest or to maintain an unchanging speed and direction of motion whenever no force is exerted on it. Quantitatively, a body’s inertia is its degree of resistance to acceleration when a force is exerted on it. infrared radiation Created by the thermal motion of molecules. Not visible to the human eye. input temperature See heat engine. instantaneous speed (speed) The average speed during a time interval that is so short that the speed hardly changes. Speedometers measure this. Measured in meters per second. See also average speed. insulator See electrical insulator. intelligent design The view that life is too complex in certain regards, such as complex cellular structures, to have evolved by Darwinian processes and that they must have therefore been created by an “intelligent designer.” Its key idea is that complex structures could not evolve through intermediate nonfunctional steps. Scientists overwhelmingly reject intelligent design as pseudoscientific and false. Intergovernmental Panel on Climate Change (IPCC) Thousands of cooperating international scientists who, on the basis of their study of the scientific literature, reported their conclusions regarding the causes and implications of global warming. Their reports, regarded as the scientific consensus on this topic, were issued in 1990, 1995, 2001, and 2007. internal combustion engine A heat engine in which burning occurs within the hot gases that push directly on mechanical parts, such as a piston, to provide useful work. ion Any atom having an excess or deficiency of electrons. ionizing radiation Radiations (including electromagnetic radiation but also material radiations from radioactive materials) having sufficient energy to ionize biological molecules. Includes higher alpha rays, beta rays, gamma rays, X-rays, and higherenergy ultraviolet rays. The biological damage is measured in a unit called the sievert. A millisievert (mSv) is one-thousandth of a sievert. The main types of damage are radiation sickness, mutation, and cancer. IPCC See Intergovernmental Panel on Climate Change. irreversibility The second law implies that most processes are irreversible, for example, that physical systems proceed spontaneously toward states of higher entropy and will not proceed spontaneously in the reverse direction. This principle is responsible for the difference between forward and backward in time. isotope A particular type of nucleus, having a particular number of protons and of neutrons. Isotopes are specified by their

GLOSSARY

atomic number (number of protons) and mass number (total protons and neutrons). A symbol like 146C represents an isotope with atomic number 6 and mass number 14. isotope separation, or enrichment, of uranium Any process that increases the percentage of 235U relative to 238U. One method is by use of spinning centrifuges. Weapons-grade uranium is highly enriched to about 90% 235U. joule (J)

The metric unit of energy. See also work.

Kepler’s theory

The theory that the planets orbit the sun in ellipses with the sun at one focus. This theory agrees with Brahe’s observations. kg See kilogram. kilo- (k) Prefix meaning one thousand. kilogram (kg) A unit of mass. The mass (or inertia) of the object known as a standard kilogram. Any object that has the same inertia as the standard kilogram has a mass of 1 kilogram. kilometer (km) One thousand meters. kiloton The amount of energy that would be released in the explosion of one thousand tons of TNT. kilowatt-hour See energy. 1 kinetic energy Energy due to motion: KinE = A 2 B mv2. Lamb shift

A small change in the energy levels of the hydrogen atom that is caused by vacuum energy fluctuations in the space surrounding the atom. Large Hadron Collider (LHC) Currently the world’s largest particle accelerator. It accelerates two narrow beams of protons in different directions around a circular ring 27 km long lying 100 m underground near Geneva, Switzerland. The beams collide to create many kinds of particles and phenomena. Each collision has an energy of 14 trillion electron-volts. law See theory. law of conservation of charge Although charge can be moved around and although charged particles can be created or destroyed, no net charge (positive minus negative) can be created or destroyed. law of conservation of energy The total energy of the participants in any process must remain unchanged throughout that process. There are no known exceptions. law of conservation of momentum The total momentum of any system remains unchanged, regardless of interactions among the system’s parts, so long as no part of the system is acted upon by forces external to that system. law of entropy See second law of thermodynamics. law of force pairs Forces always come in pairs: Whenever one body exerts a force on a second body, the second exerts a force on the first. The two forces are equal in strength but opposite in direction. law of heat engines See second law of thermodynamics. law of heating See second law of thermodynamics. law of inertia A body that is subject to no external forces maintains an unchanging velocity (or remains at rest). length contraction See relativity of space. LHC See Large Hadron Collider. light clock A clock whose timekeeping is based on the motion of a light beam.

lightspeed 300,000 km/s, or 3 * 108 m>s. light-year The distance that light travels in one year. limitations of Newtonian physics Newtonian physics gives

incorrect predictions for fast-moving objects (near lightspeed), strong gravitational forces or large distances (intergalactic), and small objects (atomic dimensions). Special relativity, general relativity, and quantum physics, respectively, do give correct predictions for each of these three classes of phenomena. line spectrum A spectrum that contains only separated precise frequencies. See also spectrum. linear growth Straight-line growth; it increases by the same amount (rather than the same percentage) in each unit of time. liquid See three states of matter. macroscopic

Big enough to be visible to the naked eye. See also

microscopic. magnetic field

Exists everywhere a moving charged object would feel an electric force if such an object were present. magnetic force See magnetic force law. magnetic force law Charged objects that are moving exert and feel an additional force, called the magnetic force, in addition to the electric force that exists when they are at rest. magnetic force law (field version) A magnetic field surrounds every moving charged object. Moving charged objects feel magnetic forces whenever they are placed in a magnetic field. magnetic poles The ends of a permanent magnet. There are two types, north and south; like poles repel, and unlike poles attract. Manhattan Project The U.S. project during World War II to build fission bombs. mass A body’s mass is its amount of inertia and also (for bodies at rest) its quantity of matter. We find a body’s mass in kilograms by comparing its inertia with the inertia of a standard kilogram placed at rest. See also inertia. mass and weight See weight and mass. mass number The mass number of a nucleus is the number of particles (protons plus neutrons) it contains. See also atomic number. materialism The philosophy that only matter is real and that everything is determined by its impersonal workings. The early Greek atomists were atomic materialists. Newtonian physics is compatible with this philosophy. matter Material substances such as wood, soil, ice, water, steam, air, and gold. Matter has nonzero rest-mass and moves at less than lightspeed, in contrast to radiation, which has zero restmass and moves at lightspeed. matter–antimatter annihilation The transformation of matter into high-energy radiation that occurs when a subatomic particle such as an electron is brought close to its antiparticle (such as a positron). matter field A new type of field that was discovered during the 1920s. It is quantized, and its quanta are called “electrons,” “protons,” “neutrons,” etc. This field is seen, for example, in the double slit experiment with electrons. Also called “psi,” “wave function,” and “electron field.” See also quantized field. matter wave A wave in a matter field. See wave theory of matter and matter field. measurement See observation and measurement (in quantum physics).

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GLOSSARY measurement (in quantum physics)

Any situation in which a microscopic particle interacts with a macroscopic device such as a viewing screen in such a way as to create a macroscopically observable mark such as a flash. A human observer need not be present. mechanical universe The philosophical view, accompanying Newtonian physics, that the clocklike workings of atoms precisely and predictably determine everything else, including the entire future of the universe. medium The material or nonmaterial substance through which a wave travels. Examples: The medium for water waves is water. The medium for electromagnetic waves is the electromagnetic field. mega- (M) Prefix meaning one million. megaton The amount of energy that would be released in the explosion of one million tons of TNT. meltdown The melting together of nuclear reactor fuel into a solid radioactive mass during a nuclear power accident. metabolic rate The rate, usually measured in Cal/s, at which an animal transforms its bodily chemical energy into other forms of energy. meter (m) The basic metric unit of distance, about 39 inches. metric system The system of measurements based on the meter, second, and kilogram. Used by all nations except the United States. metric ton (tonne) 1000 kilograms, which is about 2200 pounds. micro- Prefix meaning millionth. microscopic Too small to be seen with the unaided eye, as opposed to macroscopic, or visible to the unaided eye. microscopic disorganization and the second law The second law of thermodynamics results from the fact that microscopic disorganization is overwhelmingly likely to increase rather than decrease. microscopic interpretation of warmth Temperature is associated with disorganized, or random, microscopic motions that are not visible macroscopically. Higher temperature means greater microscopic kinetic energy. Milky Way See galaxy. milli- (m) Prefix meaning one-thousandth. millimeter (mm) One-thousandth of a meter. millisievert See ionizing radiation. model See theory. models of the atom The Greek atom is a tiny indestructible object, like a small and rigid pea. The planetary atom is made of parts, including a tiny central nucleus containing protons and neutrons and one or more electrons orbiting far outside the nucleus. The quantum theory of the atom is based on the postNewtonian quantum theory. molecule See chemical compound. momentum The momentum of an object is its mass times its velocity; its direction is the same as the direction of the velocity. The total momentum of a system is the sum of the individual momenta of all the objects in the system, added together as “vectors” (added like arrows placed tip-to-tail). mSv Abbreviation for “millisievert.” See ionizing radiation. muon, tau These two particles are identical to the electron except for the facts that they are heavier and are unstable (they have short lifetimes). Like the electron, they are point particles (so far as we know). mutation See ionizing radiation.

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Nagasaki See Hiroshima. natural motion Unassisted motion. Aristotelian physics says

that falling is one form of natural motion, and horizontal motion is always unnatural, or violent. According to Newtonian (and current) physics, motion at an unchanging speed in a straight line is natural motion, and falling is not natural motion. natural radiation Ionizing radiation from natural sources such as radon gas, cosmic rays, the ground, and internal consumption. See also artificial radiation. negative charge See electrically charged object. negative feedback See feedback. net force The total, overall force on an object. The net force due to two forces acting in the same direction is the sum of the two. The net force due to two forces acting in opposite directions is the difference between the two and acts in the direction of the stronger force. neutrino A uncharged particle that experiences only the weak and gravitational forces and hence penetrates easily through matter. At least two of the three types of neutrinos are now known to have a tiny, but nonzero, mass. neutrino transformation The spontaneous change of a neutrino’s identity among the three types of neutrinos (electron-, muon-, and tau-neutrino). See also neutrino. neutron One of the fundamental particles. A composite particle made of three quarks. neutron star A compact star a few kilometers in diameter, resembling a giant nucleus made of neutrons. It spins rapidly, sending out radio beeps and light flashes. When massive stars (precollapse masses of 10 to 20 solar masses) run out of fusion fuel, they explode, and the remaining remnant collapses to become a neutron star. newton (N) A unit of force. The amount of force that can give a 1 kg mass an acceleration of 1 m>s2. Newton’s theroy of gravity Between any two objects is an attractive force proportional to the product of the two objects’ masses and proportional to the inverse of the square of the distance between them. Newton’s law of motion An object’s acceleration is proportional to the net force exerted on it by its surroundings and is proportional to the inverse of its mass. The direction of the acceleration is the same as the direction of the net force. In the appropriate units (m>s2, newtons, kilograms) it is a = F>m. Newtonian physics The ideas about motion, force, and gravity developed by Isaac Newton and others around 1700. Newtonian physics, limitations See limitations of Newtonian physics. Newtonian physics and democracy All humans are fundamentally equal, because all are ultimately governed by the same universal natural laws. Newtonian attitudes toward natural law pervade the democratic developments of the past several centuries. Newtonian worldview The philosophical notions associated with Newtonian physics, especially the mechanical universe and the democratic ideals implied by universal natural laws. Key features: Tiny indestructible particles form the fundamental reality; the future is precisely predictable from the past; nature can be understood by analyzing it into simple individual components. See also quantum worldview. newton-meter The unit of work and of energy. Also called the joule. nonlocality See quantum nonlocality.

GLOSSARY nonlocality principle

Entangled particles cooperate in a way that can be explained only by the existence of real, nonlocal connections between the particles, so that a measurement of one particle causes a real physical instantaneous change in the other. Entanglement of this sort is predicted by quantum theory and has been confirmed by experiments. nonrenewable resource A natural resource that can be used up. Its use begins exponentially, levels off, and declines. normal force The force, perpendicular to a solid surface, that is exerted by any solid surface on any object touching it. nuclear energy The energy resulting from the structure of a material’s nuclei. It is energy due to nuclear structure. nuclear energy curve A graph showing the energies of the different nuclei versus their mass number. The graph shows a lowest point at mass number 56 (iron), indicating that nuclear energy can be released by the fusion of nuclei lighter than iron and by the fission of nuclei heavier than iron. nuclear fission A nuclear reaction in which a large, single nucleus splits into two roughly equal smaller nuclei. Nuclear energy is released whenever a heavy nucleus is fissioned into two nuclei that are both heavier than iron. nuclear fusion A nuclear reaction in which two nuclei combine to form a single, larger nucleus. Nuclear energy is released whenever two light nuclei are fused to create a nucleus that is lighter than iron. nuclear power A way to get large-scale energy from the nucleus. This energy is obtainable from uranium using the world’s present uranium-fueled nuclear reactors, from plutonium using future plutonium-fueled reactors and breeder reactors, or from hydrogen using yet-to-be-developed fusion reactors. nuclear power plant sabotage One of the four possible forms of nuclear terrorism. nuclear power reactor A device in which chain-reacting nuclei transform nuclear energy into thermal energy for electric power. Its main components are fuel to provide energy, neutron-absorbing control rods to control the reaction, and a coolant to transfer thermal energy from the fuel. Most reactors are enclosed in a thick, concrete containment dome to prevent the escape of radioactivity into the environment. nuclear reaction A change in nuclear structure. The major types of nuclear reactions are radioactive decay, fusion, and fission. nuclear reactor A device that controllably transforms nuclear energy into other energy forms. nuclear terrorism Terrorism using nuclear materials. See also seizing a bomb, seizing bomb material, nuclear power plant sabotage, and dirty bomb. nuclear waste See high-level nuclear waste. nuclear weapon An explosive device fueled by nuclear fusion or nuclear fission. See also fusion bomb and fission bomb. nuclear weapons proliferation The spread of nuclear weapons to additional nations and to terrorists. nucleus The tiny center of an atom, made of protons and neutrons. objectivity An experiment is objective if its outcome is not influenced by humans. The Newtonian worldview assumes that perfect objectivity is possible, at least in principle. observation The fact-gathering process. A measurement is a quantitative observation, and an experiment is a controlled observation.

ohm The measurement unit for electrical resistance. Ohm’s law The current in a circuit element (such as a lightbulb

or toaster) is proportional to the voltage across that element. Ohm’s law is usually written V = IR, where the proportionality constant R is called the circuit element’s “resistance.” open universe See geometry of the universe. outer space The universe outside Earth and its atmosphere and outside other astronomical bodies. ozone The O3 molecule. A dilute layer of ozone fills the stratosphere, 10 to 50 km overhead. Ozone absorbs and shields biological life from most ultraviolet radiation. Ozone Treaty Treaty that called for a nearly total phaseout by 2000 CE of CFCs and most other ozone-destroying chemicals. particle accelerator

A device to accelerate microscopic parti-

cles to high energies. passive solar energy

Energy obtained from solar radiation, natural air flows, and energy storage to provide direct solar heating. peak production See production peak. per In each. periodic table See chemical element. photoelectric effect Light and other radiation shining onto a metal surface can dislodge electrons from their parent atoms. This effect provides evidence that light is quantized and is the basis for photovoltaic electricity. photon When an EM field deposits a quantum of energy in an object such as a viewing screen, it does so all at once and at a specific point on the screen. The resulting tiny impact is called a photon. A photon can be considered to be a particle, but of a very non-Newtonian sort since it really only exists at the time of impact. Considered as a particle, each photon moves at speed c, has zero rest-mass, and carries one quantum of energy. See also quantum theory of radiation. photon exchange According to quantum field theory, charged particles exert the electromagnetic force on each other by means of exchanging photons. photosynthesis This chemical reaction in plants combines atmospheric carbon dioxide with water to form carbon-based molecules such as glucose, along with oxygen. photovoltaic cell A device made of semiconducting material such as silicone, designed to use the photoelectric effect to convert solar radiation (photons from the sun) directly into usable electricity. It’s usually disk-shaped, a few inches across, and connected to other cells in a flat array. photovoltaic electricity Electricity generated from solar radiation using the photoelectric effect. Sunlight causes electrons to flow across two thin layers of semiconducting materials— materials having properties lying midway between conductors and insulators—and then around an electric circuit. See also photoelectric effect. physics The branch of science that studies the most general principles underlying the natural world. piston The part of an internal combustion engine that is pushed on by expanding gases in order to do work. Planck energy See Planck scale. Planck length See Planck scale. Planck mass See Planck scale. Planck scale The range or scale at which physicists expect typical quantum-gravitational events to occur. Specifically, such events are expected to occur within regions about as big as the

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GLOSSARY

Planck length, with a duration of about the Planck time, and an energy about equal to the Planck energy. The Planck mass is the mass of this much energy. Planck time See Planck scale. Planck’s constant See quantum theory of radiation. planet To the Greeks, these were objects that looked like stars but that wandered, out of step with the stars. Today, we view planets as objects that orbit the sun in nearly circular orbits. planetary atom See models of the atom. planetary model of the atom The atomic model in which tiny electrons, conceived of as Newtonian particles, move in planetlike orbits around a tiny nucleus. This model cannot explain line spectra and predicts that atoms will lose energy until they collapse. plug-in hybrid car A gasoline-electric hybrid car (with a small gasoline engine that generates electricity for a battery that runs the car electrically) in which the battery is a large storage battery that can be plugged in and recharged for all-electric power for trips up to a few tens of kilometers but that must then be recharged by running the small engine. Its average gasoline consumption is even lower than a “standard” hybrid car. point particle A particle whose force field is centered on a single point and that itself takes up no volume. All of the fundamental particles described by quantum field theory appear to be point particles. See also standard model. pole See magnetic poles. positive charge See electrically charged object. positive feedback See feedback. positron The electron’s antiparticle. Identical to the electron except that it carries a positive charge. power The rate of doing work. Units: joule/second, Watt (= joule>second), horsepower; power = work>time. power of 10 10 raised to some positive or negative power. Powers of 10 are used to express huge or tiny numbers. primary qualities See dualism. principle See theory. principle of the constancy of lightspeed Light (and other electromagnetic radiation) has the same speed for all nonaccelerated observers, regardless of the motion of the light source or of the observer. principle of mass–energy equivalence All mass has energy, and all energy has mass. A system with m units of mass has mc2 units of energy. A system with E units of energy has E>c2 units of mass. principle of relativity Every nonaccelerated observer observes the same laws of nature, regardless of their reference frame. “Unless you look outside, you can’t tell how fast you’re moving.” probability An event’s fractional number of occurrences in a long series of trials. Probabilities apply to both Newtonian situations such as a coin flip where the outcome is predetermined and could in principle be predicted, and to quantum situations such as radioactive decay where the outcome is not predetermined and cannot be predicted even in principle. production peak The maximum annual production of a nonrenewable resource. Production typically follows a bell-shaped curve, rising at first, then reaching a production peak, then falling. Once the production peak is reached, prices rise and continue rising as demand increases while production levels off and then declines, causing economic dislocation and hardship. proliferation See nuclear weapons proliferation.

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proportional One quantity is proportional to a second quantity if, whenever the second is multiplied by some number, the first is multiplied by the same number. One quantity is proportional to the square of a second quantity if, whenever the second is multiplied by some number, the first is multiplied by the same number squared. proportional to the inverse A quantity is proportional to the inverse of another quantity if the first is proportional to (equal to some number times) 1 divided by the second quantity. proportional to the square See proportional. proton One of the fundamental particles. It is a composite particle made of three quarks. pseudoscience Claims presented so that they appear scientific even though they lack supporting evidence and plausibility. Ptolemy’s theory An Earth-centered theory in which the planets move in circles within circles, or loop-the-loops. It was a good theory that survived for 1500 years. quanta Discrete bundles of energy associated with the interaction of any quantized field (such as a quantized EM field) with any other system (such as a viewing screen). Examples: Photons are quanta of the EM field, and electrons are quanta of the matter field for electrons. quantitative risk estimatation The quantitative evaluation of human-made and natural risks, especially for the purpose of comparing different risks. quantization of charge Electric charge comes in discrete amounts rather than any arbitrary amount. When you charge an object, it always gains or loses some whole number multiple of the charge on one electron. quantized EM field An EM field that is allowed to have only certain specific amounts of total energy. quantized field A continuous, space-filling field that is subject to the laws of quantum physics. A quantized field’s range of possible energies is “digitized,” with only certain specific energy values allowed. Examples: quantized electromagnetic field, quantized matter field. quantized matter field See quantized field. quantum See quantum theory of radiation. quantum computer A possible future device that would exploit the quantum uncertainty and quantum entanglement of individual microscopic systems (such as ions trapped in EM fields) called qubits to make powerful calculations. The power of qubits comes from the fact that microscopic systems can be in two different quantum states at the same time, in contrast to the macroscopic devices (such as switches) called bits used in ordinary computers. quantum electrodynamics The quantum field theory of electrons and photons (i.e., of the electron matter field and the EM field). According to this theory, when we say that a particle is electrically charged, we mean that it has the ability to emit and absorb photons. Particles exert electric forces on each other in tiny quantized increments, by photon exchanges in which one particle emits a photon that is then absorbed by the other particle. quantum of energy The smallest amount of energy that a quantized field can gain or lose; the energy difference between adjoining energy levels in a quantized field. When a quantized field interacts with an object such as a viewing screen, energy is deposited in particle-like quanta, each carrying one quantum of energy.

GLOSSARY quantum entanglement

Two particles are said to be entangled when their matter fields form a single, inseparable matter field, so that any alteration of the matter field of one particle instantly alters the matter field of the other. See also quantum nonlocality. quantum field theory Everything is made of quantized fields that obey special relativity and quantum theory. All the particles of nature are field quanta. A field’s intensity represents the probability of finding the particles that are the quanta of that field. quantum jump An instantaneous change of an atom’s matter field from one quantum state to a different quantum state, during which the atom’s energy also quantum-jumps from one energy level to another. quantum model of the atom The atomic model in which an atom’s electrons are standing matter waves surrounding the nucleus. This model agrees with all experiments so far. quantum nonlocality When a quantized field (EM field or matter field) interacts with an object such as a viewing screen, the entire spread-out field instantaneously shifts to a new quantum state, even though some parts of the field might be at a great distance from the point at which the interaction occurred. See also quantum entanglement. quantum physics The physical theory of the microscopic behavior of matter and radiation. quantum states of the hydrogen atom The various possible configurations of the matter field for a hydrogen atom’s electron. Each quantum state is a standing-wave pattern that obeys Schroedinger’s equation. quantum theory of the atom See models of the atom. quantum theory of fields See quantum field theory. quantum theory of matter Like EM fields, matter fields are quantized. For example, the matter field for electrons is allowed to possess enough energy for either zero electrons, one electron, two electrons, and so on. Thus, electrons are the quanta of matter fields. This is why there are electrons and other material particles. See also matter field. quantum theory of radiation All EM fields are quantized. Their allowed total energies are 0, hf, 2hf, 3hf, and so on, where f is the frequency of the radiation carried by the field and h = 6.6 * 10 - 34 J>Hz (or J-s), called Planck’s constant. The smallest allowed energy increment, hf, is called a quantum of energy. quantum uncertainty In the microscopic world, identical conditions often produce different outcomes. The different outcomes are unpredictable, or uncertain, although the overall statistics— the likelihood of each of the various possible outcomes—is predictable. This uncertainty is inherent in the microscopic world and has no known cause. quantum worldview In contrast to the Newtonian worldview, quantum physics asserts that the universe is made of malleable (capable of being changed), nonmaterial fields, the nature of microscopic systems depends on the presence of macroscopic detectors, the future is inherently nonpredictable, and nature is deeply interconnected and indivisible. See also Newtonian worldview. quark Fundamental particle, thought to be a point particle. Protons and neutrons are each made of three quarks of two different types, known as “up” and “down.” qubit See quantum computer.

radiant energy Energy carried by an electromagnetic wave. radiation Radiation has zero rest-mass and moves at lightspeed,

in contrast to matter, which has nonzero rest-mass and moves at less than lightspeed. radiation emitted by an atom See emission of radiation by an atom. radiation sickness See ionizing radiation. radio waves Created by humans in such forms as AM and FM radio, TV, radar, and microwaves. radioactive dating Determining the ages of old objects by using radioactive methods. radioactive decay See radioactive nucleus. radioactive fallout Dust that falls to the ground carrying radioactive isotopes from a nuclear explosion or nuclear accident. radioactive isotope An isotope that is radioactive. See also isotope and radioactive nucleus. radioactive nucleus A nucleus that is not stable and thus will eventually change its structure even if left undisturbed. Such a spontaneous change in structure is called radioactive decay. radon gas A radioactive gas that can seep into buildings from underground. See also natural radiation. range of possibilities The range of possible positions and velocities that a microscopic particle can have at any particular time, as determined by the particle’s matter field. This range cannot be smaller than is permitted by the uncertainty principle. See also uncertainty principle. reactor See nuclear power reactor. redshift The stretching of the wavelength of radiation caused by the stretching of space that results from the expansion of the universe. As radiation travels through expanding space, its wavelength lengthens, or shifts, toward the red end of the spectrum. reference frame The laboratory or other surroundings within which an observer makes measurements. Measurements made in a particular reference frame are said to be relative to that frame. relative motion Two objects are in relative motion whenever they have different velocities. relativity of mass An object’s inertia (in other words, its mass) increases with its speed, so its mass is different for different observers. relativity of space Moving objects are contracted along their direction of motion, so an object’s length is different for different observers. Also called length contraction. relativity of time The elapsed time (the number of seconds) between two particular events, such as two ticks on a particular clock or the birth and death of a person, is different for two observers who are in relative motion. The duration of one clock tick is longer for observers who are moving relative to the clock than it is for observers for whom the clock is at rest. Thus, moving clocks run slowly. See also time dilation. release of nuclear energy Any transformation of nuclear energy into other forms of energy. renewable resource A natural resource, such as solar energy, that is continually replaced by natural processes. Its use begins exponentially, then levels off at some sustainable level (provided it is not overconsumed). reprocessing Extraction of the plutonium from used nuclear reactor fuel rods in order to make fuel for a reactor or for a bomb.

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GLOSSARY resistance

The tendency of any circuit element (such as a lightbulb or toaster) to cause a reduction in electric current around the circuit. Quantitatively, it’s defined as the “R” (measured in units called “ohms”) in Ohm’s law, V = IR, where V is the voltage across the element and I is the current through the element. resistive force Any force that acts on a moving body in a direction opposite to the body’s motion. resource See nonrenewable resource and renewable resource. respiration This chemical reaction in animals combines oxygen with carbon-based molecules such as glucose to generate useful energy, along with carbon dioxide and water. rest-mass The mass of an object when it is at rest. Rest-mass represents quantity of matter. retrograde motion A temporary change in the direction that a planet moves relative to the stars, as seen from Earth. rocket propulsion When material is ejected from a vehicle, it exerts a reaction force back on the vehicle because of the law of force pairs. This force accelerates the vehicle, which is then said to be “rocket propelled.” See also law of force pairs. rolling resistance The resistive force by a surface on a rolling object. satellite

A body in orbit around a larger astronomical body. Inertia keeps satellites moving, and the gravitational force exerted by the central body holds satellites in their orbits. Schroedinger’s equation An equation that predicts the matter wave for material particles in a wide variety of situations. science The observation and theoretical understanding of the natural world. See also scientific process. scientific process The dynamic interplay between experience (experiments and observations) and ideas (theories and hypotheses). See also science. second law of thermodynamics Describes the tendency of nonthermal energy to end up as thermal energy. This law can be stated in three logically equivalent forms: The law of heating states that thermal energy flows spontaneously from higher to lower temperatures. The law of heat engines states that any cyclic process that uses thermal energy to do work must have a thermal energy exhaust. The law of entropy states that the total entropy of all the participants in any physical process must either increase or remain unchanged. See also biology and the second law. secondary qualities See dualism. seizing a bomb One of the four possible ways that nuclear terrorism could occur. seizing bomb fuel One of the four possible ways that nuclear terrorism could occur. semiconducting materials Materials having properties lying midway between conductors and insulators. short circuit An electrical circuit in which a low-resistance circuit element (such as a piece of metal wire) is placed across a battery or wall socket, resulting in a huge current in the circuit. sievert See ionizing radiation. solar heating Using sunlight for warmth. solar radiation Electromagnetic radiation from the sun. It is concentrated mainly in the infrared, visible, and ultraviolet. solar system The sun and the objects that orbit the sun, including the nine planets and their moons. solar-thermal electricity Energy generated from thermal energy created by the sun.

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solid See three states of matter. space See outer space. spacetime Space and time together, thought of as a single

entity instead of two different entities. special theory of relativity Einstein’s theory based on the principle of relativity and the principle of the constancy of lightspeed. In this theory, time and space are not absolute, and light has the same speed in all nonaccelerated reference frames. This theory applies only to nonaccelerated observers, whereas the general theory of relativity applies also to accelerated observers. spectroscope A device that measures the spectrum, or set of frequencies, emitted by a radiation source. spectrum The set of frequencies emitted by a radiation source. speed See instantaneous speed. stable nucleus A nucleus that, if left undisturbed, will remain unchanged forever. standard kilogram See kilogram. standard model The theory of the electroweak and strong forces. See also electroweak force and strong force. standing wave A wave in which the medium vibrates in a wave pattern but the pattern does not move. star birth Stars form from collapsing gas clouds. Gravitational collapse heats the gas, which initiates nuclear fusion in the center, which stops the collapse. steam–electric power plant Use of thermal energy from an external source such as burning coal to turn water into steam that pushes on a steam turbine that provides work to generate electricity. The device that converts the rotational motion of the turbine into electricity is called an electric generator. Since the steam is heated by fuel that burns outside of the boiler, the plant is an external combustion engine. steam turbine See steam–electric power plant. stratosphere The upper atmosphere, 10 to 50 km overhead. string See string hypothesis. string hypothesis A promising hypothesis that unifies general relativity with quantum theory but that has as yet no direct experimental verification. Its key idea is that a fundamental particle such as an electron is not concentrated at one infinitely small point but is instead a tiny loop called a string. This spreading out of the point-particle model smoothes its effects on the space around it enough so that strings can fit into general relativity. Strings are comparable in size to the Planck distance. One odd thing about strings is that they exist in 10 spatial dimensions, 7 of which are “rolled up” so that we do not observe them in the macroscopic world. Although all strings are identical, they can vibrate in a variety of ways, and each different mode of vibration is a different elementary particle. strong force One of nature’s fundamental forces. It holds the nucleus together, acts between nuclear particles (protons and neutrons), and is strongly attractive at separations of around 10 - 15 and negligible at larger distances. The quanta (or exchange particles) of the strong force field are gluons. The quanta of the strong matter field are the up quark (u) and the down quark (d). In addition, there are two more strong matter fields corresponding to a second and third generation of particles: the c-quark and s-quark, and the t-quark and b-quark. Only the first generation is stable and contributes to ordinary matter: Protons are made of u-u-d, and neutrons are made of u-d-d. The other two generations are unstable and transmute quickly into other particles. Quarks are not found in isolation because any attempt to isolate them creates more quarks.

GLOSSARY strong force field See strong force. strong matter field See strong force. supernova explosion The explosion of a giant star. Supernovae

spread the chemical elements into space and so are the source of the elements heavier than helium in our solar system. sustainability A practice or policy is sustainable if it meets the needs of people today without endangering the prospects of future generations. tau See muon. technological imperative

The tendency to build whatever tech-

nology is possible. technological momentum

The tendency to continue a technological project once it is started. temperature A quantitative measure of warmth. The units normally used to measure temperature are called degrees Celsius. Any device that measures temperature is called a thermometer. theory A well-confirmed idea or group of ideas that explains or unifies a range of observations. A model is a theory that can be visualized. A principle or law is a single idea, often within a larger theory. theory of relativity Any theory that provides answers to questions about observers in relative motion. See also relative motion. thermal energy Energy due to temperature. Equivalently, thermal energy is microscopic energy, the kinetic (and other) energy of molecules that cannot be directly observed macroscopically. This microscopic motion is called thermal motion. thermal motion The disorganized microscopic motion of molecules that is associated with temperature. thermodynamics The study of the general properties of energy. Thermal energy plays a central role in understanding these properties. thermometer See temperature. thermonuclear reaction A self-sustaining fusion reaction that creates the thermal energy needed to sustain itself. Three Mile Island Site of the most significant U.S. nuclear power plant accident. Little radioactivity escaped even though the fuel suffered a meltdown—the fuel melted together into a solid radioactive mass that slumped downward inside the reactor. three states of matter Nearly every substance can exist in any of the three states. The molecules of a solid are locked closely together in a regular pattern, the molecules of a liquid are close together but not fixed in position, and gas molecules are far apart and move around rapidly. time Time is defined by clocks, in other words, by the operations we perform to measure time. The light clock, based on the motion of light beams, is a simple instrument to define time. time dilation See relativity of time. time travel An observer who accelerates to a high speed and then returns to the initial reference frame experiences a shorter elapsed time than does an observer who remains in the initial frame. So objects in the initial reference frame have aged more than the traveler has. This effect makes it possible to travel to stars that are many light-years distant in only a few years’ travel time. It also makes one-way travel to the future possible, by going on a fast trip and returning. tonne See metric ton. trace gases Gases that form only a minute fraction of the atmosphere. Examples: ozone, carbon dioxide, and water vapor.

transportation efficiency Useful output (such as distance traveled, passengers moved, freight moved, or mass moved) per unit of fuel input. Tycho Brahe’s observations Highly accurate data on planetary positions that disproved both Ptolemy’s and Copernicus’s theories. UFO Unidentified object in the sky. See also UFO beliefs. UFO beliefs Two popular beliefs about unidentified flying

objects are that (1) UFOs are visitations by aliens today and (2) aliens visited Earth within the past few thousand years. There is no evidence to support either belief; scientists overwhelmingly reject them as pseudoscientific and false. ultraviolet radiation Radiation created by higher-energy motions of electrons in atoms that have sufficient energy to damage biological matter, can cause mutations and cancers, and is not visible to the human eye. Higher-energy ultraviolet is one type of ionizing radiation. uncertainty See quantum uncertainty. uncertainty principle Every material particle has an inherent uncertainty in position, ¢x, and in velocity. Although either ¢x or ¢y can take on any value, the two are related through the fact that their product must approximately equal h/m. See also quantum uncertainty. uniform circular motion Motion in a circle at an unchanging or uniform speed. unit A standard, relative to which a quantity such as the length of a table or the weight of a rock, is measured. For example, you might measure length in inches, feet, or miles, or in the metric system in centimeters, meters, or kilometers. u-quark See strong force. uranium enrichment The process of increasing the proportion 235 U of to 238U in natural uranium. vacuum

A region that contains no matter (no material particles). According to quantum field theory, fields exist even in vacuum. Since these fields are quantized, there is some probability that field quanta—photons, or particle-antiparticle pairs—will pop into and out of existence, even in vacuum. Furthermore, quantum uncertainties allow the energy present at any point in vacuum to undergo random energy fluctuations around its longterm average value. velocity The combined instantaneous speed and direction of motion. visible light Detectable by the human eye. Created by lowerenergy motions of electrons in atoms. Colors are due to different wavelengths, ranging from red (longest) to violet (shortest). volt The measurement unit for voltage. voltage A battery’s voltage is a measure of the amount of electrical energy the battery gives to each electron as the electron passes through the battery. Measured in units called “volts.” W + and W - particles See electroweak force. warmth, microscopic interpretation of See microscopic inter-

pretation of warmth. warped space See gravity and warped space. watt See power. wave A disturbance that travels through a medium and that

transfers energy without transferring matter.

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GLOSSARY wave interference

The effects that occur when two waves of the same type are present at the same time and place. Interference can be either constructive or destructive, depending on whether the two waves reinforce or cancel each other. wave packet A matter field for a single material particle, moving through space and spread out over only a limited distance, ¢x. wave theory of matter Every type of material particle, such as electrons or protons, has a wave associated with it. It’s wavelength is h/mv, where m and v are the mass and velocity of the particle. These waves are called matter waves. See also quantum theory of matter. wavelength The distance from any point to the next similar point along a continuous wave. wavespeed The speed at which a disturbance (a wave) moves through a medium. weak force One of the four fundamental forces; a nuclear force that plays a role in radioactive beta decay. weapons of mass destruction Nuclear, chemical, or biological weapons. weight The weight of an object is the net gravitational force exerted on it by all other objects. weight versus mass An object’s weight is the force on it due to gravity, whereas its mass is its quantity of inertia. Weight is measured in newtons (or pounds); mass is measured in kilograms. An object’s weight depends on its environment, but an object’s mass

14

is the same everywhere. For example, a kilogram has a mass of 1 kilogram regardless of whether it is on Earth or on the moon, but its weight is about 10 N (or 2.2 pounds) on Earth and only 1.6 N (or 0.36 pounds) on the moon. weightlessness Bodies are (nearly) weightless only when they are far from all other bodies. Bodies in orbit around Earth are not weightless, but they seem weightless because they are falling freely (i.e., gravity is the only force acting on them) around Earth. white dwarf An Earth-sized, compact star. When stars having about the sun’s mass run out of fuel, they flare up and then collapse to become white dwarfs. wind energy The kinetic energy of moving air. Wind turbines capture this energy and convert it to electricity. wind turbine Device for capturing wind energy and converting it to electricity. work Object A does work on object B if A exerts a force on B while B moves in the direction of that force. Unit: newton-meter (N # m) = joule (J). work–energy principle Work is an energy transfer. X-rays Created by the highest-energy motions of electrons in atoms. X-rays are one type of ionizing radiation. Z particle

See electroweak force.

The Way of Science Experience and Reason

From Chapter 1 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Way of Science Experience and Reason

I believe that ideas such as absolute certitude, absolute exactness, final truth, etc., are figments of the imagination which should not be admissible in any field of science.... This loosening of thinking seems to me to be the greatest blessing which modern science has given us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world. Max Born, Physicist

1 STARDUST: AN INVITATION TO SCIENCE

W

e came from the stars. We are made of atoms created and blown into space by ancient stars, a fact that’s only one strand in a network connecting us with the rest of the universe. Science—observing and understanding the natural world—is a path toward embracing that network. An expanding awareness of nature is discernible in the long history of life on Earth. There is good reason to believe that our planet formed about 5 billion years ago and that the earliest simple living organisms formed nearly 4 billion years ago. Since then, organisms have evolved biologically to interact with their environment in increasingly complex ways. Looked at from the human perspective (an amoeba might look at it differently), humankind is the latest in a sequence of increasingly aware biological organisms. We could even say that through biological evolution, the universe has become more aware of itself. Education and science can be viewed as an extension of this process. And you, as you learn about the universe, are part of that process of expanding awareness. Albert Einstein spoke of this widening circle of awareness when he wrote: A human being is a part of the whole, called by us “Universe,” a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest—a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security.

I hope that Physics: Concepts & Connections will help you discover many links between you and the universe. In writing this text, my constant criterion has been “Is this material relevant to readers who want to participate fully in our

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The Way of Science

science-based culture but who won’t necessarily use science in their professional lives?” I’ve tried to use language that’s meaningful to literate nonscientists. There are no extraneous technical terms and no extraneous mathematics—in particular, no algebra. The text does, however, make wide use of numbers, proportionalities, graphs, and numerical estimates because quantitative tools are essential to meaningful communication today. Literate people must also be numerate. I’ve discussed one reason for learning science: expanded awareness. A second reason is to develop social values appropriate to the scientific age. Take a moment to list a dozen problems that are important to the nation or the world. A typical list might include population growth, poverty, crime, species destruction, illiteracy, global warming, urban decay, drugs, war, air pollution, AIDS, and famine. Every one of these problems has a science component. Now try listing solutions to these problems. A typical list might include birth control, economic growth, education, sustainable farming, democracy, international law, environmental protection, disease control, better government, rational use of energy, more understanding among people, and concern for the environment. All of these have a science component. The problems and the solutions of our times are bound up with science and its close relative, technology.1 That’s why we call this the scientific age. To solve these problems, the world needs your help. We dare not simply entrust these critical issues entirely to experts or governments. In his book Of a Fire on the Moon, about humankind’s first venture to the moon, novelist and journalist Norman Mailer wrote pessimistically:

For any man to abdicate an interest in science is to walk with open eyes toward slavery. Jacob Bronowski, Philosopher-Scientist

Scientific activity is one of the main features of the contemporary world and, perhaps more than any other, distinguishes our times from earlier centuries. Science for all Americans, A Report to the American Association for the Advancement of Science

The [twentieth] century would create death, devastation and pollution as never before. Yet the century was now attached to the idea that man must take his conception of life out to the stars.... A century devoted to the rationality of technique was also a century so irrational as to open in every mind the real possibility of global destruction.... So it was a century which moved with the most magnificent display of power into directions it could not comprehend. The itch was to accelerate—the metaphysical direction unknown.

If we are to resolve today’s problems, we must find our metaphysical direction in this scientific age. You use the power of science daily when you switch on a light, a television set, an automobile, or a computer. Such devices have powerful effects on the world, both good (light to read by) and bad (pollution from electric-generating plants). The classic moral dilemma of the scientific age—a dilemma symbolized, for example, in Mary Shelley’s nineteenth-century novel Frankenstein—is the problem of understanding and dealing responsibly with these powerful technologies. To accept technology’s power without also accepting the responsibility to use that power wisely is to invite death, devastation, and pollution—the monster’s retaliation against its maker. I will focus on that part of science called physics, along with its human connections. You have heard of most of the major sciences: biology, geology, chemistry, astronomy, physics, and others. When people ask me “What is physics?” I like to pick up something and drop it. Most things fall when you

The dangers that face the world can, every one of them, be traced back to science. The salvations that may save the world will, every one of them, be traced back to science. Isaac Asimov, Scientist and Writer

We need people who can see straight ahead and deep into the problems. Those are the experts. But we also need peripheral vision and experts are generally not very good at providing peripheral vision. Alvin Toffler, Writer and Futurist

1

Technology is the application of science to achieve useful human goals. This text often uses the single word science to refer to science and technology.

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The Way of Science

drop them.2 You can drop a rock, a frog, a cabbage, or a king and they all fall. Physics is the study of phenomena that, like falling, are universal. Geologists study rocks and Earth’s structure, biologists study frogs and other living organisms, while physicists study the general principles obeyed by rocks and frogs and everything else. How does science operate? This is the crucial question for us to answer if we are to understand and cope with our scientific age. In most of the remainder of this chapter, I’ll answer this question by means of a significant case study: the early history of astronomy. This begins in Section 2 with commonsense conclusions about the night sky. The next three sections present three theories about the way the heavens are organized: the ancient Earth-centered theory, Copernicus’s sun-centered theory, and Kepler’s sun-focused theory. Section 6 discusses what this history teaches us about science, and Section 7 looks at the cultural implications of all of this. Finally, Section 8 studies fake science or “pseudoscience,” focusing on three important examples.

2 OBSERVING THE NIGHT SKY Teach me your mood, O patient stars! Who climb each night the ancient sky, Leaving no space, no shade, no scars, No trace of age, no fear to die. Ralph Waldo Emerson, Poet

It’s hard to see a forest when you’re standing in the middle of the trees. In the same way, it’s hard to fit science and technology into perspective because our culture is so immersed in them. This text’s most important theme is the study of the nature of science itself.3 How does it operate? What are its values? How valid are its conclusions? You will see that science is more a path, a way of learning, than it is a body of knowledge. The “scientific method” or, as I will call it, the scientific process, is often described as several activities that scientists sometimes practice: observing, hypothesizing, testing, and so forth. But such a cookbook prescription doesn’t capture how science works in real life. In fact, you use aspects of the scientific process whenever you use your own experience to reason through a problem. Science is simply a careful application of experience (often called observation and experimentation) and reason (often called hypothesis, theory, principle, and scientific law) to answer questions. For perspective on how science really operates, we’ll study a historical example: the early history of astronomy. Astronomy, the scientific study of the stars and other objects in space, has usually been closely associated with physics. The starry sky seems a more perfect place than our daily world. Life is full of clatter, the stars are serene: life is brief, the stars are forever. It is not surprising that ancient priests looked to the stars. Here was timeless knowledge. And so for at least as long as there have been records to tell the story, we have looked to the sky for the time to plant and to reap, for omens of war and peace, for life’s meaning, and for our gods (Figure 1). Although astrology, the belief that the positions of the stars significantly influence human affairs, has been a discredited superstition for two centuries, human fascination with the stars may be greater today than ever (Figure 2). In these high-technology times, we sometimes fail to see the stars. On some clear night, get away from city lights and take an hour or two to track the stars across the sky. If you’re in the Northern Hemisphere, find the moon, the Big Dipper, the North Star, any group of stars on the eastern horizon, and a group of stars on the western horizon 2 3

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There are exceptions: helium balloons, for example. Besides this theme, three others reappear throughout the text: modern physics and its significance, the social impacts of physics, and energy.

UPI/Corbis-Bettmann

The Way of Science

Figure 1

Four thousand-year-old testimony to our reverence for the stars: the remains of Stonehenge, in England. Humans hauled the huge stones for more than 200 miles to make these monuments. These stones are the remains of a much larger structure used for religious purposes and to predict astronomical events, particularly solstices (longest and shortest days) and equinoxes (equal-length days and nights). Stonehenge perhaps also predicted eclipses of the moon, an impressive feat for people who did not use writing. Eclipses occur in an irregular and apparently random pattern that repeats itself only over a 56-year cycle. Even to have been aware that a repeated pattern exists required enormous dedication and attention to detail.

(Figure 3). Observe all of these every 15 minutes for one or more hours. What happens? You should be able to see that the moon and stars move westward, that stars rise in the east and set in the west, that different stars maintain their positions relative to one another while moving as a group across the sky, that the North Star remains fixed, and that stars near the North Star move in circles around the North Star (Figure 4). There are several small and unusually bright starlike objects that do not keep pace with the stars. If you observe them for a week or more, you’ll see that they slowly shift their positions relative to the stars. These objects are called planets (wanderers in Greek). Five planets are visible without a telescope. The moon and the sun also move at a different pace from the stars. From such observations, most people would conclude that the stars, sun, moon, and planets travel in circles around Earth, with their axis of rotation fixed in the direction of the North Star. Figure 4 is rather convincing evidence of this notion. This is the conclusion most observers drew centuries ago, and it’s surely the conclusion that observers draw today unless they learn differently in school. Such observations and conclusions are typical of science’s two main processes: observation and rational thought. Science is not really different from a lot of other human endeavors. Whenever you observe your surroundings and develop ideas based on what you observe, you are acting scientifically.

North Star

Little Dipper

Big Dipper

Figure 3

Look for these two constellations and the North Star in the northern night sky.

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The Way of Science Figure 2

NASA/Johnson Space Center

Our fascination with the stars seems greater than ever. (a) The Hubble Space Telescope, launched into space in 1990. For some of its astonishing photographs, see Figure 24.

European Southern Observatory

(b) The European Southern Observatory’s four-telescope array, known as the “Very Large Telescope,” in Chile. Each telescope contains a near-perfect mirror eight meters in diameter. The telescopes are connected by “light pipes” that allow them to coordinate their four different views of a single object and use waveinterference effects to greatly improve the resolution of the image. The array saw “first light” in 1998. (b)

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The Way of Science Figure 2 (continued)

ICRR Institute for Cosmic Ray Research

NASA Headquarters

(c) Many telescopes receive nonoptical signals from space. This large radio telescope in Arecibo, Puerto Rico, receives radio signals emitted by objects that pass overhead as Earth rotates.

(d) The Super-Kamiokande underground neutrino detector, or neutrino telescope, being filled up with water. Thousands of photomultiplier tubes surround the inside of this tank of pure water, ready to record light when neutrinos from the sun or from distant exploding stars interact with atoms in the water. Neutrinos are subatomic particles that travel through space and also travel nearly uninhibited through objects such as Earth at nearly the speed of light. Neutrinos can enter the detector and be recorded from any direction: top, bottom (after coming through the entire Earth), or sides.

(d)

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National Optical Astronomy Observatories

The Way of Science

Figure 4

Time-exposed photograph showing the “star trails” near the North Star. Observations such as this appear to provide convincing evidence that the stars move in circles around Earth.

3 ANCIENT GREEK THEORIES: AN EARTH-CENTERED UNIVERSE

All things are numbers. Pythagoras, Sixth Century BCE

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At least as early as 3000 BCE, people were aware of the differing motions of the stars, sun, moon, and the five planets then known. Beginning around 500 BCE, a few Greeks sought a new kind of understanding of these motions. They desired to go beyond the observed facts, to grasp how the system worked. Figure 5 indicates the early Greek concept of the cosmic architecture. In agreement with the observations described above, the figure shows the heavenly objects circling a motionless Earth. Because the stars all keep pace with one another, the Greeks supposed that they all were attached to the inside surface of a single transparent (invisible) spherical shell centered at Earth’s center and rotating around Earth once a day, carrying the stars with it. The Greeks imagined that each of the other seven objects—sun, moon, and five visible planets—was attached to this transparent spherical shell centered on Earth, one sphere for each object. Each of the seven spheres rotated at an unchanging, or uniform, rate around Earth roughly once each day. These spheres rotated at slightly different rates about the same axis through Earth’s center. A philosophical–mathematical–religious group led by Pythagoras developed this tentative theory or hypothesis. These Pythagoreans formed a secretive cult that believed passionately in the importance of abstract ideas. An idea is, in a sense, eternal. A real table, for example, eventually rots and turns to dust, but the idea of

The Way of Science Sphere of the stars

Figure 5

The earliest Greek conception, around 500 BCE, of the layout of the universe.

Jupiter

Mars

Moon Earth

Mercury

Venus

Sun Saturn

“table” or “tableness” seems eternal. Pythagoras believed that the most perfect ideas were mathematical because they could be stated so precisely yet abstractly. The idea of a table is rather imprecise—a flat rock might be considered a table, or it might be just a rock. But mathematical ideas like a straight line, a circle, or the number 5 were precise, pure. For example, a circle is all of the points on a flat surface that are at the same distance from some fixed point on the surface. CONCEPT CHECK 1 To check your understanding of the preceding definition of a circle, try answering this multiple-choice question: The “fixed point” and the “distance” referred to in the definition are known, respectively, as the (a) center and diameter; (b) axis and radius; (c) sine and cosine; (d) center and radius; (e) center and hypotenuse.

Although this definition is precise, if you draw a circle that follows this definition (Figure 6), there will always be imperfections. Indeed, the Pythagoreans Figure 6

If you try to draw a circle, there will always be imperfections.

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The Way of Science

Let no one without geometry enter here. Inscription over the Entrance to Plato’s Academy, Fourth Century BCE

believed that it was the idea of a circle, rather than any particular representation of it, that was pure and eternal. These mathematical mystics discovered how to describe many features of the natural world by mathematical ideas. The famous “Pythagorean theorem” is one example, and the simple numerical relationships between tones in the common musical intervals is another.4 They believed that the universe is based on mathematical principles or “harmonies” analogous to the numerical relationships between the common musical intervals, and that when one studies mathematics one studies the mind of God. It isn’t surprising, then, that the Pythagoreans sought a beautiful geometric scheme for the heavens. And what geometrical forms could be more fitting for the stars than the sphere and the circle? After all, the sphere is the only perfectly symmetric (the same from all vantage points) shape in space, and the circle is the only perfectly symmetric shape on a flat surface. And as befits the timeless stars, circular paths have no beginning or end. Other Greeks regarded all of this suspiciously. The Pythagoreans were persecuted and eventually banished. But their thinking had a deep influence on subsequent Greek philosophers such as Plato and Aristotle, and on Western civilization. In line with their picture of a universe made of eight transparent Earth-centered spheres within spheres, these early Greeks had the startling notion that Earth itself was a sphere residing motionless at the center of the transparent spheres. The Pythagorean concept of a spherical Earth, although not their idea of a motionless Earth, survives to this day. How do we know that Earth is round? Science is based on observable evidence. So scientists are always skeptical, always asking, “How do we know?” I will frequently ask this question. How do we know that Earth is spherical rather than flat? The evidence is fairly direct today (Figure 7), but what evidence might the ancient Greeks have had? Take a minute, to think about this. (This is a minute, for thinking.) The Greek philosopher Aristotle, living two centuries after Pythagoras, stressed the importance of evidence. He gave many good observational reasons to believe that Earth is spherical rather than flat. For one thing, ships sink little by little below the horizon as they go out to sea (Figure 8). For a second thing, Greek travelers reported that in northern lands the noontime sun is lower in the sky. For a third, the shadow cast by Earth on the moon, as observed during an eclipse of the moon, is the shape that would be expected if both Earth and the moon were spherical.

But there was a problem. Because the spheres rotated uniformly, the transparent spheres hypothesis predicted that each planet moved at a uniform rate around Earth. But careful observation showed that they do not. Instead, their rate of rotation, as seen from Earth, changes. Figure 9 diagrams this effect for a single planet such as Mars. The diagram is drawn relative to the background stars, so it does not show the nightly rotation of Mars and the stars. Relative to the stars, Mars generally moves from west to east, but at a variable rate. Occasionally, Mars even changes directions and moves east to west relative to the stars, a phenomenon known as retrograde motion. 4

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The Pythagorean theorem states that in any triangle having a 90-degree or right angle, if you draw three squares, each one based on one of the triangle’s three sides, the sum of the areas of the two smaller squares will equal the area of the larger square. As an example of the relationships between musical tones, if you create a musical tone by plucking a string and then precisely halve the string’s length and pluck it again, the two notes you create will be exactly one octave apart. Other simple string ratios, such as 3 to 2 or 4 to 3, produce the other musical intervals that sound harmonious.

The Way of Science Figure 7

NASA Headquarters

A whole-world view showing Africa and Saudi Arabia taken 7 December 1972 as Apollo 17 left Earth’s orbit for the moon. The cultural impact of photos like this, showing Earth as a single, freely moving ball in space, may be among the space program’s most important benefits.

Horizon

The Greek philosopher Plato, convinced that an elegant mathematical reality lay behind the heavenly motions, challenged his students with the problem of finding a geometric scheme that would explain the observed motions. They constructed a hypothesis similar to Pythagoras’s but far more elaborate, involving multiple transparent spheres for each planet. One Greek thinker, Aristarchus, proposed that the sun and not Earth was at rest at the center of the universe, that Earth and the five planets circled the sun, and that Earth spun on its axis. It was a radical hypothesis, and few astronomers took it seriously because it seemed absurd for several reasons: Earth seems nothing like the heavens, so how could Earth be a planet like the heavenly planets? It seems absurd to believe that Earth moves. It’s too big! What immense force could be pushing it to keep it moving? If it does move, it seems that objects such as birds and clouds that are not attached to the ground should be left behind. If Earth spins on its axis, objects should be hurled off, just as a stone is hurled from a rotating sling. These things were not observed, and so for reasons that made sense at the time, Greeks rejected Aristarchus’s hypothesis. It would be 2000 years before a sun-centered hypothesis would again be considered. Another problem arose. The Greeks noticed that during a planet’s retrograde motion it appeared brighter than at other times, as though it were closer to Earth during this time. Yet Plato’s hypothesis, with each planet on an Earth-centered sphere, implied that each planet maintained a fixed distance from Earth. *

* *

Jan Oct

Feb East

*

Sep

*

*

*

Aug Dec

Nov *

*

Jul

Jun *

*

*

* * West

Earth

Figure 8

Evidence that Earth’s surface is spherical. As a ship sails out to sea, an observer on shore sees it sink little by little below the horizon.

Figure 9

The motion of a planet such as Mars, relative to the background stars. Relative to the stars, Mars usually moves from west to east. In this illustration, Mars moves more slowly during July–August than it does during June–July. It slows to a stop by October and then reverses direction during October–December and regains its normal direction during December–February.

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The Way of Science For its subtlety, flexibility, complexity, and power the epicycle–deferent technique... has no parallel in the history of science until quite recent times. In its most developed form the system of compounded circles was an astounding achievement. Thomas Kuhn, Historian and Philosopher of Science

To explain the varying brightness of the planets, the Greeks tried something rather different. Instead of moving on multiple spheres, each planet now moved around Earth in a circle within a circle. As shown in Figure 10, a planet such as Mars moved uniformly around a circle whose center was on another circle that was centered on Earth. The small outer circle was called the planet’s “epicycle,” and the inner circle centered on Earth was called the planet’s “deferent.” The center of the epicycle moved uniformly along the deferent, so that Mars moved in two circles at the same time. This produced a loop-the-loop orbit for each planet (Figure 10). In agreement with observation, the theory predicted that there would be occasional periods of retrograde motion (on the inside of the loops) and that the planet would be closest to Earth during retrograde motion and so should appear brightest. It was a satisfying picture, and it explained the observations. It was a good theory. You’ve probably noticed that I’m using the word theory here rather than hypothesis. Whereas a hypothesis is a tentative scientific idea without a lot of evidence, a theory is a scientific idea that is well-confirmed by evidence. Figure 11 pictures this theory greatly simplified. This theory was finally refined and summarized around 100 CE by Ptolemy, antiquity’s greatest astronomer (Figure 12). In order to agree with the known observations, Ptolemy introduced two new ideas: the displacement or “eccentricity” of the centers and the “equant point” from which the motion appears uniform.5 The details of these are not crucial here. To agree with the observations, each planet needed lots of epicycles—more than 80. Thirteenth-century Spanish king Alfonso X commented that “if the Lord Almighty had consulted me before embarking upon the creation, I should have recommended something simpler.”

Path followed by Mars

Earth Deferent Epicycle

Mars

Figure 10

The orbit of Mars around Earth, according to the epicycle theory.

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None of these ideas were original with Ptolemy, but he was the first to put them all together in a consistent and quantitatively correct theory.

The Way of Science Figure 11 Sphere of the stars

Ptolemy’s Earth-centered epicycle theory (around 100 CE) of the layout of the universe, according to which the five visible planets move on epicycles around Earth. The epicycles of the two innermost planets, Mercury and Venus, are centered on the line joining Earth to the sun.

Saturn Mars

Sun

Jupiter Venus Mercury

Moon Earth

How did we know planetary positions before there were telescopes? Ptolemy checked this elaborate theory with many quantitative (numerical) measurements of the heavens. Telescopes hadn’t been invented yet, so the measuring devices were long sighting rods with a scale to measure the angular position of a planet. The sighting devices were accurate to within about 0.2 degrees (recall that there are 360 angular degrees in a complete circle). To within this accuracy, Ptolemy’s theory agreed with all observations of the stars, sun, moon, and five known planets. It survived, with modifications, for 15 centuries and was used by navigators, astronomers, and mystics such as astrologers. Not bad.

CONCEPT CHECK 3 Venus often appears as the morning star (the last-seen “star” near the rising sun) or the evening star. Ptolemy’s explanation for this observation would be that (a) Venus’s orbit around the sun lies close to the sun; (b) the center of Venus’s epicycle lies on the line between Earth and the sun; (c) Venus and Mercury orbit the sun while the other planets orbit Earth; (d) Venus is attracted to the sun’s manly appearance. (Hint: See Figure 11.)

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CONCEPT CHECK 2 The ancient Greeks believed that the stars and other astronomical objects shine by means of their own light. Can they have believed this of every astronomical object that can be seen with the naked eye? (a) Yes. (b) No.

Figure 12

The ancient astronomer Ptolemy, 85–165 CE. Using epicycles and many other theoretical devices, he perfected the Earth-centered theory of the layout of the universe.

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4 COPERNICUS’S THEORY: A SUN-CENTERED UNIVERSE

American Institute of Physics/ Emilio Segre Visual Archives Figure 13

Polish astronomer Nicolaus Copernicus, 1473–1543. Finding Ptolemy’s system to be “neither sufficiently absolute nor sufficiently pleasing to the mind,” he devised a simpler theory. Copernicus’s theory placed the sun at the center of the universe, with Earth moving around it. The odd idea that Earth moved and was a planet like the other planets met with much resistance because it conflicted with the intuitive notion that Earth is at rest at the center of things and with prevailing philosophies. In the centre of everything rules the sun; for who in this most beautiful temple could place this luminary at another or better place whence it can light up the whole at once?... In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise. Copernicus

We live on a great round wonder rolling through space. Walt Whitman, American Poet

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The birth year of modern science is often taken as 1543 CE. In that year, an old man in Poland, on his deathbed, signed the first printed copy of his life’s work, On the Revolutions of the Heavenly Spheres. Nicolaus Copernicus (Figure 13)— astronomer, mathematician, linguist, physician, lawyer, politician, economist, and canon in a Catholic cathedral—had kept the manuscript locked up for 30 years, fearing the criticism it would unleash. With this book, the sun was setting on the medieval world. During the Middle Ages (about 500 to 1500 CE in Europe), philosophers such as St. Augustine and Thomas Aquinas had linked Greek thought, including Ptolemy’s astronomy, to Christian theology. But in 1543 the times were changing. During the past century the intellectual and artistic flowering known as the Renaissance had germinated in Italy and spread to all of Europe. Martin Luther had led a frontal assault on the Catholic church’s authority. Christopher Columbus had made a memorable voyage. These trends had a liberating effect on thoughtful minds. Copernicus and others were enthused by the new art, new religious thought, and new explorations. As a result, Copernicus was uncomfortable with Ptolemy’s theory. Not that Copernicus was a revolutionary. Quite the contrary: Copernicus objected to Ptolemy’s theory on the grounds that with its many epicycles, eccentrics, and equants, Ptolemy had strayed far from ancient Pythagorean ideals. Ptolemy’s system lacked the simple elegance that scientists have always sought. Here’s how Copernicus put it: The planetary theories of Ptolemy and most other astronomers, although consistent with the data, seemed to present no small difficulty. For these theories were not adequate unless certain equants were also conceived; it then appeared that a planet moved with uniform motion neither on its deferent nor about the center of its epicycle. Hence a system of this sort seemed neither sufficiently absolute nor sufficiently pleasing to the mind. Having become aware of these defects, I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent inequality would be derived and in which everything would move uniformly about its proper center, as the rule of absolute motion requires.

Note that like all thinkers since Pythagoras, Copernicus believed that the heavenly motions were circular and uniform. He stated adamantly that “it would be unworthy to suppose such a thing [as noncircular motion] in a Creation constituted in the best possible way.” As a Renaissance man. Copernicus adopted a broad outlook. Just as Renaissance artists looked beyond Christian art and as Columbus looked beyond Europe, Copernicus looked beyond Earth itself to imagine it as an object in space, an object that he believed to be similar to other objects in space. To Copernicus, and to science since Copernicus, the ancient idea that the universe is centered on Earth seemed narrow-minded, provincial. So Copernicus asked a broader question than had been asked before: What is the most elegant geometric scheme for the motion of the stars, sun, moon, five observed planets, and Earth that will fit the known measurements of the heavens? Given this change of focus, Copernicus soon discovered “a more reasonable arrangement of circles” in which the planets and Earth move in uniform circular motion around the sun and only the moon circles Earth. Figure 14 shows Copernicus’s theory. Copernicus obtained the east-to-west daily motion of the

The Way of Science Sphere of the stars

Figure 14

Copernicus’s sun-centered theory of the layout of the universe, 1543 CE. The diagram is simplified; the planets all move on epicycles, similar to those in Ptolemy’s theory, but here there are far fewer epicycles, and no equants.

Jupiter Mars

Mercury

Venus Sun

Moon Earth

Saturn

stars, sun, moon, and planets by allowing Earth to spin from west to east, rather than by allowing the sphere of the stars to rotate from east to west. How do we know that Earth and the other planets go around the sun? There were still no telescopes in Copernicus’s day, and data were gathered with star-sighting devices. With properly chosen radii, rotation rates, and eccentrics for the planetary orbits, Copernicus obtained quantitative agreement with the data. His theory explained many things, such as retrograde motion (Figure 15 and Concept Check 5). But as Copernicus admitted, Ptolemy’s theory was also “consistent with the data.” Both theories agreed with the data. There were good objections to the new theory, like those that had earlier confronted Aristarchus’s hypothesis. Being so large, how can Earth move? What keeps it moving? Why aren’t birds and clouds left behind? Why aren’t objects hurled off Earth? Copernicus didn’t have an answer. Instead, he pointed out that such problems loomed even larger for Ptolemy’s great spinning sphere of stars than for Copernicus’s smaller spinning Earth. In making this argument, Copernicus was assuming that the stars were subject to natural laws like those operating on Earth. Nobody had looked at it in this way before. The objections to Copernicus’s theory were not answered for more than a century, when Isaac Newton and others devised a radically new view of motion. In fact, Newton’s physics arose partly because of these questions.

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The Way of Science Figure 15

The Copernican theory’s explanation of retrograde motion. As Earth passes another planet, such as Mars, the other planet appears to move backward as seen against the background stars, because of the rotation of the Earth-based observer’s line of sight. Using this figure, you can demonstrate this by following the instructions in Concept Check 5. A similar effect occurs when you pass a car moving down a straight highway. Viewed against distant background trees and houses, the slower car appears for a few seconds to move backward, because of the rotation of your line of sight.

There is perhaps no other example in the history of thought of such dogged, obsessional persistence in error, as the circular fallacy which bedeviled astronomy for two millennia. Arthur Koestler, Twentieth-Century Writer and Historian of Science

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Mars 1 Earth

A decisive blow against Ptolemy’s theory and for a sun-centered theory did not come until Galileo introduced the telescope into astronomy, some 70 years after Copernicus’s death.6 Among other things, Galileo observed that Venus goes through phases similar to the moon’s phases (new moon, quarter moon, full moon, and the like). This means that Venus shines not by its own light but by light reflected from the sun. In Ptolemy’s theory, the center of Venus’s epicycle must be fixed on the line joining Earth to the sun (Figure 11), in order to explain the fact that Venus is never seen far from the sun. As shown in Figure 16, this means that we should never see a “full Venus” phase from Earth. On the other hand, the sun-centered theory predicts that we should see a full Venus whenever Earth and Venus are on opposite sides of the sun. Galileo observed that the phases of Venus included a full Venus.

CONCEPT CHECK 4 When you say that “the sun rises in the east,” you really mean (from the Copernican point of view) that (a) due to the sun circling around Earth, the sun begins to appear above the eastern horizon; (b) due to Earth circling around the sun, the sun begins to appear above the eastern horizon; (c) due to the sun rotating (or spinning) on its axis, the sun rotates into view above the eastern horizon; (d) Earth rotates eastward around its axis to bring the sun into view; (e) Earth rotates westward around its axis to bring the sun into view. CONCEPT CHECK 5 Figure 15 shows the positions (numbered from 1 to 9) of Earth and Mars at nine different times. As you can see, Earth is passing Mars during this time. Draw lines of sight from Earth through Mars to the background stars at each of these nine times. Based on this drawing, Mars is in retrograde motion during (a) times 4 to 6; (b) times 3 to 5; (c) times 1 to 5; (d) times 4 to 7; (e) none of the time; (f) lunchtime. CONCEPT CHECK 6 Following up on the preceding question, if Mars were viewed from the sun it would appear to move in (a) retrograde motion during times 4 to 6; (b) retrograde motion during times 1 to 5; (c) retrograde motion during times 5 to 9; (d) retrograde motion the entire time; (e) normal (forward) motion the entire time. 6

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Although Galileo did not invent the telescope, he was the first to make significant scientific use of it and the first to use it to study the heavens.

The Way of Science Figure 16

Sun

Ptolemy’s theory predicted that an Earth-based observer would never see a “full” phase of Venus because Venus’s epicycle lay between Earth and the sun. Copernicus’s theory predicted that a nearly full Venus could be seen whenever Venus was on the far side of the sun in its orbit around the sun, as it is in Figure 14. Galileo observed that the phases of Venus included a full Venus, thereby disproving Ptolemy’s theory.

Sun's orbit

Venus, in different phases

Venus's epicycle Earth

5 KEPLER’S THEORY: A SUN-FOCUSED UNIVERSE

How do we know more accurate planetary positions? Brahe’s elegant sighting devices (Figure 18) were so accurate that his data are sometimes used today. Before Brahe, the best measurements had inaccuracies (possible errors) of at least 10 arcminutes (an arc-minute is 1/60th of 1 degree). Brahe’s measurements had inaccuracies of only 2 arc-minutes. When Brahe began his project, there were two competing theories of the universe: Ptolemy’s and Copernicus’s. Despite their great dissimilarity, both theories agreed with the data known at that time. Would Brahe’s measurements be able to distinguish between them and so determine which one was correct? For the next 20 years, Brahe cataloged accurate data on the positions of the sun, moon, and planets. It soon became obvious that both theories disagreed with Brahe’s observations by several arc-minutes!

Just 18 months before Brahe died, the 29-year-old Johannes Kepler (Figure 19) managed to gain employment with the famous astronomer. Kepler was born to a ne’er-do-well father who abandoned his family and to a mother who was later tried for being a witch. Furthermore, “The boy was precocious above all in illness, being beset by small pox, headaches, boils, rashes, worms, piles, the mange, and worst of all for an aspiring astronomer, defective eyesight. His visual problems included double vision in one eye and myopia in both eyes.”7 The hardships of his youth seem to have toughened Kepler for the challenges to come. A philosopher, mathematician, astronomer, and astrologer, Kepler was devoted to the Pythagorean notion

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Tycho Brahe (Figure 17), born three years after the death of Copernicus, loved the night sky. A skillful fund-raiser, he obtained financing from the king of Denmark to build a large astronomical observatory.

Figure 17

Tycho Brahe, 1546–1601. By making measurements of the planetary positions that were five times more accurate than were previous measurements, he overthrew two theories of the architecture of the heavens.

Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution (New York: Dover Publications, Inc., 1990).

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American Institute of Physics/Emilio Segre Visual Archives

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Figure 18

Figure 19

An instrument that Brahe used for measuring the angular altitudes of the planets. The two wooden arms are joined together. The lower arm is placed horizontally, as determined by the string and weight hanging vertically from the upper end of the scale. The upper arm is raised until the arm points toward the planet. The planet’s angular position above the horizontal is then read from the graduated scale.

Johannes Kepler, 1571–1630. He contemplated the Copernican theory with “incredible and ravishing delight,” although the scientific facts compiled by Brahe forced him to alter that theory in ways that would have displeased Copernicus. This scientist/mystic has been described by philosopher and novelist Arthur Koestler as the watershed between medieval science and modern science.

of elegant mathematical order, and he harbored another devotion that could only be described as sun worship. Regarding mathematical order, Kepler proclaimed: Why waste words? Geometry existed before the Creation, is coeternal with the mind of God, is God Himself; geometry provided God with a model for the Creation.

Regarding the sun: The sun in the middle of the moving stars, himself at rest and yet the source of motion, carries the image of God the Father and Creator. He distributes his motive force through a medium which contains the moving bodies even as the Father creates through the Holy Ghost.

Given these beliefs, it’s not surprising that Kepler was the first astronomer to openly support the Copernican system, a theory whose beauty he contemplated with “incredible and ravishing delight.” Kepler’s words and thoughts convey the scientist’s passion to understand the universe. Although he was a convinced Copernican, Kepler found that Brahe’s data for Mars were impossible to fit to Copernicus’s theory, even though Kepler tried reintroducing the equant device that Copernicus had so despised. The calculations were tedious. Kepler spent four years on this project, filling 900 notebook pages with finely handwritten calculations. But the Copernican orbit coming closest to Brahe’s data for Mars was still off by 8 arc-minutes. Before Brahe, this could have been ascribed to observational error. But Kepler, toughened by the confrontation with his master’s hard-won data, knew that neither observational error nor further tinkering

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would make uniform circular motion agree with the observed facts. Kepler rejected the Copernican theory. A less passionate person would have given up. Worse yet, a less tough-minded person would have found a way to fudge the data to get them to agree with the Copernican preconceptions that Kepler had believed most of his life. But the everfervent Kepler, writing “on this 8-minute discrepancy, I will yet build a theory of the universe,” began anew. He began studying planetary motions that, for the first time in history, were not based on combinations of uniform circular motions. Copernicus, and all previous astronomers, would have been horrified. Sixteen years later, Kepler finally had his answer: The planets don’t move in circles. They move, instead, in ellipses. He was able to fit an ellipse to Brahe’s data and thus resolve the 8-minute discrepancy that had plagued him for so long. And the data for all the planets fit into elliptical patterns. Kepler’s theory states that rather than moving in sun-centered circles, each planet moves in a sun-focused ellipse: an ellipse having the sun at one of its two “foci.” There is nothing at the other focus. Figure 20 shows how to draw an ellipse.8 You could describe it as a squashed circle. The planetary orbits are only slightly elliptical, which is why sun-centered circles come so close to fitting the observations. The ellipse has just the kind of elegance Kepler had sought. He was elated: What sixteen years ago I urged as a thing to be sought, that for which I joined Tycho Brahe... at last I have brought to light and recognize its truth beyond my fondest expectations.... The die is cast, the book is written, to be read either now or by posterity, I care not which. It may well wait a century for a reader, as God has waited six thousand years for an observer.

Figure 20

You can draw an ellipse with the help of a loop of string and two thumbtacks. The thumbtacks represent the two foci.

CONCEPT CHECK 7 You could use the tack-and-string construction of Figure 20 to construct a circle (a) by moving the two thumbtacks far apart; (b) by adding a third thumbtack, midway between the two thumbtacks shown; (c) by placing the two thumbtacks together.

6 SCIENCE: A DIALOGUE BETWEEN NATURE AND MIND Let’s draw some conclusions from all this history. The most important conclusion is that science is based on direct experience—observation and experiment—and on rational thought to organize and understand this experience. Science’s foundation in experience and reason distinguishes it from other forms of knowledge based on belief, intuition, personal authority, or authoritative books. Although observation is the beginning of the scientific process, a catalog of observed facts does not add up to an understanding of nature, any more than a telephone book adds up to an understanding of a city. To understand—literally, to “stand beneath”—means to perceive a framework. A framework of scientific ideas is called a theory. In the development of astronomy, observations stimulated speculations that led to theories, and these theories in turn suggested new observations to check the theories and suggest new speculations. This interplay between observations and theories is the essence of science. Figure 21 illustrates this dialogue with nature. 8

I measured the skies, now the shadows I measure. Skybound was the mind, earth-bound the body rests. Kepler’s Epitaph, Composed by Kepler

Here is the exact definition: An ellipse is all the points on a flat surface for which the sum of the distances of each point on the ellipse from two fixed points (the two “foci”) is constant. The construction shown in Figure 20 follows this definition.

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The Way of Science Figure 21

How we began to learn where we are in the universe. The figure illustrates the dynamic interplay between observations and theory that is the essence of science. In science it often happens that scientists say, “You know that’s a really good argument; my position was mistaken,” and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn’t happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. Carl Sagan, Astronomer and Science Writer

A Summary of the Early History of Astronomy Observations

Typical Dates

Stars, sun, moon, and planets are moving overhead.

3000 BCE

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Pythagorean hypothesis: Earthcentered transparent spheres.

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Plato’s hypothesis: multiple transparent spheres.

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Aristarchus’s hypothesis: sun-centered circles.

Each planet moves at a varying rate; retrograde motion.

Heaven and Earth seem different; Earth seems motionless, apparently contradicting Aristarchus’s hypothesis.

200 Planets are brighter during retrograde motion. 100

Physical theory without experiment is empty. Experiment without theory is blind. Heinz Pagels, Physicist

The whole of science is nothing more than a refinement of everyday thinking.... The scientific way of forming concepts differs from that which we use in our daily life, not basically, but merely in the more precise definition of concepts and conclusions, more painstaking and systematic choice of experimental material, and greater logical economy. Albert Einstein

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Theories

Detailed quantitative measurements show need for small corrections.

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Hypothesis of Earth-centered epicycles.

Ptolemy’s theory: Earthcentered epicycles, equants.

100 CE 1500 Copernicus’s theory: suncentered circles. Brahe’s accurate measurements disprove Ptolemy’s and Copernicus’s theories. 1600

Kepler’s theory: sun-focused ellipses.

Galileo’s telescopic observations disprove Earth-centered theories.

Observation refers to the data-gathering process. A measurement is a quantitative observation, and an experiment is an observation that is designed and controlled by humans, perhaps in a laboratory. A scientific theory is a well-confirmed framework of ideas that explains what we observe. A model is a theory that can be visualized, and a principle or law is one idea within a more general theory. The word law can be misleading because it sounds so certain. As you will see, scientific ideas are never absolutely certain. Note that a theory is a well-confirmed framework of ideas. It’s a misconception to think that a scientific theory is mere guesswork, as nonscientists occasionally do when they refer to some scientific idea as “only a theory.” Theories—wellconfirmed explanations for what we observe—are what science is all about and are as certain as any idea can be in science. The correct word for a reasonable but unconfirmed scientific suggestion (or guess) is hypothesis. For example, Kepler’s first unconfirmed suggestion that the

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planets might move in elliptical orbits was a hypothesis. Once the data of Brahe and others confirmed Kepler’s suggestion, elliptical orbits took on the status of theory rather than mere hypothesis. Figure 22 shows the general form of Kepler’s theory of the solar system (the sun and its planets), extended to include all eight planets known today. This theory explains all of Brahe’s data and all preceding observations and unifies these data into a few principles such as the principle of elliptical orbits. As you can see, a theory represents an enormous simplification or reduction of many observations into a few simple ideas. But Kepler’s theory does more than describe known data. It also predicts new observations. For example, when the new planets Uranus and Neptune were discovered, Kepler’s theory predicted, correctly, that they too would move in elliptical orbits. A theory having no predictive value, which needs to be patched up to account for every new observation, isn’t worth much. For example, Ptolemy’s theory could doubtlessly be amended with enough new epicycles to make it agree with all of Brahe’s data, but the result would be a confusing mess with little predictive ability. Most importantly, Kepler’s theory suggested further developments. Isaac Newton, born a few years after Kepler’s death, built on Kepler’s theory in developing his own theories of motion and gravity. Another misconception about theories, especially if they happen to be called “laws,” is that they are absolutely certain and hence that scientific knowledge is absolute. Let’s look at history. Ptolemy’s theory correctly predicted the planetary observations, and so did Copernicus’s theory. Both were, and are, good theories for many purposes. But new, more accurate observations by Brahe contradicted both theories, opening the way for Kepler’s theory. Did Kepler, then, discover the true motion of the planets? Not necessarily. In the future, astronomers might discover that the planets have begun severely deviating from their elliptical paths, as could happen if, for example, another star passed close to our sun. It is always possible that new data will contradict any general theory. Good science is always provisional, nondogmatic. All theories dangle by the slender thread of evidence.

The great intellectual division of mankind is not along geographical or racial lines, but between those who understand and practice the experimental method and those who do not understand and do not practice it. George Sarton, Historian of Science

The aim of science is not to open the door to everlasting wisdom, but to set a limit on everlasting error. Bertolt Brecht, Playwright, in The Life of Galileo

Figure 22

The arrangement of the solar system as it is now known. Uranus and Neptune are visible only with a telescope. The orbits are elliptical, although their ellipticity is too small to be visible in this diagram. Saturn

Sun

Uranus

Mars Earth Venus Mercury

Jupiter

Neptune

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[The scientific process is] designed to counter human selfdeception. People always think they’re right, and powerful people will tend to use their authority to bolster their prestige and suppress inconvenient opposition. You try to set up the game of science so that the truth will out despite this ugly side of human nature. Steven Pinker, Harvard, Cognitive Psychologist, Author of The Modern Denial of Human Nature

In fact, today’s highly accurate observations show that the planets move along orbits that actually do deviate slightly from precise ellipses. According to Isaac Newton’s theories, Kepler’s elliptical orbits are caused by gravity acting between the sun and each planet. The main cause of the deviations from elliptical motion is gravity acting between the different planets. Interplanetary dust and many other things also cause small deviations. Nevertheless, scientists have retained Kepler’s theory because it’s a good and useful approximation. Perhaps we should describe theories as good or useful rather than true. The fact that theories are never absolutely certain is a strength, not a weakness, of science. Absolute certainty can foster dogmatism and a rigid inability to change what needs changing. Theories can be good, useful, fruitful, or compelling, but they are never certain. If a theory cannot be tested against observations, then it tells us nothing about the observable universe and is not a scientific theory at all. Scientific theories must be testable by observations that could conceivably contradict the theory. For example, a notion such as “undetectable alien creatures are living among us” is not a scientific statement, not because this notion seems odd (most scientific theories are odd), but because the creatures are said to be undetectable. Scientifically, this statement is not true and it’s not even false. Being untestable, it is outside science. Nonscientific ideas can, of course, have their own validity. “Beethoven’s music is sublime,” or “May God bless this home,” can be meaningful statements, but they lie outside science. The elegant tools of Brahe and the inspired theories of Pythagoras and Kepler show that science thrives on creativity. It is one of nature’s mysteries that these beautiful inventions actually turn out to produce a consistent picture of the universe. Scientists generally believe in the Pythagorean ideal of a universe based on simple and elegant principles. Copernicus adopted a sun-centered theory over the hallowed Earth-centered theory because it was “pleasing to the mind.” Scientists such as Kepler strove passionately to perceive such an elegant framework. When creating his theories, Einstein used to ask himself how he would have constructed the universe if he were God. The scientific process of observing and theorizing is not very different from our ways of coping with daily life. In science, as in life, we learn from experience and by thinking carefully. It’s a very human activity. To summarize: The Scientific Process Science is a process, a way of learning, rather than a set of conclusions. It is the process of using evidence (experiments and observations) and reason (hypotheses and theories that correlate the evidence) to develop testable knowledge about the natural world. This basis in evidence and reason distinguishes science from other forms of knowledge based on belief, intuition, personal authority, or authoritative books.

I will return frequently to the theme of the scientific process. CONCEPT CHECK 8 The idea that proved fruitful (or useful) for Kepler as he developed his own ideas was (a) Copernicus’s theory; (b) Aristarchus’s hypothesis; (c) Ptolemy’s theory; (d) Plato’s hypothesis; (e) Newton’s theory. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house. Jules Henri Poincaré, Scientist and Mathematician, 1854–1912

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CONCEPT CHECK 9 William is absolutely certain of a particular scientific principle. You can conclude from this that (a) this principle is correct; (b) this principle is wrong; (c) this principle is irrelevant; (d) William is being scientific; (e) William is being unscientific; (f) William is a blithering idiot.

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7 THE COPERNICAN REVOLUTION: DAWN OF THE MODERN AGE The scientific age has its roots in two historical developments. One is the Pythagorean belief in natural harmonies, an idea that captivated Greek philosophers and then spread to Europe and the world. Its central premise is that the universe is organized in a framework of principles that can be uncovered by observation. The second is the rejection of the “geocentric illusion” that Earth is at the center of, and therefore fundamentally different from, the rest of the universe. Copernicus started this development, which is justly called the Copernican revolution. Its thrust is that, just as Earth is a planet similar to the other planets, the natural world is fundamentally the same everywhere, differing in details at different places and times but always following the same general principles. When stated in this form, you can see a kind of symmetry in the Copernican viewpoint. Symmetry is an important theme throughout science. An object is commonly said to have symmetry when it can be viewed from several perspectives and still look the same. For instance, a square can be viewed from four directions and still look the same. The thrust of the Copernican viewpoint is that, no matter where you are in the universe, the fundamental operating principles are the same there as they are here on Earth. Others began thinking along these lines. It became apparent that the sun—considered by Copernicus and Kepler to be central to the universe—was a star like the other stars. We now know that the visible stars belong to a vast revolving aggregation of some 400 billion stars spread out in the shape of a giant pizza. Our sun, one of the stars in the outreaches of this aggregation, circles the center every 200 million years. But the center of this aggregation is not at the center of the universe, either. Instead, there are hundreds of billions of other similar aggregations of stars throughout the observable universe. And according to current theories, none of these aggregations is at the center, because the universe has no center—an odd idea that is the ultimate extension of Copernican astronomy. Each of these aggregations is called a galaxy. Ours is the Milky Way galaxy. Figure 23 shows a typical galaxy, one much like our own. The cloudlike glow in the night sky that is called the Milky Way is our galaxy seen from our position

NASA Headquarters

Figure 23

The Andromeda galaxy, photographed through a telescope. This is the nearest large galaxy outside of our own Milky Way galaxy. Like our galaxy, Andromeda is made of billions of stars, each one somewhat similar to our sun, whirling around a bright star-filled center. Andromeda is nearly invisible to the unaided eye and lies far beyond the visible stars of our own galaxy. Since light takes about 2.5 million years to reach here from there, you are looking at 2.5-million-year-old history.

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Humanity has perhaps never faced a greater challenge; for by [Copernicus’s] admission [that humanity is not the center of the universe], how much else did not collapse in dust and smoke: a second paradise, a world of innocence, poetry and piety, the witness of the senses, the conviction of a religious and poetic faith...; no wonder that men had no stomach for all this, that they ranged themselves in every way against such a doctrine. Johann Wolfgang Von Goethe, Nineteenth-Century German Poet and Dramatist

within it—it’s like standing in the middle of a giant pizza and looking into the dough. The glow comes from the stars in only a small, local portion of our entire galaxy. The center of our galaxy lies far beyond the visible Milky Way, in the direction of the constellation (group of stars) known as Sagittarius. There are lots of galaxies out there. Figure 24 is a photograph of the very distant galaxies in a typical narrow speck of sky containing hundreds of galaxies. In the entire observable universe—that part of the universe from which we can receive light—there are something like 100 billion galaxies. There are about as many galaxies in the observable universe as there are stars in our Milky Way galaxy! It’s a big place. Copernicus sowed the seeds of many revolutions. Once Copernicus announced that Earth is a planet, Isaac Newton could unify the heavens and Earth in a new physics based on principles that were uniform throughout the universe. And just as Copernicus unified Earth with the other planets, Charles Darwin conceived an evolutionary biology that unified all life and included humankind as one species among many. The Copernican/Newtonian conception of natural laws that apply democratically everywhere and to all people helped to propel the political transition from medieval authority to constitutional law and democracy. The U.S. Declaration of Independence, for example, refers to the “Laws of Nature” that entitle the people to assume a separate and equal station with their former rulers. This notion that natural law applies equally to all people stems partly from the universality of Newtonian physics. Copernican astronomy was correctly perceived as revolutionary by religious and philosophical authorities. Ptolemy’s system had been developed in parallel with Earth-centered Aristotelian physics, and Aristotle’s thinking was a foundation of Catholic theology. The perfection of heaven, the imperfection of Earth, and humankind’s centrality to God’s plan for the universe were threatened by the loss of the Ptolemaic system. Seventy years after Copernicus’s death, the Catholic church pronounced his theory “false and erroneous,” “altogether opposed to Holy Scripture,” and “heretical.” Science historians believe that during this period, science and religion fell out into two noncommunicating camps that still, today, feel they are at odds with each other.

This view of distant galaxies was taken with the Hubble Space Telescope. Nearly every object in the photograph is an entire galaxy, most of them so far away that the light we see from them started on its journey about 13 billion years ago. This is around the time we believe the galaxies were formed, and only about 1 billion years after the origin of the universe. The view covers only a narrow speck of sky one-thirtieth the diameter of the full moon, and reaches deeper into space than any previously visible image. Although this view shows a very small sample of sky, it is considered a typical representative of the distribution of galaxies in space because the universe, statistically, looks the same in all directions.

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NASA Headquarters

Figure 24

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This situation is a far cry from the Pythagoreans, who considered science and religion to be the same thing. Champions of the Copernican theory were denounced and persecuted by religious authorities.9 Leaders of the Protestant Reformation were even more extreme in denouncing the new astronomy. The main Protestant objection was that the new theory ran counter to a “literal” reading of the Bible. The Bible frequently mentions a moving sun and a fixed Earth, contrary to the Copernican theory. Even before publication of the new theory, Protestant leader Martin Luther heard about Copernicus’s ideas and condemned them for contradicting the Bible. In Luther’s opinion, “The fool [Copernicus] will turn the whole science of astronomy upside down. But, as the Holy Writ declares, it was the sun and not the Earth which Joshua commanded to stand still.” It is not surprising that Copernicus, prudent by nature, withheld publication of his planetary theory until his dying day. CONCEPT CHECK 10 Which of the following represent a continuation of the basic thrust of the Copernican revolution? (a) The universe was made for humans. (b) The moon is probably made of material that split off of Earth. (c) Our sun is just one star among billions of similar stars. (d) Our Milky Way galaxy is at the center of the universe. (e) The human species is not very different biologically from the other species. (f) Our galaxy is just one among billions of similar galaxies. CONCEPT CHECK 11 The most characteristic feature of science is (a) the use of precise mathematical relations; (b) precise quantitative observations; (c) the absolute truth of the scientific laws; (d) the mutually supporting relationship between theory and observation.

8 PSEUDOSCIENCE As part of understanding what science is, we need to understand what it’s not. Because science is so widely accepted today, it has become common for all manner of charlatans to hawk their wares by alleging some scientific basis for them. Thus we’ve been treated, during the past century or so, to a proliferation of pseudoscientific claims—claims presented so as to appear scientific even though they lack supporting evidence and plausibility and therefore aren’t scientific. Typically, pseudoscientists reverse the scientific process by assuming their desired conclusion at the outset and then searching for evidence that supports that conclusion while ignoring evidence and arguments to the contrary. Using such a biased and backwards approach, it’s possible to “prove” (in the eyes of the convinced believer) anything, including some of the most absurd nonsense imaginable. Pseudoscience comes in many guises (Table 1). Although some of the supposed phenomena in Table 1 are not entirely ruled out by the evidence, there is no real scientific evidence that actually supports any of them. Although they might have other, non-scientific virtues, these beliefs lie outside of science because they have not received support from the scientific process. It’s a significant issue. Pseudoscientific views are alarmingly popular: 52% of American adults believe astrological “predictions,” 46% believe in extrasensory perception, 42% believe that people can communicate with the dead, and 35% actually believe in ghosts. One-and-a-half centuries after Darwin’s The Origin of 9

Early in 1926 [the magician] Houdini made a pilgrimage to Washington to enlist the aid of President Coolidge in his campaign “to abolish the criminal practice of spirit mediums and other charlatans who rob and cheat grief-stricken people with alleged messages.” From Houdini, by B. R. Sugar

Every science that is a science has hundreds of hard results; but search fails to turn up a single one in “parapsychology.” John A. Wheeler, Physicist

In 1984, the Vatican stated that church officials had erred in condemning Galileo and called for increased dialogue between science and religion. Then in 1992, the pope announced that the church had wrongly accused Galileo, laying the blame on seventeenth-century church authorities who interpreted the Bible too literally.

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The Way of Science Table 1 A few of the better-known pseudosciences ancient astronauts

extrasensory perception

orgone boxes

astrological birth control

Falun Gong

parapsychology

astrology

flying saucers

perpetual motion machines

Bermuda Triangle

fortune-telling

phrenology

Big Foot

ghosts

psychic surgery

channeling

holocaust denial

psychokinesis

creationism

homeopathy

pyramid power

crop circles

intelligent design

quantum mysticism

crystal healing

Kirlian aura

remote viewing

crystal power

levitation

séances

dianetics

lost continent of Atlantis

spoon bending

dowsing

Noah’s flood

Velikovsky’s colliding worlds

emotions in plants

occult chemistry

witches

extraterrestrial visitations

To the best of my knowledge there are no instances out of the hundreds of thousands of UFO reports filed since 1947—not a single one—in which many people independently and reliably report a close encounter with what is clearly an alien spacecraft. Carl Sagan, Astronomer, Physicist, Educator, and Author

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Species, 46% believe that human beings did not develop from earlier animals. And 43% believe it likely that some of the reported unidentified flying objects are really space vehicles from other civilizations. More fundamentally, pseudoscience is a kind of mind pollution. By pretending to be what it’s not (namely science), pseudoscience weakens one’s ability to think honestly and rationally. Let’s look at three typical pseudoscientific beliefs: extraterrestrial visitations, astrology, and creationism. UFOs are unidentified objects in the sky, or “unidentified flying objects.” Two UFO beliefs have gained a following in the popular media. The first is that some UFOs are visitations by contemporary aliens; the second is that aliens visited Earth in the past. The problem with these ideas is not that UFO beliefs themselves are inherently antiscientific. The problem, instead, is in the nonscientific way these beliefs are supported. Let’s examine the evidence. There have been thousands of reports of sightings of strange lights, strange aircrafts, and people being captured by aliens. Upon investigation, these reports fall into three categories. Most have normal explanations: automobile headlights reflected off high-altitude clouds, a flight of luminescent insects, unconventional atmospheric effects, unconventional aircrafts, aircrafts using searchlights for meteorological observations, aerial refueling operations, orbiting satellites, sunlight reflecting from objects that are dropped from aircrafts, or the setting planet Venus distorted by the atmosphere. Although these are honest reports, “seeing what you want to believe” is common. For example, the U.S. Air Force collected 30 UFO reports in 1968 when a satellite reentered the atmosphere and broke into burning pieces in the night sky. Of these, 57% reported that the objects were flying in formation, implying intelligent control, and 17% claimed that the glowing objects were attached to a black “cigarshaped” or “rocket-shaped” object, sometimes with glowing windows. Other reports are hoaxes, often for profit. For example, a 1968 University of Colorado study, headed by physicist Edward Condon, established that many of the classic UFO photos are either fakes or photos of known natural phenomena. Nevertheless, these photos continue to reappear in new UFO publications. Great Britain’s widely publicized “crop circle” phenomenon reported around 1990 was caused by pranksters.

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Finally, a few UFO reports cannot be explained. In any investigation of unusual phenomena, there will always be cases that remain unexplained because of lack of data, false reporting, self-deception, and so forth. The unexplained UFO reports offer no positive evidence, such as unambiguous photographs or unambiguous sightings by many observers or an artifact (a tool or piece of material) left behind by aliens. Such a residue of unexplained cases, with no positive evidence, is not surprising and offers no support for UFO beliefs. In fact, the evidence points the other way. The only real evidence we have is negative: Extraterrestrials have not come right out and revealed themselves to us. So if they exist, they prefer to conceal themselves. Any extraterrestrial civilization able to mount a journey to Earth would surely be able to conceal themselves from us if they wanted to and would not make simple mistakes like flying around in visually observable vehicles. So reports of UFO sightings are inherently implausible. Furthermore, it’s surprising that such beings would want to conceal themselves. It seems more reasonable that they would want to contact and investigate us. At least, this is what human explorers have done when they discovered new cultures. A common fallacy of many UFO reports is that far from being overly fantastic, they are not nearly fantastic enough to be believable. The reported technologies are always just a little in advance of, or even behind, the current technology on Earth. The aliens are reported to have curiously humanlike features. But there is little reason to expect that alien technologies, or alien body features, would resemble ours. These are some of the reasons that scientists who have thought about this matter overwhelmingly reject the hypothesis that we are being visited. The second UFO belief, that we have been visited in the past, has even less supporting evidence. Ancient legends of superior beings mean little: Most cultures have had such legends, based on either real humans or stories promoted by the priesthood. An ancient legend containing “futuristic” information, such as instructions for an electronic circuit, might be convincing. Also convincing would be an ancient artifact that could not have been made by the ancient civilization, like an electronic microchip or an advanced metallic alloy. But such evidence hasn’t been found. Popular UFO mythology illustrates several common features of pseudoscience: mistaken observations attributed to exotic causes when simpler explanations suffice, deliberate fraud, using a small number of unexplained cases as proof of an exotic hypothesis, and self-deception caused by a desire to believe. It is for precisely such reasons that scientists ask, How do we know? What is the evidence? Astrology, the belief that events on Earth are influenced by the positions of the planets, began in ancient Babylonia. It seemed reasonable in an era that believed the planets existed for human purposes. Its central belief is that the configuration of the sun, moon, and planets at the moment of a person’s birth affects his or her personality or fortune. A simplified form of astrology, based only on the position of the sun, is the mainstay of newspaper astrology columns. Today, astrology is scientifically implausible, to say the least. The only known physical influences exerted on Earth by the planets are gravitational effects and electromagnetic radiation. It is hard to imagine how these effects at birth could influence our lives. For example, the gravitational effects10 exerted on a baby by the doctor and nurse and furniture in the delivery room far exceed the effects of the planets, the walls of the delivery room shield us from many radiations, and the variations in the sun’s radiation output (variations that are unrelated to a person’s astrological sign) are far larger than the total radiation received from the moon and all the planets added together. 10

In the prehistoric period, the human civilization sometimes lasted long, sometimes short. Some human civilization lasted very long. Mankind in every cycle takes a different way in the development of science. In fact, the moon was made by the prehistoric human beings. It is hollow inside. From Zhuan Falun, Volume II, Literature of the Chinese Cult Known as Falun Gong, by Falun Gong Leader Li Hongzhi, 1998.

The effects referred to here are “tidal effects,” by which the moon and sun cause tides in bodies of water on Earth. Tidal effects cause similar, but smaller, distortions in all objects on Earth.

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The Way of Science

Virtually every major move... the Reagans made was cleared in advance with a woman in San Francisco who drew up horoscopes to make certain that the planets were in a favorable alignment for the enterprise. Nancy Reagan seemed to have absolute faith in... this woman.... At one point, I kept a color-coded calendar—highlighted in green for “good” days, red for “bad” days, yellow for “iffy” days—as an aid to remembering when it was propitious to move the President from one place to another, or schedule him to speak in public, or commence [foreign] negotiations. Donald Regan, Chief of Staff to Former President Ronald Reagan

Science is the great antidote to the poison of ... superstition. Adam Smith, in The Wealth of Nations

For us, not to believe in inerrancy is not to believe in God.... [T]he Bible is literally without error in all respects—in history and science as well as religion.... Adam and Eve were real people. The historical narratives of the Bible are accurate. Miracles of the Bible were supernatural events. The authors stated by all the books were the authors of the book. Rev. M. H. Chapman, President of the Nation’s 14.9 Million Southern Baptists, 1990

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How do we know astrology is not credible? Despite its scientific implausibility, can we find any evidence that astrological predictions are correct? A number of researchers have studied this question, some of them using astrological predictions based on horoscopes (charts showing the orientation of the planets at the moment of birth) for thousands of people, and found no evidence that astrology has any power to predict personalities or lives. If astrology were valid, such evidence should be easy to find. For example, University of California educator and physicist Shawn Carlson conducted a rigorously controlled investigation of astrology that was published in the 5 December 1985 issue of the journal Nature. He studied 30 astrologers considered by their peers to be among the best practitioners of their art. Carlson asked the astrologers to interpret birth charts for 116 real-life but unseen “clients.” With each client’s chart, astrologers were provided three personality profiles, one from the client and two others chosen at random, and asked to choose the one that best matched the birth chart. Contrary to the astrologers own predictions that they would spot the correct chart significantly more often than the “guessing” frequency of one-third, Carlson found that they could correctly match only one of every three charts—the proportion predicted by chance. Even when astrologers expressed strong confidence in a particular match, they were no more likely to be correct. Carlson comments that astrologers may be successful because they draw clues about their clients from body language and verbal responses, but not because astrology itself has any scientific validity.

Even though astrology is incredible theoretically and disproved observationally, half of American adults say they believe in it; newspapers continue their daily astrological predictions; there are many times more professional astrologers than astronomers; and former president Ronald Reagan’s scheduled activities were determined partly by astrological horoscopes (see marginal quotation). Will humankind outgrow its most harmful instincts and develop a mature culture able to control its own technology? Facts such as these give little cause for optimism. Creationism is the belief that the Bible’s Old Testament can be read literally, as scientific and historical truth, and that Earth and the main biological organisms, including humans, all were created separately and at roughly the same time, just a few thousand years ago. Creationism, including its variations such as “intelligent design” (see below), is perhaps the most harmful pseudoscience in the United States because it is believed by so many people, it is fervently championed by many powerful religious organizations, and it tries to cast doubt on science education, especially biology education. For example, in 1999, creationists in Kansas removed from the state science standards all mention of the big bang, radioactive dating, continental drift, the age of Earth, global warming, and biological evolution. Like astrology, creationism was credible until a few centuries ago, and many scientists believed it. But today it conflicts with the observations and principles of astronomy, physics, chemistry, geology, biology, paleontology, and archaeology. There is a broad scientific consensus, supported by a consistent network of evidence from many sciences, that Earth is billions of years old, that humankind is millions of years old, and that humans are related through biological evolution to all other living creatures. Although scientific ideas are never certain, and honest doubts about established theories should never be arbitrarily dismissed, creationist arguments have found essentially no scientific support. Creationist beliefs are in direct conflict with physics on several counts. According to one creationist argument, biological evolution conflicts with the second law of thermodynamics, because evolution describes an increasingly organized biological realm while the second law says that things become more disorganized. But the same question arises in the growth of a leaf, which creates organization out

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of disorganized water and carbon dioxide. The answer to this apparent dilemma is that the leaf is not an isolated system but instead gets crucial assistance from the sun’s radiation, whereas the second law applies only to isolated systems. The same is true of the evolution of all life. The biological realm could not exist without the sun’s radiation to both energize and organize all life on Earth. Evolution does not violate the second law. This creationist argument, based on the second law, is an excellent example of pseudoscience because it sounds scientific but is in fact a misleading distortion of science. Other points of conflict between creationism and physics include the big bang and the conclusions of radioactive dating and other methods of determining the ages of objects. Four independent lines of evidence point to the big bang creation of the universe about 14 billion years ago. There is an enormous and consistent body of radioactive and nonradioactive evidence showing that Earth is billions of years old and dating the geological ages in a manner that confirms evolution but disproves creationism. One creationist view, known as intelligent design, put forth recently is that life is too complex in certain regards, such as complex cellular structures, to have evolved by Darwinian processes. Intelligent design’s key idea, that complex structures could not evolve through intermediate nonfunctional steps, is a new version of the old “argument from design” first proposed 200 years ago and discredited long ago by biologists. The intelligent design view argues (unconvincingly, in the view of the vast majority of biologists) against evolutionary explanations of complexity, but without putting anything in its place. If complex structures did not originate through the evolutionary process, then how did they originate? Arguing that an “intelligent designer” (in other words, God) did it explains nothing, tends to stifle further scientific research, and is beside the point because it doesn’t tell us how a complex structure came to be complex. It’s important to note that science is compatible with a belief in God and with many other religious beliefs. Many scientists are Christians, and many more believe in God. Science has nothing to say about the existence or nonexistence of God, because science studies only natural processes, not supernatural processes. Many scientists harbor a deep conviction that both science and religion are part of a single larger truth. In 2005, the American Association of Physics Teachers adopted a statement on the teaching of evolution and cosmology that demonstrates an admirable understanding of the scientific process. It says, in part:

It is our conclusion that creationism ... is not science. It subordinates evidence to statements based on authority and revelation.... Its central hypothesis is not subject to change in light of new data or demonstration of error. Moreover, when the evidence for creationism has been subjected to the tests of the scientific method, it has been found invalid. National Academy of Sciences, Committee on Science and Creationism, 1984

Nothing in biology makes sense except in the light of evolution. Theodosius Dobzhansky, Geneticist

No scientific theory, no matter how strongly supported by available evidence, is final and unchallengeable; any good theory is always exposed to the possibility of being modified or even overthrown by new evidence. That is at the very heart of the process of science. However, biological and cosmological evolution are theories as strongly supported and interwoven into the fabric of science as any other essential underpinnings of modern science and technology. To deny children exposure to the evidence in support of biological and cosmological evolution is akin to allowing them to believe that atoms do not exist or that the Sun goes around the Earth. We believe in teaching that science is a process that examines all of the evidence relevant to an issue and tests alternative hypotheses. For this reason, we do not endorse teaching the “evidence against evolution,” because currently no such scientific evidence exists. Nor can we condone teaching “scientific creationism,” “intelligent design,” or other non-scientific viewpoints as valid scientific theories. These beliefs ignore the important connections among empirical data and fail to provide testable hypotheses. They should not be a part of the science curriculum.

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School boards, teachers, parents, and lawmakers have a responsibility to ensure that all children receive a good education in science. The American Association of Physics Teachers opposes all efforts to require or promote teaching creationism or any other non-scientific viewpoint in a science course.

© Sidney Harris, used with permission.

CONCEPT CHECK 12 Creationists sometimes argue that all the evidence that Earth is billions of years old was actually created just a few thousand years ago in order to make Earth appear old without really being old. Is this argument scientific? (a) Yes, even though it is not especially credible. (b) Yes, even though it is impossible to prove. (c) Yes, even though it is impossible to disprove. (d) No, because it is impossible to prove. (e) No, because it is impossible to disprove.

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The Way of Science Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions

18. According to Kepler’s theory, what geometric shape fits the planetary orbits?

OBSERVING THE NIGHT SKY

THE SCIENTIFIC AND COPERNICAN REVOLUTIONS

1. What two reasons does this chapter give for studying science? 2. What is physics? 3. Distinguish astronomy from astrology. 4. What astronomical objects can you normally see in the night sky? Describe their motion as seen from Earth.

ANCIENT GREEK THEORIES 5. What did the Pythagoreans believe, and how did these beliefs influence the development of science? 6. According to the earliest Greek hypothesis, the planets orbit Earth in uniform circular motion. In what way does this hypothesis disagree with simple observations made without telescopes? 7. Give two observational reasons for believing that Earth is curved rather than flat. 8. How does Ptolemy’s theory explain the retrograde motion of the planets and the fact that planets are brighter during retrograde motion? 9. Did Ptolemy’s theory agree with the quantitative observations known in Ptolemy’s time? How were these observations made?

COPERNICUS’S THEORY 10. “Copernicus rejected Ptolemy’s theory because it disagreed with the data, and he proposed a new sun-centered theory that did agree with the data.” True or false? Explain. 11. Use Copernicus’s theory to explain the retrograde motion of the planets and the fact that they are brighter during retrograde motion. 12. Why did Copernicus propose his theory? 13. State at least one plausible argument against the notion that Earth moves around the sun. 14. How did new telescopic evidence decisively disprove Ptolemy’s theory?

KEPLER’S THEORY 15. “Kepler was attracted to Copernicus’s theory because the known data supported that theory.” True or false? Explain. 16. Describe Brahe’s work and its effect on the theories of Copernicus and Ptolemy. 17. What aspect of Kepler’s theory would have horrified all previous astronomers?

19. What is the most characteristic and significant feature of science? 20. Describe several characteristics of a good scientific theory. 21. Can a scientific theory be proved (can we show that the theory is certainly true)? Can it be disproved? Explain. 22. Strictly speaking, Kepler’s theory has been disproved. What has been found wrong with it? Why, then, do we still use it? 23. How does a hypothesis differ from a theory? 24. Distinguish between the Copernican theory and the Copernican revolution. 25. In what sense can evolutionary biology be said to be “Copernican”?

PSEUDOSCIENCE 26. What is pseudoscience? List several examples. 27. What are the two popular UFO beliefs? What is the scientific consensus about them, and why? 28. What is astrology? What is creationism? 29. Why do scientists consider UFO beliefs to be pseudoscientific? Answer the same question for astrology and for creationism.

Conceptual Exercises OBSERVING THE NIGHT SKY 1. How can you tell, from naked-eye observation alone, whether a particular object in the sky is a planet? 2. Draw a diagram showing the positions of Earth, the moon, and the sun at new moon, crescent moon, nearly full moon, and full moon. 3. Are the stars in Figure 4 circling clockwise or counterclockwise? A time-lapse photograph made in the Southern Hemisphere, looking toward the South Pole, would also show the stars moving in a circle around a fixed point in the southern sky. Would the stars in the southern view be circling clockwise or counterclockwise?

From Chapter 1 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Way of Science: Problem Set

ANCIENT GREEK THEORIES 4. Describe a naked-eye observation you could make to disprove the theory that the planets orbit Earth in a simple, uniform, circular motion. 5. Describe a naked-eye observation you could make to disprove the theory that the planets orbit Earth attached to transparent spheres that rotate in a complicated fashion but that are always centered on Earth. 6. In seeking an explanation of retrograde motion, why didn’t the Greeks just allow the planets to change their speed and direction of motion as the planets moved along circular paths around Earth, instead of resorting to circles within circles?

10. Use Copernicus’s theory to explain why Venus often appears as the morning star or the evening star.

KEPLER’S THEORY 11. Which aspects of Kepler’s theory would Copernicus have liked? Disliked? 12. Would Kepler’s theory have agreed with the data available in Ptolemy’s time? In Copernicus’s time? 13. Did Brahe’s data prove that planets move in ellipses? Explain. 14. Is there anything in Kepler’s theory that resembles the displaced centers of Ptolemy and Copernicus? 15. Who is the “observer” mentioned by Kepler? 16. Kepler says that God has waited 6000 years. Why 6000? 17. Explain how to get a highly elliptical (elongated) orbit from the tack-and-string construction of Figure 20.

COPERNICUS’S THEORY 7. Is it possible that on some evenings the planet Mars is the evening star? Is this very likely? (see figure below) 8. Use Copernicus’s theory to predict whether Mars goes through moonlike phases. Do we ever see a “full Mars”? A “new Mars”? 9. It is possible, but difficult, to see the planet Mercury with the unaided eye. How, then, would you go about finding it?

Sphere of the stars

Copernicus’s sun-centered theory of the layout of the universe, 1543 CE. The diagram is simplified; the planets all move on epicycles, similar to those in Ptolemy’s theory, but here there are far fewer epicycles, and no equants.

Jupiter Mars

Mercury

Venus Sun

Moon Earth

Saturn

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Figure 14

The Way of Science: Problem Set

THE SCIENTIFIC REVOLUTION 18. Because Darwinian evolution is only a theory, we need not take it seriously. Comment on this statement. 19. What is the most important and characteristic feature of science? 20. Can two different theories both be true in the sense that at some particular time in history, they correctly predicted the known data? Defend your answer with a historical example. 21. “If Earth is curved, it must have a spherical shape, because a sphere is the most perfect curved solid form.” Does an aesthetic argument like this have any place in science? 22. A sensationalist tabloid “news”paper carries this headline “SCIENTISTS PREDICT THAT THE UNIVERSE AND EVERYTHING IN IT WILL DOUBLE IN SIZE AT THE BEGINNING OF THE NEXT NEW YEAR!” Is this a testable hypothesis? If so, how could you test it, and if not, why not? Is this good science, bad science, or neither? 23. What is the scientific attitude toward beliefs such as astrology, dianetics, extrasensory perception (ESP), visitations by extraterrestrials, a 6000-year-old Earth, the Bermuda Triangle, and pyramid power? 24. Aristotle, a careful observer of living organisms, wondered where the material that contributes to the growth of a plant comes from. He hypothesized that all of it comes from the soil. Based on your knowledge of biology, do you consider this hypothesis to be correct? Propose an experiment to test this hypothesis. 25. Some people believe that plants will grow better if they are talked to. Is this a testable hypothesis? If so, propose an experiment to test it. 26. “Certain people are gifted with extrasensory perception (ESP), such as the ability to move material objects with their own minds. However, ESP is so delicate that every attempt to verify it always destroys it.” Is this a scientific hypothesis? 27. Isaac Newton predicted that because of its spinning motion, Earth would bulge out near the equator and be flattened near the poles. In 1735 the French Academy of Sciences sent an expedition to the Arctic to measure the exact shape of Earth. When they returned, reporting the predicted results, the philosopher Voltaire mocked them with the following couplet: To distant and dangerous places you roam To discover what Newton knew staying at home. Was Voltaire’s sarcasm justified? Why or why not? 28. Consider the flat Earth hypothesis. Give evidence for this hypothesis. Give evidence against it.

THE COPERNICAN REVOLUTION 29. Since there are some 100 billion stars in a typical galaxy, and since there are at least 100 billion galaxies in the known parts of the universe, how many stars are there in the known universe? Write this number out. 30. An astronomical unit (AU) is the distance from Earth to the sun. The radius of the approximately circular orbit of Mars is about 1.5 AU. As Earth and Mars orbit the sun, what is their greatest and least distances apart, measured in AU? 31. A light-year (LY) is the distance light travels in one year. Our nearest neighboring star is 4 LY away. Using the fact that light gets here from the sun in 8 minutes, how many AU (preceding exercise) is it to our nearest neighboring star?

32. The astronomical object known as the Crab Nebula is the remnant of an exploded star. The explosion was seen, by the Chinese, in 1054 CE. However, the Crab Nebula is about 3500 LY (preceding exercise) distant from Earth. In what Earth year did the star actually explode?

PSEUDOSCIENCE 33. Jeane Dixon, who also claims to have forecast John F. Kennedy’s assassination, once claimed that an incredible vision informed her that aliens from another planet in our solar system would visit Earth the following August and announce their arrival to the entire Earth. She claimed that this other planet lies directly on the other side of the sun, which is why we have never seen it. Give one good scientific argument against the existence of any such planet. 34. Continuing Exercise 33: One answer is that any such planet should have a gravitational effect on the other planets and that this effect has not been observed. Suppose that Jeane Dixon then replied, “But these aliens are so advanced that they have been able to completely mask the effects of their planet’s gravity, as well as all other observable effects of their planet.” What is your response to this explanation? Does this supposed planet fall within the realm of science? 35. Continuing Exercise 34: Jeane Dixon’s forecast was published on the front page of the National Enquirer on September 14, 1976. Have you heard of any reports, the following August, that her forecast was correct? Do you suppose that the National Enquirer then printed a front-page story reporting that her forecast was wrong? Can you recall any instance when such forecasts were later reported as false when they turned out to be false? 36. Some supporters of ESP (extrasensory perception—for example, mind reading, causing objects such as spoons to move by means of mental concentration, and the like) claim that ESP really exists but that it cannot be checked scientifically because scientific experiments always cause the ESP effect to vanish. What is your response to this argument?

Answers to Concept Checks 1. No looking until you’ve formed your own answer! The

answer is (d). 2. The moon’s phases (new, crescent, quarter, and so on) show

that it shines by means of reflected light from the sun, (b). 3. Ptolemy’s theory, Figure 11, places the centers of the orbits 4. 5. 6. 7. 8. 9. 10. 11. 12.

of Mercury’s and Venus’s epicycles on the line joining Earth with the sun, (b). (d) (a) (e) (c) Note that this shows that a circle is a particular kind of ellipse. (a) A scientific idea is never absolutely certain, because the next observation could disprove it, (e). Answers (c), (e), and (f) are correct, because each one says that our particular place in the universe is not unique. (d) (e)

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The Way of Science: Problem Set

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Follow its position in the sky for a few weeks. If its position relative to the surrounding stars changes, it is a planet. 3. We are looking northward, and stars rise in the east (righthand side of photo) and set in the west (left-hand side), so the stars in the photo are circling counterclockwise. If we were looking southward, toward the South Pole, the stars would be circling clockwise around a point in the southern sky. 5. Follow a planet every night until it noticeably brightens or dims—an indication that it is closer to or further from Earth. 7. This is possible, if Mars happens to lie a little to the east of the sun in the sky (in other words, close to a line joining Earth to sun in Figure 14) and if Venus is below the horizon. However, this combination of events isn’t very likely. 9. Look near the rising or setting sun, just before it rises and just after it sets. If the sun is visible above the horizon, the dim light from Mercury will be obliterated by the light from the sun. 11. Aspects Copernicus would have liked: Earth is a planet; Earth goes around the sun; Kepler’s theory is fairly simple and straightforward (compared to Ptolemy’s theory). What Copernicus would not have liked: In Kepler’s theory the planets do not move in circles or in combinations of circles. 13. Specific data can never prove a general theory, so Brahe’s data could not prove that planets move in ellipses. 15. The observer is Brahe. 17. Move the thumbtacks far apart.

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19. The interplay between theory and observation. 21. Yes, in fact the theories of Ptolemy, Copernicus, and Kepler

were partly based on aesthetic considerations. 23. Scientifically, the best attitude is “let’s look at the evidence.”

25.

27. 29. 31.

33. 35.

Does the “theory” make clear-cut observational predictions? Can they be checked? What are the results? From the purely theoretical standpoint, one should also ask whether the “theory” is clear and logically consistent. This is testable. To test it, ask a neutral person (one who could care less about talking to plants—so as not to bias the experiment) to raise two identical plants in identical surroundings, with the sole significant difference that one plant is talked to and the other is not. To draw any firm conclusion, this experiment should be repeated several times. Do the talked-to plants actually grow significantly better, on the average? Voltaire’s sarcasm was not justified. New scientific predictions must be verified by observation, even though they are sometimes first predicted by theory. 100 billion times 100 billion = 10,000,000,000,000,000,000,000 (a one followed by 22 zeros). Divide 4 years by 8 minutes. First, we must express 4 years in minutes: 4 yrs * 365 days>year * 24 hrs>day * 60 min>hr = 374,400 min. Then 374,400>8 = 46,800. Thus the distance is 46,800 AU. Any such planet should have a gravitational effect on the other planets, and this effect has not been observed. There were no such reports. There were no stories reporting this fact. Generally, when far-fetched predictions such as this are made, there is little or no attempt to follow up on them.

Atoms The Nature of Things

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is Á that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling each other upon being squeezed into one another. In that one sentence Á there is an enormous amount of information about the world. Richard Feynman, Physicist

L

et’s turn now from stars to atoms.

One of science’s key principles is that everything is made of imperceptibly small particles. As Richard Feynman points out above, this explains an extraordinary range of observations. We’ll learn that science profoundly changed its view of atoms during the twentieth century, a development crucial to one of this text’s four themes:1 modern physics and its significance. Section 1 presents the 2500-year-old idea that everything is made of small particles. Section 2 discusses the atom as chemists have understood it for 200 years and distinguishes atoms from molecules. Section 3 explores the wide-ranging explanatory power of the atomic idea. In order to discuss atoms quantitatively, Section 4 takes a brief excursion into “powers of 10” and metric units. Section 5 ponders the incredible tininess of atoms. Section 6 looks at the philosophical implications of the atomic idea. Section 7 compares this chapter’s model of the atom with two other models. Finally, Section 8 explores some significant examples of “chemical reactions”—combining and recombining atoms.

1 THE GREEK ATOM: THE SMALLEST PIECES The ancient Greeks produced an astonishing number of original thinkers. They wanted to think their way to the bottom of everything. Because of their prointellectual attitude, this small group of people, during just two centuries centering on the

1

The three other themes are the scientific process, the social context of physics, and energy.

From Chapter 2 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Atoms

fifth century BCE, laid the foundations for most of the Western world’s great ideas. One thing they thought about was the nature of matter: material substances such as wood, cotton, sausage, ice, water, soil, and gold. They speculated about the underlying unity that they believed lay behind the different substances. What do sausage and gold have in common? What is matter? One Greek, Democritus, sharpened his focus on this question with a “thought experiment,” an imagined experiment that seemed possible in principle but difficult in practice. Suppose, he argued, you cut a piece of gold in half, and then cut one of the halves in half, and so forth. How far could you continue making such divisions? Either the divisions could go on forever, or there would be a limit at which no further divisions would be possible. That is, matter is either continuous—divisible without limit—or it is made of particles that cannot be divided. The first alternative seemed absurd to him. Matter, he concluded, is made of imperceptibly small, “a-tomic” (Greek for “not divisible”) particles. He called these smallest particles “atoms.”2 CONCEPT CHECK 1 Today, this idea should be classified as (a) a scientific fact; (b) an experimental observation; (c) a hypothesis; (d) a scientific theory; (e) scientifically false; (f) gibberish.

I’ll call this idea

The Atomic Theory of Matter All matter is made of tiny particles, too small to be seen.

This is a good example of a scientific principle or law or theory: a well-confirmed idea that explains a broad range of observations. In Democritus’s time, the atomic idea had not yet been confirmed by observations; rather, it was an educated guess or hypothesis. When observations confirmed it during the nineteenth and twentieth centuries, it then became an established theory. A general idea like this cannot, however, be called a fact, no matter how often observations may have confirmed it, because we cannot observe every possible material object to prove for certain that everything really is made of atoms. Theories are never certain. What do your thumbnail, beer, an acorn, Saturn, the Amazon River, and the period at the end of this paragraph have in common? Each is made of atoms. This is the kind of underlying unity that the Greeks loved and that scientists seek.

2

50

“Atom” is used in a slightly different sense today. Today, the “atom” or “chemical atom” is the smallest particle of a chemical element. This chemical atom is actually made of smaller, subatomic parts: electrons, protons, and neutrons. In fact, the protons and neutrons are themselves made of quarks. As far as we know, electrons and quarks are the smallest particles, of which the others are made. These smallest parts are what the Greeks meant by an atom.

Atoms

How do we know that things are made of atoms? Science’s power comes from its “show-me” attitude, its insistence on evidence. So I will frequently ask, “How do we know?” The ancient Greeks had no direct microscopic evidence for atoms, but Democritus had some ingenious indirect evidence. He argued that since we can smell a loaf of bread from a distance, small bread particles must break off and drift into our noses. This is still an acceptable explanation of odors today (Section 4). John Dalton discovered the first specific evidence for atoms around 1800. He found that whenever certain substances combine chemically to form other substances, they combine in simple ratios by weight. For example, when hydrogen and oxygen combine to form water, the ratio of the weights of the two substances is always 1 to 8. Such ratios are difficult to understand if matter is infinitely divisible, but there is a simple explanation if matter is made of atoms. If, for example, one atom of hydrogen and one atom of oxygen have a simple weight ratio, and if these atoms always combine in simple ratios to create water, the weight ratios of hydrogen and oxygen in water will be simple numbers also. Today we know that individual atoms of hydrogen and oxygen have a weight ratio of 1 to 16 and that it always takes two hydrogen atoms for every one oxygen atom to form a water molecule. So you can see, today, why the weight ratio should be 1 to 8. So the atomic theory explains Dalton’s simple ratios. But does this prove the theory? The answer is no! It’s possible that atoms don’t exist and that there is some other explanation for the simple ratios. Observations cannot prove a general theory, but they can make it more plausible. A few decades after Dalton, botanist Robert Brown, using a microscope, observed that tiny pollen grains suspended in liquid move around erratically (Figure 1), even though the liquid itself had no observable motion. His first hypothesis was that the grains were alive. But lifeless dust grains suspended in liquid executed the same erratic dance, disproving the hypothesis. Hypotheses and theories cannot be proved but they can be disproved. It was suggested that submicroscopic motions of atoms (or “molecules,” as we’ll see later) caused this Brownian motion. The idea was that atoms moved around constantly and Brownian motion resulted from numerous atoms colliding with each pollen or dust grain every second. This hypothesis got strong support in 1905 from an unknown young physicist, Albert Einstein. He used an already established theory to calculate how particles such as dust grains are jostled when bombarded randomly by moving atoms. He made several quantitative (numerical) predictions, such as the rate at which a collection of grains should spread out in a liquid. Such predictions could be checked by measurements, and the measurements agreed with Einstein’s predictions. It was difficult to dispute this evidence. Either unseen atoms really did cause Brownian motion, or Einstein’s calculations were fabulously lucky in giving all the right numbers. Since Einstein’s work, scientists have not questioned the atomic theory.

CONCEPT CHECK 2 A sulfur atom has twice the weight of an oxygen atom. When sulfur and oxygen combine to form sulfur dioxide, one sulfur atom is required for every two oxygen atoms. In the formation of sulfur dioxide, the weight ratio of sulfur to oxygen is (a) 4 to 1; (b) 2 to 1; (c) 1 to 1; (d) 1 to 2; (e) 1 to 4. CONCEPT CHECK 3 Following up on the preceding question: In the formation of sulfur trioxide, the weight ratio of sulfur to oxygen is (a) 6 to 1; (b) 3 to 1; (c) 3 to 2; (d) 2 to 3; (e) 1 to 3; (f) 1 to 6.

Figure 1

Brownian motion. This erratic path is typical of a small particle such as a single dust grain, suspended in water, observed under a microscope. The atomic theory explains this behavior by the ceaseless, rapid, random motion of water molecules. Although the molecules are far too small to be seen even under a microscope, the effect of numerous molecules impacting a dust grain every second can be seen in the erratic motion of the grain.

2 ATOMS AND MOLECULES Think of all the different material substances around you: this paper, your shirt, your hair, and so forth. You could list hundreds. Nineteenth-century chemists found that they could transform most substances into a much smaller number of simpler

51

Atoms

substances but that they could not further transform this small number. Any process3 that changes a single substance into other simpler substances is called a chemical decomposition of the original substance. An example: By passing electricity through it, water can be decomposed into two distinct substances, called hydrogen and oxygen, neither of which are anything like water. But hydrogen and oxygen turn out to be among that small (fewer than 100) group of substances that nineteenth-century chemists could not decompose. No matter how they tried to decompose hydrogen, it remained hydrogen, and the same was true for oxygen. Apparently, these roughly 100 substances that cannot be chemically decomposed are particularly fundamental. They are called chemical elements, or simply elements. By studying the weight ratios just discussed, Dalton and others soon recognized that each element was made of only one kind of atom and that elements differed because their atoms differed. So an atom is the smallest particle of a chemical element. But water is compounded of two kinds of atoms, hydrogen and oxygen, which is why you can decompose water but not oxygen or hydrogen. Today, 117 elements are known—117 different kinds of atoms. Eighty-eight of these occur naturally on Earth, while the remaining 29 are created in laboratories. The most recently discovered, but yet unnamed, element is number 118, created in 2006 when a total of just three atoms of it were produced in the lab during a 1080-hour high-energy physics experiment. Each atom existed for only about 0.89 milliseconds (0.00089 seconds). Element number 117 is predicted but not yet observed. Each number, known as the element’s atomic number, represents a particular kind of atom. Higher atomic numbers correspond to heavier atoms. Scientists found that certain groups of elements have similar properties. For example, elements 2, 10, and 18 (helium, neon, and argon) are “inert gases,” meaning that they are gases that will not combine chemically with other elements. For another example, elements 3, 11, and 19 (lithium, sodium, and potassium) are soft, silver-white metals melting at moderate temperatures. If we list these groups having similar properties vertically and also list the elements in order of increasing atomic number, the result is the periodic table. This table is a nice example of the regularities that scientists find in natural phenomena. Scientists use it as a predictive device, by noting the table’s unfilled gaps and searching for elements with properties that just fit those gaps. What about all the other substances, those made of more than one element? A pure substance, such as pure water (with no impurities like salt or dirt), that is made of more than one element is called a chemical compound. Imagine dividing a cup of water into smaller and smaller amounts. If the water is pure, you will always get just water—not something else such as salt or dirt. Working downward in size, you will eventually arrive at the smallest particle of water. In pure water, every one of these smallest particles must be a particle of water, and so they should be identical. And every particle must contain atoms of both hydrogen and oxygen, because we know that water can be chemically decomposed into these elements. This reasoning shows that every pure chemical compound must be made of tiny particles that are identical and that are themselves made of two or more atoms

3

52

More precisely, any low-energy (lower than nuclear energies) physical process.

Atoms

attached together into a single identifiable unit. Such a particle, the smallest particle of a compound that still has the characteristics of that compound, is called a molecule. Chemists can deduce a compound’s molecular structure by decomposition and by combining it with other compounds. Such experiments show, for example, that the water molecule is made of two hydrogen atoms and one oxygen atom (Figure 2). Some elements are made of two-atom molecules. For example, a molecule of hydrogen gas is made of two hydrogen atoms (Figure 3).4 Helium gas, on the other hand, is made of individual helium atoms (Figure 4). The common forms of oxygen gas and nitrogen gas are made of two-atom molecules. Air (Figure 5) is made primarily of these two kinds of molecules. We represent compounds and elements by abbreviated formulas. For example, water is represented by H 2O, where the subscript 2 belongs to the symbol preceding it and indicates the number of atoms of that type in each molecule. Hydrogen gas is represented by H 2, oxygen gas by O2, and helium by He. Molecules can get pretty complicated, especially the molecules of life, such as your protein and DNA. Biological molecules are among the most varied and complicated known. Hemoglobin, the protein responsible for the red color of blood, has the formula C3023H 4816O872N780S8Fe 4. DNA molecules contain millions of atoms and vary from one individual to the next. They carry the instructions that make you you.

Figure 2

A simplified drawing of liquid water, magnified 50 million times. In a liquid the molecules are in close contact and slide past one another. Each water molecule is made of one oxygen atom (blue) and two hydrogen atoms (black). This and other microscopic drawings in this chapter view only a tiny region within a much larger container.

CONCEPT CHECK 4 Which of the following elements are chemically similar to chlorine? (a) Iodine. (b) Sulfur. (c) Xenon. (d) Bromine. (e) Krypton. (f) Fluorine.

4

Figure 3

Figure 4

Figure 5

A simplified drawing of hydrogen gas. Each molecule of hydrogen is made of two hydrogen atoms. Each molecule moves rapidly in a nearly straight line, changing direction only when it collides with another molecule or with the container wall.

A simplified drawing of helium gas. Each molecule of helium is simply an unattached atom of helium.

A simplified drawing of air, magnified 50 million times. Air is a mixture mostly of nitrogen (gray) and oxygen (green) molecules, both two-atom molecules.

However, outside Earth’s atmosphere nearly all the universe’s hydrogen is in the “atomic” (single-atom) form rather than the “molecular” (two-atom) form, because the universe began with atomic hydrogen and these atoms are separated so widely in space that they never combined into molecules. These “primordial” hydrogen atoms have not been altered in 14 billion years (the age of the universe)!

53

Atoms

CONCEPT CHECK 5 What elements, and how many atoms of each, does the simple sugar C6H 12O6 (“glucose”) contain? (a) 6 chlorine, 12 helium, 6 ozone. (b) 6 carbon, 12 hydrogen, 6 oxygen. (c) 1 chlorine, 1 hydrogen, 1 oxygen. (d) 1 carbon, 1 hydrogen, 1 oxygen. (e) 1 carbon, 2 hydrogen, 1 oxygen. CONCEPT CHECK 6 The chemical formula for carbon dioxide is (a) CaO; (b) Ca2O; (c) CO; (d) CD; (e) C2O; (f) CO2.

3 THE ATOM’S EXPLANATORY POWER: THE ODOR OF VIOLETS5

The power of the atomic theory, and the virtues of careful observation, are both illustrated by the question “What are smells?” Have you ever thought about this? Please stop reading and think about it for a moment.... Observation shows that you are surrounded by an invisible substance, air. You know it’s there because you can feel the wind. The atomic theory tells us every material substance, anything you can pick up or touch, is made of atoms. It’s reasonable to suppose that air is a material substance, too, because you can feel it blow on you. A careful measurement would show that air has weight, further confirming our hypothesis. We conclude, from the atomic theory, that air is made of atoms. As you know from the Brownian motion experiment, the atoms in a liquid move all the time, even when the liquid appears to be motionless. So it’s reasonable to suppose that air molecules are in constant motion, too, even in still air. Consider the odor of violets. Among a violet’s various molecules, there must be some that make it smell the way it does. Chemists have learned how the violet’s odor molecule is strung together (Figure 6). Scientifically, at least, that’s what the smell of violets is—those molecules. In order for a violet’s smell to spread out, odor molecules must break loose from the violet. Once in the air, moving air molecules knock odor molecules around, causing odor molecules to spread out in all directions. Eventually, they reach your nose. Think about that the next time you smell something. The atomic theory links human-scale or macroscopic phenomena that you can see to phenomena at the unseen microscopic level. The microscopic perspective is especially helpful in understanding the states of matter. Water, for example, comes in three states: ice, liquid, and vapor (or steam). We call these the solid state, liquid state, and gas state of water. Nearly every substance can exist in any one of these three states.6 At the macroscopic level, the three states of matter are distinguished by the shapes they assume when placed in a container. In a closed container, a solid maintains its shape; a liquid spreads out over the bottom; and a gas fills the volume. How do they differ at the microscopic level? A little thought, guided by the atomic theory and by some simple macroscopic observations, can answer this. As I hope Figure 6

The odor of violets, in air. The funny-looking thing is the odorof-violets molecule, made of carbon (horizontal stripes), hydrogen (black), and a single oxygen atom (green).

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5

6

This section is partly based on Richard Feynman’s Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. I, Chapter 1, where the odor of violets example was first presented. Although these three are the normal states of matter on Earth, many other states are common throughout most of the universe. Such “exotic” states of matter include plasma (electrically charged gas, common in stars), three kinds of superdense matter (found in white dwarf stars, neutron stars, and black holes), and supercold states in which substances display large-scale “quantum” behavior (superfluids, superconductors, and Bose-Einstein condensates).

Atoms

you’ll discover throughout this text, it’s amazing what careful thought guided by simple observations can accomplish! Because solids maintain a fixed shape, their molecules must be locked into a fixed arrangement. Because solids are difficult to compress into a smaller volume, their molecules must be crowded against one another. The precise arrangement is determined by the ways in which the substance’s molecules push and pull on one another when they get close together. If you have ever seen a large number of balls tossed one by one into a big box, or gunshot (BBs) filling a small container, you can guess that molecules tend to lock into an orderly pattern that repeats itself throughout the solid.7 Orderly molecular patterns are responsible for the regular surfaces and beautiful symmetries seen in macroscopic crystals such as diamonds. Figure 7 shows the microscopic six-sided crystal pattern of ice, and Figure 8 shows the macroscopic snowflake crystals that are formed from it (note the hexagonal, or six-sided, symmetry). Because liquids have no fixed shape, their molecules must not be rigidly attached to one another. But liquids are about as difficult to compress into a smaller volume as are solids, so we expect that a liquid’s molecules are crowded together about as closely as possible. This reasoning leads us to a microscopic picture of a liquid that is similar to a jumbled bowlful of marbles that assume different shapes depending on the shape of the bowl. The molecules in a liquid are free to migrate throughout the liquid by sliding past one another. Most liquids take up slightly more volume than do the solids of the same substance, but water is an exception to this rule; because of its open crystal structure (Figure 7), ice takes up slightly more volume than does liquid water. Because gases can be compressed into a much smaller volume, their molecules must be widely separated. Gas molecules dart back and forth, bouncing off the container’s walls and colliding and rebounding from one another. From this microscopic picture we would expect that, because of the continual torrent of gas molecules hitting the surrounding surfaces, a gas should press outward against its container. This outward press is called gas pressure. It’s as though hundreds of baseballs were thrown at a wall, pressing the wall backward. You can see the effect of gas pressure when you blow up a balloon; the elastic material is pressed outward by trillions of gas molecules hitting the inner surface every second. Figure 9 shows the differences between solids, liquids, and gases. A complete absence of air and all other forms of matter is called a vacuum. A perfect vacuum is impossible to achieve in any ordinary macroscopic volume on Earth, but it is not difficult to achieve a partial vacuum in which the container holds far less air than it would if filled with air at its normal density. A good vacuum in a laboratory still contains a trillion molecules in every cubic centimeter! But in space the large regions between galaxies are nearly perfect vacuums—neighboring molecules are some 2 meters apart! When you warm a substance, what happens to its molecules? With our understanding of solids, liquids, and gases, we’re in a position to answer this important question. Consider an air-filled balloon tied shut so that no air enters or leaves. What happens if you heat or cool it? Try it! First put the balloon in the freezer for a few minutes. Then hold it over boiling water. What happens? The balloon expands as the air warms inside it. Returning to our microscopic picture of a gas, you can 7

Figure 7

Ice. Compare this diagram of solid water with that of liquid water in Figure 2. In the solid state, atoms vibrate around their average position in the crystal pattern but they do not migrate throughout the material as they do in the liquid state.

National Oceanic and Atmospheric Administration/Seattle Figure 8

The hexagonal symmetry we see in snowflakes mirrors their underlying microscopic symmetry (compare Figure 7).

However, some solid materials, including plastics and glasses, have an irregular arrangement at the microscopic level.

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Atoms

(a)

(b)

see that as the air in the balloon warms, the molecules inside must bounce harder off the inner walls in order to cause the expansion. This means that, as the air warms, the molecules move faster. Experiments amply confirm this hypothesis. It’s true not only in gases such as air but also in liquids and solids. That is, molecules are always in random (or disorganized) motion, whether in a solid, liquid, or gas, and those motions get faster as the solid, liquid, or gas gets warmer. Warmth is measured quantitatively by devices called thermometers. In a simple household thermometer the liquid inside responds to warmth by changing its volume in a measurable way when placed into a solid, liquid, or gas. The resulting reading is called the temperature of the solid, liquid, or gas. This connection between warmth and molecular motion is so close that scientists consider warmth (or temperature) and molecular motion to be, respectively, the macroscopic and microscopic aspects of the same phenomenon. Because of this connection, this molecular motion is called thermal motion. Summarizing this important idea: The Microscopic Interpretation of Warmth At the microscopic level, warmth (temperature) is the random, or disorganized, motion of a substance’s molecules. This thermal motion cannot be directly observed macroscopically but is observed instead as temperature or warmth.

The atomic theory explains and unifies the odor of violets, the three states of matter, chemical compounds, gas pressure, warmth, and much more. It’s a good theory.

(c)

Figure 9

Microscopic views of the (a) solid, (b) liquid, and (c) gas states of matter.

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CONCEPT CHECK 7 Which of the following observations confirm that you are surrounded by air? (a) Trees bending in the wind. (b) Your ability to observe light. (c) Air that you can feel entering your nose as you breathe. (d) A breeze brushing against your cheek. (e) An air-filled balloon. (f) A rock falling when you drop it.

4 METRIC DISTANCES AND POWERS OF 10 Before discussing atoms quantitatively in Section 5, we need to take a brief excursion into metric units and powers of 10. When you measure a quantity such as the length of a table or the weight of a rock, that measurement is made relative to a particular standard or unit. For example, you might measure length in inches, feet, or miles, or in the metric system in centimeters, meters, or kilometers. If you wanted to tell someone the distance to the next town, you wouldn’t say “53.” You must give the unit, for example 53 kilometers or 53 miles. One curious feature of American life is its use of the “English” system of measurements, based on feet and pounds and so forth. Since only Liberia, Burma, and the United States use it officially anymore (it’s still used unofficially in the United Kingdom and Ireland), I’ll henceforth call it the U.S. system of units. We’ll shun this confusing traditional system (inches, feet, yards, miles, horsepower, pounds, ounces, pints, quarts, gallons, degrees Fahrenheit, etc.), a modern patchwork codification of medieval trade units. This quaint system can be costly: During NASA’s

Atoms

Mars Climate Orbiter space probe in 1999, one engineering group used U.S. units for navigation while another assumed the numbers were metric. This caused problems. The $125-million spacecraft veered off course while approaching Mars, lost contact with Earth, and crashed. Not good. For further excellent reasons why the United States should convert to all-metric units, see Concept Check 10 and the marginal quotation by Valerie Antoine. The basic metric distance unit is the meter (abbreviated m). It’s about 39 inches, a little over a yard. Table 1 lists other metric distances and relates them to the meter. The most important are the kilometer (km), centimeter (cm), and millimeter (mm). Table 2 lists six common prefixes that can be attached to any metric unit. For example, the kilowatt is 1000 watts, and the megawatt is 1 million watts (later, we’ll see what’s a watt). For handling large and small numbers, a technique known as powers of 10 is invaluable. A power of 10 means 10 raised to some power. So 102 means 10 * 10, which equals 100, and 105 means 10 * 10 * 10 * 10 * 10 = 100,000. For example, the solar system’s diameter (distance across) is 12,000,000,000,000 m. You can write this as 1.2 * 10,000,000,000,000 m or 1.2 * 1013 m. Each multiplication by 10 moves the decimal point one place to the right, so to write out 1.2 * 1013, you begin with 1.2 and move the decimal point 13 places to the right. The number in front (the 1.2) is usually written as a number between 1 and 10. If there is no number in front, you can think of a 1 in front; for instance, 105 is the same as 1 * 105. Negative powers are used for small numbers. For instance, 10-2 means 1/102, which equals 1/100, or 0.01, and 10-5 means 1/105 = 0.000 01. The minus sign indicates that the power of 10 is to be divided into 1. For example, the diameter of an atom is about 0.000 000 000 11 m, which can be written as 1.1 * 10-10 m. Since each division by 10 moves the decimal point one place to the left, to write 1.1 * 10-10, you begin with 1.1 and move the decimal point 10 places to the left. Thousand 11032, million 11062, billion 11092, and trillion 110122 all represent various powers of 10. Similarly, thousandth 110-32, millionth 110-62, and so forth represent negative powers of 10. To multiply two powers of 10, just add their powers. For instance, 102 * 105 = 2+5 10 = 107, and 102 * 10-5 = 102 + 1-52 = 10-3. The numbers in front of the power of 10 can be grouped together first, before multiplying. For example,

Benefits to U.S. industry if it converts to metric usage Á can be summed up in one word: survival. Overseas countries already are refusing entry to some U.S. inch–pound goods, Á our industries will lose the buying power of 320 million people in the European Community (EC) if we don’t wake up and begin producing to the EC metric standards Á U.S. industry must convert to metric production if it wants to survive. Valerie Antoine, Executive Director of the U.S. Metric Association

11.5 * 1022 * 13 * 1052 = 11.5 * 32 * 1102 * 1052 = 4.5 * 107 To divide two powers of 10, subtract the denominator’s power from the numerator’s power. For instance, 102/105 = 102 - 5 = 10-3, and 102/10-5 = 102 - 1-52 = 107. Table 2

Table 1

Metric prefixes

Metric distances Name of unit

Kilometer (km)

Distance 3

1000 m = 10 m

Meter (m) Centimeter (cm)

0.01 m = 10-2 m

Millimeter (mm)

0.001 m = 10-3 m

Micrometer 1mm2 Nanometer (nm)

0.000 001 m = 10

Conversion to U.S. units

Giga (G)

one billion, 109

1 km = 0.62 mi, 1 mi = 1.6 km

Mega (M)

one million, 106

1 m = 3.3 ft = 39 in., 1 ft = 0.30 m

Kilo (k)

one thousand, 103

1 cm = 0.39 in., 1 in. = 2.5 cm

Milli (m)

one-thousandth, 10-3

Micro 1m2 -6

m

0.000 000 001 m = 10

Nano (n) -9

one-millionth, 10-6 one-billionth, 10-9

m

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Atoms

Numbers in front of the powers of 10 can be grouped together first, before dividing them. For example, 11.5 * 1022/13 * 1052 = 11.5/32 * 1102/1052 = 0.5 * 10-3 = 5 * 10-4 Using powers of 10, you can calculate all sorts of fabulous things. For example, the solar system’s diameter divided by an atom’s diameter (the ratio of the two diameters) is 1.2 * 1013 m/1.1 * 10-10 m = 11.2/1.12 * 11013/10-102 = 1.1 * 1013 - 1-102 = 1.1 * 1023

This number, 110,000,000,000,000,000,000,000, is the number of atoms you would have to line up side by side in order for them to stretch across the solar system. Is that fabulous or what? CONCEPT CHECK 8 The universe is only seconds old, a million trillion seconds old, in fact. In powers of 10, this is (a) 1014 s; (b) 1015 s; (c) 1016 s; (d) 1017 s; (e) 1018 s. CONCEPT CHECK 9 The diameter of an atomic nucleus is about a hundredth of a trillionth of a meter. In powers of 10, this is (a) 10-10 m; (b) 10-12 m; (c) 10-14 m; (d) 10-15 m; (e) 10-16 m; (f) 10-18 m. CONCEPT CHECK 10 Answer either one of the following two questions, without using a calculator. For those of you who prefer U.S. units: How many inches are there in 6 miles? For those who prefer metric units: How many centimeters are there in 6 kilometers? Answers (U.S. system): (a) 463,173 in. (b) 380,160 in. (c) 263,150 in. Answers (metric system): (a) 6,000,000 cm; (b) 600,000 cm; (c) 60,000 cm.

Did you choose to answer Concept Check 10 in U.S. units? Do I make my point clear?

5 THE INCREDIBLE SMALLNESS OF ATOMS The most convincing evidence for atoms is to see one. But it’s impossible to see atoms with ordinary light, even with the best optical microscopes. The reason lies in the nature of light. Light is a wave, similar in some ways to water waves on the surface of a pond. The wavelength of light, the distance from one crest to the next, is very small—10 to 100 times smaller than the smallest visible dust particle. That’s small, but a single atom is 5000 times smaller still. To visualize this, imagine that light has a wavelength of 5 meters. On this scale, an atom would be a speck just 1 millimeter across! So light waves are too big to respond to tiny individual atoms. How do we know that atoms exist? Before 1970, Brownian motion was probably the closest we had come to seeing atoms. In 1970, scientists developed a more direct way: the scanning electron microscope. It shoots a steady stream, or beam, of tiny material particles called electrons at the object to be detected. Similarly, your television set sprays an electron beam across the inside of the screen’s face to make each picture. An electron beam is fundamentally different from a light beam because electrons are made of matter—material substance having weight—whereas light is not made of matter. During

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Atoms the 1920s, physicists discovered that every particle of matter, such as an electron, has a certain kind of wave, called a “matter wave,” associated with it. Matter waves are terrific for detecting individual atoms, because they have wavelengths thousands of times smaller than the wavelength of light. As an electron microscope’s electron beam sweeps over, or “scans,” atoms, the beam’s matter wave is disturbed. The disturbed matter wave is monitored by devices that collect and record the patterns made by the electrons. An even more precise device called the scanning tunneling microscope was developed in 1983. It employs a tiny probe, shaped like a sharp pencil tip a few atoms wide, that scans a surface from just above the surface. In order to sense the microscopic structure of the surface, electrons move across the narrow gap between the surface and the probe in a uniquely quantum process called “tunneling.” Figure 10 shows a typical image. Because the tip of the probe can pick up individual atoms and drag them from place to place, scanning tunneling microscopes can perform the thought experiment that Democritus could only imagine 2500 years ago. In 1990, scientists picked up 35 individual atoms of xenon gas and rearranged them to spell out the name of their laboratory (Figure 11).8 They had divided xenon gas into its individual atoms, just as Democritus had imagined.

Although atoms are small, the nucleus at the atom’s center (see Section 7) is smaller still (Figure 12). The electron, also found within the atom, is known to be smaller than the smallest distance yet measured, which makes it at least 100,000 times smaller than the nucleus. Since it might in fact have zero size, the electron does not appear in Figure 12. At the other end of the scale, galaxies are among the largest objects known. Larger still are clusters of galaxies, forming thin “sheets” of galaxies that can individually stretch across as much as 1% of the known universe. The largest structures ever detected are the ripples in the faint afterglow of the big bang origin of the universe, stretching across two-thirds of the known universe. Humankind stands roughly in the middle, somewhere between the atoms and the stars (Figure 12). Atoms and molecules are pretty small. If you put a million atoms side by side, the lineup would be no longer than the period at the end of this sentence. The head of a pin contains more than 1018 atoms. One breath of air, about 1 liter (1000 cm3, about a quart), contains more than 1022 molecules. Now, 1022 also happens to be about the number of liters of air in Earth’s atmosphere, which leads to an interesting conclusion. Any particular parcel of air, such as the liter of air you will exhale in your next breath, mixes throughout Earth’s atmosphere within a few years. This means that of the air you exhaled a few years ago in any particular breath, about one atom is now in every liter of air on Earth and inside the lungs of every person on Earth! And about one atom that was breathed out by every person on Earth, in any particular breath, is in your lungs now. One from George Washington’s first breath, one from his dying breath, and one from every other breath that dear George ever took are in your lungs right now, along with atoms from each of the breaths of all the other people who have ever lived. You are a walking museum of history. Atoms are forever. Earth’s atoms have been here since Earth formed 5 billion years ago, and very few have changed during that time.9 It is only the connections

8 9

National Institute for Materials Science, Japan Figure 10

Scanning tunneling microscope (STM) image of a horizontal layer of silicon “dimers” (pairs of silicon atoms) with a single tungsten atom that the STM has deposited onto the surface. Note the nanometer (nm) distance scale.

IBM Corporation Figure 11

Thirty-five individual xenon atoms have been manipulated into position by the tip of a scanning tunneling microscope. The distance between atoms in the pattern is about 10-9 m—one-billionth of a meter, or 10 times the width of a single atom.

Xenon atoms do not combine easily with other atoms, making them easy to manipulate. Only those relatively few atoms that have been involved in radioactive decay, fission, or fusion have changed into different types of atoms.

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Atoms Meters 1025

1020

Size of known universe Ripples in cosmic background radiation Clusters and sheets of galaxies Milky Way galaxy

between atoms that have changed. A particular oxygen atom might be part of a nerve cell in your brain today, part of an atmospheric water molecule a century from now, and part of a tree a century after that. “Your” atoms, the ones you are carrying around right now, have just been borrowed from the air, from Earth, to be given back perhaps soon, perhaps later, to be given back entirely when you die. MAKI NG ESTI MATES

1015

Distances to nearby stars Solar system

1010

Sun Earth

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1

Tall mountain Tall building Human

10⫺5

Fine dust particle Wavelength of light

10⫺10

Typical atom

10⫺15

Smallest nucleus

10⫺20

Of all the molecules you have ever exhaled, about how many will your class instructor inhale during his or her next breath? This sounds hard. However, it’s surprisingly easy to make a rough estimate. In estimating very large numbers, an estimate to the nearest power of 10 is usually good enough: Is the answer closer to 10, or 100, or 1000, and so on? Such estimates are called “order-of-magnitude estimates.” We will make such estimates of all sorts of things throughout this text, but don’t expect a single correct answer. Different people will make different estimates, but all should be in the same ballpark. Suppose you exhale 12 times per minute (measure it!). Note how per is used—it always means “in each.” Multiplying by 60 minutes per hour, 24 hours per day, and 365 days per year, you’ll get your number of exhales per year. Since we want only a rough estimate, round off these numbers for easy multiplication: 10 * 60 * 25 * 400 = 6 * 106 exhales per year. If you are 20 years old, you have exhaled 20 * 6 * 106 or about 100 million times. How many of these exhaled molecules will your instructor inhale in one breath? As discussed above, he or she will inhale about one molecule from every one of your exhaled breaths. So the answer is 100 million! And in that same breath, he or she will also inhale some 100 million molecules from the exhaled breaths of each person living on Earth and from each person who has ever lived on Earth. And all of this will only be a tiny fraction of the total number of molecules your instructor will inhale in that breath. It’s something to consider when you take a breath.

Smallest distance yet measured

10⫺25

Figure 12

The range of sizes in the universe.

MAKI NG ESTI MATES About how many millimeters thick is one sheet of paper? (Hint: Roughly how thick is a 500-sheet package of typing paper?) My solution is at the bottom of the page. MAKI NG ESTI MATES

The U.S. national debt is about $12 trillion. If you stacked this up in new $100 bills, about how many kilometers high would the stack be? (Hint: Assume that they stack like typing paper and see the preceding question.)

6 ATOMIC MATERIALISM: ATOMS AND EMPTY SPACE Every time you drink a glass of water, you are probably imbibing at least one atom that passed through the bladder of Aristotle. A tantalizingly surprising result, but it follows [from the simple] observation that there are many more molecules in a glass of water than there are glasses of water in the sea. Richard Dawkins, Zoologist, Oxford University

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From 1550 to 1700, the revolutionary ideas of Copernicus and others became widespread, and educated people no longer viewed Earth as the central focus of the universe. Humans became passengers on one planet among many, inhabitants of a less SO LUTION TO MAKI NG ESTI MATES A 500-sheet package of typing paper is about 4 to 6 cm (a few inches) thick, say 5 cm. So the thickness of one sheet is about 5 cm/500 = 0.01 cm = 0.1 mm. SO LUTION TO MAKI NG ESTI MATES The number of $100 bills needed is 12 * 1012/100 = 1.2 * 1011. We saw in the preceding question that the thickness of one bill is 0.01 cm = 10-2 cm = 10-4 m. The height of the stack is 1.2 * 1011 * 10-4 m = 1.2 * 107 m = 12,000 km, which is more than twice the distance across the United States.

Atoms

personal universe (Figure 13). The new view stimulated an advancing scientific tide whose high point was Newtonian physics, the remarkably effective ideas about motion, force, and gravity developed by Isaac Newton (1642–1727) and others. During 1700 to 1900, its cultural influence spread far beyond science, affecting the way people thought about themselves, their society, and their place in the universe. Today, the Newtonian worldview still dominates our culture. In summing up his scientific career, Isaac Newton once stated, “If I have seen farther than others, it is by standing on the shoulders of giants.” Two such giants, René Descartes (1596–1650) and Galileo Galilei (1564–1642), helped establish the philosophy behind Newton’s physics. Descartes, Galileo, and Newton were the leading founders of science as we know it today. Although in Newton’s time there was very little evidence for atoms, the atomic idea underlies much of Newtonian physics. It was an idea that went pretty deep, a philosophical idea. As Democritus put it: By convention sweet is sweet, bitter is bitter, hot is hot, cold is cold, and color is color. But in reality there are only atoms and empty space. That is, the objects of sense are supposed to be real, and it is customary to regard them as such, but in truth they are not. Only the atoms and empty space are real.

All these things being considered, it seems probable to me that God in the Beginning formed Matter in solid, massy, hard, impenetrable, movable Particles, of such Sizes and figures, and with such other Properties, and in such Proportion to space, as most conduced to the end for which he formed them. Isaac Newton, 1704

Corbis/Bettmann

This goes far beyond the atomic theory. Democritus is saying that not only matter but everything is made of atoms and that atoms are all there is. So when you say

Figure 13

When medieval beliefs gave way to the new science of Copernicus and Newton, the cozy pre-Newtonian universe was replaced by a vast impersonal mechanical universe. This woodcut was made during the nineteenth century, long after the transition had taken place.

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“the water is hot” or “the shirt is red,” you really mean that the atoms in the water and shirt are moving in a certain way. There really is no such thing as hot or red— there are only atoms. According to Descartes, sense impressions such as hot and red are merely “secondary qualities” that exist only in our minds. The real universe, the universe outside our minds, contains only the atoms and their physical properties, such as weight and size. Descartes calls these the “primary qualities.” For Descartes, science’s task is to study the primary realm and explain it by means of atoms. Because such views about what is real go beyond what can be observed, they lie outside of science. They are philosophical, rather than scientific, views. These views are one version of materialism, the philosophy that matter is the only reality and that everything is determined by its mechanical motions. Not that Descartes, Galileo, or Newton were materialists themselves. They all subscribed to nonmaterialistic religious beliefs such as a belief in God. But the new scientific philosophy provided little room for the God of the Middle Ages, a God who is continually and intimately involved in the world. Instead, the founders of modern science believed in a God who created the universe and established the physical laws all at once, and who then merely maintained those laws. Newtonian physics is a remarkable achievement that is incredibly effective in explaining countless observed phenomena. Are its materialistic philosophical underpinnings then necessarily correct? Is it true that atoms are all there is? One reassuring thing about philosophy is that, for most good philosophical ideas, there are also good arguments to refute those ideas. As physicist Niels Bohr put it, “The hallmark of a profound idea is that its converse is also profound.” And so it is with atomic materialism. The respectable arguments on the other side include the following: 1. Science always starts from evidence, which comes ultimately from sense impressions. Materialism, which says that atoms are primary and sense impressions only secondary, has the cart before the horse. Theoretical ideas such as atoms are secondary to sensory evidence, rather than the other way ’round. 2. Although materialism is rooted in science, science is only one way of viewing reality. Other views—religious, aesthetic, intuitive—have equal claim to being “real.” Scientists themselves cover the gamut of religious views, from devout to atheistic. 3. All scientific ideas are only tentative, including atomic materialism. 4. Since 1900 scientists have found that Newtonian physics is only approximately correct over only a limited range of phenomena. Outside that limited range it is not even approximately correct. For example, we’ll find that some things (such as light) are nonmaterial and not made of atoms and that matter itself is made of nonmaterial “fields.” Whereas Newtonian physics is congenial to materialism, recent theories are more neutral or even uncongenial to materialism.

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Atoms

7 THREE ATOMIC MODELS: GREEK, PLANETARY, AND QUANTUM Science’s way of working back and forth between observations and theories comes with a kind of guarantee of success. If an observation agrees with a theory, that’s fine for that theory. And if an observation disagrees with a theory, that’s too bad for that theory, but it’s fine for science because science makes its greatest progress by repairing, or replacing, disproved theories. The atomic theory of matter is a good example. Science’s notion of the nature of atoms has changed several times. In the original Greek model of the atom, an atom was an unchangeable, single object like a small rigid pea. The Greek atom was also Newton’s way of looking at the atom, and it got support from the nineteenthcentury discoveries of elements, compounds, and Brownian motion. Around 1900, experiments with electricity showed that an “atom,” as that word was understood in 1900, was more complex than the Greek model of the atom. Electricity had been studied throughout the nineteenth century. Nobody suspected that an entirely new model of the atom would be needed to explain these experiments until, in 1897, scientists discovered a new, very lightweight, “electrified” particle. It was the first discovery of a particle that weighed less than an atom. It was, apparently, one part of the so-called atom (remember, the word means “indivisible”). This particle was the electron. A few years later, in 1911, physicists discovered that an atom is itself nearly entirely empty space and that nearly all of an atom’s material substance resides in a tiny central core, or nucleus. Experiments indicated that each atom also contained electrons moving through the large empty regions outside the nucleus. Scientists developed the theory that electrons orbit the nucleus much as planets orbit the sun. Later, scientists learned that the nucleus itself is made of two kinds of subnuclear particles, protons and neutrons. Figure 14 shows an atom of the element helium and an atom of the element carbon according to this planetary model of the atom. During the 1920s, new experiments involving electrons contradicted the planetary model and even contradicted the principles of Newtonian physics itself. An entirely new theory of matter called ”quantum theory” was needed to explain the new results. To date, no disagreements have been found between experiments and the new quantum theory of the atom. So our understanding of the atom has evolved through at least three different theories. At each stage, new experiments disproved the old theory, and scientists invented a broader theory that explained both the old and the new observations. But scientists did not discard the Greek and planetary models, despite their shortcomings, because these models are useful within their proper range. For instance, we can use the Greek atom to explain many common observations like air pressure. We need not resort to the planetary atom or the quantum atom to explain these things, because the atom’s internal structure and its quantum nature are irrelevant to these phenomena. Restricted to its proper range, the Greek atom is just fine. Once again, theories are best described as useful rather than true.

Helium

Carbon

Figure 14

An atom of helium and an atom of carbon, according to the planetary model of the atom. The small black dots are electrons in orbit around the nucleus, and the blue circles and white circles represent protons and neutrons in the atom’s nucleus. This is not drawn to scale! The nucleus should be 100,000 times smaller than the electron orbits, and electrons might have no size at all.

CONCEPT CHECK 11 The quantum theory of the atom agrees with every experiment to date. (a) Thus it can now be called an accepted fact rather than merely a theory. (b) Thus it can now be called a scientific hypothesis. (c) Thus it is now known to be certainly true, although we still refer to it as a “theory.” (d) Nevertheless, it remains

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Atoms

only a theory and thus is basically just a guess. (e) Thus it is properly called a scientific theory although, like all theories, it is somewhat tentative. (f) Nevertheless, it could still be disproved by future experiments.

8 CHEMISTRY AND LIFE: WHAT DID ATOMS EVER DO FOR YOU? You can get atoms to do fantastic things by connecting them in sufficiently subtle ways. It’s possible, for example, for a pile of atoms to acquire additional atoms from its environment, to move itself from one place to another, to respond to external events such as the presence of particular molecules, and to create copies of itself. We would call such a pile of atoms alive. Indeed, you are just such a pile of atoms. The pile of atoms that is you has an especially surprising property: It is aware of itself, and in this scientific age it is even aware that it is a pile of atoms. It’s something to think about. The chemical element that gives life its powerful abilities is carbon, which is plentiful on Earth and connects readily to a variety of other plentiful elements. Other elements that are abundant in biological molecules are oxygen, hydrogen, and nitrogen (remember “COHN”). Any rearrangement of molecules into new molecular forms is called a chemical reaction. As examples, this section looks at three chemical reactions that are important in your life: burning, respiration, and photosynthesis. It was once believed that fire was one of the substances of which things are made and that a burning object was releasing the fire that it already contained. The prevailing theory said that this intangible and nonmaterial substance—fire—had weight and carried its weight away when any object burned. Around 1780, Antoine Lavoisier studied burning more closely. He accurately weighed all the materials involved when an object burned, including the gases consumed and given off. Although the prevailing theory predicted that the weight should decrease, Lavoisier found that there was no net change in weight. This disproved the prevailing theory and initiated the modern science of chemistry—the study of the properties and transformations of substances (chemical compounds). The key to this new science was the principle that chemical reactions are rearrangements of atoms that are themselves changeless and indestructible. It followed that the total amount of matter involved in any chemical reaction is the same before and after the reaction. This idea is known as conservation of matter. We now know that, although it’s a useful theory that is very nearly correct in chemical reactions, experiments have proved it entirely wrong in other situations. Most burnable substances are derived from biological materials that contain carbon or hydrogen. As you can demonstrate by placing an inverted jar over a burning candle, burning requires air. Air is not a pure substance but is a mixture of many different substances. Nitrogen and oxygen dominate: Nearly 80% of air’s molecules are nitrogen 1N22, about 20% are oxygen 1O22, and 1% are single argon atoms (Ar). All the other gases added together total far less than 1%. These “trace gases” include all sorts of compounds. Some, such as water vapor 1H 2O2 and helium (He), are natural. Others, such as carbon dioxide 1CO22 and ozone 1O32, come from both

64

Atoms

natural and industrial sources. And still others, such as carbon monoxide (CO), come almost entirely from industry. For burning,10 the crucial component needed from air is oxygen. Carbon from the burning substance combines with oxygen from the air to form carbon dioxide. We abbreviate the preceding sentence symbolically as C + O2 ¡ CO2 The plus sign means “combined with,” and the arrow means “changes into.” If the fuel contains hydrogen, it too combines with oxygen to form water vapor. For example, methane gas, CH 4, is the simplest of the hydrocarbon (hydrogen and carbon) fuels. It is the main component of natural gas. It burns in air to form carbon dioxide and water vapor:11 CH 4 + O2 ¡ CO2 + H 2O An important feature of any chemical reaction is its energy balance. For now, I’ll use the important word energy to mean either of two things: the ability to move things around, and heat or, as I’ll call it, “thermal energy.” Thermal energy is related to, but not the same thing as, warmth. As you know, warmth—perhaps from friction or a burning match—is needed to start a substance burning. Once it starts, the burning reaction itself creates more than enough thermal energy to maintain itself, so excess thermal energy is given off. Including thermal energy, the reaction formula for burning a typical fuel such as methane is CH4 + O2 ¡ CO2 + H2O + excess thermal energy Turning to biology, animals get their bodily material and their energy from the food they eat and the air they breathe. Your blood absorbs carbon-based molecules from food and oxygen from air and ferries them all over your body. When they arrive at, say, your thumb, they enter a biological cell there. In a reaction known as respiration, the cell uses these substances to create biologically useful energy. In a typical case, a simple sugar called glucose reacts with oxygen to create carbon dioxide and water: C6H12O6 + O2 ¡ CO2 + H2O + useful energy As you can see, this is similar to burning. Animal life is a slow burn. In respiration, part of the useful energy goes into making a high-energy molecule known as ATP, and the rest appears as thermal energy. ATP is the energy carrier in animals; it can remain in storage, or it can move from place to place within the cell. It can be used for all sorts of things, like bending your thumb. As you can see from the reaction formula, respiration generates water and carbon dioxide as wastes that are excreted in your sweat, urine, and exhaled breath. Plants and animals have different energy strategies. Whereas animals gather energy by eating plants and other animals, plants use energy directly from the sun. Plants gather carbon dioxide and water from their surroundings and put them 10 Burning

is one form of combustion, which means any chemical reaction that generates warmth and light. formula is not quantitatively “balanced.” For example, there are four Hs on the left, but only two on the right. The balanced formula is CH 4 + 2O2 ¡ CO2 + 2H 2O. Since we are not interested here in how much of each compound enters into a reaction, we omit these numbers.

11 This

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Atoms

together to form high-energy carbohydrates (carbon compounded with water) such as glucose. From the formula for respiration, you can see that this process in plants is exactly the reverse of respiration in animals! Since respiration generates useful energy, the reverse reaction in plants must require an input of energy. Plants have worked out a complicated process that gets this needed energy from the sun. Since animals consume oxygen, we also expect that plants must generate oxygen. So a typical reaction is CO2 + H2O + solar energy ¡ C6H12O6 + O2 It’s called photosynthesis (putting together by light). Animals depend on plants not only for food and fuel but also for oxygen, the crucial component of the air we breathe. Nearly all of Earth’s oxygen comes from photosynthesis and did not exist in large, breathable amounts until after the rise of photosynthesizing bacteria some 2.7 billion years ago. Without plants, animals would soon be out of food, fuel, breath, and luck.

© Sidney Harris, used with permission.

CONCEPT CHECK 12 Some people have suggested that another substance, other than carbon, might conceivably be the key element in forming living organisms elsewhere in the universe. Which of these is the most plausible choice? (a) silicon. (b) oxygen. (c) chlorine. (d) argon. (e) neon. (f) peanut butter. (Hint: See the periodic table. Note: Scientists have rejected this suggestion as unrealistic.)

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Atoms Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions THE GREEK ATOM 1. What macroscopic evidence is there for atoms? 2. What light-based microscope evidence is there for atoms? 3. What experiment did the ancient Greek atomists imagine doing, and what did they believe the result would be? 4. An experiment such as the Greeks (previous question) imagined was actually carried out recently. Describe it. 5. Which is bigger, an atom or the wavelength of light? A little bigger or a lot?

ATOMS AND MOLECULES 6. From the microscopic point of view, what is the difference between an element and a compound? 7. From a macroscopic point of view, what is the difference between an element and a compound? 8. What is the difference between an atom and a molecule? 9. Why is the periodic table arranged in the way that it is? 10. If you chemically decompose water, will you get anything like water? What will you get?

THE ATOM’S EXPLANATORY POWER 11. Describe the microscopic process by which a flower gives off an odor that you can smell some distance away. 12. How do solids, liquids, and gases differ macroscopically? Microscopically? 13. Which is easiest to compress: solids, liquids, or gases? Why? 14. Is a perfect vacuum ever attained on Earth, over a volume as large as 1 cubic centimeter? Elsewhere? 15. What is the microscopic difference between hot water and cold water?

ATOMIC MATERIALISM AND ATOMIC MODELS 16. Name several things that people ordinarily regard as real but that, according to atomic materialism, are not real. 17. Describe the philosophy of materialism. 18. Give arguments for the materialist philosophy. 19. Give arguments against the materialist philosophy. 20. Name three different models of the atom. Describe two of them.

CHEMISTRY AND LIFE 21. What is meant by a chemical reaction? 22. Name three different chemical reactions. 23. Is air a single substance (a single compound)? Describe its chemical composition. 24. Describe an experiment involving burning that supports the notion of conservation of matter. 25. In what types of experiments is the conservation of matter correct to a very good approximation? 26. Describe the following reactions: burning, respiration, and photosynthesis.

Conceptual Exercises THE GREEK ATOM 1. Is the atomic theory known, for certain, to be true? 2. Carbon atoms are about 25% lighter than oxygen atoms (the ratio of their weights is 3 to 4). What is the weight ratio of the carbon and oxygen that go into the formation of carbon monoxide? Answer the same question for carbon dioxide. 3. A carbon atom is 12 times heavier than a hydrogen atom. If methane 1CH 42 is chemically decomposed, what will be the ratio of the weights of the resulting carbon and hydrogen? 4. A carbon atom is 12 times heavier than a hydrogen atom, and an oxygen atom is 16 times heavier than a hydrogen atom. If glucose 1C6H 12O62 is chemically decomposed, what will be the ratio of the weights of the resulting elements?

ATOMS AND MOLECULES 5. How many atoms are in a molecule of H 2SO4 (sulfuric acid)? 6. How many atoms are in the alcohol molecule C2H 5OH? 7. Which of these is a pure compound, which is an element, and which is neither: helium gas, carbon dioxide, polluted water, C6H 12O6, gold, steam? 8. Which of these is a pure compound, which is an element, and which is neither: pure water, oxygen gas, liquid mercury, H 2SO4, U, air? 9. Suppose you obtained the smallest single particle of each of the following substances. In which cases would this particle be a molecule made of more than one atom, and in which cases would it be a single unattached atom: pure water, oxy-

From Chapter 2 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Atoms: Problem Set

10. 11.

12.

13. 14. 15. 16.

17.

gen gas in the form found in Earth’s atmosphere, H 2SO4, U, He, carbon dioxide, H 2, H? Helium is an inert gas, meaning that it does not readily enter into chemical reactions with other substances. List five other substances that you would expect to also be inert gases. Chlorine has a strong tendency to combine with a single hydrogen atom to form HCl. Look in the periodic table and list at least three other elements that you would expect to combine with hydrogen the way that chlorine does. Consider a pure chemical substance A. Suppose that it can be chemically decomposed into two other pure substances B and C. Can we then conclude that B and C must be elements? That B and C must be chemical compounds? That A must be a chemical compound? What is the chemical formula for methane (carbon and four hydrogens)? What is the chemical formula for sulfur dioxide? What is the chemical formula for carbon tetrachloride (tetra means “four”)? On the simplifying approximation that oxygen and carbon atoms have the same weight, how many tons of carbon dioxide gas are formed when 1 ton of coal burns (coal is nearly pure carbon)? In a typical large coal-fed electrical generating plant, a ton of coal is burned every 10 seconds. About how many tons of carbon dioxide enter the atmosphere every hour from such a plant?

THE ATOM’S EXPLANATORY POWER 18. Why can’t you observe Brownian motion in easily visible objects such bits of paper floating in water? 19. What is the chemical formula for the odor of violets (see Figure 6)? 20. A dog follows an escaped convict’s trail by putting its nose to the ground. Explain this from a microscopic point of view. 21. If air is put into a sealed container that is then compressed (reduced in volume), what do you predict will happen to the air pressure on the container walls? Explain this from a microscopic point of view. 22. If air is put into a sealed container and warmed, what do you predict will happen to the air pressure on the container walls? Explain this from a microscopic point of view. 23. If a balloon is partially filled with air (so that it isn’t fully expanded), sealed, and then warmed, what do you predict will happen to the balloon? Explain this from a microscopic point of view. What if the balloon is cooled instead? 24. Why is it so difficult to remove the lid from a vacuumsealed jar? 25. Suppose that you observe the Brownian motion of tiny pollen grains floating in still air enclosed in a glass bottle. What would happen if you increased the amount of air? What would happen if you warmed the air? 26. Why does the air pressure in a tire increase as you add air? Why does the air pressure in a tire increase as you warm the tire? 27. Suggest an experiment that would show that air has weight. 28. What if, in addition to its random molecular motion, all the air molecules in some volume of air had an overall collective motion, all of them moving, say, eastward. Could this collec-

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Figure 6

The odor of violets, in air. The funny-looking thing is the odorof-violets molecule, made of carbon (horizontal stripes), hydrogen (black), and a single oxygen atom (green).

tive motion be observed macroscopically? What would we call it?

METRIC DISTANCES AND POWERS OF 10 29. Write as ordinary numbers: 109; 1026; 3.6 * 1013; 5.9 * 10-8. 30. Write in powers of 10 notation: 3 trillion; five-thousandths; 730,000,000,000,000; 0.000 000 000 082. 31. The distance to the moon is 384,000 km. Express this using powers of 10. How far is this in meters? In millimeters? 32. Our Milky Way galaxy contains perhaps 400 billion stars. Suppose that 0.05% (i.e., 0.000 5) of these stars have planetary systems containing at least one Earthlike planet (one that could conceivably support Earthlike life). Express these two numbers using powers of 10, and then multiply them together to find how many Earthlike planets there are in our galaxy. Express this number in words (thousands or millions, etc.). 33. The universe is a million trillion seconds old. Write this number in ordinary (not powers of 10) notation.

Atoms: Problem Set

THE SMALLNESS OF ATOMS 34. Put these in order from lightest to heaviest: water molecule, oxygen atom, raindrop, hydrogen atom, glucose molecule, electron, DNA molecule. 35. Put these in order from lightest to heaviest: H 2 molecule, methane molecule, fine dust particle, hemoglobin molecule, proton, glucose molecule. 36. How old are a baby’s atoms? Are they older than an old person’s atoms? What about a baby’s DNA molecules? 37. MAKING ESTIMATES One sheet of paper is about 0.1 mm thick. An atom is about 10-10 m across. About how many atoms thick is one sheet of paper? 38. MAKING ESTIMATES The average weight, per atom, of the atoms in your body is about 10-26 kg 12 * 10-26 pounds2. About how many atoms are there in your body? 39. MAKING ESTIMATES The smallest dust particle visible to the unaided eye measures about 0.05 mm across. About how many atoms across is this? In other words, if we line up atoms side by side, about how many would it take to make a line of atoms 0.05 mm long? 40. MAKING ESTIMATES Referring to the preceding exercise: Assume the small dust particle is shaped like a cube. About how many atoms does it contain?

CHEMISTRY AND LIFE 41. What is the chemical reaction formula for burning hydrogen gas in air? What substance is created by this reaction? 42. For safety, gas-filled balloons are filled with helium instead of hydrogen. What does this tell you about the behavior of helium in the atmosphere? 43. Gasoline is a hydrocarbon fuel. What are the two main compounds created when gasoline burns in a car engine? 44. NOX (nitrogen oxide and nitrogen dioxide) is one pollutant from automobiles. What elements must combine to form NOX? 45. Gasoline contains neither oxygen nor nitrogen. So where must these elements come from when NOX is formed in car engines? 46. Are there any molecules in your body that you could claim are “your” molecules, unique to your body and probably unlike any other molecules in the universe?

Answers to Concept Checks 1. [Are you reading this before forming your own answer? If

2. 3. 4. 5. 6.

so, do you exercise by watching somebody else jog? Exercise your mind by providing your own input to the Concept Checks!] In Democritus’s time, this was a hypothesis, but today it is an established scientific theory, (d). It is incorrect to call a general idea, such as this one, a fact or observation. The weight of one sulfur atom is the same as the weight of two oxygen atoms, so the ratio is 1 to 1, (c). Now the ratio is 1 to 1.5, which is the same as 2 to 3, (d). (a), (d), and (f) (b) (f)

7. (a), (c), (d), and (e). Note that we can observe the light

8. 9. 10. 11. 12.

from stars [answer (b)], despite the absence of air in outer space. And a rock would still fall [answer (f )] even if there were no air. 106 * 1012 = 1018, (e) 10 - 2 * 10 - 12 = 10 - 14, (c) (b) (e) and (f). Note that answer (d) is wrong: A hypothesis is an educated guess, but a theory is far more than that. Silicon, (a), in the same column with carbon in the periodic table.

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. No. General scientific principles are never certain. 3. 12 to 4, in other words 3 to 1. 5. 2 + 1 + 4 = 7. 7. Helium is an element, carbon dioxide is a pure compound, polluted water is neither (it is a mixture), C6H12O6 is a pure compound, gold is an element, and pure unpolluted steam is a pure compound (H2O). 9. Molecule made of two or more atoms: pure water (H2O), atmospheric oxygen (O2), H2SO4, carbon dioxide (CO2), H2. Single unattached atom: U, He, H. 11. The elements lying in the same column with chlorine in the periodic table are fluorine, bromine, iodine, astatine. 13. CH4. 15. CCl4. 17. Since 1 ton of coal is burned every 10 seconds, about 3 tons of CO2 enters the atmosphere every 10 seconds. In 1 hour there are 3600 seconds, or 3600>10 = 360 of these 10-second intervals. So the number of tons of CO2 entering the atmosphere in 1 hour is roughly 3 * 360 = 1080 tons. 19. Figure 6 shows that the molecule is made of 14 carbon atoms (C), 22 hydrogen atoms (H), and 1 oxygen atom (O), so the chemical formula is C14H22O. 21. When the container’s volume is reduced, an individual air molecule hits the inner walls of the container more often because it has less space in which to move around. So the walls will be struck more often by moving air molecules. In other words, the pressure will increase. 23. When the air is heated, the balloon will expand a little because the molecules are moving faster and hit the walls harder, pushing the walls further apart (since the balloon is not fully expanded to begin with). When the air is cooled, the balloon will shrink a little. 25. Since there are now more air molecules, the pollen grains will be hit more often, and they will not travel as far between hits (changes in velocity). If we heat the air, the air molecules will be moving faster, the pollen grains will be hit harder, and the pollen grains will gain greater speeds. 27. Weigh two identical rigid containers, one containing air and one that has had some of its air removed. If air has weight, the container with more air should weigh a little more.

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Atoms: Problem Set 29. 109 = 1,000,000,000

31. 33. 35. 37. 39.

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10 - 6 = 0.000 001 3.6 * 1013 = 36,000,000,000,000 5.9 * 10 - 8 = 0.000 000 059 3.84 * 105 km, 3.84 * 108 m, 3.84 * 1011 mm. 1,000,000,000,000,000,000 seconds. Proton, H2, methane (CH4), glucose molecule (C6H12O6), hemoglobin molecule, dust particle. How many times does 10 - 10 m go into 0.1 mm? Since -4 - 10 = 0.1 mm = 10 - 4 m, the answer is 10 >10 10 - 4 + 10 = 106 atoms, or one million atoms thick. An atom is about 10 - 10 m across (Section 3). Since 0.05 mm = 5 * 10 - 5 m, the number of atoms needed to -5 - 10 = stretch across a dust particle is 5 * 10 >10

5 * 10 - 5 + 10 = 5 * 105 atoms, or 500,000 atoms (half a million). 41. Hydrogen and oxygen come in the two-atom form, H2 and O2. They combine to give water: H2 + O2 : H2O. 43. Hydrocarbons are made of hydrogen (H) and carbon (C). When these burn in air containing O2, the H should combine with O2 to create H2O, and the C should combine with O2 to create CO2. 45. From the atmosphere, which contains an abundance of N2 and O2. These elements don’t combine at normal atmospheric temperatures, but at the high temperatures prevailing in automobile engines they do combine.

How Things Move

From Chapter 3 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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How Things Move Galileo Asks the Right Questions

I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use. Galileo

W

hen you look around, your eye falls on a book, a flower, your foot. What are these things made of? The ancient Greeks answered that things are made of atoms. You notice that the book falls, the flower sways, your foot taps. Why, and how, do things move? Again, the ancient Greeks asked such questions (and so did others, such as Chinese naturalists of that same time). The Greek philosopher and scientist Aristotle (Figure 1) developed the earliest theory of motion. His theory was intuitively plausible and had some observational support, but later scientists such as Galileo and Newton discarded Aristotelian physics in favor of powerful new ideas that then dominated science for three centuries. Beginning in 1900, science again changed its view of motion, when the relativity and quantum theories altered most of Newtonian physics. Although we now know that these ideas are inaccurate outside of the situations encountered in everyday life on Earth, Newtonian physics continues to be useful for understanding the way the macroscopic world around us works and forms the basis for many of the technologies we rely on every day. Perhaps more importantly, Newtonian views have retained their powerful cultural influence. After a look at Aristotelian physics (Section 1), this chapter discusses Galileo’s ideas about motion. Section 2 presents Galileo’s objections to Aristotelian physics and the experimental background for the law of inertia, the foundation of Newtonian physics. Section 3 examines this law. Sections 4 and 5 explore speed, velocity, and acceleration, ideas needed to describe motion. Section 6 applies all of this to a familiar phenomenon, falling.

1 ARISTOTELIAN PHYSICS: A COMMONSENSE VIEW Aristotle’s physics agrees with most people’s common sense. But these plausible notions are precisely the ones that Newtonian physics discarded. Because Aristotelian physics is so ingrained in our intuitions, we had best see where it went wrong.

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Aristotle noticed that some motions maintain themselves without assistance, and he called these natural motions. For example, a rock pushed off a ledge falls toward the ground with no obvious assistance, so he considered the fall of a solid object to be a form of natural motion. In his view, solid objects fall because they are made of the Aristotelian element “earth” and thus seek to get as close as possible to their natural resting place, which is the center of the solid Earth. In addition to solid objects falling, Aristotle perceived three other sorts of natural motion on Earth: water falling or running downhill, air rising, and flames leaping upward. All these natural motions are downward or upward. Horizontal motions seem different. When you pull a cart along a road, throw a stone horizontally, or push a box along the floor, your activity maintains the motion: Pushes and pulls are needed to keep the cart, the ball, and the box moving. Aristotle believed these pushes and pulls were needed because objects must be forced to behave contrary to their own natural motion. Aristotle classified such motion as “violent motion,” meaning that an external push or pull was needed to maintain it. He believed that all motion on Earth was either natural or violent, but he perceived in the heavens an entirely different kind of motion. He believed that the moon, sun, planets, and stars were made of a substance called ether (from the Greek word for “blaze”), which was not found on Earth. Ether had no weight and was incorruptible (unchangeable, eternal). Perfect in every way, ether’s natural place was in the heavens, and it naturally moved in perfect circles around Earth. This third kind of motion was called “celestial motion.” Aristotle’s theory explained lots of observations. It gained wide acceptance, partly because of its plausibility. It does seem to us that a rock falls all by itself, that a push is needed to maintain horizontal motion, and that motion in the heavens really is different from motion on Earth. But as you will see, Newtonian physics contradicts all three of these notions.

Erich Lessing/Art Resource, N.Y.

How Things Move

Figure 1

The Greek philosopher and scientist Aristotle, 384–322 BCE. He developed the earliest theory of motion. His theory, which agreed with our common intuitive notions, was replaced by the far less intuitive theory of Newton.

2 HOW DO WE KNOW? DIFFICULTIES WITH ARISTOTELIAN PHYSICS Aristotelian physics had its weaknesses. You can demonstrate some of these for yourself. Drop a piece of notebook paper to the ground. Now crumple it into a tight ball and drop it again. Does it fall faster?1 Aristotelian physics has a hard time explaining this result. After all, the crumpled paper is still the same paper, so it should “seek” Earth’s center equally as strongly as the flat sheet, and should fall no faster than the flat sheet. Now try dropping two objects that have the same shape but very different weights, such as a rock and a tightly crumpled piece of newspaper of about the same size (Figure 2). What do you find? According to Aristotelian physics, the heavier object, containing more of the element “earth,” should seek out Earth’s center more strongly, and so should fall noticeably faster. But it does not. If you do this experiment carefully and from a high place such as a second-story window, you might detect that the heavier object actually does fall a little faster, but not a lot faster as is predicted by Aristotle’s physics. Today’s theories predict that for two objects of the same shape, the lighter one will fall a little slower because of 1

Figure 2

Hold a rock and a wadded-up piece of paper above the ground and drop them simultaneously. What does Aristotelian physics predict? What do you observe?

Please do these simple experiments when they are suggested, to reinforce your learning. There’s nothing like observing the real thing!

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How Things Move

air resistance—the resistance to the motion of an object through the air due to the object’s collisions with numerous air molecules. According to today’s theories, air resistance also explains why a flat sheet of paper falls slowly. One can test the hypothesis that these small differences in falling are due to air resistance by letting two objects fall in a vacuum, perhaps inside a container from which the air has been removed. One then finds that the light and heavy objects fall at precisely the same speed. A feather dropped in a vacuum falls as fast as a rock, in clear contradiction of Aristotelian predictions (Figure 3)! Since Galileo Galilei was one of the first scientists to challenge Aristotle on this point, I’ll summarize these conclusions as:

Galileo’s Law of Falling If air resistance is negligible, then any two objects that are dropped together will fall together, regardless of their weights and their shapes, and regardless of the substances of which they are made.

Figure 3

Editorial Photocolor/Art Resource, N.Y.

A feather dropped in vacuum falls as fast as a rock.

Figure 4

Galileo Galilei, 1564–1642. He helped overthrow Aristotelian physics, helped formulate the law of inertia, made astronomical discoveries that supported the Copernican view of the universe, and much more. But his most important contribution might have been his development of the scientific process: the notion that we learn not from authority but rather from experience and rational thought.

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This is an amazingly general statement. It applies to any two objects. Each object could be anything: cannon ball, frog, feather, helium-filled balloon, even an individual atom,2 just as long as air resistance is negligible. Aristotle’s concept of violent motion also has problems. If you shoot an arrow, it can travel a great distance horizontally while hardly slowing down. A brief strong push from the bowstring starts it, but what external assistance keeps it moving once it is released from the bow? Aristotle himself had difficulty reconciling this sort of example with his own theory, and later scientists had similar difficulties. Galileo (Figure 4) was a brilliant, cocky Italian who supported Copernican astronomy, issued sarcastic opinions about Aristotelian physics, and generally annoyed the authorities. His writings eventually earned him a visit by the Catholic Inquisition, which “persuaded” the now elderly man to “confess” and then confined him to house arrest for his remaining 10 years of life. Even under house arrest, the irrepressible Galileo pursued his experiments and wrote a large physics book. To focus his thinking, Galileo imagined the following experiment: Let a ball roll down an incline. Its speed will increase. Now give the ball a starting push and let it roll up an incline. It slows down (then stops and rolls back down). Suppose we make the inclines nearly horizontal (Figure 5). If you have ever let a ball roll down a very slight incline, you know that it’s likely to slow down and come to rest, even though it’s going downhill. Galileo understood that this slowing is due to the roughness of the incline and ball. Today it’s called friction. Galileo’s crucial step was to idealize the experiment by neglecting, at least in his mind, the effect of friction. He saw that if there were no friction, the ball would speed up on any downward incline, no matter how slight, and would slow down on any upward incline. Then he took another brilliant step: He imagined the “limiting case” of slight inclines, namely, a perfectly horizontal surface. On a frictionless horizontal surface, the ball could neither speed

2

In 1999, researchers were for the first time able to compare the motion of freely falling individual atoms with the fall of a macroscopic object such as a rock. It was not an easy experiment because, in order to observe only their falling, the atoms’ thermal motion had to be removed by cooling them to within two-millionths of a degree of “absolute zero” (the lowest temperature allowed by the laws of physics). The atoms fell just like rocks.

How Things Move

(a)

(b)

(c)

Figure 5

A smooth ball on a smooth incline always (a) speeds up going down and (b) slows down going up, even for a very slight incline. In the limiting case (c) of a perfectly smooth and level surface, the ball should keep going forever.

up nor slow down because the surface was intermediate between downhill and uphill. Galileo concluded that in absence of friction, a ball that once started rolling on a horizontal surface would roll forever. This radically contradicted Aristotle’s theory, which stated that continued pushing or pulling was needed to maintain violent (that is, horizontal) motion, and led directly to the law of inertia (next section), the foundation of post-Aristotelian physics. Galileo’s methods have been crucial to science ever since. They included the following: • Experiments, designed to test specific hypotheses. • Idealizations of real-world conditions, to eliminate (at least in one’s mind) any side effects that might obscure the main effects. • Limiting the scope of the inquiry by considering only one question at a time. For example, Galileo separated horizontal from vertical motion, studying only one of them at a time. • Quantitative methods. Galileo went to great lengths to measure the motion of bodies. He understood that a theory capable of making quantitative predictions was more powerful than one that could make only descriptive predictions, because quantitative predictions were more specific and could be experimentally tested in greater detail. Galileo was one of the first people to practice what we recognize today as the scientific process: the dynamic interplay between experience (in the form of experiments and observations) and thought (in the form of creatively constructed theories and hypotheses). This notion that scientists learn not from authority or from inherited beliefs but rather from experience and rational thought is what makes Galileo’s work, and science itself, powerful and enduring.

The Holy Spirit intended to teach us in the Bible how to go to heaven, not how the heavens go. Galileo

A grain of sand falls as rapidly as a grindstone. Galileo

3 THE LAW OF INERTIA: THE FOUNDATION OF NEWTONIAN PHYSICS Galileo and other scientists eventually arrived at a profound non-Aristotelian insight. It involved an extreme idealization: Suppose you could get away from the effects of friction and air resistance and also gravity. It isn’t easy to imagine such a

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How Things Move

Oh, my dear Kepler, how I wish that we could have one hearty laugh together! Here at Padua is the principal professor of philosophy, whom I have repeatedly and urgently requested to look at the moon and planets through my glass, which he perniciously refuses to do. Why are you not here? What shouts of laughter we should have at this glorious folly! And to hear the professor of philosophy at Pisa labouring before the Grand Duke with logical arguments, as if with magical incantations, to charm the new planets out of the sky. Galileo, in a Letter to Kepler, Commenting on Libri, Teacher of Philosophy at Padua, Who Refused Even to Look into Galileo’s Telescope in Order to View the Newly Discovered Moons of Jupiter

Libri did not choose to see my celestial trifles while he was on Earth; perhaps he will do so now he has gone to Heaven. Galileo’s Further Comment on Libri, Who Died Soon After the Telescope Incident

thing, because gravity is so omnipresent that you scarcely notice it. French philosopher and scientist René Descartes was the first to imagine the absence of gravity and understand its consequences. What if you could turn off gravity? This question would have been meaningless to Aristotle, because for him there was no such thing as gravity. Objects just fell, by themselves, because that was their nature. But Descartes realized that, if you released a stone in midair and there were no gravity or friction or air resistance, the stone would not fall. It would hang, motionless, in midair. And if you flicked that motionless stone with your finger, it would coast in a straight line with no change in speed, forever! Descartes is saying that without gravity or friction or air resistance, an object that was moving to begin with would keep moving without external assistance. And an object that was at rest to begin with would stay at rest; it would hang in midair, for instance. This is strange, counterintuitive. Because gravity, friction, and air resistance are all around us, our intuition tells us that objects can keep moving only if they are pushed or pulled, and objects can hang in midair only if something holds them up. As a way of holding on to our intuitive notion that something must assist an object if it is to keep moving, scientists give a word to an object’s tendency to keep moving or to remain at rest: “inertia.” In other words, an object’s inertia is its tendency to maintain its state of motion, whether moving or remaining at rest. This word inertia doesn’t really explain anything; it is simply a word that stands for the unexplainable fact that unassisted objects do keep moving. I’ll summarize all of this as: Law of Inertia3 A body that is subject to no external influences (also called external forces) will stay at rest if it was at rest to begin with and will keep moving if it was moving to begin with; in the latter case, its motion will be in a straight line at an unchanging speed. In other words, all bodies have inertia.

You see the law of inertia in action in any motion that is horizontal (to eliminate the effect of gravity) and nearly frictionless, such as a bowling ball rolling slowly down a bowling alley, or an object coasting on a cushion of air. Figure 6a is a multiple-flash photograph of such an air-coaster (see Figure 6b), made in a completely dark room with a camera whose shutter remained open, using a rapidly flashing light to illuminate the coaster only briefly at several equally spaced times. As you can see by checking the meter stick next to the coaster, the coaster is moving in a straight line at an unchanging speed: It moves the same distance (so far as it is possible to measure this in the photo) in each time interval. Although careful measurement would show that air resistance slows the coaster slightly, this example is close enough to Galileo’s ideal case that if you view it in a lab, it will give you an intuitive feel for the law of inertia. Outer space furnishes lots of nice examples. Outer space refers to those regions of the universe outside Earth and outside other astronomical objects, where “Earth” 3

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This is often called Newton’s first law, even though Descartes invented it, because Newton listed it first among his three basic principles of motion. I will refer to these three principles as the law of inertia, Newton’s law of motion, and the law of force pairs, rather than by their more common but less accurate, less descriptive, and more boring titles: Newton’s first law, Newton’s second law, and Newton’s third law.

Uri Haber-Schaim

How Things Move

Uri Haber-Schaim

(a)

(b)

Figure 6

(a) Multiple-flash photo of the motion of an air coaster on a smooth horizontal surface, viewed from above. (b) The coaster at rest.

includes the atmosphere. The atmosphere thins out at higher altitudes, becoming so thin above 100 km that the drag (air resistance) on satellites is nearly negligible. Beyond about this altitude lies outer space. Figure 7 puts this altitude into perspective. Let me clarify some common misconceptions about the word space. Space is all around you. There is space between you and objects on the far side of the room you are in. The space within a few miles of Earth’s surface is filled with air—but not completely filled because the empty spaces between the air’s molecules are far larger than the molecules themselves. There’s nothing dramatically different about this near-Earth space and the outer space that lies above Earth’s atmosphere. The major difference is simply that there’s far less air up there than down here; that is, outer space is closer to being empty space than is the space in your room. But the same laws of physics, such as the law of inertia and the law of gravity, that operate down here also operate up there. When astronauts traveled to the moon, their spacecraft’s rocket engines first boosted (pushed) them up and into orbit around Earth. Then they fired their rocket engines for a few minutes to leave Earth’s orbit and start toward the moon. Then they shut down their engines and coasted, for three days, to the moon. The spacecraft became a long-distance coaster and a great example of the law of inertia. But this coasting was not entirely free of external influences. Although there is no significant air resistance in outer space, there is still significant gravity unless the spacecraft is extremely far from all large bodies such as Earth, the sun, and the moon. Gravity has a very long-range effect. For example, at one-sixth of the distance to the moon, gravity is still 1% as strong as it is on Earth’s surface—a muchreduced effect but still not negligible. The spacecraft to the moon slowed during the first part of its journey because of the pull of Earth’s gravity and then sped up during the last part because of the moon’s pull.

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How Things Move Layer of very thin atmosphere, too thin for breathing, about 90 km high Black line represents the thin layer of breathable air, 10 km high. This is the height of Mount Everest.

A typical low-orbit satellite, greatly enlarged.

Radius of solid Earth, 6000 km Outer space begins here, at about 100 km above Earth’s solid surface.

Figure 7

The solid Earth, Earth’s atmosphere, and outer space. The drawing is roughly to scale, except that the artificial satellite is far too large. A real orbiting satellite, several meters in size, would be a microscopic dot on this diagram.

A big difficulty for the sun-centered astronomy proposed by Copernicus around 1550 was the problem of how Earth could keep moving with nothing to push it. This problem perplexed Copernicus, and it gave his opponents powerful ammunition. The answer came a century too late to help Copernicus. Earth is a coaster in space! Like astronauts coasting to the moon, Earth coasts around the sun. It keeps going because there’s nothing to stop it. But why, you might ask, does it move in a circle rather than in a straight line at unchanging speed? And what started it moving in the first place? The answers are that the sun’s gravity bends Earth’s path into a circle, and Earth started moving because the gas and dust from which it was formed were already moving. Another difficulty for a moving-Earth theory of astronomy is that it seems as though birds and other objects not attached to the ground should be left behind as Earth moves through outer space. The answer is that birds have inertia too. A bird standing on the ground is participating in Earth’s 30-kilometer-per-second coaster

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ride around the sun, so when the bird takes to the air, it is already moving at this speed around the sun, and the law of inertia says that there’s no reason for it to stop. CONCEPT CHECK 1 According to Aristotelian physics, which outside influences act on a stone while it falls? (a) Air resistance (b) Inertia (c) Gravity (d) The tooth fairy (e) There are no outside influences. CONCEPT CHECK 2 According to Newtonian physics, which outside influences act on a stone while it falls to the ground? (a) Air resistance (b) Inertia (c) Gravity (d) There are no outside influences. CONCEPT CHECK 3 Suppose that, because of unknown causes, the sun suddenly appeared to “stand still” in the sky. From the viewpoint of Copernican astronomy, this would mean that (a) Earth stopped spinning around its own center; (b) Earth stopped moving in its orbit around the sun; (c) the sun stopped moving in its orbit around the center of the Milky Way Galaxy; (d) the sun stopped moving from east to west; (e) the sun stopped moving from west to east.

4 MEASURING MOTION: SPEED AND VELOCITY Sometimes quantitative methods are needed to get at nature’s deeper secrets. At other times, quantitative details are superfluous and qualitative descriptions are preferable. For a clear understanding of motion and related topics like force and energy, you need to think both qualitatively and quantitatively. And quantities (numbers) are needed to understand important practical matters such as world energy problems. Scientists like to specify their measurements in terms of just a few basics. To describe motion, only two are needed: distance and time. For example, suppose you want to describe quantitatively the motion flash-photographed in Figure 6 using only the meter stick shown and a clock. Suppose the flasher flashes steadily at 0.40-second intervals and that you start the clock at the first flash, when the coaster is at the 10-centimeter (cm) mark. Then successive flashes occur at 0.40 seconds (s), 0.80 s, 1.20 s, 1.60 s, 2.00 s, and 2.40 s. Table 1 tabulates these data, with distances estimated to the nearest millimeter (0.1 cm) from Figure 6. How can you use these data to describe how fast the coaster is moving? In other words, how can these data tell you what a speedometer attached to the coaster would read? A speedometer tells you the distance traveled per (in each) unit of time, such as the number of kilometers per hour or the number of centimeters per second. So if you were to walk 6 kilometers (km) in 2 hours, the number of kilometers in each hour would be 6 divided by 2, or 3 km per hour. From this, you can see that speed is distance divided by time. Returning to Table 1, during each 0.40-s time interval the coaster travels 14.1 cm. So a speedometer attached to the coaster should register 14.1 cm divided by 0.40 s, or 35.2 centimeters per second. I’ll call this the coaster’s speed. I’ll abbreviate it as 35.2 cm/s, where the divide sign (/) is to be read “per” or “in each.” But there’s a catch. Suppose you ride your bicycle 24 km in 3 hours. According to this definition, your speed would be 8 km/hr. But surely you did not maintain exactly this speed during every minute of the 3-hour trip. Rather, the 8 km/hr is an

Table 1 Positions and times for air coaster of Figure 6 Clock time (s)

Position (cm)

0.00

10.0

0.40

24.1

0.80

38.2

1.20

52.3

1.60

66.4

2.00

80.5

2.40

94.6

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overall speed, actually the speed you would have had to maintain in order to make the 3-hour trip at an unchanging speed. I’ll call this the average speed for the trip. But a car’s speedometer gives a value at every instant of time. What does a speedometer read? A speedometer is based on wheel rotation rates. If you look closely at the way it operates, you will find that it actually reads only an average speed during some time interval, but that this time interval is very short—so short that the speed is practically unchanging during this time interval. This average speed during a time interval so short that the speed hardly changes is called the instantaneous speed. It’s defined just like the average speed, but with the understanding that the time interval is short. It’s what a speedometer reads. I will use the unmodified word speed to mean “instantaneous speed,” and I’ll use average speed when that's what I mean. Quantitative statements, such as our definition of average speed, are often easier to grasp if written as an abbreviated formula: average speed =

distance traveled traveling time

This can be further abbreviated using symbols. We can choose the symbols to suit ourselves. I will use s to represent instantaneous speed, s for average speed, d for distance traveled, and t for traveling time. Then the formula is s =

d t

Please don’t be intimidated by formulas like this. A formula is just an abbreviation for words. It’s the idea, not the formula, that’s essential. And many of the most important principles, such as the law of inertia, are best stated without formulas. In fact, if you do use a formula, be sure you can first state it carefully in words, because otherwise you could fool yourself into thinking you understand the idea when all you’ve done is memorize some symbols. For example, the t in the speed formula’s denominator is not just any arbitrary time—it means something very specific: the duration of the time interval during which the object traveled the distance indicated in the numerator. When you travel, it makes a difference which direction you move. Jogging at 10 km/hr northward will get you to a different place than will jogging at 10 km/hr westward. Speed and direction of motion occur together so frequently in physics that it’s useful to have a separate word for the combination. I will use the word velocity to mean speed and direction. The words speed and velocity are interchangeable in everyday language, but in physics they are not. Test your understanding of speed and velocity by trying these questions: CONCEPT CHECK 4 A car travels 12 km in half an hour, while a bicyclist “sprints” for 1 minute at a steady 30 km/hr. The one with the higher average speed is (a) the car; (b) the bicyclist. CONCEPT CHECK 5 In which of the following cases is the car’s speed increasing? (a) A car covers longer and longer distances in equal time intervals. (b) A car takes longer and longer time intervals to cover equal distances. (c) A car covers equal distances in equal time intervals. (d) A car covers equal distances in shorter and shorter time intervals. (e) A car takes equal time intervals to cover equal distances. (f) In equal time intervals, a car covers shorter and shorter distances.

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CONCEPT CHECK 6 Two bicyclists, both moving at 10 km/hr, pass each other on a straight road, one moving north and the other moving south. These bicyclists have (a) the same speeds and the same velocities; (b) different speeds and different velocities; (c) different speeds but the same velocities; (d) the same speeds but different velocities.

5 MEASURING MOTION: ACCELERATION The law of inertia says that a body that feels no external forces must either move at unchanging speed in a straight line or remain at rest if it were at rest to begin with. But remaining at rest is just a special case of an unchanging speed (the speed remains zero), so we can state the law of inertia as simply “a body that feels no external forces must move at unchanging speed in a straight line.” But motion in a straight line at an unchanging speed is motion at an unchanging velocity, and the condition of remaining at rest is also a condition of unchanging velocity. So we can state the law of inertia more concisely: Law of Inertia (more concise form) A body that is subject to no external forces must maintain an unchanging velocity.

Now suppose that there are external forces (external influences). How will they affect an object’s motion? It’s not too difficult to guess the answer once you understand the law of inertia: External forces must cause changes in velocity. Any object whose velocity is changing is said to be accelerated. Concept Check 7 will exercise your thinking about this idea. Remember: An object is accelerated only if its velocity is changing, and velocity refers to the combined instantaneous speed and direction. CONCEPT CHECK 7 During a trip, a car executes several kinds of motion. In which of the following cases is the car accelerated? (a) Moving along a straight, level road at a steady 70 km/hr. (b) Moving along a straight, level road while slowing down from 70 km/hr to 50 km/hr. (c) Rounding a curve at a steady 50 km/hr. (d) Moving uphill along a straight incline at a steady 50 km/hr (Figure 8). (e) Rounding the top of a hill at a steady 50 km/hr (Figure 9). (f) Starting up from rest along a straight, level road.

You have seen how to describe velocity in terms of measured quantities. What about acceleration? To answer this, imagine a car moving north along a straight, level highway. Suppose it speeds up, say from 60 km/hr to 72 km/hr. Its change in speed is then 12 km/hr. Imagine how this would feel to you if you were in the car. It would make a difference to you how fast this change took place. If it took place over an entire hour, you would hardly notice it, but if it occurred during one-tenth of a second, you could wind up with a whip-lashed neck! So the rate at which the speed changes—the amount of speed change per second—is important. Suppose that the time interval is 8 s. Then the amount of speed change per second is 12 km>hr

Figure 8

Illustration for Concept Check 7.

Figure 9

Illustration for Concept Check 7.

8s

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or 1.5 “kilometers per hour per second.” These units tell us that in every second, the speed changes by 1.5 km/hr. We’ll write this as 1.5 (km/hr)/s. This useful quantity, which measures the rate of speeding up, is called the “acceleration” of the car. But remember that an object is said to be accelerated whenever its velocity changes and that the velocity changes not only when the object speeds up but also when it slows down or changes direction. This means that an object’s acceleration is its change in velocity (and not simply the change in speed) divided by the time to make the change. Written as a formula, acceleration =

change in velocity time to make the change

Please note that this physicists’ definition is a little different from the popular definition. The scientific meaning includes not just speeding up (the common meaning of acceleration) but also slowing down (commonly called deceleration) and changing direction. Definitions of words like acceleration are arbitrary, in the sense that nature does not tell us that we must define these words in any particular way. Physicists define their words for maximum convenience. The distinction between velocity and acceleration is important and often misunderstood. “Velocity” refers to motion itself—an object has a velocity whenever it is moving. But “acceleration” refers only to changes in velocity. CONCEPT CHECK 8 Which of these have a high velocity and low acceleration? (a) A speeding bullet moving through air. (b) A race car just as it begins to “dig out” from rest. (c) A fast train as it moves around a long and gentle curve. (d) A fast car as it collides with a brick wall. (e) A golf ball at the instant it is struck by a fastmoving golf club. CONCEPT CHECK 9 In the preceding question, which ones have a low velocity and high acceleration?

6 FALLING Galileo’s law of falling tells us that, because all objects fall in the same way, we can learn about the fall of any object by studying the fall of just one particular object— a book, for example. How do we know objects speed up as they fall? Hold a book, flat, above the floor, and let it go. ——— This is a pause, for dropping your book. What is the numerical value of the book’s speed at the instant you release it? ——— Another pause, to think about that. While you are holding it, the book’s speed is zero, so its speed at the instant of release must also be zero. But does its speed remain zero? Obviously not. At the beginning of the motion, the speed increases from zero to something bigger than zero. So the book must accelerate, at least at the beginning. But does your book accelerate all the way down—does its speed keep on changing? To answer this, drop your book from about half a meter above the floor. Pick it up and drop it again from about 2 m above the floor. Listen as it hits the floor. Did it hit noticeably harder

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How Things Move the second time? If so, the book must have been moving faster at the end of the second drop. Apparently, objects keep on moving faster and faster as they fall farther. So falling objects accelerate all the way down. The preceding paragraph demonstrates the power of careful observation. As the Yankee catcher and famous sage Yogi Berra put it, “You can learn a lot just by looking.”

The multiple-flash photo in Figure 10 shows how to measure falling. A billiard ball falls past a 2-m stick while being photographed at several equally spaced times. The time interval between photos is 1/30 s. You can see the ball’s acceleration: The images get farther and farther apart. Figure 11 is an idealized drawing of a ball falling through a larger distance, neglecting air resistance. A real object falling farther than about 20 m is strongly affected by air resistance because air resistance becomes stronger as an object moves faster. We will, however, imagine that there is no air resistance, in order to focus on the effects due to gravity alone. An object like this whose falling is influenced by gravity alone is said to be in free fall. Suppose you measure distances downward from the release point and that a speedometer attached to the ball measures the ball’s speed as it falls. At the instant of release, you start a clock that tells you the time elapsed since the ball was dropped. Figure 11 gives some of the data you would get in this idealized experiment. In order to highlight the pattern, the actual experimental data are rounded.4 You can see, in three different ways, that the ball accelerates: First, you can see directly from the drawing that the distances fallen during each successive second (0 to 1 s, 1 to 2 s, and so on) get larger and larger. Second, the speed is greater at the end of each successive second, so the ball is moving faster and faster. Third, if you look closely at the distance data, you’ll see that the distances covered during each successive time interval grow larger and larger. For instance, the distance covered during 0 to 1 s is 5 m, and the distance covered during 1 to 2 s is 15 m. How big is this acceleration? Recall that the acceleration is the change in velocity divided by the duration of the time interval. Now look at each successive 1-s time interval. All the changes in speed are precisely the same! During 0 to 1 s, the speed change is 10 m/s. During 1 to 2 s, the speed changes by 10 m/s. And so forth. So, calculating the acceleration for any one of these time intervals, acceleration =

10 m>s change in speed = time interval 1s

which is 10 (m/s)/s, abbreviated as 10 m/s2. This means that the speed changes by 10 m/s in every second. So the acceleration is the same, 10 m/s2, all the way down. And Galileo’s principle of falling tells us that it must be the same for every freely falling object. The numerical value of this acceleration due to gravity is, more accurately, 9.8 m/s2. There is a pattern in the speed data. At times of 0 s, 1 s, 2 s, 3 s, 4 s, and 5 s, the speed (in m/s) is 0, 10, 20, 30, 40, 50, and so on. Just by looking at this string of Figure 10 4

The rounding process introduces a 2% error. More precise distances are 4.9 m, 19.6 m, 44.1 m, 78.4 m, and 122.5 m. More precise speeds are 9.8 m/s, 19.6 m/s, 29.4 m/s, 39.2 m/s, and 49 m/s. Using these more accurate numbers, the calculated acceleration is (9.8 m>s)>(1 s) = 9.8 m>s2.

Multiple-flash photo of a falling billiard ball. The position scale is in centimeters, and the bulb flashed every 1/30 s.

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0s 1s

Approximate distance 0m 5m

2s

20 m

20 m/s

3s

45 m

30 m/s

Time

Approximate speed 0 m/s 10 m/s

numbers, you can guess what should come next: 60. The reason this can be guessed is that there is a recognizable pattern here. Patterns are what scientists look for in nature! Your expectation that the sun will rise tomorrow is also based on a pattern in nature. One way to describe this pattern is with proportionalities. One quantity is proportional to a second quantity if doubling the first means you must double the second, tripling the first means you must triple the second, and so forth. In general, whatever you multiply the first quantity by, you must also multiply the second quantity by. Looking at the speed data, doubling the time (from 1 to 2 s, say) results in doubling the speed (from 10 to 20 m/s), and similar proportionalities hold throughout the data. So, for free fall, speed is proportional to time; s r t

4s

80 m

40 m/s

5s

125 m

50 m/s

Figure 11

A freely falling ball dropped from the top of a tall building. The effect of air resistance is neglected in this illustration.

The symbol r means “is proportional to.” Note that a proportionality such as s r t is not the same thing as an equation. Distance cannot equal time, for the same reason that apples cannot equal oranges. Similarly, speed is proportional to the time for any object that starts from rest and moves in a straight line with unchanging acceleration. For example, an object dropped onto the surface of the moon falls freely (there’s no air resistance on the moon, because there’s no air) with an unchanging acceleration of 1.6 m/s2. So a falling object reaches a speed of 1.6 m/s at the end of 1 s of falling, 3.2 m/s at the end of 2 s, 4.8 m/s at the end of 3 s, and so forth. As on Earth, speed is proportional to time. The pattern in the position data of Figure 11 is not as easy to recognize. To make it easier to find, let’s express the position data in multiples of the position at 1 s, in other words, in 5-m units. The data tell us that at 2 s, the position (the total distance fallen) is 20 m, or 4 of these units; it is 9 units at 3 s, 16 units at 4 s, 25 units at 5 s. So the positions, measured in 5-m units, are 0, 1, 4, 9, 16, 25. What’s the next number in this sequence? Have you got it? Each of the numbers is a perfect square: 02, 12, 22, 32, 42, 52. Next comes 62, or 36 of our 5-m units! To get the distance in meters, multiply this by 5, getting 180 m. This pattern can also be described quantitatively with proportionalities. The distances, in meters, are proportional to the square of the time. This means that doubling the time multiplies the distance by 4, tripling the time multiplies the distance by 9, and so forth. In general, whatever number you multiply the time by, you must square this number and then multiply it by the distance. For instance, if you multiply the time by 3 (from 1 to 3 s, say), then you must multiply the distance by 32, or 9. So for free fall: distance fallen is proportional to the square of the time; d r t2 Again, this is a proportionality that is valid for any case of unchanging acceleration. For instance, distance is proportional to the square of the time for an object falling freely onto the moon.5 5

With further analysis, we could arrive at two equations for the speed and position of any object that starts from rest and moves in a straight line with unchanging acceleration s = at,

1 d = a b at2 2

where a represents the acceleration. For freely falling objects on Earth, a = 9.8 m>s2.

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CONCEPT CHECK 10 In four times as much time, a freely falling object dropped from rest falls (a) twice as far; (b) 4 times farther; (c) 8 times farther; (d) 12 times farther; (e) 16 times farther; (f) into your soup. CONCEPT CHECK 11 Would the answer to the preceding question be altered if the object were falling freely onto the surface of Mars? (a) Yes. (b) No. CONCEPT CHECK 12 In four times as much time, a freely falling object gets going (a) twice as fast; (b) 4 times faster; (c) 8 times faster; (d) 12 times faster; (e) 16 times faster.

© Sidney Harris, used with permission.

CONCEPT CHECK 13 For a freely falling object, (a) the total distance covered (distance fallen) keeps increasing; (b) the distance covered during each second keeps increasing; (c) the speed keeps increasing; (d) the change in speed during each second keeps increasing; (e) the acceleration keeps increasing.

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How Things Move Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions ARISTOTELIAN PHYSICS 1. Describe the four kinds of motion that Aristotle considered to be natural on Earth. 2. Give two examples that Aristotle considered to be violent motions. 3. According to ancient Greek thought, in what fundamental way does Earth differ from the heavens? 4. Give an example of a motion that contradicts Aristotelian physics. 5. According to Aristotelian physics, why does a stone fall when it is released above the ground? According to Newtonian physics? 6. Describe at least one principle of Aristotelian physics that seems intuitively plausible but that Newtonian physics rejects.

THE LAW OF INERTIA 7. What does it mean to say that an object has inertia? 8. What does the law of inertia say about the velocity of a body that is subject to no external influences? What does this law say about such a body s acceleration? 9. Which of the following describes how high you must go before you will first reach outer space : anywhere above the ground, about 100 m, about 1 km, about 100 km, beyond the moon, beyond the solar system? 10. Is there air in outer space? 11. Give at least one example that demonstrates, at least approximately, the law of inertia in others words, an example of unassisted motion at constant, or nearly constant, velocity.

SPEED AND VELOCITY 12. Describe how you could use a clock and a meter stick to measure a moving object s speed. 13. When we say 5 centimeters per second, what does the per mean? 14. What is the difference between speed and average speed? In what circumstances are they the same? 15. Can you give an example in which the speed is unchanging but the velocity changes? If so, give one. 16. Can you give an example in which the velocity is unchanging but the speed changes? If so, give one.

ACCELERATION 17. A car speeds up along a straight line. Describe how you could use clocks and meter sticks to measure its acceleration. 18. How is acceleration related to velocity? 19. If an object s position is changing, can we be certain that it has a nonzero velocity? Can we be certain that it has a nonzero acceleration? 20. If an object is moving in a circle at an unchanging speed, is it accelerated? 21. If an object is slowing down, is it accelerated?

FALLING 22. An object is released above the ground and falls freely. At which of the following places during the fall is its velocity greatest: the top, the midpoint, or a point near the bottom? At which position is its acceleration greatest? 23. What is the meaning of the phrase acceleration due to gravity ? What is its approximate value on Earth? 24. What does speed is proportional to time mean? 25. In twice the time, does a freely falling object fall (from rest) twice as far? Does it gain twice as much speed?

Conceptual Exercises ARISTOTELIAN PHYSICS 1. You roll a ball. It soon rolls to a stop. How would Aristotle interpret this? How would Galileo interpret it?

THE LAW OF INERTIA 2. Most meteoroids pebble-sized to boulder-sized rocks in outer space have been moving for billions of years. What, if anything, keeps them moving? 3. If you ride on a smooth, fast train at an unchanging speed and throw a baseball upward inside the train, will the baseball then get left behind and come down toward the rear of the car? Explain. 4. If a ball is moving at 20 m/s and no forces ever act on it, what will its speed be after 5 s? After 5 years? 5. Do you suppose that the photo of Earth shown in Figure 7a was taken from a low-orbit satellite (see Figure 7b on next page)?

From Chapter 3 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright ' 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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How Things Move: Problem Set Figure 7a

NASA Headquarters

A whole-world view showing Africa and Saudi Arabia taken 7 December 1972 as Apollo 17 left Earth s orbit for the moon. The cultural impact of photos like this, showing Earth as a single, freely moving ball in space, may be among the space program s most important benefits.

Layer of very thin atmosphere, too thin for breathing, about 90 km high Black line represents the thin layer of breathable air, 10 km high. This is the height of Mount Everest.

A typical low-orbit satellite, greatly enlarged.

Radius of solid Earth, 6000 km Outer space begins here, at about 100 km above Earth’s solid surface.

Figure 7b

The solid Earth, Earth s atmosphere, and outer space. The drawing is roughly to scale, except that the artificial satellite is far too large. A real orbiting satellite, several meters in size, would be a microscopic dot on this diagram.

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How Things Move: Problem Set 6. In order to experimentally verify the law of inertia, would you need to be able to measure time? Weight? Distance? 7. When a moving bus comes rapidly to a stop, why do the riders who are standing lurch toward the front of the bus?

SPEED AND VELOCITY 8. Can you drive your car around the block at a constant velocity? 9. Mary passes Mike from behind while bicycling. As she passes him, do the two have the same velocity? The same speed? 10. Mary is bicycling straight north at 15 km/hr, and Mike is bicycling straight south at 15 km/hr. As they pass each other, do they have the same velocity? The same speed? 11. Figure 12 represents a multiple-flash photo of two balls moving to the right. The figure shows both balls at several numbered times. The flash times are equally spaced. Which ball has the greater acceleration? The greater speed? The greater velocity? Does either ball pass the other, and if so, when? 1

1

2

3

2

5

4

3

4

6

6

Figure 12

12. The automobile beltway around many cities is approximately circular. Suppose that you start driving at point A on the east side of the beltway and drive counterclockwise at an unchanging 90 km/hr (Figure 13). As you pass point B on the north side, what is your speed? Your velocity? B

C

City

1

1

2

2

3

4

3

5

4

5

6

6

7

7

8

Figure 14

7

5

17. Is the motion sickness that some people get in a car actually due to motion per se or to something else? Describe one form of motion that would not make people sick. 18. When you drive a car, might you depress the accelerator pedal without actually accelerating? Could you accelerate without having your foot on the accelerator? Explain. 19. One car goes from 0 to 30 km/hr. Later another car goes from 0 to 60 km/hr. Can you say which car had the greater acceleration? Explain. 20. Figure 14 represents a multiple-flash photo of two balls. Describe each ball s motion. Does either ball pass the other? When? Do they ever have the same speed? When?

A

Figure 13

13. Referring to the preceding exercise, as you pass point C on the west side, what is your speed? Your velocity? 14. In Figure 12, suppose the large divisions on the measuring rod are centimeters and that the time intervals each have a duration of 0.20 s. Find the speed of each ball. 15. Find the average speed of a jogger who jogs 3 km in 15 min. Give your answer in km/hr.

ACCELERATION 16. A French TGV train cruises on straight tracks at a steady 290 km/hr (180 mi/hr). What is its acceleration?

21. In each of the following cases, is the motion accelerated or not accelerated? (a) A rock falling freely for 2 m. (b) A meteoroid (a rock in outer space) that is so far from all planets and stars that gravity is negligible. (c) An artificial satellite orbiting Earth at a steady 30,000 km/hr. (d) The moon. (e) An ice-skater coasting on smooth ice, neglecting friction and air resistance. 22. Can a slow-moving object have a large acceleration? Can a fast-moving object have a small acceleration? 23. Which devices in a car are designed to cause acceleration? 24. For an unassisted (unforced, or isolated) moving object, which of the following quantities change, and how do they change: distance (from the starting point), speed, velocity, acceleration? 25. An automobile moves along a straight highway at an unchanging 80 km/hr. During the motion, which of the following quantities change, and how do they change: distance (from the starting point), speed, velocity, acceleration? 26. A ball rolls down a straight ramp. During the motion, which of the following quantities change, and how do they change: distance (from the starting point), speed, velocity? 27. A bicyclist increases her speed along a straight road from 3 m/s to 4.5 m/s, in 5 s. Find her acceleration. 28. A car accelerates from 0 to 100 km/hr in 10 s. Find its acceleration. Drag racers can get to 400 km/hr from rest in 5 s. How big is this acceleration? 29. Find the acceleration of a car as it speeds up from 70 to 82 km/hr in 4 s. From 70 to 82 km/hr in 16 s. From 70 to 94 km/hr in 8 s. From 70 to 76 km/hr in 8 s.

FALLING 30. Multiple choice: Two metal balls are dropped from a thirdstory window at the same time. They are the same size, but one weighs twice as much as the other. The time to reach the ground will be (a) about twice as long for the heavy ball; (b) about twice as long for the light ball; (c) about the same for both; (d) considerably longer for the heavy ball, but not necessarily twice as long; (e) considerably longer for the light ball, but not necessarily twice as long.

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How Things Move: Problem Set 31. A falling object has a speed of 10 m/s at t = 1 s. So it seems that it should move 10 m in 1 s. Yet the data say that the object moves only 5 m in 1 s. What is wrong here? 32. Figure 15 represents a multiple-flash photo of a falling ball. Neglect air resistance. At which point, A or B, is the ball s acceleration larger? At which point is its velocity larger?

A

B

Figure 15

33. By how much does a freely falling object s speed increase during its third second of fall (from t = 2 s to t = 3 s after release)? During its fourth second of fall? 34. For an object that is freely falling to Earth, which of the following quantities increase during the fall: distance (from the starting point), speed, velocity, acceleration? 35. As an object falls freely, what will be its speed at the end of the first second? Second second? Third second? 36. As an object falls freely, what will be its acceleration at the end of the first second? Second second? Third second? 37. An astronaut on another planet, one that has no atmosphere, drops a rock off a cliff. How much faster is the rock moving at the end of 3 s as compared with 1 s? How much farther (measured from the release point) does the rock fall in 3 s as compared with the distance it falls in 1 s? 38. Neglecting air resistance, would the answers to the preceding exercise be different if the rock is dropped on Earth? Neglecting air resistance, would the distance fallen in 3 s on Earth be likely to be the same as the distance fallen in 3 s on the other planet?

1

Problems VELOCITY 1. Worldwide sea levels are predicted to rise at a rate of at least 5 mm per year during the next century, due to global warming. At this rate, how long will it be before sea levels have risen by 0.5 m? 2. It takes light about 8 minutes to travel here from the sun. Given that the speed of light is 300,000 km/s, how far is it to the sun? 3. It is 3.8 * 108 m to the moon. How long does it take a radar beam, traveling at the speed of light (300,000 km/s), to get from Earth to the moon and back? 4. You wish to travel from downtown New York City (NYC) to downtown Washington DC (DC), a distance of 330 km. You consider two options: train and plane. The high-speed train takes 1.5 hr, plus 30 min in stations. The airplane flies the 330 km (airport to airport) in just 30 min, but the drive to the NYC airport takes 30 min, you must arrive 2 hr before departure time, the plane waits 15 min for takeoff, and it takes 45 min to get your luggage and drive into DC. Find the train s track speed, the plane s flying speed, the total travel time for each option, and the overall average speed for each option. 5. You drive from New York City to Washington DC by car. You drive in traffic for the first hour at an average of 50 km/hr. You cover the next 250 km in 3.0 hr, and then drive the remaining 30 km into Washington in 30 min. Find your total time and average speed.

ACCELERATION1 6. A car starts from rest and maintains an acceleration of 4.5 (km/hr)/s for 5 s. How fast is it going at the end of the 5 s? 7. A car is moving at 30 km/hr. The driver then presses harder on the accelerator, causing an acceleration of 2.25 (km/hr)/s, which she maintains for 4 s. How fast is the car going at the end of the 4 s?

FALLING 8. You drop a rock off a cliff and note that it hits the ground below in 6 s. How high is the cliff, assuming that the air is so thin that air resistance can be ignored during the entire fall? Unless the air is extremely thin, air resistance will not be negligible. What does this tell you about your calculation of the cliff s height: Is the cliff actually higher, or is it lower, than your calculated answer? 9. In the preceding problem, how fast is the rock moving when it hits the ground, still assuming negligible air resistance?

With further analysis, we could arrive at two equations for the speed and position of any object that starts from rest and moves in a straight line with unchanging acceleration s = at,

1 d = a bat2 2

where a represents the acceleration. For freely falling objects on Earth, a = 9.8 m>s2.

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How Things Move: Problem Set 10. You drop a rock down a well and hear a splash 3 s later. As Charlie Brown would say, the well is 3 seconds deep. But how many meters deep is it, assuming that air resistance is negligible and that the time for sound to travel back up the well is also negligible? 11. In the preceding problem, how fast is the rock moving when it hits the water? 12. You drop an apple out of a third-story window. When does it pass the second-story window 4 m below? 13. When does the apple in the preceding question hit the ground 8 m below? 14. A car speeds up from rest, along a straight highway. Its acceleration is unchanging. How much farther (measured from the starting point) does it get in 10 s, as compared with 1 s? 15. In the preceding problem, how much faster is it moving in 10 s, as compared with 1 s? 16. On the planet Mars, a free-falling object released from rest falls 4 m in 1 s and is moving at 8 m/s at that time. How fast would such an object be moving after 2 s? 3 s? 17. In the preceding problem, how far would such an object fall in 2 s? 3 s?

Answers to Concept Checks 1. Artistotle believed that it was part of the nature of stones and 2. 3.

4. 5. 6. 7.

8. 9. 10. 11. 12. 13.

other heavy objects to fall, so no outside influence was required, (e). (a) (if the stone is falling through air) and (c). (a) It s interesting to note that, because of Earth s daily spin, a typical point on Earth s surface moves around Earth s center at about 1600 km/hr (1000 mi/hr). So the law of inertia tells us that, if Earth suddenly stopped spinning, people and houses would find themselves sliding across Earth s surface at a speed of 1600 km/hr. Eventually, friction would bring them to rest. Most objects would slide for a few minutes across a distance of about 25 km (15 miles) and their surfaces would be heated by friction to nearly the boiling point of water. The car s average speed is 24 km/hr, which is less than the bicycle s 30 km/hr, (b). (a) and (d) (d) The car is accelerated when its velocity is changing that is, whenever either the speed or the direction of motion is changing. Answers: (b) (speed is decreasing), (c) (direction of motion is changing), (e) (direction of motion is changing), (f) (speed is increasing). Note that there is no acceleration in (d), because neither the speed nor the direction is changing at the instant shown. (a) and (c) (b) and (e) (e) (b) (b) (a), (b), and (c)

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Aristotle: This is the ball s natural motion. Galileo: Friction slowed it to a stop. 3. The baseball keeps up with the train and comes back down in your hand, just as though you were standing still on Earth s surface. Explanation: Because of the law of inertia, the ball keeps moving in the forward direction with no change in its forward speed, even though you have released the ball. Your throw simply gives the ball an upward (and then downward) motion, on top of the forward motion that the ball had before you threw it. 5. Judging from Figure 7b, an observer in low orbit would see only a small portion of Earth. Thus Figure 7a must have been taken from a much greater distance. 7. They lurch forward because of their own inertia their bodies have a tendency to keep on moving. 9. They must have different speeds, because she is passing him. Since their speeds are different, their velocities are different, because velocity means speed and (not or) direction; that is, both the speeds and the directions of motion must be the same before we can say that the velocities are the same. 11. Neither ball has any acceleration. The lower ball has the larger speed and the larger velocity. It starts out behind the upper ball, catches up at time 2, and then passes the upper ball. 13. Speed 90 km/hr, velocity 90 km/hr toward the south. 15. Speed = 3 km>0.25 hr = 12 km>hr. 17. It is due to bouncing, or shaking back and forth. These are accelerations. Nonaccelerated motion would not make people sick. 19. No, you cannot say, because you don t know how long each acceleration took. 21. (a) Accelerated. (b) Not accelerated. (c) Accelerated, since it is moving in a circle. (d) Accelerated, since it is moving in a circle. (e) Not accelerated. 23. Accelerator pedal, brake, steering wheel. 25. The object moves with an unchanging velocity. Thus, distance changes; it gets larger and larger, at a steady rate. Speed does not change. Velocity does not change. Acceleration remains zero, so it does not change. 27. accel = change in speed>time

(4.5 m>s - 3 m>s) 5s 1.5 m>s = 0.3 (m>s)>s = 5s 12 km>hr = 3(km>hr)>s 29. 4s 12 km>hr = 0.75(km>hr)>s 16 s 24 km>hr = 3(km>hr)>s 8s 6 km>hr = 0.75(km>hr)>s 8s =

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How Things Move: Problem Set 31. The object begins with a speed of 0 m/s and speeds up to a

speed of 10 m/s by the end of the first second, so its average speed during the entire first second (from 0 to 1 s) is only 5 m/s. 33. By 10 m/s. By 10 m/s. 35. 1st second: about 10 m/s. 2nd second: about 20 m/s. 3rd second: about 30 m/s. 37. Three times as fast, because speed is proportional to time; nine times as far, because distance is proportional to the square of the time. Problems 1. 0.5 m = 500 mm. Solving v = d>t for t gives t = d>v. So the number of years until the level has risen 500 mm is 500 mm>(5 mm>y) = 100 y. 3. The distance to the moon and back is 7.6 * 108 m. The speed is 300,000 km>s = 3 * 105 km>s = 3 * 108 m>s. Solving d = st for t, we get t = d>s = (7.6 * 108)> (3 * 108 m) = 2.5 s.

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5. total time = 1.0 hr + 3.0 hr + 0.5 hr = 4.5 hr.

7.

9. 11. 13. 15. 17.

total distance = 50 km (during first hr) + 250 km + 30 km = 330 km. average speed = 330 km>4.5 hr = 73 km>hr. The change in speed is at = 2.25(km>hr)>s * 4 s = 9 km>hr. This must be added to the initial speed of 30 km/hr. Thus the final speed is 30 km>hr + 9 km>hr = 39 km>hr. s = at = (9.8 m>s2) * (6 s) = 59 m>s. s = at = (9.8 m>s2) * (3 s) = 29 m>s. d = (1>2)at2. Solving for t, t = 2(2d>a) = 2(2 * 8>9.8) = 1.28 s. Speed is proportional to time, so the car is moving 10 times faster after 10 s than after 1 s. Distance is proportional to the square of the time, so it has moved four times as far, or 16 m, after 2 s. It has moved nine times as far, or 36 m, after 3 s.

Why Things Move as They Do Nature and nature’s laws lay hid in night; God said, “Let Newton be,” and all was light. Alexander Pope, Eighteenth-Century British Poet

T

he world changed in 1687. In that year, Isaac Newton (Figure 1) published his Mathematical Principles of Natural Philosophy. To take just one example, by making Descartes’s and Galileo’s law of inertia the foundation of his work, Newton undermined our intuitive view of how things move, a view accepted by all educated people for 2000 years. The Newtonian world is surprisingly simple. Using only a few key principles, Newton was able to give quantitative explanations for all manner of things: planets, moons, comets, falling objects, weight, ocean tides, Earth’s equatorial bulge, stresses on a bridge, and more. It was an unparalleled expansion and unification of our understanding of nature. Newton’s influence ranged far beyond physics and astronomy. Not only the sciences but also history, the arts, economics, government, theology, and philosophy were shaped by the general patterns of Newtonian physics. For example, the ideals of inalienable human rights that inspired the American and French revolutions stemmed largely from a populace steeped in a Newtonian culture of universal natural law that applied equally to all people, to commoners and kings alike. Newtonian physics worked almost too well. Unchallenged for over two centuries, it was eventually regarded as absolute truth. The very word understand came to mean “to explain in terms of Newtonian physics.” Most importantly, people eventually took for granted many subtle Newtonian habits of mind that had profound but unstated and unexamined implications having to do with determinism, cause and effect, the mechanical nature of the universe, and other philosophical conclusions.1 Eventually, everyone from the laborer to the scholar assumed that Newton had laid the framework for all human knowledge. During the twentieth century, relativity and quantum physics superseded Newtonian physics. But Newtonian cultural habits remain, partly because there is no agreed-upon philosophical framework for the new physics and partly due to the failure of science educators to teach the new physics to all people. Thus, our culture remains largely Newtonian while our science is post-Newtonian...not a healthy situation. In order that 1

Two classic historical studies of physical science from the early Greeks through Newton examine the transition to the new worldview. The very title of Arthur Koestler’s The Sleepwalkers (New York: Universal Library and The Macmillan Company, 1963) refers to the philosophically naive manner in which the Newtonian view developed. E. A. Burtt’s The Metaphysical Foundations of Modern Science (originally published in 1932; reissued by Humanities Press, Atlantic Highlands, NJ, 1980) is a close examination of the history and implications of these unstated philosophical assumptions.

From Chapter 4 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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you may develop the tools to help pull all of us into the post-Newtonian age, I’ve chosen modern post-Newtonian physics and its significance as one of the themes of this text. Newton’s physics starts from only a few concepts and principles. You have already learned two concepts, velocity and acceleration, and two principles, the law of inertia and the law of falling. Newton’s other key concepts are force and mass (Sections 1 and 2). His other key principles are the law of motion (Sections 3 and 4), the law of force pairs (Section 5), and the law of gravity. Section 6 applies these ideas to the motion of a device that has, for better or worse, reshaped our cities, our landscapes, and our lives: the automobile. Section 7 presents another way of looking at Newtonian physics based on the concept of “momentum.” American Institute of Physics/ Emilio Segre Visual Archives Figure 1

Isaac Newton, 1642–1727. His Mathematical Principles of Natural Philosophy, summarizing his, Descartes’s, and Galileo’s studies on the motion of material objects on Earth and in the heavens, may well be the single most important book in the history of science. Newton was not only the greatest genius that ever existed, but also the most fortunate, inasmuch as there is but one universe, and it can therefore happen to but one man in the world’s history to be the interpreter of its laws. Pierre-Simon De Laplace, Scientist

Figure 2

Both Sam and Sally are exerting a force on the ball, but the ball is not accelerating. When we say “Sam exerts a force on the ball” we mean that Sam would cause the ball to accelerate if no other forces were acting. In the case pictured, Sally’s force on the ball prevents Sam’s force from causing it to accelerate.

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1 FORCE: WHY THINGS ACCELERATE We have used the word force synonymously with “external influence.” Now I need to be more specific. Since the law of inertia says that bodies having no external influence (no force) on them are unaccelerated, it is natural to define a force as any external influence that causes a body to accelerate. So a body “exerts a force on” another body whenever the first body causes the second body to accelerate. Some examples: If a ball is at rest on a table and you push it with your hand, the ball will accelerate into motion. If the ball is already moving across a table and you push it briefly from behind, it will speed up. If you “pat” a moving ball lightly on the front side, toward the rear, it will slow down. If you pat it lightly sideways, it will change directions. In all four cases, your hand push accelerated the ball. In fact, a little experimentation shows that you cannot push the ball without accelerating it.2 So every hand push is a force. When you use the word force, it is useful to remember that a force is like a push. There are many misconceptions about the word force. Just like the word push, a force is an action rather than a thing. An object cannot be a force or possess force. Instead, force is something that one object does to another, just like “pushing.” A body can “exert a force on” another body. Pulling is another example. Starting with a ball at rest on the table, you can grasp it and pull it toward you, accelerating it into motion. So pulls are forces. Instead of pulling the ball with your hand, you could attach a string and pull the string, which pulls on the ball to accelerate the ball. So strings, when they pull, exert forces. Now suppose that Sam and Sally both push on a ball in opposite directions (Figure 2). If they adjust their pushes, they can get them to balance so that the ball remains at rest. Yet both are pushing on the ball. Even though the ball is unaccelerated, we will say that Sam exerts a force on the ball and that Sally does, too. In cases involving more than one force, a body exerts a force on another body if, in the absence of the other forces, the first body would cause the second body to accelerate. You could tap a ball with a hammer instead of pushing or pulling it with your hand. Since the hammer tap accelerates the ball, it exerts a force on the ball. Try

2

Assuming that there is only one push at a time. Two simultaneous pushes in opposite directions could cancel each other.

Why Things Move as They Do

tapping a motionless or moving ball from various directions yourself, and observe it carefully. Exactly when is it accelerating? ———This is a pause for finding a ball and a hammer and trying this. Observe carefully. The ball accelerates only during the fraction of a second when the hammer is touching it. So the hammer exerts a force on the ball only during this fraction of a second. After the tap, the ball moves at an unchanging speed in a straight line, so there is no force exerted on it. Note that the moving ball does not “have force” and it does not “carry force along with it.” A force is like a push. You wouldn’t say that the ball “has push.” Friction and air resistance are two more forces. If you briefly shove a book and let go so that it slides across a table, the book will slow down as it slides. Some force must cause this acceleration (recall that slowing down is one type of acceleration). This force results from the contact between the book and the tabletop, and is exerted by the tabletop on the bottom of the book. This force exists because both surfaces are rough or uneven at the microscopic level, as you can verify by sliding the book across a smoother surface and observing that the (de-)acceleration is reduced. Such a force, by one surface on another surface due to the roughness of the surfaces, is called friction. A fast bullet moving horizontally through air slows a little, so there must be a force on the bullet. This force is caused by the bullet hitting air molecules as it travels. It is called air resistance. Air resistance is similar to friction: The bullet slides through the air in somewhat the same way that a book slides across a table. You know that an apple falling freely to the ground accelerates all the way down. Since the apple accelerates, there must be a force on it, commonly called the force of gravity. But remember that forces are always actions by one object on another object. Gravity is a force on the apple, but what is this force exerted by? The answer is that it is exerted by planet Earth. The experimental evidence for this is that no matter where you go on Earth, a falling apple always accelerates downward, toward Earth’s center. You can think of a gravitational force as a pull, although not a human, muscular pull. It’s a pull by Earth on nearby bodies. There’s an interesting difference between gravitational forces and the other forces we’ve looked at. Hand pushes, hand pulls, hammer taps, string pulls, friction, and air resistance all are contact forces: forces exerted by an object that is touching another object. The gravitational force by Earth on a falling apple is different, because Earth is not actually touching the apple while it falls. Air is touching the apple, but you could imagine removing the air and the apple would still fall. The gravitational force acts at a distance, across empty space.

I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. Newton

2 CONNECTING FORCE AND ACCELERATION The crux of Newton’s theory of motion is really simple: forces cause accelerations. It’s a surprising idea. Our Aristotelian intuitions tell us that outside influences are needed to keep something moving, that is, that forces cause (or maintain) velocities. But Newton says no force is needed to keep a thing moving, and that forces instead cause accelerations. Newton formulated the specific relation between force and acceleration. To follow his reasoning, suppose that you put a smooth ball on a smooth table and tap it once with a hammer. As you know, it accelerates during the tap. Experience

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shows that the more strongly you tap, the faster it will be moving after the tap. So stronger forces cause larger accelerations. When this kind of experiment is done quantitatively, it is found that as the force on an object increases, the object’s acceleration increases in exactly the same proportion: A doubled force causes a doubled acceleration, a tripled force causes a tripled acceleration, and so forth. So an object’s acceleration is proportional to the total force exerted on it. In symbols, a r F How do we know that acceleration is proportional to force? The proportionality between acceleration and force can be demonstrated by using a setup such as Figure 3: A coaster glides without friction, pulled by a spring. Measuring the coaster’s acceleration with clocks and rulers, one finds that an unchanging pulling force (Figure 3a) causes an unchanging acceleration and that a doubled pulling force (Figure 3b) causes a doubled acceleration.

Now imagine exerting forces on a light ball and a heavy ball. You’ll find that, if you give them equal taps, the light ball accelerates into faster motion than does the heavy ball. So the light ball has a larger acceleration during the tap. It’s useful to extend the concept of inertia to this situation. Recall that an object’s inertia is its ability to maintain its velocity. Since the heavier ball changes its velocity the least, we say that it has more inertia than the light ball, using the word inertia to mean a body’s resistance to acceleration. It might seem, offhand, that “inertia” means pretty much the same thing as “weight,” because the heavier or “weightier” ball has more inertia. And in fact an object’s inertia and its weight are pretty much the same thing so long as the object is near Earth’s surface. However, weight and inertia are actually different things. Convincing evidence of this key fact comes from the study of objects in outer space, objects such as the many isolated rocks moving through our solar system. If you were in distant space holding such a rock in your hand, and then released it, the rock wouldn’t “fall”; it would instead remain “floating” in front of you. But if you Doubled force Unchanging force

Unchanging acceleration

Doubled acceleration

Air coaster

(a)

(b)

Figure 3

Quantitative demonstration that acceleration is proportional to force. (a) An unchanging pulling force causes an unchanging acceleration of a frictionless coaster along a horizontal surface. (b) If the pulling force is doubled, the acceleration is also doubled.

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push it with your hand, you’ll find that it resists your push. A huge push is needed to get a large boulder moving at even a slow speed. A rock in space has inertia, even though it has no weight. Such an object has no weight because weight is the force of gravitational attraction and is too small to notice in deep space. It’s useful to define inertia quantitatively. When inertia is made quantitative, it’s called mass. That is, the mass of an object is its amount of inertia. To establish a measurement scale for mass, scientists choose one particular object, called the standard kilogram, and define its mass to be one kilogram, abbreviated kg (Figure 4). There are good duplicates of it in most physics laboratories. Any object having the same inertia as the standard kilogram is said to have a mass of 1 kilogram. And any object having the same inertia as 2 kilograms bundled together has a mass of 2 kilograms. The mass of any object is defined in this way, by comparing its inertia with that of 1 or more kilograms (or with half a kilogram or some other fraction). Now, suppose you conducted further “coaster” experiments such as those shown in Figure 3, but that this time you maintained an unchanging pulling force while varying the amount of material being pulled (Figure 5). Figure 5a shows a single coaster being pulled, and Figure 5b shows a double coaster (two identical coasters linked together) being pulled by the same force. The acceleration should be smaller in case (b), because the greater amount of material has greater inertia. But how much smaller? The experimental answer turns out to be that the doubled coaster has half as much acceleration as the single coaster. And three coasters would have onethird as much acceleration, and so forth. We express this by saying that an object’s acceleration is proportional to the inverse of its mass. Since the inverse of a number is 1 divided by that number, this is abbreviated as a r 1>m. You learn something else from this experiment: An object’s mass (its inertia) is a measure of the “quantity of matter” (amount of material, number of atoms) it contains. For example, there is twice as much matter in the doubled coaster as in the single coaster, and also twice as much mass.

Acceleration Force

National Institute of Standards and Technology Figure 4

The U.S. National Standard Kilogram no. 20, an accurate copy of the International Standard Kilogram kept at Sèvres, France. It is stored inside two bell jars from which air has been removed.

Half as much acceleration Force Two coasters

(a)

(b)

Figure 5

Quantitative demonstration that acceleration is inversely proportional to mass. (a) Pulling on an air coaster causes the coaster to accelerate, as in Figure 3. (b) Pulling on two air coasters (twice as much mass), with the same force as in (a), causes half as much acceleration.

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Our two proportionalities, a r F and a r 1>m, can be put together to read acceleration r force>mass;

a r F>m

In words: An object’s acceleration is proportional to the force exerted on it divided by its mass. We need a measurement scale for force. The unit of force, called the newton (abbreviated N), is defined as the amount of force that can give a 1 kg mass a 1 m/s2 acceleration. So the proportionality becomes an equality: acceleration = force>mass;

a = F>m

This formula gives the acceleration in m/s2, provided the force is in N and the mass in kg. In the U.S. system of units, force is measured in pounds. One newton is a little less than a quarter of a pound. Think of a quarter-pound (a single stick) of butter. CONCEPT CHECK 1 A giant rock several kilometers across is at rest in outer space, far from all outside influences. A small, slow-moving pebble lightly “taps” the rock and bounces off. What does the rock do? (a) It accelerates up to a slow speed during the tap, and then comes quickly back to rest. (b) It accelerates up to a slow speed during the tap, and then comes gradually back to rest. (c) It accelerates up to a slow speed during the tap, and then continues moving at that speed. (d) It doesn’t accelerate at all. (e) It accelerates up to a high speed during the tap, and then continues moving at that speed. (f ) It turns into a frog. CONCEPT CHECK 2 Imagine you are in space and so far from all astronomical bodies that gravity is negligible, with two blocks of metal in front of you. They look identical, but you have been informed that one is made of aluminum and the other of lead (which, on Earth, would be much heavier than aluminum). You could determine which one is which by (a) giving them equally strong hammer taps—the one that then moves more slowly is aluminum; (b) giving them equally strong hammer taps—the one that then moves more slowly is lead; (c) holding them in your two hands—the heavier one is aluminum; (d) holding them in your two hands—the heavier one is lead; (e) actually, none of these methods would work.

3 NEWTON’S LAW OF MOTION: CENTERPIECE OF NEWTONIAN PHYSICS I must discuss two other points about Newton’s theory of motion. First, what happens when more than one force acts on an object, perhaps pushing or pulling it in different directions? In this text, we’ll only be concerned with situations in which the individual forces all act along a single straight line. When the individual forces all act in the same direction, their effects simply add up, and the overall effect is the sum of the individual forces. What if two forces act in opposite directions on the same object? If the forces are of equal strength (Figure 2) you know from experience that the object will not accelerate, so the overall effect must be zero. This suggests subtracting the two forces. This suggestion is correct.

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So two or more forces acting in the same direction have the same overall effect as a single force equal to their sum, while two forces acting in opposite directions have an overall effect equal to their difference and acting in the direction of the larger force. We call this overall effect the net force. For instance, if you push your book along a tabletop with a force of 10 N and the tabletop exerts a 3 N frictional force on the book (Figure 6), the net force on the book is 7 N. These 7 newtons represent the net, overall effect of the external environment pushing and pulling on the book. It is this 7 N net force, and not just your 10 N pushing force, that accelerates the book. The second point is the direction of the acceleration. Since forces have directions, and since acceleration is proportional to force, it is not surprising that acceleration should have a direction, too. So far, the only accelerations I have discussed quantitatively were ones in which an object was speeding up along a straight line. In this case, the direction of the acceleration is forward, because the change in velocity is in the forward direction (Figure 7). What about an object slowing down along a straight line? Since the velocity gets smaller, the change in velocity is backward (Figure 8). This means that the acceleration is backward, opposite to the velocity. Since an object’s acceleration is determined by the net force on it, it seems plausible that the acceleration’s direction should be the same as the net force’s direction. Simple experiments verify this: If you give a motionless ball a brief hammer tap, it will accelerate into motion along the direction in which you tapped, so the acceleration is along the direction of the force. If the ball is already moving and you tap it from behind, it will speed up; the acceleration is forward, again along the direction of the force. And if you tap a moving ball lightly from in front, the ball will slow down; this is a backward acceleration, which again is along the direction of the force.

Initial velocity

10 N push

Figure 6

How strong and in what direction is the net force on the book?

2

1

Change in velocity

Initial velocity

Final velocity

1

3N friction

Change in velocity Final velocity

2

Figure 7

Figure 8

When an object speeds up along a straight line, its change in velocity is along the direction of the motion.

When an object slows down along a straight line, its change in velocity is opposite to the direction of the motion.

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In summary: Newton’s Law of Motion3 An object’s acceleration is determined by its mass and by the net force exerted on it by its environment. The direction of the acceleration is the same as the direction of the net force. Quantitatively, the acceleration is proportional to the net force divided by the mass: acceleration r

net force ; mass

a r

F m

If force is measured in newtons, mass in kilograms, and acceleration in m/s2, the proportionality becomes an equality: acceleration =

net force ; mass

a =

F m

CONCEPT CHECK 3 A slow car moves at a steady 10 km/hr down a straight highway while another car zooms past at a steady 120 km/hr. Which car has the greater net force on it? (a) The slower one. (b) The faster one. (c) The one having the greater air resistance and rolling resistance. (d) None of the above. CONCEPT CHECK 4 You push your 2 kg book along a tabletop, pushing it with a 10 N force. If the book is greased so that friction is negligible, the book’s acceleration (a) is 5 m/s2; (b) is 10 m/s2; (c) is 20 m/s2; (d) is 0.2 m/s2; (e) keeps getting larger and larger as long as you keep pushing; (f) keeps getting smaller and smaller as long as you keep pushing. CONCEPT CHECK 5 Follow-up on Concept Check 4: A nongreased book also has a mass of 2 kg and is pushed with a 10 N force, but now there is a 4 N frictional force. The book’s acceleration is (a) 12 m/s2; (b) 20 m/s2; (c) 28 m/s2; (d) 3 m/s2; (e) 5 m/s2; (f ) 2 m/s2.

4 WEIGHT: GRAVITY’S FORCE ON A BODY As you know, Earth exerts a gravitational force on objects that are falling to the ground. This force is called “weight.” An object still has weight even when it’s not falling, as when it’s at rest on the ground. We’ll discover that the sun, moon, planets, stars, and all other astronomical bodies exert gravitational forces, too. It’s useful to extend the meaning of the word weight to include all such possibilities. In other words, the weight of an object refers to the net gravitational force exerted on it by all other objects. Since weight is a force, it can be measured in newtons. In U.S. units, weight is measured in pounds. Weight and mass are related concepts, but they certainly are not the same thing. An object’s weight is the force on it due to gravity, whereas its mass is its quantity of inertia. Weight is measured in newtons (or pounds, in U.S. units) while mass is measured in kilograms. An object’s weight depends on its environment; for 3

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Often called, boringly, Newton’s second law.

Why Things Move as They Do

instance, an object’s weight is less when it is on the moon than when it is on Earth, because the force of gravity is smaller on the moon than on Earth. But an object’s mass is a property of the object alone and not of its environment, so its mass is the same on the moon as on Earth. For example, a kilogram has a mass of 1 kilogram regardless of whether it is on Earth or on the moon or in distant space, but its weight is about 10 N (or 2.2 pounds) on Earth, only 1.6 N on the moon, and essentially zero in distant space. If you drop a stone and a baseball, Galileo’s law of falling tells us that their accelerations will be the same (neglecting air resistance). If the stone and baseball happen to have the same mass, Newton’s law of motion tells us that the forces on them are the same. But this force is just the force of gravity, which means that their weights are equal. This is a plausible and important conclusion: Two objects of equal mass also have equal weight, so long as you measure both weights at the same place (you wouldn’t want to measure one on Earth and the other on the moon). So you can compare masses by comparing weights, for instance on a balance beam (Figure 9). Any object that balances a kilogram has a mass of 1 kilogram, for example. The metric ton, or tonne (it’s always spelled this way), equal to 1000 kilograms, is useful for measuring larger masses. The similar U.S unit—the ton—is 2000 pounds. On Earth, the mass of a ton is about 900 kilograms, so a ton is a little less massive than a tonne. As you can see, the U.S system gets needlessly confusing, so you’ll perhaps be glad to hear that I’ll henceforth dispense with it entirely. For example, consider a book resting on a table. Suppose it weighs 12 N, meaning that the gravitational force by Earth on the book is 12 N. This force has a downward direction. But the book is obviously not accelerating downward through the table. Since the book’s acceleration is zero, Newton’s law of motion tells us that the net force on it must also be zero. So there must be an upward force of 12 N acting on the book to balance the downward weight. The table must exert this force, because if the table vanished the book would fall. It may seem strange that an inanimate object could exert a force. Why should a table push on a book? The tabletop doesn’t seem to be doing anything. A microscopic view is enlightening. The upward force is exerted by the atoms in the tabletop on the atoms in the book’s bottom.4 When the book presses against the tabletop, the tabletop is squeezed down and slightly deformed. And like a squeezed spring, the atoms then push upward against the book (Figure 10). The direction of this force by the tabletop is directly away from the surface, perpendicular to it. A force similar to the upward force by the table on the book is exerted when any object touches a solid surface. Physicists call any such force a normal force, because “normal” means perpendicular. Figure 11 shows the forces exerted on the book. Each force is represented by an arrow. A force diagram like this can help in analyzing forces and motion. When you draw a force diagram, show every one of the individual forces acting on whatever object is of interest. Show each force as an arrow pointing in the direction in which that force pushes or pulls on the object, and name each force. As another example, suppose that a rocket at liftoff weighs 150,000 N and has a mass of 15,000 kg and that the rocket engines exert a 210,000 N “thrust” force on

Figure 9

You can compare masses by comparing weights, for instance on a balance beam. Since they balance, the stone and the baseball have equal masses.

Figure 10

As an explanation of the normal force by a table on a book, imagine that the tabletop is covered with small springs. When the book rests on the table, it squeezes the springs, causing the springs to push back against the book. Normal force on book

Weight of book

Figure 11 4

More precisely, this force is an electric force by the electrons in the table’s atoms on the electrons in the book’s atoms. Electrons repel one another strongly when they get very close together.

The forces exerted on a book at rest on a table.

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Thrust, 210,000 N

the rocket (Figure 12). (You’ll learn more about the thrust force in the next section.) How large is the net force on the rocket, and how big is the rocket’s acceleration? Solution: The net force is 210,000 N – 150,000 N = 60,000 N upward. It is only this 60,000 N that actually accelerates the rocket. To find the acceleration, Newton’s law of motion says to divide the net force by the mass: 60,000 N/l5,000 kg = 4 m/s2. CONCEPT CHECK 6 Suppose the rocket develops a thrust of only 165,000 N. The acceleration is then (a) 4 m/s2; (b) 3 m/s2; (c) 2 m/s2; (d) 1 m/s2; (e) 0 m/s2.

Weight, 150,000 N

CONCEPT CHECK 7 An astronaut on Earth has a mass of 70 kg and a weight of 700 N. On the moon, the astronaut’s mass and weight will be (a) 11 kg and 700 N; (b) 70 kg and 110 N; (c) 11 kg and 110 N; (d) 70 kg and 700 N. CONCEPT CHECK 8 Would it be easier to lift a book on Earth or on the moon? (a) On the moon, because the book’s weight would be smaller. (b) On the moon, because the book’s mass would be smaller. (c) On Earth, because the book’s weight would be smaller. (d) On Earth, because the book’s mass would be smaller. (e) Same in both places.

5 THE LAW OF FORCE PAIRS: YOU CAN’T DO JUST ONE THING

Figure 12

The forces exerted on a rocket during liftoff. Note that the diagram shows only the individual forces and not the 60,000 N net force. The 60,000 N net force is not an individual force (it is the sum of all the individual forces) and hence is not shown.

How do we know that forces always come in pairs? Try these: Slap a tabletop with your hand. Grasp the edge of a table and pull hard on it. Now push hard on it. Find two balls of any kind; place one at rest on a smooth surface and roll the other one toward it so that they collide. ———Pause. I hope you’re actually doing some of this stuff that I suggest. It keeps your brain awake. When you slap a table, it slaps back, as you can feel when it stings your hand. This slap by the table is a force, because it accelerates your hand (by stopping your hand). When you pull on a table, the table pulls you toward it. And when you push on the table, the table pushes you away. These are forces exerted by the table on you. When the balls collide, the ball you rolled (call it the first ball) exerts a force on the second ball, as you can see from the fact that the second ball accelerates into motion. But the second ball exerts a force on the first ball, too, as you can see from the fact that the first ball’s velocity changes. These experiments indicate that whenever one object exerts a force on a second object, the second exerts a force on the first: Forces always come in pairs, called force pairs. Do things still work out this way even if the two objects are not touching? You could investigate this with a pair of magnets. Place the magnets on a smooth surface and hold them at rest with their poles near each other but not touching. When you release them, they both accelerate (if they don’t then find a smoother surface). So each exerts a force on the other.

Physicists like to think of every force as an interaction between two objects, rather than as something one object does to another. If you think of slapping a table as an interaction between your hand and the table, it’s natural to conclude that each exerts a force on the other.

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Touch your friend’s face. Your hand is touched by your friend’s face. You cannot touch without being touched.5 Slap lightly on a tabletop. Now slap hard. The table slapped back harder the second time, right? This gives us quantitative information about force pairs: When one member of a force pair grows bigger, so does the other. In fact, quantitative experiments show that the two members of any force pair have the same strength. If one of them is, say, 3.71 newtons, the other one will be 3.71 newtons too. The directions of the two forces in a force pair are not the same, however. In fact, our examples show that they are in opposite directions. For instance, when you pull a table toward you, the table pulls you toward it (Figure 13). Newton recognized this idea as a key physical principle. I’ll summarize it as follows: The Law of Force Pairs6 Every force is an interaction between two objects. Thus, forces must come in pairs: Whenever one body exerts a force on a second body, the second exerts a force on the first. Furthermore, the two forces are equal in strength but opposite in direction.

The fact that the two forces always have exactly the same strength is surprising. This says, for example, that a bug hits a car with the same force that the car hits the bug! Surprising—but true. However, these equal forces cause vastly different responses in the bug and the car: The bug feels an enormous acceleration, while the car experiences a barely measurable acceleration. The reason for this difference is Newton’s law of motion, and the vastly different masses of the bug and the car. Figure 14 illustrates an interesting point. Since Earth exerts a gravitational force on an apple, the law of force pairs says that the apple must exert a gravitational force on Earth! Furthermore, the strengths of these two forces must be equal: If Earth exerts a 2 N force on the apple, then the apple must exert a 2 N force on Earth. This might seem surprising. Why haven’t you noticed this force, by apples and other objects, on Earth? Why doesn’t Earth accelerate toward the apple?

Force by table on you

Force by Earth on apple Apple

Force by apple on Earth

Force by table on you

Force by you on table Force by you on table

Earth (a) Pulling on the edge of the table.

(b) Pushing on the table.

Figure 13

When you pull or push on a table, it pulls or pushes on you in the opposite direction. Figure 14 5

6

Thanks to my friend Paul Hewitt, author of Conceptual Physics, 10th ed. (New York: Addison Wesley 2006), for this nice way of putting it. Often called, boringly, Newton’s third law.

Earth and a falling apple: Which one exerts the larger force? (Answer: They are the same).

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The answer is that an apple causes only a slight acceleration of Earth because Earth’s mass is so large. You can’t use an apple to noticeably accelerate a planet. Large astronomical objects, however, can noticeably accelerate a planet. For example, scientists can detect Earth’s acceleration in response to the motions of the moon. CONCEPT CHECK 9 Your hands push a heavy box across the floor. The other member of the force pair is (a) friction pushing backward on the box; (b) gravity pulling downward on the box; (c) the box pushing backward against your hands; (d) the box pushing downward against the floor.

As you can see from Concept Check 9, the two forces in a force pair always act on different objects; your hands exert a force on the box, while the box pushes back against your hands. Similarly, if a rope pulls forward on a water skier, the skier pulls backward on the rope. So both the skier and the rope feel forces. The first force keeps the skier moving forward, while the second force keeps the rope taut. CONCEPT CHECK 10 A big truck and a small car collide head on. Regarding the forces: (a) the truck exerts a larger force on the car than the car does on the truck; (b) the car exerts a larger force on the truck than the truck does on the car; (c) the truck and car exert equally large forces on each other. CONCEPT CHECK 11 Regarding the accelerations in the preceding question: (a) The truck’s acceleration is largest; (b) The car’s acceleration is largest; (c) The truck and the car have equally large accelerations.

6 NEWTON MEETS THE AUTOMOBILE You can’t get anywhere by pulling on your nose. Try it (Figure 15)! You might pull your nose out of joint, but you won’t go anywhere because your nose pulls back on your hand, and both pulls are on your body, so they result in zero net force on your body—they “cancel out.” The same argument shows that you can’t get anywhere by pushing or pulling anywhere on your own body. If you want to accelerate, something outside of you—something in your environment—must exert a force on you. That’s why Newton’s law of motion says that an object’s acceleration is determined by the net force exerted on it by its environment. This presents an interesting dilemma when you consider self-propelled7 objects such as an automobile or an animal that accelerates itself into motion. How can they get themselves going if things cannot push or pull themselves into motion? Try this: Stand up and walk just one step, noting carefully the sensations in your legs, especially along the bottom of the foot that is accelerating you. Your foot pushes backward against the floor.8 You can demonstrate this more convincingly by accelerating rapidly from standing to running on a dusty dirt road. Your feet push dust backward, showing that they exert a backward force on the road. The law of force pairs tells us that when your foot pushes backward on the ground, the ground pushes forward on your foot. Voila! We’ve discovered the force Figure 15

You can’t get anyplace by pulling on your nose.

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7

8

“Self-propelled” means that the energy to propel the object comes from within the object itself. But, as we’ll soon see, the force to propel it comes from the outside. ... if you are barefoot. Otherwise, your foot pushes backward against your shoe, which in turn pushes backward against the floor.

Why Things Move as They Do

that accelerates you forward! It’s the ground pushing forward on your foot. This force arises from friction between the two surfaces (the surface of the ground and the bottom of your foot), as you can demonstrate by accelerating quickly from rest to a fast run on a nearly frictionless surface such as a smooth sheet of ice (be careful!). Automobiles are useful applications of Newtonian principles. What’s more important, automobile technology has drastically reshaped the social fabric of the modern world. Like all powerful technologies, cars have important social pros and cons. They provide unparalleled freedom of movement, have transformed our cities, use most of our petroleum, create much of our pollution, and are the leading cause of death of Americans under 35. They will come in for lots of discussion in this text. Before reading further, try listing or drawing the forces exerted on a car by its environment while traveling along a straight, level road. ———(A pause, for listing or drawing.) As shown in Figure 16, one force is the gravitational force, or weight of the car, exerted downward by Earth on the car. A second force is the normal force, exerted upward by the road on the car. These two forces act vertically. Since a car on a level road has no acceleration in the vertical direction, the net vertical force must be zero. So these two vertical forces must be of equal strength. The three horizontal forces relate more directly to the car’s motion. Two backward resistive forces act on the car: The atmosphere exerts the force of air resistance already discussed in Section 1, and the contact between tires and road creates another backward force known as rolling resistance. Rolling resistance is caused by flattening of the tire where the rubber meets the road. It turns out that the force that the road exerts on the deformed tire acts to slow the tire’s rotation, so the road exerts a retarding (backward) force on the car. This is most pronounced in more flexible, air-filled tires. Hard tires rolling on a smooth, hard surface, such as steel wheels on steel tracks, reduce rolling resistance to a minimum—one reason trains are far more energy efficient than cars. Rolling resistance also explains why underinflated tires reduce your gas mileage. High-mileage cars such as the Toyota Prius use special low-rolling-resistance tires for this same reason. The four forces discussed so far act even on a car that is coasting with its engine shut off. If these are the only forces on the car, then the net force must be backward, so the acceleration is backward and the car must slow down. But when a car is driving instead of coasting, there is an additional force on it. It’s a misconception to think that this force is exerted by the engine, because things cannot accelerate themselves and the engine is part of the car. Instead, the engine causes the drive wheels to turn; the drive wheels exert a frictional force backward against the road; and (because of the law of force pairs) the road in turn exerts a frictional force forward against the drive wheels. If the car moves at an unchanging velocity, there is no acceleration. Newton’s law of motion tells us that the net force must then be zero, which means that the five forces shown in Figure 16 must balance. In this case, the forward force on the drive wheels must equal the sum of the two resistive forces. In order for the car to speed up, the forward frictional force on the drive wheels must be larger than the sum of the two resistive forces; in order for the car to slow down, this forward force must be smaller than the sum of the resistive forces. Most other self-propelled objects are similar to this: A swimmer pushes backward on the surrounding water, and the water pushes forward on the swimmer. A motorboat’s propeller pushes backward on the water, and the water pushes forward on the propeller. An airplane’s propeller pushes backward on the surrounding air,

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Why Things Move as They Do Figure 16 Normal force by road on car

The five forces on an automobile. Air resistance by air on car

Rolling resistance by road surface on car Drive force, a second force by surface of road on drive tires Gravitational force by Earth on car

and the air pushes forward on the propeller. A jet airplane pushes air backward, too. As a jet engine moves through air, the air flowing into its front end heats by combustion with jet fuel, and the heated gas expands and rushes out of the back end at high velocity. One nice thing about space travel is that there are no resistive forces in space, so you don’t need a forward force by the environment on the spaceship to keep going. Your spaceship keeps going because of the law of inertia. But if you want to accelerate your spaceship—by changing its direction for instance—you have a problem. It’s difficult to get the surroundings to exert a force on your spaceship because there’s nothing around to push against! You would have a similar problem if you were stranded in the middle of a smoothly frozen pond. If the ice were absolutely smooth, you could not walk off it because, with no friction, you could not push backward on the ice. How could you get off? You could fan the air, pushing air backward in the way that a swimmer pushes water backward. That would work. But suppose that, as in space, there were no air. What then? Well, suppose you had something with you that you could throw away—your physics book, or a shoe. While throwing your shoe, you would push on the shoe, so it would push in the other direction on you, so your body would accelerate away from the shoe. When you let go of the shoe, you would have acquired a velocity. So you would slide along the pond. This is the principle of rocket propulsion. Rockets take along their own material just to have something to push against. Shoes would work, but they aren’t terribly practical (Figure 17). The rocket fuel for the U.S. space shuttle’s main rocket engines is hydrogen and oxygen, stored as low-temperature liquids. When combined, their combustion produces steam, which accelerates rapidly out the back end of the engine. Thanks to the law of force pairs, this backward push by the shuttle on the steam means that the escaping steam must push the shuttle forward. There are about 1000 large “near Earth asteroids” in our solar system—rocks more than 1 kilometer in diameter that orbit the sun and can cross Earth’s orbit and can therefore hit us, possibly dealing civilization a death blow. People are thinking

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about methods to nudge such rocks off course in case one of them is discovered heading for Earth. One suggested method: Send a space probe to attach itself to the asteroid, scoop up rock, and hurl it away. Thus is just like hurling shoes: The asteroid would react by moving in the opposite direction, deflecting it from its collision course. The law of force pairs comes to the rescue! CONCEPT CHECK 12 A car weighing 10,000 N moves along a straight, level road at a steady 80 km/hr. Air resistance is 300 N, and rolling resistance is 400 N. The net force on this car (a) is 10,000 N; (b) is 9300 N; (c) is 10,700 N; (d) is 700 N; (e) cannot be determined without knowing the strength of the drive force; (f ) is zero. CONCEPT CHECK 13 In the preceding question, the strength and direction of the drive force are (a) 10,000 N forward; (b) 700 N backward; (c) 700 N forward; (d) 400 N forward; (e) zero. Figure 17

Shoe power.

7 MOMENTUM An object’s momentum is defined as its mass times its velocity. It’s conventional to abbreviate it with the symbol “p” (I have no idea why): momentum = mass * velocity p = mv Momentum measures an object’s “amount of motion”—how much mass is moving how fast. It’s useful in connection with any “system” (this word simply means a collection of objects) of two or more objects that interact with each other via “internal” forces—forces exerted by objects in the system on other objects in the system. A good example is two colliding pool balls. When they collide, each ball exerts a brief force on the other during the short time they’re in contact. As a result of these forces, both balls accelerate—usually changing both the magnitude (speed) and direction of their velocity. To keep things simple, suppose the balls collide head-on so that all motion occurs along a single direction, call it the x-axis (Figure 18). One reason momentum is important in physics is that it’s one of nature’s “conserved quantities,” in other words a system’s total momentum remains unchanged throughout collisions such as is shown in Figure 18, despite the changes in both balls’ velocities during the collision. Here’s why:

v1 1

v2 2 x

Figure 18

Two pool balls, moving along the x-axis in the + and – direction, respectively, about to collide.

How do we know momentum is conserved? During the short impact time, which we’ll call ¢t, each ball experiences a change in velocity, which we’ll call ¢v1 and ¢v2. (The symbol ¢ is often used to mean “a change in”). According to the definition of acceleration, the accelerations of ball 1 and ball 2 during the impact are ¢v1>¢t and ¢v2> ¢t . Using Newton’s law of motion and Newton’s law of force pairs and making

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Why Things Move as They Do the important assumption that the only significant forces acting on either ball during the collision are the force by ball 1 on ball 2 and the force by ball 2 on ball 1, a little algebra9 shows that the change in the quantity m1 v1 is equal in magnitude but opposite in direction to the change in the quantity m2 v2. In symbols, ¢ (m1 v1) = - ¢ (m2 v2) The minus sign means “in the opposite direction along the x-axis.” In other words, the change in the first object’s momentum is the negative of the change in the second object’s momentum. But this means that the sum of the two momenta (plural of momentum) doesn’t change at all during the collision.

Momentum has a direction, namely the same direction as the velocity. For motion along a single axis, the direction can be indicated by a + or – sign: A positive momentum is along the +x direction, while a negative momentum is along the –x direction. I showed above that the total momentum p1 + p2 remains unchanged throughout the collision, where total momentum means the sum of the two individual momenta, with the directions (+ or –) included. This important result is known as conservation of momentum. Remember that it only applies so long as there are no external forces (forces other than the internal forces by each object on the other) on the system. For instance, suppose that ball 2 is initially at rest and ball 1, moving with a velocity of +3 m/s (the + emphasizes that it’s in the +x direction), hits it. Then the system’s total momentum before collision is m 1v1 + m 2v2 = m * (3 m>s) + m * 0 = (3 m>s) m, where “m” means the mass of either ball (pool balls all have the same mass). Conservation of momentum says that the total momentum after collision must also be 3 m: p1 + p2 = (3 m>s) m or mv1 + mv2 = (3 m>s) m or (with simple algebra) v1 + v2 = 3 m>s 9

Newton’s law of motion applied to each ball tells us

¢v1> ¢t = F (on ball 1)>m1 and ¢v2> ¢t = F (on ball 2)>m2.

Multiply both sides of the first equation by m1 and both sides of the second equation by m2 to get m1 ¢v1>¢t = F (on ball 1) and m2 ¢v2> ¢t = F (on ball 2)

But Newton’s law of force pairs says that the force on 1 by 2 and the force on 2 by 1 are equal and opposite, in other words F (on ball 1) = -F (on ball 2). It follows that m1 ¢v1 = -m2 ¢v2. But m1 is just a fixed number, so m1 times the change in v1 is the same as the change in m1 v1, and the same goes for ball 2. So the previous equation says that ¢ (m1v1) = - ¢ (m2v2).

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where v1 and v2 now represent the two balls’ final velocities. This result could be useful: If you knew one of the two final velocities, you could find the other. For instance, suppose ball 1 stops when it collides with ball 2. Then v1 = 0 and our result says that v2 = +3 m>s. So ball 2 takes off with the same velocity ball 1 had just before the collision. For another instance, suppose the balls are made of soft clay and that they stick together after collision. Then v1 = v2 and so v1 + v2 = 3 m>s tells us that 2v1 = 3 m>s. Simple algebra then says that v1 = v2 = +1.5 m>s. CONCEPT CHECK 14 If ball 2 takes off with a velocity of 2 m/s, ball 1’s final velocity is (a) 0 m/s; (b) 0.5 m/s; (c) 1 m/s; (d) –1 m/s (in the –x direction); (e) 1.25 m/s.

For yet another oddball (so to speak) instance, suppose both balls are covered with a small amount of gunpowder, in such a way that a small explosion occurs when they collide. And suppose that the explosion sends ball 2 zooming off with a velocity of +10 m/s. Notice that momentum must be conserved even in this situation, because all the significant forces on the balls during the collision/explosion (including the explosive force) are by 1 on 2 and by 2 on 1. If you worked through Concept Check 14, I’ll bet you’ll be able to work through this problem and conclude that v1 = -7 m>s. Both balls are now moving faster than ball 1 was moving before collision. The system gained kinetic energy (energy of motion), and this kinetic energy came from the chemical energy of the gunpowder. For a violent but instructive example involving objects of different mass, suppose that a 30,000 kg “18 wheeler” truck moving at 20 m/s (72 km/hr) collides head-on into a small 1000 kg car moving in the opposite direction at 20 m/s. Suppose that the car and truck become enmeshed in each other, so that they stick together. How fast is the combined wreckage moving just after the collision (before the frictional force by the road has had time to begin to slow the wreckage)? It’s easiest if you let the x-axis be in the direction of the truck’s initial motion, so that the car’s velocity is negative. ——— A pause, for figuring. The result is that the truck is hardly slowed by the collision; it slows from its initial +20 m/s to +18.7 m/s (the speed of the wreckage). But the car changes its velocity from –20 m/s to +18.7 m/s. This is a huge velocity change of +38.7 m/s in a small fraction of a second, and implies an enormous acceleration and hence (see Newton’s law of motion) enormous forces by the windshield, seats, etc., on the car’s occupants. Ouch. Notice that the forces on the car driver’s body would be much smaller if the driver’s velocity change of 38.7 m/s occurred in a much longer time, such as one second instead of a small fraction of a second. This is why air bags and vehicle front-ends designed to crumple slowly upon collision are a good idea. The truck driver, on the other hand, suffers a much more mild velocity change of only 1.3 m/s. This example gives you a feel for the momentum concept. Momentum involves both mass and velocity, so more massive objects possess more of it, and faster objects possess more of it. Despite the equal speeds of the car and the truck, the truck has far more momentum because of its larger mass. Momentum is a measure of the tendency of an object to keep moving despite forces (such as collisions) that act to change the velocity: The truck slows only slightly, while the car changes its velocity radically. Conservation of momentum applies to an amazing variety of situations. Here are a few.

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First, suppose the pool ball collision is a glancing collision, so that the two balls shoot off into different directions (Figure 19). The collision is then “twodimensional,” not along a single line but still on the surface of the pool table. Conservation of momentum is still valid; in fact, it applies to each of the two directions on the table (since in this text we’re staying away from something ominously called “vectors,” I won’t go into exactly what this means). Now suppose there are more than two balls; for instance, suppose the collision is between a cue ball and a rack of 15 pool balls. It’s amazing (at least I’ve always found it amazing) but true that momentum is conserved: The total momentum of all 16 pool balls just after collision equals the momentum of the cue ball just before collision. The 16 balls might be scattering all over the place, but if you add up all 16 momenta10 you’ll find that the result is equal, in both magnitude and direction, to the magnitude and direction of the initial momentum mv of the cue ball! But notice that momentum is conserved only from just before to just after the collision, before any “external forces” such as friction from the table top or bounces from pool table walls have had time to change any of the 16 velocities. The balls could all have different sizes and masses, and momentum would still be conserved. In fact, I allowed for two different masses in arriving (above) at the principle of conservation of momentum for two pool balls. The objects needn’t physically collide (bang against each other) at all. The “collision” could be between two magnets sliding on a frictionless surface, never touching but simply influencing each others’ motion magnetically, or an encounter between two stars that exert gravitational forces on each other and remain millions of miles apart. The two stars’ interaction (“collision” isn’t the appropriate word here) could take years, but so long as external forces (by other stars, for instance) don’t interfere, the total momentum of the two stars remains the same throughout the entire interaction. We’ll find that Newton’s laws are far from absolute. They break down for fastmoving (comparable to the speed of light) objects, for small objects such as individual molecules, and in situations involving strong gravitational forces or distances stretching across many galaxies. Since Newton’s laws break down, it’s natural to question the principle of conservation of momentum in these situations. But surprisingly, physicists have checked a wide variety of such situations and found that momentum is always conserved. In fact, a very broad argument based simply on the notion that the laws of physics are the same everywhere in the universe leads to the conclusion that momentum must be conserved in any system that has no external forces exerted on it, regardless of whether Newton’s laws are valid. Figure 19

y

A cue ball glancing off another ball, viewed from above. The second ball is initially at rest. Arrows show the initial velocity of the cue ball and final velocities of both balls. Arrows point in the direction of the velocity; longer arrows represent greater speeds. (a) Just before collision. (b) Just after collision.

v2 2 1

x (a)

10

110

2

v1

1

x v1

(b)

Since the collision occurs in two dimensions, the 16 momenta must be added using something called “vector addition,” which means roughly that you should add up 16 arrows whose lengths and directions represent the magnitudes and directions of the 16 balls’ momenta.

Why Things Move as They Do

Conservation of momentum seems to be one of the universe’s most fundamental principles. To summarize: The Law of Conservation of Momentum The total momentum of any system remains unchanged, regardless of interactions among the system’s parts, so long as no part of the system is acted upon by forces external to that system.

© Sidney Harris, used with permission.

Contemporary physicists have learned that many of nature’s deepest principles are conservation laws in which some quantity such as momentum remains unchanged over time. We’ll encounter two other conservation laws: conservation of energy and conservation of electric charge.

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Why Things Move as They Do Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions FORCE 1. How can we tell whether a body is exerting a force on another body? 2. Can an object have force? Can an object exert a force? Can an object be a force? Can an object feel a force? 3. List at least six specific examples of forces. Try to list examples that are significantly different. 4. What is a resistive force? Give two examples. 5. Give two examples of forces that act at a distance.

NEWTON’S LAW OF MOTION 6. What does Newton say that forces cause? What does Aristotle say? 7. What do we mean when we say that one object has “more inertia” than another object? 8. When you move an object from Earth to the moon, does its inertia change? Does its weight change? Does its mass change? Does its amount of matter change? Does its acceleration differ while falling freely? Does it respond differently to a net force of 1 N? 9. Forces of 8 N and 3 N act on an object. How strong is the net force if the two forces have opposite directions? The same directions? 10. Is an object’s acceleration always in the same direction as its velocity (its direction of motion)? If not, give an example in which it is not. Is an object’s acceleration always in the same direction as the net force on the object? If not, give an example in which it is not. 11. As you increase the net force on an object, what happens to its acceleration? What if you double the net force? As you increase the mass of an object (for example, by gluing additional matter to it), what happens to its acceleration? What if you double the mass?

16. Draw a force diagram showing the forces on a rocket during liftoff. Which force is largest? What is the direction of the net force? 17. Where is it easiest to lift your automobile: on Earth or on the moon? Where is the automobile’s mass larger?

LAW OF FORCE PAIRS 18. Describe several experiments demonstrating that forces come in pairs. 19. Do you exert a gravitational force on Earth? How do you know? What direction is this force? 20. Describe the other member of the force pair for each of the following forces: the normal force on a book lying on a table, the weight of an apple, the force by a bat against a baseball, the force by a baseball hitting a catcher’s mitt.

THE AUTOMOBILE 21. Describe four examples of forces that propel “self-propelled” objects. 22. Draw a force diagram showing the forces on a car driving along a straight, level road. How would this force diagram be altered if the car were coasting? What if the car were braking? 23. What is the main difference between propeller-driven airplanes and jet airplanes? 24. How does the forward force on a car compare with the resistive forces when the car maintains a constant speed? When the car is speeding up? Slowing down? 25. When a car moves at constant speed along a straight road, is the forward force (the force that moves the car forward) zero? Is the net force zero? Is the acceleration zero? Is the speed zero? 26. What is the main difference between the force that propels a rocket and the force that propels airplanes and automobiles?

MOMENTUM WEIGHT 12. What is weight? Is it the same as mass? If not, what is the difference? 13. Describe a simple way to determine, in a lab, whether two objects have equal masses. Would this method work in distant space? What would work in distant space? 14. Find the gravitational force on a 1 N apple. Would it still weigh 1 N if we took it to the moon? 15. Draw a force diagram showing the forces on an apple at rest on a table. Find the net force on the apple.

27. Conservation of momentum follows logically from two other laws of physics. Which two? 28. Which of the following quantities do you need to know in order to calculate the magnitude of the momentum of an object, and how do you do the calculation: weight, mass, acceleration, velocity, location, length? 29. True or false: Every system’s total momentum is always conserved. (Recall that a “system” is any collection of physical objects). Explain your answer.

From Chapter 4 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Why Things Move as They Do: Problem Set 30. A hunter fires a rif le bullet northward and then spins and fires a second bullet (from the same rif le) southward. Do the two bullets have the same momentum? Explain. 31. Which has greater momentum, a truck at rest or a slowrolling pool ball? 32. What is the magnitude of the momentum of a 7 kg bowling ball rolling at 3 m/s?

Conceptual Exercises FORCE 1. Is any force exerted on you when you speed up along a straight line? When you slow down along a straight line? How do you know? 2. Is any force exerted on you while you move in a circle at unchanging speed? How do you know? 3. A smooth ball rolls on a smooth table. Initially, no horizontal forces are exerted on the ball. Then you bring a magnet near the rolling ball, but you are not sure whether the magnet actually exerts a magnetic force on the ball. How can you tell whether the magnet is exerting a horizontal force on the ball? 4. Does a high-speed bullet contain force? Does a stick of dynamite contain force?

NEWTON’S LAW OF MOTION 5. You place your book on a table and hit it horizontally with a hammer, strongly but briefly. Do not neglect friction. Describe the motion of the book, beginning from just before you hit it with the hammer. Describe the direction and strength of the net force on the book during the entire motion. 6. If you exert a force on an object and then exert three times as strong a force on the same object, what (if anything) can you say about the object’s acceleration during the exertion of each force? Assume no other force acting on the object. 7. A ball weighing 8 N is thrown straight upward. Disregarding air resistance, find the direction and strength of the net force on the ball as it moves upward. What is the direction of the ball’s acceleration? Are the net force and the acceleration in the same direction in this case? Can they ever be in different directions? 8. An object moves with unchanging speed in a straight line. Does it then have no forces acting on it? Explain. Does it have no net force acting on it? 9. An object is at rest. Does it then have no forces acting on it? Explain. Does it have no net force acting on it? 10. When you stand on the floor, does the floor exert a force on your feet? In which direction? Why, then, don’t you accelerate in that direction? 11. You push on a solid concrete wall. Is your push the only horizontal force on the wall? How do you know? What can you say about the net force on the wall? 12. A car starts up from rest, moving along a straight highway with an acceleration of 1 m/s2. A second car comes racing past at a steady 120 km/hr. Which car has the larger net force acting on it?

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13. A 40 tonne truck and a small 1 tonne car maintain a steady speed of 80 km/hr on a straight highway. Which vehicle has a larger net force exerted on it? Which vehicle has the larger normal force exerted on it? 14. A 40 tonne truck and a small 1 tonne car maintain a steady speed of 80 km/hr on a straight highway. Which vehicle has the larger drive force exerted on it? The larger air resistance force? The larger net force? 15. A 3 kg rock rests on the ice. You kick it, briefly exerting a 60 N force. Find the rock’s acceleration, assuming that there is no friction. Still assuming no friction, what will be the rock’s acceleration after your foot is no longer in contact with the rock? Will the rock have a (nonzero) speed at this time? 16. In the preceding question, assume now that a frictional force of 6 N acts on the rock whenever it is moving across the ice. Find the net force on the rock and the rock’s acceleration. What can you say about the net force on the rock after your foot is no longer in contact with it? 17. Ned the skydiver weighs 600 N and has a mass of 60 kg. How large must be the force of air resistance acting on Ned in order for Ned to maintain an unchanging speed while falling through the air? 18. In the preceding question, what would be Ned’s acceleration if there were no air? 19. A car weighing 8000 N moves along a straight, level road at a steady 80 km/hr. The total resistive force on the car is 500 N. Find the net force on the car and the acceleration of the car. 20. In the preceding question, find the drive force on the car.

WEIGHT 21. Roughly, what is your weight in newtons? 22. Which has the greater mass, a tonne of feathers or a tonne of iron? Which has the greater weight? Which has the larger volume? 23. Would you rather have a hunk of gold whose weight is 1 N on the moon or one whose weight is 1 N on Earth—or wouldn’t it make any difference? 24. Would you rather have a hunk of gold whose mass is 1 kg on the moon or one whose mass is 1 kg on Earth—or wouldn’t it make any difference? 25. A standard kilogram in your physics lab weighs (approximately) 10 N, or 2.2 pounds. What are its mass and weight in distant space? 26. Find the strength and direction of the net force on an apple weighing 2 N, neglecting air resistance, in each of the following cases: The apple is held at rest in your hand. The apple is falling to the ground. The apple is moving upward, just after you threw it upward. 27. An apple is accelerated upward by your hand. Which is larger, the apple’s weight or the upward force by your hand? What if you accelerate the apple downward while it is in the palm of your hand? What if you lift the apple at an unchanging velocity? What if you lower the apple at an unchanging velocity? 28. Would it be easier (in other words, would it require less thrust and less rocket fuel) to lift a rocket off the moon’s surface than off Earth’s surface? Why? 29. An astronaut on the moon picks up a large rock. Would it be easier, or harder, or neither for him to pick up the same rock on Earth?

Why Things Move as They Do: Problem Set 30. An astronaut on the moon kicks (horizontally) a large rock. What if she kicked the same rock on Earth? Neglecting frictional effects, would it hurt her foot more, or less, or just as much? 31. Neglecting friction and air resistance, would it be easier to set this book into horizontal motion at 5 m/s on Earth, or on the moon, or in distant space?

LAW OF FORCE PAIRS 32. “Planet Earth is pulled upward toward a falling boulder with just as much force as the boulder is pulled downward toward Earth.” True or false? Why? 33. “Planet Earth is pulled toward a falling boulder with just as much acceleration as the boulder has as it moves toward Earth.” True or false? Why? 34. A large truck breaks down on the highway and receives a push back into town by a small car. While moving at unchanging speed, does the car exert any force on the truck? Does the truck exert any force on the car? If so, is this force weaker or stronger than the force that the car exerts on the truck? 35. A car collides head-on with a large truck. Which vehicle exerts the stronger force? Which has the larger force exerted on it? Which experiences the larger acceleration? 36. When a rifle fires, it accelerates a bullet along the barrel. Explain why the rifle must recoil. 37. A 2 N apple hangs by a string from the ceiling. Describe the two forces on the apple. How strong is each of these forces? Do these forces form a single force pair? If not, then for each force, describe the other member of that force’s force pair. 38. A horizontally moving bullet slows down. Is anything exerting a force on it? How do you know? Is it exerting a force on anything? How do you know? 39. I push you away from me. Do you also push (exert a force on) me? Which force is stronger—or does it depend on which of us is heavier? 40. A pitcher exerts a force on a baseball while throwing it. Describe the other member of the force pair. 41. A rope pulls forward on a water skier. Describe the other member of the force pair. 42. As we know, “weight” is a force, and force is an interaction. In the case of your own weight, name the two objects that are involved in this interaction. 43. Describe the two forces that act on a book that rests in the palm of your hand. Are these two forces equal but opposite to each other? Are these two forces part of one force pair? 44. Continuing the preceding question, suppose you accelerate the book into upward motion. How many forces act on it? Are these two forces equal but opposite to each other? 45. A freely falling apple has a weight of 1 N. Earth’s mass is 6 × 1024 kg. How strong is Earth’s force on the apple? 46. In the preceding question, how strong a force does the apple exert on Earth? 47. Still continuing the preceding question, how big is the apple’s acceleration? Find the acceleration that the apple would cause Earth to have if the apple was the only object exerting a force on Earth.

THE AUTOMOBILE 48. Since the law of inertia states that no force is needed to keep an object moving in a straight line at an unchanging speed, why is a force needed to keep a car moving? 49. While driving your car on a straight, level road, you slam on your brakes. Draw a force diagram of the car during braking. What is the direction of the net force? Draw a force diagram for a car that is coasting without braking. In which of the two cases is the net force stronger? 50. Why is it easier to pedal a bicycle with hard high-pressure tires as compared with soft balloon tires? 51. When you hold your foot on a car’s accelerator pedal, is the car necessarily accelerating? Could it be accelerating? Could it have a forward acceleration? Could it have a backward acceleration? 52. There are three acceleration devices on any car. What are they, and what kinds of acceleration does each one give to the car? 53. If a jet airplane were above Earth’s atmosphere, could it then accelerate? What about a rocket-driven plane? 54. Magnetic forces can levitate railroad trains a short distance above the tracks, making friction practically negligible. Suppose such a “maglev” train runs inside an evacuated (emptied of most air) tunnel from New York City to Chicago. If friction and air resistance are negligible, during what parts of the trip would an external horizontal force act on the train? Discuss the direction of this force during each part of the trip.

MOMENTUM 55. Which has greater momentum, a 1000 kg small car moving 10 m/s or a 1 kg artillery shell shot at 10 times the speed of sound (the speed of sound is 330 m/s)? 56. Which has greater momentum, you steadily jogging one kilometer in 6 minutes or a 5-gram rifle bullet moving at 1000 m/s? 57. Why is it so much harder to stop or turn a moving supertanker than a small speedboat? 58. Can a swarm of flying insects have a total momentum of zero? Explain. 59. A stationary firecracker explodes, breaking into two parts of equal mass. One part is moving north at 20 m/s. What is the velocity of the other part? 60. Explain, in terms of momentum, why guns recoil. 61. Are there any kinds of situations in which momentum is not conserved? Explain. 62. An artillery shell explodes in midair into many fragments. Is the total momentum of the fragments just after the explosion equal to the momentum of the shell just before the explosion? Explain.

Problems NEWTON’S LAW OF MOTION 1. You push on a 2 tonne (2000 kg) vehicle on level pavement with a force of 250 N. Find the vehicle’s acceleration.

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Why Things Move as They Do: Problem Set 2. How large is the acceleration of a 60 kg runner if the friction between her shoes and the pavement is 500 N? 3. In order for a 60 kg runner to accelerate at 8 m/s2, what must be the frictional force between her shoes and the pavement? 4. A 747 jumbo jet of mass 30,000 kg accelerates down the runway at 4 m/s2. What must be the thrust of each of its four engines? 5. What would a skydiver’s acceleration be if air resistance were half as large as the skydiver’s weight? What if air resistance were as large as the skydiver’s weight? 6. How much force must a pitcher exert on a 0.5 kg baseball in order to accelerate it at 50 m/s2? 7. Find the force acting on a 0.01 kg bullet as it is accelerated at 1 million m/s2 (100,000 times larger than the acceleration due to gravity!) down a rifle barrel. 8. A 2 kg flower pot weighing 20 N falls from a window ledge. How large must air resistance be in order that the pot fall with an acceleration of 8 m/s2? 9. An 80 kg firefighter whose weight is 800 N slides down a vertical pole with an acceleration of 3 m/s2. What is the frictional force on the firefighter? 10. A black box and a white box accelerate at the same rate across the floor despite the fact that the net force on the black box is four times larger than the net force on the white box. Which box has the larger mass, and how much larger? 11. A 70 kg runner speeds up from 6 m/s to 7 m/s in 2 s. Find the runner’s acceleration and the frictional force by the ground on the runner during this time. 12. A 1 tonne (1000 kg) automobile experiences 100 N of air resistance and 200 N of rolling resistance. How large a forward force must the road exert on the drive wheels in order for the automobile to accelerate at 0.5 m/s2?

THE LAW OF FORCE PAIRS 13. Wearing frictionless roller skates, you push horizontally against a wall with a force of 50 N. How hard does the wall push on you? 14. In Problem 13, if your mass is 40 kg, then what is your acceleration? 15. Your friend (mass 80 kg) and you (mass 40 kg) are both wearing frictionless roller skates. You are at rest, behind your friend. You push on your friend’s back with a force of 60 N. How hard does your friend’s back push on you? 16. In the preceding question, what is your acceleration? What is your friend’s acceleration? 17. A small car having a mass of 1000 kg runs into an initially stationary 60,000 kg 18-wheeled truck from behind, exerting a force of 30,000 N on the truck. How big, and in what direction, is the force that the truck exerts on the car? 18. In the preceding question, find the car’s acceleration. Is this a “speeding up” or a “slowing down” type of acceleration? Find the truck’s acceleration. Is this of the “speeding up” or “slowing down” variety? 19. You press downward with a 100 N force on a brick weighing 40 N that rests on a table. With what force, and in what direction, does the brick press against your hand? Draw a force diagram similar to Figure 16, with an arrow representing each force acting on the brick.

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20. In the preceding question, how big is the net force on the brick? Find the force (how big and in what direction) that the table exerts on the brick. How hard is the brick pressing down against the table?

MOMENTUM 21. A 1000 kg car moving at 20 m/s slams into a stationary 27,000 kg truck from the rear, and sticks to the rear end of the truck. Assuming the truck is free to roll, how fast is the wreck moving after the collision? 22. A 27,000 kg truck moving at 20 m/s slams into a stationary 1000 kg car. The two stick together. Assuming the car is free to roll, how fast is the wreck moving after the collision? 23. A 50 kg boy and a 30 kg girl are standing on ice skates on a smoothly frozen pond. The boy gives the girl a push and she slides at unchanging speed to the edge of the pond, 20 m away, in 4 seconds. What happens to the boy? 24. A 30 kg girl standing on slippery ice catches a 0.5 kg ball thrown with a speed of 16 m/s. What then happens to the girl?

Answers to Concept Checks 1. The rock accelerates only when the pebble is pushing (tap2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

ping) it; since the rock has a large mass, its acceleration will be small, (c). If you tap them, Newton’s law of motion tells us that the one with the larger mass will accelerate less, (b). (d), because neither car is accelerating, so both cars have zero net force on them. acceleration = force>mass = 10>2 = 5 m>s2, (a). The net force is now 10 - 4 = 6 N, so acceleration = 6>2 = 3 m>s2, (d). (d) The mass must stay the same, but the weight is far less than on Earth, (b). (a) (c) (c) (b) Since the acceleration is zero, the net force must also be zero, (f ). Since the net force is zero, the forward drive force must be equal to the sum of the backward forces, (c). Since v1 = +2 m>s, v1 + v2 = 3 m>s tells us that v1 + 2 m>s = 3 m>s, so v1 = +1 m>s, (c).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. A force must be exerted on you, both when you speed up and when you slow down, in order to accelerate you. Newton’s law of motion says so.

Why Things Move as They Do: Problem Set 3. If the ball accelerates (speeds up, slows down, or changes 5.

7.

9.

11.

13. 15. 17. 19. 21. 23.

25. 27.

29. 31. 33. 35.

37.

direction), it must have a force on it. Initially, the book is at rest; then it quickly speeds up during the fraction of a second that the hammer is actually in contact with the book. After the hammer is no longer touching the book, the book gradually slows down to a stop. There is no net force on the book before the hammer hits it; then there is a large force in the forward direction while the hammer is in contact with the book. Then there is a smaller force in the backward direction while the book is slowing down. Since gravity is the only force acting on the ball, the net force on the ball is 8 N downward. Thus the ball’s acceleration is also downward, opposite to the ball’s upward velocity, because Newton’s law of motion says that the acceleration is in the direction of the net force. Acceleration and net force are always in the same direction. The object could have several forces on it, adding up to zero net force. For example, an object at rest on a table has two forces on it: weight acting downward, and normal force by the table acting upward. The object has no net force on it. No, your push cannot be the only force on the wall. Because the wall doesn’t accelerate, the net force on the wall must be zero, and so there must be another force (provided by the concrete structure) pushing back in the other direction on the wall. Each vehicle has zero net force on it. The truck has the larger normal force on it. a = F>m = 60 N>3 kg = 20 m>s2. After the kick, the acceleration must be zero (the law of inertia). The rock will have a non-zero speed. 600 N, acting upward, to balance the force of gravity. The net force is zero, because the car is not accelerated. The acceleration is zero. Since 1 N is about 1/4 pound, multiply your weight in pounds by 4 to get your approximate weight in newtons: 100 pounds is roughly 400 N, etc. You would be better off having a hunk of gold whose weight is 1 N on the moon, because it would be a more massive hunk of gold (containing more gold atoms) than one whose weight is 1 N on Earth. Mass = 1 kg, weight = 0. The upward force by your hand must be larger, because the net force on the apple must be upward to provide the upward acceleration. For the downward acceleration, the apple’s weight must be larger. For the unchanging velocity (both lifting and lowering), the upward force by your hand and the downward force of gravity have equal strengths. Harder, because it would weigh more. Same in all three places, because the book has the same mass in all three places, and there are no resistive forces in any of the three places. False. The boulder has a much larger acceleration than does Earth, because the boulder’s mass is much smaller than Earth’s mass. The two vehicles exert equally strong forces on each other, and the two vehicles feel equally strong forces from the other vehicle. The car experiences the larger acceleration, because it has the smaller mass. The string pulls upward on the apple, and Earth’s gravitational force pulls downward. Each force has a strength of

39. 41. 43. 45. 47.

49.

51.

53.

55. 57. 59. 61.

2 N. These do not form a force pair. The other members of the two force pairs are (1) the apple pulling downward on the string and (2) the apple’s gravitational force pulling upward on Earth. Yes, you push on me too. The two forces are equally strong. The backward pull by the water skier on the rope. Your hand pushes upward on the book. Earth’s gravitational force pulls downward on the book. These two forces are equal and opposite, but they are not part of one force pair. Earth exerts a 1 N force on the apple. The apple’s acceleration is 9.8 m>s2. Earth’s acceleration would be a = F>m = 1 N>6 * 1024 kg = 1.7 * - 25 2 10 m>s , which is so small that it is not measurable. The diagram should show a large frictional force, acting backward, in addition to the forces of air resistance (backward), gravity (downward), and the road’s normal force (upward). The net force is backward. For a car coasting without braking, the forces are rolling resistance, air resistance, gravity, and the normal force. The net force is strongest in the case of braking. No, the car could be moving at a constant velocity. However, it could be accelerating. The acceleration could be forward (if the car is speeding up) or backward (if the car is slowing down). No, a jet plane could not accelerate (except for the “natural” acceleration of 9.8 m>s2 downward due to gravity). A rocketdriven airplane could accelerate. For the car, For the shell, p = 104 kg m>s. p = 3.3 * 103 kg m>s. The car’s momentum is larger. The supertanker’s huge mass gives it a much larger momentum than the speedboat. Conservation of momentum says that the two parts must have equal and opposite momenta, and they have the same masses so they must have the same speeds. 20 m/s south. A system having external forces acting on it does not necessarily have an unchanging momentum.

Problems 1. a = F>m = 250 N>2000 kg = 0.125 m>s2. 3. a = F>m, where F is the frictional force. Solving for F, F = ma = 60 kg * 8 m>s2 = 480 N. 5. Air resistance would reduce the downward net force to half of the skydiver’s weight, so the skydiver would accelerate downward at half of the acceleration of gravity: 4.9 m>s2. If air resistance were as large as the skydiver’s weight, the skydiver’s acceleration would be zero, i.e., he or she would be falling at an unchanging speed. 7. Solving a = F>m for F, F = ma = 0.01 kg * 106 m>s2 = 104 N = 10,000 N. 9. The net downward force is F = ma = 80 kg * 3 m>s2 = 240 N. But the net downward force is F = weight - f, where f means “the upward force due to friction.” Thus, weight - f = 240 N. Solving, f = weight - 240 N = 800 N - 240 N = 560 N. 11. a = (change in speed)>(time to change) = (7 m>s - 6 m>s)>2 s = (1 m>s)>2 s = 0.5m>s2 frictional force = net horizontal force = ma = 70 kg * 0.5 m>s2 = 35 N 13. The wall pushes with 50 N.

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Why Things Move as They Do: Problem Set 15. Your friend’s back pushes on you with a force of 60 N. 17. The truck exerts a 30,000 N force on the car, in the backward

direction. 19. The brick presses upward against your hand, with a 100 N force.

Table pushing upward

Gravity pulling downward

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Your hand pushing downward

21. Using kg, m, and s: Initial momentum = 1000 * 20 =

20,000. Final momentum = 1000 v + 27,000 v = 28,000 v. So conservation of momentum says 28,000 v = 20,000. So v = 20,000>28,000 = 0.96 m>s. 23. The initial momentum of the system (boy plus girl) is zero. The girl’s momentum after the push is (30 kg) * (20 m > 4 s) = (30 kg) * (5 m>s) = 150 kg m>s . Since momentum is conserved, the boy must be sliding the other way with this same momentum. So 50 v = 150, from which v = 3 m>s.

Newton’s Universe

From Chapter 5 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Newton’s Universe

And from my pillow, looking forth by light Of moon or favouring stars, I could behold The antechapel where the statue stood Of Newton with his prism and silent face, The marble index of a mind for ever Voyaging through strange seas of Thought, alone. William Wordsworth. P r e l u d e (Book III), 1850

T

he law of inertia might be history’s most fruitful scientific idea. Besides unifying natural motion on Earth and in the heavens, undermining Aristotelian views, promoting the idea of universal natural law, and leading to Newton’s law of motion, it also led Newton to look in a new way at one specific kind of force: gravity. Because gravity is all around us all the time, it’s difficult to even notice it. This has made it difficult for scientists to properly conceptualize it. From Aristotle until Newton, people believed that every solid body had a natural tendency to seek out Earth’s center, in the way that a thirsty person seeks out water. External influences— forces—were not needed to explain why objects fell: They fell because they “wanted” to. But the inertial view is that bodies “want” to maintain their velocity. Descartes first conceived of this new view of motion. It was a conceptual shift comparable to Copernicus’s shift to a sun-centered view. Newton then built on Descartes’s idea. If you believe that bodies have inertia, you must ask why an apple, released above the ground, falls. Newton’s answer applied to more than apples; it demonstrated that the same gravitational forces are at work in the heavens as on Earth. We live in one universe, not two. Section 1 presents the general idea of Newton’s theory of gravity, and Section 2 gives the specifics along with examples. One significant social/cultural development of the past 100 years is our increased scientific understanding of the origin and future of our universe, our planet, life, and humans. I’ll delve into such topics at several points in this text, beginning with Sections 3 and 4. Section 3 applies Newton’s theory of gravity to the birth and death of the sun and Earth. Section 4 tells of the violent gravitational collapse of stars that are more massive than the sun and the exotic objects that result from the collapse. Sections 5 and 6 return to our theme of comparing Newtonian and modern physics: Section 5 looks at broad implications of Newtonian physics, particularly the “mechanical universe.” Section 6 notes the limitations of Newtonian physics in light of modern physics.

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1 THE IDEA OF GRAVITY: THE APPLE AND THE MOON Isaac Newton, age 22, had just completed his bachelor of arts degree at Cambridge University in England. He was invited to remain, but the school then closed for 18 months because of a plague epidemic, so the graduate returned to his family’s farm. But he didn’t just snooze. During those 18 months, Newton laid the foundations for a theory of gravity and a theory of light and, in his spare time, invented calculus. Some say that greatness is partly a matter of timing. Newton lived at a time that was culturally ripe for a new view of the universe. The scientific foundations had been laid by Copernicus, Brahe, Kepler, Galileo, and Descartes. You have seen that the inertial view of Descartes and Galileo leads naturally to Newton’s law of motion. The concepts surrounding the law of motion, plus the astronomy of Copernicus and Kepler, then led Newton to the law of gravity. Newton stood, as he himself said, “on the shoulders of giants.” As Newton recounted it late in life, the central idea of his theory of gravity came to him during his stay on the family farm when an apple fell from a tree while he could see the moon in the sky. Beyond the fact that both are more or less round, it’s difficult to think of two more dissimilar objects than an apple and the moon. One is on Earth, the other in the heavens; one rots, the other seems eternal; one falls to the ground, the other remains aloft. Yet where others saw difference, Newton saw resemblance. Let’s trace Newton’s thinking. Figure 1 shows an apple falling toward the ground, accelerated by Earth’s gravitational pull. The directions of the apple’s velocity, acceleration, and gravitational force are all downward toward Earth’s center, as shown. The moon’s motion is quite different. The direction of its velocity is parallel to Earth’s surface rather than toward its center. But we are interested in the forces on each, and, according to the inertial view, forces cause accelerations, not velocities. So the forces on the two could be similar, despite the dissimilarity of the velocities. How do the forces compare? Aristotle would say that no force is needed to make the moon move in a circle because that is its natural motion, but the inertial view is that in order for the moon to deviate from straight-line motion, a force must act on it. What is the direction of Moon’s velocity is directed along its orbit

One has to be a Newton to see that the moon is falling, when everyone sees that it doesn’t fall. Paul Valery, French Poet and Philosopher, 1871–1945

Figure 1

The apple and the moon.

v

Falling apple: Velocity, acceleration, and force all are directed downward

v, a, F

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Newton’s Universe Figure 2

The moon is held into its orbit by an inward-directed force.

A

Moon’s displacement due to its inertia

C

B

Moon’s motion without gravity

Moon’s displacement due to gravity

Gravitational force Gravitational force

this force? If the moon were at point A in Figure 2 and if no force acted on it, it would move in a straight line toward point B. But instead it moves around to point C. As you can see from Figure 2, the force required to pull the moon inward—so that it arrives at C rather than B—is directed toward Earth’s center, just like the force on a falling apple. Newton hypothesized that this force has the same source as the force that pulls an apple downward: Earth’s gravitational attraction. Newton offered another argument, one that helps us understand why the moon and other satellites stay up. If you throw an apple horizontally, it will follow a curved path as it falls to the ground (Figure 3). If you throw the apple faster, it will go farther before hitting the ground. And if you throw it fast enough, it might “fall” around a large part of Earth’s surface before striking the ground (Figure 4). If the apple is launched at such a high speed that the curvature of its path just matches Earth’s curvature, it will fall all the way around. In other words, it goes into orbit. The required speed is about 8 km/s, or 29,000 km/hr. This is what any orbiting satellite does, except that the required speed is less for higher-altitude satellites because they feel a smaller gravitational pull and so don’t need to move as fast to avoid spiraling down onto Earth’s surface. For instance, the moon’s speed is only about 1 km/s. The force that shapes the moon’s path is gravity—the same gravity that pulled the apple to the ground that day on Isaac Newton’s family’s farm. It was an imaginative leap, in more ways than one. It was difficult to believe that anything at all was pulling on the moon, much less that it could be the same force that pulled on an apple. Most difficult was the notion that the gravitational force could reach across nearly 400,000 kilometers of empty space (the distance was known in Newton’s time). It’s easy to see that things exert forces on one another when they are in direct contact, but a force that acts across so great a distance seems astonishing. Figure 3

If you throw an apple horizontally, the faster you throw it, the farther it will go.

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Slower

Faster

Newton’s Universe Suborbital

Figure 4

Falling around Earth. If you throw an apple fast enough, it will fall around a large part of Earth’s surface or even go into orbit. A diagram like this appears in Newton’s notebook.

Orbital

CONCEPT CHECK 1 A 2 N apple falls from a tree. Neglecting air resistance, while it is freely falling the net force on it is (a) zero; (b) 2 N downward; (c) 2 N upward. CONCEPT CHECK 2 In the preceding question, the apple’s acceleration is (a) zero; (b) impossible to determine from the given information; (c) about 10 m/s2 downward; (d) about 10 m/s2 upward. CONCEPT CHECK 3 Suppose you throw a 2 N apple horizontally, as shown in Figures 3 and 4. Neglecting air resistance, the net force on the apple when it is in the five positions shown is (a) zero; (b) 2 N in the forward direction (along the direction of motion); (c) 2 N downward (toward Earth’s center); (d) 2 N upward (away from Earth’s center); (e) impossible to determine. CONCEPT CHECK 4 The net forces in Concept Checks 1 and 3 are the same in both magnitude and direction. So, what must be the numerical value and direction of the apple’s acceleration in Figures 3 and 4? (a) Zero. (b) Impossible to determine from the given information. (c) About 10 m/s2 in the forward direction. (d) About 10 m/s2 downward. (e) About 10 m/s2 upward.

2 NEWTON’S THEORY1 OF GRAVITY: MOVING THE FARTHEST STAR Since Earth’s gravitational pull holds the moon into its orbit, it’s reasonable to suppose that all satellites—bodies in orbit around larger astronomical bodies—are held in their orbits by the gravitational pull exerted by the larger body. Since the planets are satellites of the sun, Newton’s insight regarding the moon also resolves

1

This theory is usually called Newton’s law of gravity. But the term law, which is always inappropriate in science because every general scientific principle is subject to some doubt, is especially inappropriate here. The reason is that Newton’s theory of gravity has limitations, beyond which the theory isn’t valid. The more accurate theory, having no known limitations, is always called Einstein’s theory of general relativity. It’s ridiculous to call Newton’s theory a “law” while calling Einstein’s theory a “theory.”

What makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit.... The answer is not far from the truth. The only difference is that the angels sit in a different direction and their wings push inwards. Richard Feynman, Physicist

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Newton’s Universe Pick a flower on Earth and you move the farthest star! Paul Dirac, Physicist

Force by apple on book

Force by book on apple

Figure 5

Even ordinary-sized objects exert gravitational forces on one another. Your physics book exerts a force on an apple, and vice versa. It’s a small force, but forces like this have been measured.

the old question of why the solar system moves as it does! The planets keep moving forward because of the law of inertia, and the sun’s gravitational pull bends their orbits into ellipses. Similarly, the moons of the planet Jupiter are held in their orbits by Jupiter’s gravitational pull. But why would gravity act only between astronomical bodies and their satellites? For instance, it seems plausible that there should be a gravitational force between Earth and Mars. Such a force between planets had not been noticed yet in Newton’s day, but Newton realized that this was only because it was so much smaller than the force by the sun on the planets. Likewise, there should be a gravitational force between any two astronomical bodies, even between the farthest stars. But why should gravity be restricted to astronomical bodies? Why shouldn’t a gravitational force be exerted between smaller objects on Earth—oranges, rocks, and so forth? Your physics book, for instance, should exert a gravitational pull on an apple, and vice versa (Figure 5). You won’t notice this force, but that is only because the force between such objects is very small. So Newton reasoned that the gravitational force is universal; it’s exerted between every pair of objects throughout the universe. This is the central idea of Newton’s theory of gravity. Newton understood the importance of quantitative methods. Although his basic insight was qualitative, its expression in a quantitative form led to powerful explanations and predictions. Quantitatively, the gravitational attraction between two objects must be stronger when the objects’ masses are larger, because an apple’s weight is larger when its mass is larger (double the mass, for example, by replacing the one apple by two apples glued together, and you double the weight). And since widely separated objects attract each other only weakly, the gravitational force should get smaller when the distance between the objects gets larger. Newton put all this together (see “How Do We Know Newton’s Theory of Gravity?” later in this section) and came to the following conclusions: Newton’s Theory of Gravity Between any two objects there is an attractive force that is proportional to the product of the two objects’ masses and proportional to the inverse of the square of the distance between them: gravitational force r

(mass of 1st object) * (mass of 2nd object) square of distance between them

F r

m1 * m2 d2

If mass is expressed in kilograms, distance in meters, and force in newtons, this proportionality becomes F = 6.7 * 10 - 11

m1 * m2 d2

For our first example, let’s consider your weight—the gravitational force exerted by Earth on you. Newton’s theory of gravity tells us that this force is proportional to your mass times Earth’s mass, which means that the force is proportional to each of

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the two masses separately. So doubling your mass would double your weight, tripling your mass would triple your weight, and so forth—which certainly makes sense. But the theory also says that if you imagined that somehow Earth’s mass were doubled (without, however, changing its size), this also would double your weight; halving Earth’s mass would halve your weight; and so forth. You can reduce your weight without dieting or exercising: Simply reduce Earth’s mass! What if you altered both masses? For instance, suppose you tripled your mass while simultaneously doubling Earth’s mass. Since the force is proportional to the product of the two masses, this would multiply your weight by 6. What happens when the distance between Earth and you is changed? In fact, exactly what is meant by the “distance between the objects” in a case like this? Does the distance from Earth to your body mean the distance from the near side of Earth (the ground beneath your feet), from the far side, from the center, or from some other point? And to what point in your body should you measure the distance? Newton worked through a lot of mathematics to answer this—in fact, he invented “integral calculus” to answer it. Newton’s answer was that the distance between the “centers” of the two bodies is the correct distance to use when applying the gravitational force formula to two extended bodies. In the case of a body such as Earth that has an obvious center, distance is measured from that center. For other bodies, such as your own, the distance should be measured from the body’s “balance point”—the point at which the body would be balanced under the force of gravity. But because your body is so small compared with the distance from Earth’s center to your body, it matters little which point you choose within your body. Suppose you travel away from Earth. Since the gravitational force is proportional to the inverse of the square of the distance, the increased distance makes the force decrease—another way to reduce your weight! For instance, your weight at the top of Mount Everest, nearly 10 km above sea level, is 0.3% less than at sea level. If your weight is normally 600 N (135 lb), it will be 598 N (134.5 lb) at the top of Mount Everest. Your weight reduction is greater at an altitude of a few hundred kilometers, where low-orbit artificial satellites travel. For example, at a 200 km altitude, your weight would be reduced by 6%, so a person normally weighing 600 N would weigh only 560 N. Now you’re really losing weight (but unfortunately you’re not losing any mass). Moving to still higher altitudes, suppose you are 6400 km—1 Earth radius— above the ground. What is your weight? The proportionalities in the theory of gravity make this an easy question. If you rise 1 Earth radius above the ground, your distance from Earth’s center doubles, so the square of the distance quadruples. Since the force is proportional to the inverse of the square of the distance, the force is divided by 4. Your weight is now one-fourth of normal. Figure 6 is a graph of your weight at various distances from Earth’s center. No matter how far you are from Earth, the gravitational force by Earth on your body never reaches precisely zero. But very far away, the force becomes very small. For example, at 10 Earth radii, your weight is 1% of your normal weight. It’s a good thing for us that the force of gravity declines at larger distances in just the way it does. If the gravitational force declined a little faster, the planets would not move in ellipses but would instead spiral into the sun, and you would not be here to ask about things like gravity. And if the gravitational force declined a little more slowly, the gravity from distant stars would dominate the gravity from Earth, and again you would not be here. It’s something to think about. You can use the theory of gravity to calculate the gravitational attraction between any pair of objects, from apples and books to stars and moons. For example, the force

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Newton’s Universe Figure 6 Normal

Weight

A graph of your weight at various distances from Earth’s center. The same graph applies to the weight of any object.

1/4 of normal weight 1/9 of normal weight 1/16 of normal weight 1/100 of normal weight

2

4 6 8 Distance from Earth’s center measured in Earth radii

10

between a kilogram and another kilogram 1 meter away is found by putting these numerical values into the gravitational force formula. The answer is 6.7 * 10 - 11 newtons, or 0.000 000 000 067 newtons! It’s no wonder that the gravitational force between ordinary objects is difficult to detect. The delicate experiments needed to measure such tiny forces could not be performed until about a century after Newton’s work. When they were performed, they verified Newton’s predictions. The situation inside an orbiting satellite seems paradoxical. Judging from Figure 7, you would feel weightless in an orbiting satellite, at any altitude. But you have seen that if the satellite is in low orbit, your weight is actually only a little less than normal. Why, then, would you feel weightless, even though you are not really weightless? To answer this, let’s imagine a somewhat similar situation (Figure 8): Suppose you are in an elevator and the elevator cable breaks. The elevator is then in free fall, and so are you. After the cable breaks, your feet no longer press down against the floor. If you try to press your feet against the floor, you will simply push yourself away from the floor. A bathroom scale glued to your feet would read zero, because your feet would not press down on it. You are apparently weightless, but, because we have defined weight as the gravitational force on an object, you are not really weightless. Although you have not (I hope) actually experienced a freely falling elevator, you might have experienced a similar “weightless” effect in a roller-coaster while moving rapidly over a crest in the track. You would feel weightless in an orbiting satellite for the same reason that you would feel weightless in a freely falling elevator. As you saw in the preceding section, the satellite falls freely around Earth. You are falling freely around Earth too, regardless of whether you are inside the satellite or outside in space. Since both you and the satellite are just falling around Earth, you have the sensation of weightlessness. Your body behaves as though it were removed from the effects of gravity, but you are not really weightless. How do we know Newton’s theory of gravity? How did Newton verify his theory of gravity? The dependence on mass was not hard to deduce. Because an object’s weight is proportional to its mass (for instance, two identical apples glued together surely have twice the weight of one, so doubling the mass doubles the weight), Newton reasoned that the force of gravity must be proportional to each of the two masses. But what about the dependence on distance? Newton knew that the distance to the moon is about 60 times larger than Earth’s radius (Figure 9). Newton’s theory of gravity then implies that an object at the moon’s distance should experience a force that is 3600 (the square of 60) times smaller than the force on the same object on Earth. So

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NASA Headquarters

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NASA/Johnson Space Center

NASA/Johnson Space Center

(a)

(b)

(c)

Figure 7

Space travelers feel weightless when they are in orbit and at any other time that they are “falling” freely through space. (a) Balancing. (b) Floating. (c) Spacewalking.

(since acceleration is proportional to force) the acceleration of an object at this distance should be 3600 times smaller than the acceleration of an object falling to Earth. In other words, Newton’s hypothesis implies that the moon’s acceleration should be (1>3600) * 9.8 m>s2, or 0.0027 m/s2. But from the known distance to the moon, plus the observed fact that the moon takes 27 days to complete a circle around Earth, Newton could calculate directly that the moon’s acceleration (due to its circular motion) actually is 0.0027 m/s2. Newton’s theory agreed with the observation.

CONCEPT CHECK 5 Suppose that you were in distant space, far from all planets and stars, and you placed an apple and a book at rest in front of you, separated by

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about 1 m, and then moved some distance away in order to observe the apple and book without influencing them. The apple and the book would then (a) very slowly accelerate toward each other; (b) very rapidly accelerate toward each other; (c) move toward each other without accelerating; (d) remain at rest; (e) head for the beach.

I’m apparently weightless.

You’re apparently in trouble.

CONCEPT CHECK 6 When you are in a high-flying jet plane, (a) your weight and mass are both normal (the same as on Earth); (b) your weight and mass are both less than normal; (c) your weight is normal but your mass is less than normal; (d) your weight is less than normal but your mass is normal. CONCEPT CHECK 7 Your weight at an altitude of 2 Earth radii above Earth’s surface is (a) zero; (b) impossible to calculate without knowing Earth’s radius; (c) the same as your weight on Earth; (d) one-third of your weight on Earth; (e) onefourth of your weight on Earth; (f) one-ninth of your weight on Earth.

Figure 8

Falling freely in a freely falling elevator.

The moon is 60 times farther from Earth’s center than is the falling apple

M A K I N G EST I M AT ES

Earth’s mass is about 100 times the moon’s mass, and Earth’s radius is about 4 times the moon’s radius. From this information, use Newton’s theory of gravity to quickly estimate how much more an object weighs on Earth, as compared with its weight on the moon.

3 GRAVITATIONAL COLLAPSE: THE EVOLUTION OF THE SOLAR SYSTEM

Apple

Figure 9

The moon is 60 Earth radii away from the center of Earth.

Like you and me and everything else, stars have a beginning, they go through changes, and they have an ending. The driving force behind this “stellar evolution” is the force of gravity. Stars are made mostly from diffuse (thin) gas, mostly hydrogen atoms, that is spread throughout the universe. In some regions, this material happens to be gathered slightly more densely into great gas clouds that are the spawning grounds for stars (Figure 10). Because of the gravitational pull between all bits of matter, all gas and dust in space tends to aggregate, a process called gravitational collapse. Here is how the sun and Earth were born. Some 5 billion years ago, the atoms that would eventually form the solar system, including every atom in your body, were scattered as cold, diffuse gas and dust over a region far larger than the solar system. Then a blast of radiation and fast-moving particles from a nearby exploding star (more about this later) caused turbulence and clumping in this gas and dust. Such a clump of matter, if sufficiently dense, will gravitationally attract more gas and dust, causing still stronger gravitational forces, pulling even more matter inward, and so forth in a self-reinforcing buildup of matter. As our clump of gas and dust became more massive and more dense, atoms fell at greater and greater speeds toward the center, where they collided and formed a central region of fast-moving atoms. In other words, the center heated up. Every gas cloud spins a little, simply from the net effect of its chaotic flowing and swirling. As our gas cloud contracted, this spinning increased, just as a figure skater spins faster and faster as she brings her outstretched arms into her sides.2 As 2

This is because of something called “conservation of angular momentum,” a sort of rotational version of conservation of momentum.

SO LU T I O N TO M A K I N G EST I M AT ES In the theory of gravity, one of the masses is multiplied by 100 and R is multiplied by 4. Thus F is multiplied by 100/42 = 100/16, or about 6. So your weight is six times larger on Earth than on the moon.

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Newton’s Universe Figure 10

NASA Headquarters

Star birth. These eerie, dark, pillarlike structures are columns of cool interstellar hydrogen gas and dust that are also incubators for new stars. They are part of the Eagle Nebula, a nearby star-forming region in our own galaxy. This region is “only” 7000 light-years away (i.e., it takes light 7000 years to get here from there). The tallest pillar (left) is about 1 light-year long from base to tip—a distance that is about 800 times larger than the distance across our solar system. This is one of the many beautiful and informative photographs taken by the Hubble Space Telescope.

contraction continued, this spinning became rapid enough to flatten the outer regions of the gas ball into a disk, much as a wad of dough can be flattened to make a pizza by spinning it. Some of the gas in the outlying disk rotated fast enough to go into orbit around the larger central ball. Because it was orbiting, this material was left behind as the center collapsed. The outer region continued orbiting while cooling, condensing, and aggregating into clumps that became Earth and the other planets (Figure 11). As the warming sun got hot enough to glow, light streaming outward swept away the dust and gas that had filled the solar system. And then there was light on Earth. The central ball continued collapsing and heating until the center reached million-degree temperatures. New things happen at such temperatures: Atoms collide so violently that their electrons are stripped off, leaving a gas made mostly of bare hydrogen nuclei and electrons. The violently colliding hydrogen nuclei occasionally stick together, a process known as nuclear fusion. Nuclear fusion creates lots of heat, and the pressure from this heat then prevents the ball of gas from collapsing further. When it initiated nuclear fusion nearly 5 billion years ago, our sun turned itself on and became a normal, self-sustaining star. A similar process of star birth is going on all the time, all over the universe. The starry sky is not static. Scientists have recently learned that our sun had a violent birth amidst highenergy radiation and explosions of entire stars. Based partly on material found in meteorites that formed along with the solar system, it’s now known that one or more nearby stars must have exploded during the solar system’s formation. It’s thought

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Newton’s Universe Figure 11

Lynette R. Cook

An imaginary view of the newborn sun during formation of the solar system. Dust partially obscures the sun. As comets streak by, a planet (foreground) begins to form from the dust.

that the sun and some 50 or more other stars all formed at roughly the same time from a single huge region of gas and dust within our Milky Way Galaxy (our galaxy was already some eight billion years old by then). The upper, lit-up, portion of the left-hand “pillar” in Figure 10 is an example of such a star-forming region within our galaxy today. At least a few very massive stars, far more massive than the sun, are likely to form in such regions. Any such massive star “burns” (via nuclear fusion) very hot and therefore very rapidly, and soon exhausts itself in a giant supernova explosion (more on this in the next section). High energy radiation and ejected particles from such massive stars, as well as the blast effects from supernova explosions themselves, then initiated the formation of smaller stars as described in the preceding paragraph, and also helped shape such star formation processes. Once our sun stopped collapsing, it settled into a middle age that has been going on for nearly 5 billion years. The long-term stability of this period made it possible for atoms on one planet to gather and evolve into highly complex forms such as ourselves. Like the rest of the solar system, we came from the universe. But stars eventually die. Over billions of years, our sun’s supply of hydrogen fuel must deplete until, around the year 5,000,000,000 CE, it will no longer support nuclear fusion in its central “core.” Then the sun will enter old age. Although nuclear fusion will cease near the sun’s center, a thin outer shell of hydrogen will continue the fusion process, causing the sun to brighten and expand to three times its present size. The increased energy output will evaporate Earth’s oceans and perhaps cause a runaway greenhouse effect that could make Earth even hotter than Venus’s 500°C. During the following several hundred million years, the sun will become still brighter and 100 times larger, warming Earth to around 1000°C and killing any remaining life. By this time, the central core will have grown hot enough to ignite new, hotter nuclear reactions involving the element helium. The sun will then spend 100 million years as a helium-burning star. Then comes another disaster. After exhausting its helium, the sun will again expand, brighten, and eject its outer layers in a huge shell of glowing gas that will expand outward, engulfing all the planets and drifting outward beyond the solar system into interstellar space. After a million years of this, the sun will have entirely exhausted its energy sources.

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Gravity will assert itself for the final time. Without a nuclear heating source, there will be little to stop the sun from collapsing inward on itself. Certainly the interatomic forces that hold up solid matter against outside pressures on Earth are far too puny to stand up against the enormous inward pull of gravity in the final collapse of a star. The sun will squeeze itself far inside its present boundaries and far inside the volume it would have if it were made of ordinary solid material, squashing its atoms out of recognizable existence until only a solid, tightly packed ball of bare nuclei and unattached electrons remains. At this point, the collapse will be permanently stopped by an effect known as “quantum exchange forces” between the electrons.3 The sun’s burnt-out corpse will be hot, solid, and about Earth’s size, or onemillionth of its present volume! It will be extraordinarily compact, with many tonnes packed into each cubic centimeter. On Earth, even a solid steel platform would be unable to support a mere thimbleful of this material. The sun will warm enormously during its final collapse, but once the collapse ends there will be no further source of heating. This starry remnant will glow brightly for a while and then slowly dim like a dying ember, still orbited by the charred remains of Earth and other planets. A star the size of Earth? When such an object was first discovered in 1862, astronomers thought there must be an error in their observations. But two other such stars were soon discovered, and it’s now known that about 4% of the stars in our galaxy—some 16 billion stars—are of this type. Because of their white-hot glow they are called white dwarfs. How do we know our solar system’s past and future? Detailed quantitative theories predict the scenario just sketched. Observations of stars in the various evolutionary stages described and observations of Earth’s oldest rocks, the moon, moon rocks, meteorites, other planets, other moons, and the sun itself all support these theories. The natural place to look for star births is among thick gas clouds in space. When the Hubble Space Telescope searched the dense gas cloud known as the Eagle Nebula, it found thousands of newly minted stars (Figure 10). Just as the theory predicts, nearly all of these new stars were wrapped in disks of dust and gas, disks that are expected eventually to coalesce into planets.

CONCEPT CHECK 8 Suppose that the sun collapsed tomorrow to become a white dwarf, but without any explosions or expansion that would alter the sun’s mass or directly impact Earth. Which of the following would ensue? (a) Earth’s orbit would be altered. (b) Life on Earth would be radically affected. (c) The gravitational force by the sun on Earth would be radically altered. (d) The sun’s radiation would be radically altered. (e) None of the above.

4 GRAVITATIONAL COLLAPSE: THE DEATHS OF MORE MASSIVE STARS A star’s life cycle is determined primarily by its mass. A star needs at least 10% of the sun’s mass in order to get hot enough to initiate nuclear fusion and become a star in the first place. All stars massive enough to initiate nuclear fusion go through a middle age that is similar to the sun’s present state. Then when the hydrogen fuel 3

My suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. John B. S. Haldane, British Geneticist, 1892–1964

Quantum exchange forces have no explanation within Newtonian physics. They are far stronger than the ordinary electrical forces that maintain the solidity of normal solid matter.

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in their central cores have been used up, they enter their final phases. Stars having masses up to about 10 times the sun’s mass go through a final phase similar to the sun’s, ending as white dwarfs. But a quite different fate awaits more massive stars. Like the sun, they use up their hydrogen fuel and then contract at the center. But the larger mass makes the contraction stronger, so the center gets hotter. The high temperature initiates a wide range of nuclear reactions that eventually turn the star’s small central core into solid iron. This gets the star into serious trouble. Iron continues forming until the inner core becomes so massive that it cannot hold itself up. The entire solid iron core then abruptly collapses in just one second! As the core collapses, this unimaginably cataclysmic supernova explosion blasts the rest of the star into space. For a brief moment, the dying star glows as brightly as 4 billion suns. No supernova has been seen in our galaxy since 1604, but today astronomers are able to routinely discover them in other galaxies. The nearest of these burst into view in 1987 and was visible to the naked eye (Figure 12). It occurred in a neighboring small galaxy at a safe distance of 150,000 light-years (meaning that light travels from there to here in 150,000 years). A nearby supernova, if it were as close as 10 light-years or so, would produce various radiations that would create a fabulous light show in Earth’s atmosphere, and that would soon kill us. But not to worry: Such an event won’t happen in our corner of the Galaxy, because a candidate star for a supernova must be at least 10 times as massive as the sun and there’s nothing that massive that close. The nearest likely candidate is Betelgeuse, which has been acting unstable for years. But it’s at a safe 430 light-years away. Only 10% to 20% of the original star remains after the explosion. No further nuclear reactions can occur in this remnant, so there is little to oppose the inward pull of gravity. Within one second, this remaining massive core collapses to become one of the two densest things in the universe, a neutron star or a black hole. If the original star had a mass of between 10 and 30 suns, the final collapse is strong enough that electron exchange forces (see the previous section) can’t stop it.

(a)

(b)

National Optical Astronomy Observatories/Science Photo Library/Photo Researchers, Inc. Figure 12

The supernova of 1987, the brightest supernova in 400 years. Its light reached Earth on February 23, 1987. “Before” (a) and “after” (b) photos show the star as it looked before and shortly after the explosion. The supernova is the bright star on the right in figure (b).

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But there’s one remaining force that does stop it, the so-called “neutron exchange force,” a quantum effect similar to the electron exchange force but acting between neutrons. The collapse not only squashes atoms out of existence, it also squashes electrons out of existence by forcing them to merge with protons in the nuclei. This turns each nucleus into a collection of neutrons, and it turns the entire star into an object that resembles a giant nucleus made of neutrons. It’s called a neutron star. Nuclear physicist J. Robert Oppenheimer, who later gained fame as leader of the team that developed the atomic bomb, predicted neutron stars in 1938. None were discovered until 1967, when Jocelyn Bell (Figure 13), a sharp-eyed astronomy graduate student in England, discovered a source of radio waves in space that sent out “beeps” or “pulses” every 1.3 seconds. Some scientists thought at first that she might have discovered a radio beacon from an extraterrestrial civilization. But another was soon discovered, and by now hundreds are known, with a wide range of pulse rates. There’s little doubt that they are neutron stars. A neutron star is pretty impressive. More massive than the sun, the star is only a few kilometers across with a billion tonnes packed into each cubic centimeter! On Earth, a barely visible speck of this material would weigh as much as a large, fully loaded highway truck! The collapsing iron core spins faster and faster during its onesecond collapse, so that the remnant neutron star spins at incredible speeds for such a massive object—up to 700 times every second. The surface of such a rapidly spinning neutron star moves at an incredible 15% of the speed of light. This is staggering when you realize that the star has a mass of some 1027 tonnes. This spinning combines with magnetic effects to create the rapid pulses of visible light and radio signals observed from Earth, the signals that Bell discovered in 1967. As seen from Earth, the entire star appears to flash on and off many times every second. Figure 14 is a sequence of photographs showing two of these visible flashes. The supernova explosion that created this neutron star was seen and recorded on Earth in 1054. For a few days the light from the explosion was brighter than the planet Venus. Today, it’s called the Crab Nebula because the shape of the nebulous halo of gases blown into space by the explosion resembles a crab. Neutron stars pull hard. The star’s radius is only about 10 kilometers, which is 100,000 times smaller than the sun’s radius. Yet the star is more massive than the sun. Newton’s theory of gravity tells us that the weight of an object on the surface of a star is proportional to the inverse of the square of the star’s radius. If a collapsing star’s radius becomes 105 times smaller, an object on its surface becomes 105 * 105 = 1010 (10 billion) times heavier. That’s heavy. What about stars even more massive than those that collapse to form neutron stars—stars having a mass of over 30 suns? When such a star runs out of fuel, the ensuing collapse is so strong that no known force can stop it. According to current theories, it collapses into a single point! Its matter—its atoms and subatomic particles—is squeezed out of existence. The star retains its mass, however, and so it retains its gravitational influence on the space around it. This star pulls really hard. If you had the misfortune to get too close, you could not escape, because gravity won’t let anything escape—not even light itself. That’s why it’s called a black hole. For a typical black hole formed from a collapsing giant star, the distance within which nothing can escape is 10 to 50 km (larger for more massive black holes). You can think of this as the “radius” of the black hole. If you were within this distance of the central point and you wanted to throw an object completely away from the

Robin Scagell/Photo Researchers, Inc.

Newton’s Universe

Figure 13

Jocelyn Bell (later Burnell) discovered the first four neutron stars. Using a radio telescope that she helped build as part of her Ph.D. dissertation, Bell detected a rapid set of pulses occurring at regular intervals. She determined that the position of the unusual radio source remained fixed with respect to the stars, which meant that it was located beyond the solar system. During the course of the next few months, she discovered three more pulsating radio sources. These were later found to be rapidly rotating neutron stars.

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N P 0532

National Optical Astronomy Observatories Figure 14

A sequence of photographs of the neutron star at the center of the Crab Nebula. Portions of a surrounding gas cloud, the remnant of the supernova explosion that created the neutron star, can be seen. This sequence lasts 1/20 second and includes two flashes, the first during frames 3 and 4, and the second during frames 9 and 10.

star, you would need to throw it faster than the speed of light. But objects cannot be thrown faster than light. So nothing can escape a black hole.4 How do we know that black holes exist? Scientists detect black holes by their gravitational influence on things around them. The first black hole, Cygnus X-1, was discovered in 1972. It’s thought to be a double star, two stars orbiting each other. One is a visible giant star, the other an unseen compact (far smaller than a normal star) object. By observing its gravitational effect on the visible star, the compact object’s mass can be deduced to be 10 solar masses.5 Since theories indicate that a compact object of more than 3 solar masses can only be a black hole, astronomers believe that Cygnus X-1 is a black hole. Satellites in orbit around Earth detect X-rays from Cygnus X-1 that further confirm it to be a black hole. Apparently the invisible object’s gravitational pull is drawing gases from the visible star and accelerating them down into and around the black hole, a process that tears apart the gas atoms and causes them to emit X-rays that scientists can observe (Figure 15). Astronomers have now identified about 20 similar objects within our galaxy that are thought to be black-hole remnants of collapsed stars, and they suspect that there might be around one billion of them in our galaxy. Scientists don’t go out of their way to invent bizarre ideas like black holes. To the contrary, they look for the least strange explanation of the data. For example, people once found it strange that Earth could orbit the sun, but astronomers such as Copernicus found that this was the most natural way to account for the data. In the same manner, astronomers today find that a black hole is the most natural explanation for what they observe at Cygnus X-1. If it is not a black hole, then this object is not compact, or it does not have a mass larger than 3 suns, or compact objects of greater than 3 solar masses are not always black holes. Astronomers find it easier or “less strange” to believe that Cygnus X-1 is a black hole than to believe any of these options. There is a second kind of black hole for which the evidence is even more compelling than it is for Cygnus X-1. The centers of most galaxies contain extremely massive black holes. In 1994, for example, the Hubble Space Telescope found a tiny, bright source of

Julian Baum/New Scientist/Science Photo Library/Photo Researchers, Inc. Figure 15

In this artist’s conception, a black hole pulls matter from a companion star and accelerates it into a hot, X-ray–emitting disk before slowly swallowing it.

4

5

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More precisely, quantum theory allows black holes to emit subatomic particles, but this effect is negligible for collapsed stars. This effect is expected to be important for low-mass black holes, although such small black holes have never been observed and may not exist. The original star, before collapse, had a mass of more than 30 suns, but most of this mass blew into space during the collapse.

Newton’s Universe light at the center of a distant galaxy. Detailed analysis of this light showed that nearby gas and stars are orbiting this center so rapidly that gravity can hold them in their orbits only if the bright object has a mass of several billion suns. Given that the central object’s size is only slightly larger than our solar system, it could only be a black hole. The light apparently comes from high-energy processes occurring just outside the black hole. Study of distant galaxies reveals that the centers of most or all of them contain black holes having masses of millions or billions of suns. The distant and powerful objects known as “quasars” are powered by such giant black holes. Observation of a small portion of sky, and extrapolation to the entire sky, leads to an estimate of at least 300 billion giant black holes populating the observable universe! Observations of stars dashing in tight orbits around the center of our own Milky Way Galaxy at up to 1/30th of the speed of light imply a giant black hole lurks there. Despite having a mass of nearly 4 million suns, it is only about 20 times larger than our sun! Such giant black holes radiate X-rays and light as they swallow nearby stars and gas. Their origin is not yet understood.

CONCEPT CHECK 9 If Earth collapsed from its present 6000 km radius to only 6 km, your weight would be (a) unchanged; (b) l/1000th of your present weight; (c) 1/1,000,000 of your present weight; (d) 1000 times your present weight; (e) 1,000,000 times your present weight.

5 THE NEWTONIAN WORLDVIEW: A DEMOCRATIC, MECHANICAL UNIVERSE During the sixteenth and seventeenth centuries, the new sun-centered astronomy and inertial physics ushered in a new philosophical and religious view that I’ll call the Newtonian worldview.6 It is one of the most significant consequences of Newtonian physics. Even though Newtonian scientific ideas have been partly superseded by other more accurate theories, the worldview based on Newtonian physics retains its influence on popular culture. In the Western world, the pre-Newtonian worldview combined medieval Christianity, the Earth-centered astronomy of the ancient Greeks, and Aristotle’s physics. Central to this view was the idea of purpose, or future goals. During the Middle Ages in Europe, popular culture united with religion and science in the belief that there was a purpose for everything and that the universe’s larger purposes were tied to humans, so that humankind was central to all creation. Ancient Earth-centered astronomy and Aristotelian physics, with its goal-directed natural motions, chimed in perfectly with this traditional view. It was well attuned to the era’s hierarchical social structure, comprising a God-ordained king surrounded by a few land-holding nobles surrounded in turn by many land-working serfs and peasants. Astronomy and physics since the Middle Ages have contradicted Earth-centered astronomy and Aristotelian physics. Copernicus removed Earth from the center, Kepler replaced the planets’ “natural” circular orbits with ellipses, and Descartes declared that bodies move not because they have a goal but simply because there is nothing to stop them. The hierarchy of natural places, the notion that Earth is special, the centrality of humankind, and the scientific basis for purpose in the universe—all were swept away. It was not by chance that stirrings for religious and political freedom began at about this time. Once the hierarchical cosmology began to crumble, it was no 6

I am much occupied with the investigation of the physical causes [of the motions of the solar system]. My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork... insofar as nearly all the manifold motions are caused by a most simple, magnetic, and material force, just as all motions of a clock are caused by simple weight. Kepler

Newton, Descartes, and Galileo were among the scientists and philosophers who contributed to this view.

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longer obvious to people that they should follow the old hierarchical cultural habits. The new science established universal natural laws, rather than particular people or religious beliefs, as the ultimate framework for human behavior. Religious reformers such as Martin Luther felt freed to challenge medieval Christian traditions. Political reformer Thomas Jefferson could draw up a Declaration of Independence that threw off the divine rights of the king of England and that was permeated with the concept of “unalienable rights” flowing directly from “the Laws of Nature and of Nature’s God” to all people as the basis for human equality. Thus does our science influence, on quite a deep level, our religion, our social order, and our politics. Galileo sought only to describe how things behave, not why they behave as they do. He was not concerned with a physical phenomenon’s purpose. Analysis—the new technique of separating phenomena into their simplest components and studying those components—was one of his tools. This led to a focus on the simplest and smallest components of matter: atoms. And so atomism—the idea that nature can be reduced to the motions of tiny material particles—underlay the new physics. For example, in a view remarkably similar to Democritus’s view, Newton stated: It seems probable to me that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles... and that these primitive particles being solids are incomparably harder than any porous bodies compounded of them, even so hard as never to wear or break in pieces.... [Men are] engines endowed with wills. Robert Boyle

Now I a fourfold vision see, And a fourfold vision is given to me; ‘Tis fourfold in my supreme delight And threefold in soft Beulah’s night And twofold Always. May God us keep From Single vision And Newton’s sleep! William Blake, 1757–1827, Poet, Painter, Rebel Against the Mechanical Single Vision, or Linear Thinking, of Newton

Newton, Galileo, and Descartes believed firmly in God. What place within the new science could be found for God? Descartes reconciled the new science with traditional religion by assuming that there were two realities, a notion known as dualism. The first reality was the material world, made of matter and operating according to nature’s inflexible laws. Here, the true realities, or primary qualities, were assumed to be impersonal physical characteristics such as the motions of atoms. The second reality was spiritual, the realm of human thoughts and feelings and communication with God. These were assumed to be secondary qualities that were not part of the physical world but were merely reflections of the primary qualities. Thus did science and philosophy relegate human concerns to a shadowy secondary role in a physical universe. This left little room for God in the workings of the material universe. In the traditional view, God is continually and actively present throughout the universe, continually endowing all things with purpose. In the new view, God is, at most, an uninvolved observer. Descartes and Galileo believed that God was needed to establish the laws of nature and to start the universe moving but that once started, the whole thing would run itself.7 A machine, especially a finely tuned machine such as a clock, is an excellent analogy for the Newtonian worldview. Once the owner starts it, a clock runs itself according to its own operating principles. The founding fathers of physics thought of the universe as a clockwork mechanism whose operating principles were the laws of nature and whose parts were atoms. Because of its machinelike quality, I’ll call this view the mechanical universe. In fact, one major consequence of Newtonian physics is that every physical system is entirely predictable, like a perfectly operating clock. For a simple example, Newtonian physics can predict precisely how far a freely falling object will fall 7

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With a few exceptions, Newton also believed that God did not intervene in the universe. On certain occasions, namely in situations for which Newton himself could not find a scientific explanation, he believed that God momentarily intervened. However, this “god of the gaps” view—that every phenomenon that cannot be explained by science requires an intervention by God—becomes less and less tenable as science closes the gaps.

Newton’s Universe

during any specified time. This clocklike predictability has surprising implications. To understand them, imagine a simple, isolated, self-contained collection of atoms that move and interact in accordance with Newtonian physics. Suppose you specify the precise positions and velocities of every atom at one particular time. Then, according to Newton’s theory of motion, the entire future behavior of this system can be precisely predicted, for all time. But the Newtonian view is that the universe itself is just such a collection of atoms. Thus, the future is entirely determined by what all the atoms of the universe are doing right now or at any other time. Furthermore, since humans are entirely made of atoms, it follows that every thought or feeling that enters your head is reducible to the motion of atoms within your brain and elsewhere. Thus, all of your thoughts, feelings, and actions are entirely predetermined and predictable. You never choose to scratch your nose, for example—the laws of nature choose for you. You might believe that you choose, but this, too—this believing that you choose—was chosen for you by the laws of nature. Such a mechanistic universe, the loss of free will, and the absence of a continuously creative God strike many observers as inhuman and cold. For example, German social scientist Max Weber (1864–1920) spoke of the “disenchantment of the world” brought about by Newtonian science. Poet and painter William Blake (1757–1827) wrote disdainfully in a poem “May God us keep/From Single vision/ and Newton’s sleep!” Nevertheless, from the seventeenth into the twentieth century, these ideas influenced many educated people. Newtonian physics was so successful that the associated philosophy was accepted with little question. People absorbed the clockwork universe without knowing they were absorbing it. There are reasons today to question both the Newtonian worldview and Newtonian physics. Nevertheless, it would be surprising if these views were not still influential today. A person’s worldview tends to be absorbed thoughtlessly, as part of the cultural air of the times. It seems likely that the Newtonian worldview remains active, even (or perhaps especially) among people who have never heard of Isaac Newton. It is for you, valued reader, to determine to what extent the Newtonian worldview is valid, whether it retains a significant influence, and what difference it might make.

[It is unbelievable] that all nature, all the planets, should obey eternal laws, and that there should be a little animal, five feet high, who in contempt of these laws, could act as he pleased, solely according to his caprice.

6 BEYOND NEWTON: LIMITATIONS OF

It’s a material world.

NEWTONIAN PHYSICS

Voltaire, French Philosopher and Writer, 1694–1778

They may say what they like; everything is organized matter. Napoleon Bonaparte, 1769–1821

I never satisfy myself until I make a mechanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand. Lord Kelvin, Nineteenth-Century British Mathematician and Physicist

That Man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms;... all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. Bertrand Russell, Philosopher and Mathematician, 1872–1970

Madonna

Tested repeatedly during the eighteenth and nineteenth centuries, Newtonian physics stood up in quantitative detail to every challenge. In fact, it was so powerful and accurate that scientists began to accept it as true in an ultimate, absolute sense. But science is never absolute. Even though a scientific principle has been confirmed repeatedly, it hangs always by the slender thread of new experiments. Around 1880, experimental results began appearing that couldn’t be reconciled with Newtonian physics. The incorrect Newtonian predictions arose in four extreme situations: at high speeds, for enormous gravitational forces, at huge distances, and at tiny distances. During the first few decades of the twentieth century, Albert Einstein, Werner Heisenberg, and many others invented three new theories to account for these discrepancies: special relativity, general relativity, and quantum physics. To date, at least, scientists have found no exceptions to any of the new theories. Experiments show that Newton’s law of motion and Newtonian views of time and space break down at high speeds. The disagreement is not noticeable at slow

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speeds, but the errors become worse as speeds increase. The non-Newtonian effects are difficult to detect for automobiles, jet planes, or even orbiting satellites moving at some 10 km/s. But at 30,000 km/s (around the world in about 1 second!), Newtonian predictions are off by 0.5%. At 290,000 km/s, nearly the speed of light, typical Newtonian predictions are incorrect by a factor of 4! Scientists didn’t notice these non-Newtonian effects for 200 years because they had never closely studied such fast-moving objects. Special relativity gives correct predictions at all speeds, both low and high. These predictions become indistinguishable from Newtonian physics whenever the speeds are considerably less than the speed of light. Similarly, experiments show that Newton’s theory of gravity, Newton’s law of motion, and Newtonian views about time and space are incorrect for objects subjected to enormous gravitational forces and also over huge distances. For example, non-Newtonian gravitational effects are measurable, but small, for the orbit of the innermost planet, Mercury, which feels strong gravitational forces from the sun. Non-Newtonian gravitational effects are pronounced near neutron stars and black holes and for physical systems that range over large portions of the observable universe. General relativity gives correct predictions for all these situations and is regarded as the correct theory of gravity. The predictions of general relativity become indistinguishable from Newtonian physics whenever gravitational forces are not too strong and distances are not too large. The disagreements between Newtonian physics on the one hand and Einstein’s special and general relativity on the other stem from profoundly different ways of viewing space and time. Newton took the common intuitive view that all of us take in our daily lives: Space is infinite in extent, time is infinite in duration, and both have the same properties everywhere and at all times. Einstein, however, found that space and time are “relative,” or different for different observers, namely observers moving at different speeds. For example, the duration of a process such as the melting of your ice cream cone is different as viewed by you from its duration as viewed by your friend who is moving past you. From this, all sorts of new results emerge, such as that space can “curve,” and time runs differently in different places. Finally, experiments show that Newton’s law of motion and subtle Newtonian views concerning predictability and cause and effect are incorrect for objects of molecular dimensions or smaller. Quantum physics gives correct predictions for objects of all sizes, from microscopic to macroscopic. For macroscopic objects like footballs and apples, quantum theory’s predictions become indistinguishable from Newtonian physics. Although quantum physics represents an even more profound revolution than does relativity, it stems from a seemingly insignificant difference concerning such properties as speed, momentum, and energy. Newtonian physics allows such properties to have any numerical value whatsoever within a continuous range of possibilities, for example, the speed of a particular airplane might be anything between zero and 1000 km/h. But quantum physics states that such properties can only have specific “permitted” values, such as 0.01 km/h, 0.02 km/h, 0.03 km/h, etc. up to 1000.0 km/h.8 The speed of the airplane is said to be “quantized.”

8

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This is an exaggerated example for purposes of illustration; the differences between the permitted values would be much much smaller than this for a real airplane, and so this “quantization principle” isn’t significant for airplanes and other large objects. But for microscopic objects, these “small” differences between permitted values are more important, and so quantization makes a big difference in the microworld.

Newton’s Universe

This turns out to have surprising and profound implications, especially in the microscopic world. Figure 16 is one way of indicating, graphically, these limits of validity of Newtonian physics. The vertical axis represents the speed of individual objects. Special relativity predicts that objects cannot move faster than the speed of light— 300,000 km/s—so these speeds are forbidden. The horizontal axis shows the size of individual objects. Because a principle known as “quantum uncertainty” predicts that objects cannot be both small9 and slow moving, there is another forbidden region in the small-size, low-speed corner of the diagram. The lesson is that it’s not a Newtonian universe. Earth, where Newtonian physics works well for ordinary objects, is an exception in a universe dominated by relativistic and quantum phenomena. The conditions we regard as normal occur only rarely in the universe. Newtonian and intuitive concepts of time, space, matter, and much else are far from correct throughout most of the universe. The “real” universe— the quantum-relativistic universe—is fundamentally different, and far stranger, than our Earth-bound intuitions could have imagined.

Speed Forbidden

Speed of light, 300,000 km/s

Quantum ⫹ special relativity

Special relativity General relativity

10% of speed of light, 30,000 km/s Quantum

Newtonian

Forbidden 10⫺5 m

1022 m

Size or distance

Figure 1610

Newtonian physics is correct for common phenomena on Earth, but breaks down for objects that are very small, very large, or very fast. Newtonian physics also breaks down for strong gravitational forces, such as those near a neutron star or black hole. The quantum and relativity theories apply throughout the entire range of the phenomena observed to date. The diagram is only schematic and approximate. 9

“Highly localized” is a more accurate term than “small.” A particle such as an electron is said to be “localized” within a small region of space when it is observed (or known) to be located within that region. The quantum uncertainty principle implies that a particle that is localized within a very small region must have (on the average) a high speed. 10 Thanks to Douglas Giancoli, the author of several physics textbooks, including Physics: Principles with Applications (Englewood Cliffs, NJ: Prentice Hall, 1991), for suggesting diagrams of this type.

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© Sidney Harris, used with permission.

Newton’s Universe

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Newton’s Universe Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions THE IDEA OF GRAVITY 1. What is the direction of a falling apple’s velocity? Of its acceleration? 2. What is the direction of the moon’s velocity? Of its acceleration? 3. Does Earth exert a force on the moon? What is its direction? How would the moon move if this force suddenly vanished? 4. In what ways are the moon and a falling apple similar? In what ways do they differ?

NEWTON’S THEORY OF GRAVITY 5. Does this book exert a gravitational force on your body? 6. What would happen to this book’s weight if you managed to double Earth’s mass? What if, instead, you doubled the book’s mass? What if you doubled both? 7. In order to use Newton’s theory of gravity to calculate your weight, what data would you need? 8. If you were orbiting Earth in a satellite 200 km above the ground, would you be weightless? Would your weight be as large as it is when you are on the ground? Would you feel weightless? Explain.

GRAVITATIONAL COLLAPSE 9. What caused the sun to get hot? What keeps it hot today? 10. Describe the process that formed the planets. 11. Since gravity pulls inward on the material in the sun and since the sun is made only of gas, why doesn’t the sun collapse? 12. Are there places in our galaxy where stars are being born? 13. Name the process and also the substance that fuels the sun. 14. What will happen to the sun after it runs out of fuel? 15. Name and describe the object into which the sun will evolve after it runs out of fuel. 16. What causes different stars to evolve differently? 17. All stars eventually evolve into one of three types of objects. Name them. What kinds of stars evolve into each of the three types of objects? 18. Describe a neutron star. 19. Describe a black hole. Since nothing can come out of a black hole, how can we detect it?

THE NEWTONIAN WORLDVIEW 20. List some ways in which ancient Greek astronomy and Aristotelian physics support the medieval philosophical and religious worldview.

21. List some of the ways in which Copernican and Newtonian science are less supportive of the medieval worldview. 22. How is Newtonian physics related to democracy? 23. According to the Newtonian worldview, is a red napkin really “red”? Explain. 24. List several ways in which, according to the Newtonian worldview, the universe is similar to a clock.

BEYOND NEWTON 25. For what kinds of phenomena is Newtonian physics incorrect? Why did it take so long to discover such exceptions? 26. List the three theories that give correct predictions for the situations in which Newtonian physics is incorrect.

Conceptual Exercises THE IDEA OF GRAVITY 1. Does Earth’s gravity pull more strongly on a block of wood or on a block of iron having the same size? 2. Which one falls faster when dropped, a block of wood or a block of iron having the same size (neglect air resistance)? 3. What is the magnitude (strength) and direction of the gravitational force on you right now? 4. When you crumple a sheet of paper into a tight ball, does its mass change? Does its weight change? 5. Are you in orbit around (falling around) Earth’s center? Is there anything around which you are in orbit? 6. The moon is in orbit around two objects simultaneously. Which two? (Actually, there is a third—our galaxy’s center.) 7. Do you exert a gravitational pull on people around you? Do they exert a gravitational pull on you? 8. Do you exert a gravitational force on Earth? If so, how large is it, and in what direction is it? 9. How far does Earth’s gravitational influence extend? 10. As a spacecraft travels from Earth to the moon, does it ever entirely leave Earth’s gravitational influence? 11. A low-orbiting satellite weighs 8000 N. How big and in what direction is the gravitational force on it? How big and in what direction is the gravitational force by the satellite on Earth? 12. What would be the approximate orbital period (time for one complete orbit) for an apple placed in circular orbit around Earth at the moon’s distance from Earth? 13. If gravity suddenly shut off right now, what would be the shape of Earth’s orbit? What about the moon’s orbit? 14. What force (if any) keeps the planets moving?

From Chapter 5 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Newton’s Universe: Problem Set

NEWTON’S THEORY OF GRAVITY 15. Which is larger, the gravitational force by Earth on the moon or the gravitational force by the moon on Earth? 16. How strongly and in what direction does Earth pull on a 1 N apple? How strongly and in what direction does the apple pull on Earth? 17. Suppose you went to another planet that was identical to Earth on the surface but that was mostly hollow inside. Would this affect your weight? How? 18. Suppose you went to another planet having a larger radius than Earth but having the same total mass as Earth. Would this affect your weight? How? 19. List at least three bodies that have a detectable (measurable) gravitational effect on Earth’s motion. 20. The giant planet Jupiter is about 300 times more massive than Earth. It seems, then, that an object on Jupiter’s surface should weigh 300 times more than it weighs on Earth. But it actually weighs only about 3 times as much. Explain. 21. If you were in a freely falling elevator and you dropped your keys, they would hover in front of you. Are the keys falling? Are the keys weightless? 22. If gold were always sold by weight, could you make money buying gold at one altitude above the ground and selling it at a different altitude? Where would you want to buy—at a high altitude or a low altitude? 23. Would you weigh more in Denver or in Los Angeles? Why? 24. Is there any net force acting on the moon? 25. Is the moon accelerated? If so, in what direction is the acceleration? In what direction is the moon’s velocity?

26. Suppose that a heavy- and a lightweight satellite are put into low orbits around Earth. Could you tell, by observing the shape or speed of the two orbits, which satellite was the heavy one? 27. Suppose that two satellites are put into orbit, one around Earth and one around the moon, and suppose that the radii of the two orbits (the distance from the center of Earth and the moon) are the same. From the knowledge that Earth’s mass is larger than the moon’s mass, can you make any predictions about the speeds of the two orbits? 28. Communications satellites must be in geosynchronous orbits. That is, they must remain above a fixed point on Earth’s surface, enabling sending and receiving antennas to be aimed at a fixed point overhead. What, then, must be a communication satellite’s orbital period (the time for one complete orbit around Earth)? 29. In the “orbital” case in Figure 4, draw three arrows—labeled f, a, v—attached to the apple that show the direction of the gravitational force on the apple, the direction of the apple’s acceleration, and the direction of the apple’s velocity. 30. Figure 3 shows two possible paths for an apple that has been thrown horizontally. Assume that air resistance is negligible. For each path, draw three arrows—labeled f, a, v—attached to the apple that show the direction of the gravitational force on the apple, the direction of the apple’s acceleration, and the direction of the apple’s velocity. 31. Suppose that the gravitational force between an apple and an orange placed a few meters apart is one-trillionth (10–12) N. What would the force be if the distance were doubled? Halved? Tripled? Quartered?

Figure 4

Suborbital

Falling around Earth. If you throw an apple fast enough, it will fall around a large part of Earth’s surface or even go into orbit. A diagram like this appears in Newton’s notebook.

Orbital

Figure 3

If you throw an apple horizontally, the faster you throw it, the farther it will go.

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Slower

Faster

Newton’s Universe: Problem Set 32. Referring to the previous exercise, what would the force be if the mass of the apple were doubled? Tripled? What if the mass of the apple were tripled and the mass of the orange were quadrupled? 33. Referring to the previous exercise, what would the force be if the mass of the apple were doubled, the mass of the orange were doubled, and the distance between them were doubled?

GRAVITATIONAL COLLAPSE 34. If Earth collapsed to one-tenth of its present radius, how much would you then weigh? 35. If Earth expanded to 10 times its present radius, how much would you then weigh? 36. Find your weight at a distance of 10 Earth radii from Earth’s center. Compare with the preceding question. 37. Will Earth ever collapse to become a black hole? Why? Will the sun? 38. The orbits of all nine planets lie approximately in the same flat plane. Why?

BEYOND NEWTON 39. What theory or theories would be needed to predict the behavior of an atom moving at half the speed of light? 40. According to the most widely accepted scientific theory of the creation of the universe, the observable universe during the first few moments (much less than 1 second) of its existence was extremely hot, was full of densely packed matter, and was very tiny—smaller than an atom. What theory or theories would be needed to explain what was happening during these first few moments?

Problems NEWTON’S THEORY OF GRAVITY 1. What happens to the gravitational force between two planets when the distance between them is decreased to one-third of its previous value? 2. What happens to the gravitational force between two planets when the distance between them is increased to three times its previous value? 3. Earth’s mass is 6.0 * 1024 kg, and its radius is 6.4 * 106 m. Use Newton’s theory of gravity to find the weight of a 1 kg object lying on Earth’s surface. 4. The moon’s mass is 7.4 * 1022 kg, and its radius is 1.7 * 106 m. Use Newton’s theory of gravity to find the weight of a 1kg object lying on the moon’s surface. If you did the preceding problem, then compare the two answers. 5. A certain neutron star has a mass of 4.0 * 1030 kg (twice the sun’s mass) compressed into a sphere of radius only 10,000 m (10 km). Find the gravitational force on a cubic centimeter of water, whose mass is 1 gram, lying on the surface (in reality, this “water” would no longer be in its normal liquid state if it were on the surface of a neutron star!). 6. Find the force by the moon on Earth. Their masses are 7.4 * 1022 kg and 6.0 * 1024 kg, and it is 3.8 * 108 m between their centers.

7. In the preceding question, how large is the force by Earth on the moon? In what direction is the force by Earth on the moon? 8. Find the force by the sun on Earth. Their masses are 2.0 * 1030 kg and 6.0 * 1024 kg, and it is 150 million kilometers between their centers. 9. In the preceding question, how large is the force by Earth on the sun? In what direction is the force by Earth on the sun? 10. Find the force by a 0.1 kg apple on another 0.1 kg apple, if their centers are 2 m apart. 11. MAKING ESTIMATES Estimate the gravitational force, in newtons, that you exert on a person standing near you. Is the answer closer to 1000 N, 1 N, one-thousandth N, one millionth N, or one-billionth N?

Answers to Concept Checks 1. 2. 3. 4. 5. 6. 7. 8. 9.

(b) (c) (c) According to Newton’s law of motion, if the net force is the same, then the acceleration is also the same, (d). (a) Although your mass is unchanged, your weight is reduced because you are farther from Earth’s center, (d). You have multiplied the distance by 3, so you’ve divided the force by 9 (3 squared), (f ). (b) and (d) The radius is reduced to 1/1000th of its previous value. The square of this is 1/1,000,000, and the inverse of this is 1,000,000, (e).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Iron. They fall equally fast. 3. The magnitude is your weight (in pounds, or in newtons), and the direction is downward. 5. No, you are not in orbit around Earth’s center (although you are revolving around that center due to Earth’s spinning motion). You are in orbit around the sun. 7. Yes; yes. 9. It extends to infinity (but it is very small at great distances). 11. 8000 N, downward. 8000 N, upward. 13. A straight line; a straight line. 15. The law of force pairs tells us that these two forces are of equal strength. 17. The other planet’s mass would be less than Earth’s mass, so your weight would be reduced. 19. The sun, Earth’s moon, planets such as Mars and Venus. 21. Yes, the keys are falling, along with you. The keys have weight, although they are “apparently weightless.” 23. You would weigh more in Los Angeles, because your distance from Earth’s center would be smaller. 25. Yes, the moon is accelerated in the inward (downward) direction. The moon’s velocity is forward—along the moon’s orbit.

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Newton’s Universe: Problem Set 27. The inward force on the earth satellite would be larger

29. 31. 33. 35. 37. 39.

(because Earth’s mass is larger than the moon’s mass), so the earth satellite would have the larger acceleration (because of Newton’s law of motion). In order to have this larger acceleration, the earth satellite would have to be moving faster. f and a point directly toward Earth’s center, and v points along the path of motion. (1>4) * 10 - 12 N, 4 * 10 - 12 N, (1>9) * 10 - 12 N, - 12 16 * 10 N. The force would be unchanged. 1/100th of your present weight. No. Earth does not have sufficient mass for it to collapse this far. Neither does the sun. Special relativity and quantum theory.

Problems 1. The new force is nine times larger than it was. 3. F = 6.7 * 10 - 11 m1 * m2>d2 = 6.7 * 10 - 11(1 kg)(6.0 * 1024 kg)>(6.4 * 106 m)2 = 9.8 N

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5. F = 6.7 * 10 - 11 m1 * m2>d2

= 6.7 * 10 - 11 (10 - 3 kg) * (4 * 1030 kg)>(104 m)2 = 2.7 * 109 N (2.7 billion newtons!) 7. The answer is the same as in Problem 6, 2.1 * 1020 N. The force by Earth on the moon is directed toward Earth’s center. 9. The answer is the same as in Problem 8, 3.6 * 1033 N, directed toward Earth’s center. 11. A typical mass for a person is about 50 kg. A typical distance from you to a person next to you might be about 1 meter. So the gravitational force by one person on the other is about (6.7 * 10 - 11) * (50) * (50)>(1)2 N = 1.7 * 10 - 7 N, less than one-millionth N.

Conservation of Energy

From Chapter 6 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Conservation of Energy You Can’t Get Ahead—

Energy is the most difficult part of the environment problem, and environment is the most difficult part of the energy problem. The core of the challenge of expanding and sustaining economic prosperity is the challenge of limiting, at affordable cost, the environmental impacts of an expanding energy supply. John Holdren, President Obama’s Science Advisor

E

nergy is physics’ most important concept and, as you can see almost every day in the newspapers, energy is also highly relevant to society. In fact, we define human cultures largely by their use of energy resources. Civilization itself is nearly synonymous with the organized use of solar energy. Humankind’s first permanent villages developed 10,000 years ago because of the needs of trade and agriculture. For centuries, trade was facilitated by solar energy, which drove the winds that pushed the sails of merchant ships, warships, and exploration ships. And agriculture is the organized use of solar energy to grow food. Today, the chemically altered remains of ancient life known as fossil fuels—coal, oil, and natural gas— energize our industrial culture. Energy is one of the four recurring themes of this text. It will be the basis for analyzing all sorts of natural phenomena in this chapter and for discussing many energyrelated social issues. Our goal in this chapter is to understand what scientists mean by energy and to use this concept to understand a multitude of physical processes. Like all powerful scientific ideas, energy explains and unifies a wide variety of phenomena. Unlike Newton’s laws, the principles of energy apply to all phenomena, from subnuclear “quarks” to the cosmos, observed so far. New energy sources have been nearly synonymous with significant social changes. The coal-fueled steam engine stimulated the Industrial Revolution around 1750, with profound economic and social consequences. Because the new industrial machines were large, complex, and expensive, traditional home workshops grew into large centrally located factories run by the rich. Whereas the skills of traditional craftspeople required a long apprenticeship, even unskilled workers and children could tend the new machines. Consequently, nineteenth-century Europe and North America were marked by increased productivity, the capitalistic organization of industry, and a shift of population from farms to cities. Many political ideologies of the twentieth century—facism, communism, capitalism, socialism—grew out of the economics of the Industrial Revolution. Today, the Industrial Revolution is spreading all over the world and to new industries such as computers. The new industries stimulated nineteenth-century scientists to understand the two grand principles of energy. This chapter develops one of these principles, conservation of energy. This principle appears in Section 5, following the development in

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Sections 1 through 4 of the concepts of work and energy. Everything that happens in the universe involves an energy transformation of one sort or another. Section 6 studies several examples of energy transformations. Section 7 looks at a highly useful related idea: power, or the rate (per unit of time) of transforming energy. CONCEPT CHECK 1 We’ve never observed a violation of conservation of energy or the second law of thermodynamics. Thus, these principles of energy are (a) good theories; (b) good hypotheses; (c) certain to be correct in all future observations; (d) facts; (e) absolutely true; (f) hogwash.

1 WORK: USING A FORCE TO MOVE SOMETHING People commonly say that a material system such as a person, a flashlight battery, or a tank of gasoline, has “energy” if it has an inherent capacity to bring about changes in its environment or itself. The physicists’ definition of energy is a refinement of this notion. I’ll say a system has “energy” whenever it has the capacity to do work, where “work” refers to bringing about external or internal changes. In this section, I’ll discuss “work.” The physicist’s definition of work is a refinement of the common notion that you do work whenever you exert yourself to perform a task. In physics, work is done whenever an object is pushed or pulled through a distance. For instance, you do work on a book when you push it across a table. A magnet does work on a paper clip when the magnet pulls the clip toward the magnet. More precisely, object A (a person or any other thing) does work on object B if A exerts a force on B while B moves in the direction of that force (we won’t need to consider situations in which the motion is not in the same direction as the force). You do work on a book when you lift it. Earth does work on the book when the book falls. Notice that work is always done by one specific object on another specific object. And notice that both force and motion are needed in order for work to be done. CONCEPT CHECK 2 Jed leans against a brick wall while Ned pushes hard against it and “works up” a sweat in the process (Figure 1). Is either Jed or Ned doing any work on the wall? (a) Both are. (b) Ned is but Jed is not. (c) Neither one is. CONCEPT CHECK 3 A single electron flies through the vacuum (assume it’s a “perfect” vacuum) inside your TV picture tube, from the back to the front side, where it makes a tiny flash when it strikes the inside of the screen. Neglect the force of gravity on the electron. During the electron’s motion through the tube, (a) only air resistance does work on the electron, causing it to slow down; (b) inertia does work on the electron, causing it to move at an unchanging speed in a straight line; (c) inertia does work on the electron, causing it to slow down; (d) no work is done on the electron, which moves at an unchanging velocity; (e) no work is done on the electron, which slows down.

Anybody who has ever thought about the cost of filling a car’s gas tank, or about a car’s gasoline efficiency, knows that it’s of practical importance to be quantitative about energy. Let’s think about the quantity of work you do in various situations. If the word work is to agree roughly with common language, the work you do in lifting a load should be larger for larger loads. To see how much larger, compare lifting one

Jed

Ned

Figure 1

Is either Jed or Ned doing any work on the brick wall?

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book with lifting two identical stacked books (Figure 2). The effect is twice as big in the second case, so the work done should be twice as big. This means work should be proportional to force. Now compare pushing a book across one table with pushing it all the way across two adjoining tables (Figure 3). Again the effect is twice as big in the second case. So work should be proportional to the distance moved. So work should be proportional to both force and distance. Thus, we define the amount of work done by object A on object B as the force exerted by A on B times the distance that B moves while experiencing that force:1 work = force * distance = Fd Figure 2

It takes twice as much work to lift two books.

For instance, if you push on a book with a 3 newton force while pushing it 2 meters, you have done (3 N) * (2 m) = 6 newton-meters of work. Note that the unit of work is the newton-meter, a unit that’s so widely used that it’s been renamed the joule (J) (rhymes with school), in honor of James Prescott Joule (Figure 4). From the following Concept Checks you can see that the work done in lifting an object is the object’s weight multiplied by the height lifted. CONCEPT CHECK 4 Suppose you slowly, and at constant speed, lift a 12 N book from the floor to a shelf 2 m above the floor. While you are lifting it, the net force on the book is (a) zero; (b) 12 N; (c) 24 N. CONCEPT CHECK 5 The force by your hand against the book in the preceding question is (a) zero; (b) 12 N; (c) 24 N.

Figure 3

It takes twice as much work to push one book twice as far.

CONCEPT CHECK 6 The work done by you on the book in the preceding question is (a) zero; (b) 24 J; (c) 48 J.

2 WORK AND ENERGY: A SIMPLE EXAMPLE

American Institute of Physics/ Emilio Segre Visual Archives

Do this two-step experiment and observe carefully: First, place your book on your outstretched hand on the floor; slowly lift it to some height; hold it there a few seconds; and then slowly lower it back to the floor. Second, repeat the same lifting process to the same height, but this time suddenly remove your hand from the book so that it falls to the floor. You do work on the book when lifting it, but it does work on you when lowering back to the floor, because the book pushes downward against your hand all the way down. So the raised book has a capacity to do work and it actually does this work as it’s lowered. Let’s look more closely at the “capacity to do work.” You just saw that raised objects have this capacity. And so do moving objects. For example, suppose that you throw your book, horizontally, at a wall. One way to get work out of the moving book would be to stick a thumbtack partly into the wall, directly in line with the book’s motion, so that the book will hit the tack and drive it in farther (Figure 5). Any moving object has the capacity to do work.

Figure 4

British physicist James Prescott Joule. His experiments in the 1840s helped unravel the confusion surrounding thermal energy and so led to the first clear understanding of energy.

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This definition assumes that the motion is in a straight line in the direction of the force. If the motion and the force are not in the same direction, then in the formula we must use only that part or “component” of the force that is along the motion. We won’t need this refinement here.

Conservation of Energy

In the second step of our experiment, the book was again raised, and in the raised position it again had the capacity to do work. But then you dropped it so that it simply fell, without doing work on your hand. As the falling book lost height, it gained speed, so it retained an ability to do work. Just before hitting the floor, the book still had a capacity to do work; only now this capacity resulted from the book’s speed rather than from its height. You could get the falling book to actually do this work by sticking a tack partly into the floor and letting the book drive in the tack farther (Figure 6). So you give your book the capacity to do work when you lift it or throw it. The work you do is “stored” in the raised or moving book. You could get this work back at any time, for example by letting the book push your hand down to the floor. Physicists have a word for the capacity to do work. It’s called energy. You’ve seen that both raised objects and moving objects have energy. It’s useful to distinguish these different forms. We’ll say that a raised object has “gravitational energy,” because this energy is caused by Earth’s gravitational pull on the object, and that a moving object has “kinetic energy,” because “kinetic” is related to the Greek word for motion. As you’ll see, there are several other energy forms. As it falls, the book loses gravitational energy but gains kinetic energy and so retains energy. This retention of energy when no outside agent (such as your hand) influences the system is one example of the law of conservation of energy. These are the essential ideas about work and energy, presented in the context of a simple example. The rest of this chapter expands on these ideas.

Figure 5

One way to get work out of a moving book: Allow it to push a thumbtack into a wall.

3 A QUANTITATIVE LOOK AT ENERGY Let’s look quantitatively at the experiment described in the preceding section. Recall that the amount of work you do to lift an object is its weight multiplied by the height raised. Once the book is raised, it has gravitational energy because it can do work in pushing your hand back to the floor. How much gravitational energy does it have? Quantitatively, we define an object’s energy to be the amount of work it can do. It’s measured in joules (or newton-meters), just as work is. The energy of the raised book is the amount of work it can do in slowly pushing your hand back down to the floor, which is just the book’s weight multiplied by the distance to the floor. You can see from this that, for any raised object,

Figure 6

One way to get work out of a falling book.

gravitational energy = weight * height When you slowly lower the book, it uses up its energy while pushing your hand back to the floor. But when the book falls, its gravitational energy is transformed into kinetic energy. How much kinetic energy is possessed by a moving object such as the book? In other words, how much work can a moving object do because of its motion? It’s possible to work out the answer to this question, starting from Newton’s laws, although we won’t work it out here. The answer turns out to be 1 kinetic energy = a b * (object’s mass) * (square of object’s speed) 2 This formula tells us that a more massive object has more kinetic energy and a faster object has more kinetic energy, as we might expect. It makes sense that the formula should involve the object’s mass rather than its weight, because kinetic energy is possible even in the absence of gravity.

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wt ⫻ ht at this point

equals (1/2) ms 2 at this point

Figure 7

An amazing thing: The gravitational energy at the top precisely equals the kinetic energy at the bottom, just before the book hits the ground.

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Now comes an incredible fact, also provable from Newton’s laws: If you neglect air resistance (which I’ll deal with later), the amount of gravitational energy the book has at the beginning of its fall will precisely equal the amount of kinetic energy it has at the end (Figure 7). The book’s total capacity to do work, its total energy, is quantitatively unchanged during the falling process. Its energy is simply changed in form—transformed—from gravitational to kinetic, but its total energy remains the same. As physicists put it, energy is precisely “conserved.” This physics use of the word conserved should be distinguished from the way “energy conservation” is used socially. When the newspapers speak of energy conservation, they mean preserving certain high-value forms of energy such as oil by consuming them less. When physicists speak of the conservation of energy, they mean that the total amount of energy remains unchanged throughout some physical process. Furthermore, since energy is conserved for any distance of fall, it must be conserved at halfway down, at three-quarters of the way down, and at every other point during the fall. The loss in gravitational energy during any portion of the fall precisely equals the gain in kinetic energy during that portion (Figure 8). CONCEPT CHECK 7 How much kinetic energy does a car have when it moves at 100 km/hr, as compared with when it moves at 50 km/hr? (a) The same amount. (b) One-half as much. (c) One-fourth as much. (d) Twice as much. (e) Four times as much. CONCEPT CHECK 8 A bag of groceries having a mass of 6 kg and a weight of 60 N falls from a shelf that is 2 m high. Just as it begins to fall, its gravitational energy (relative to the floor) is (a) zero; (b) 12 J; (c) 120 J; (d) none of the above. CONCEPT CHECK 9 Refer to the preceding question. Neglecting air resistance, just before hitting the floor the bag of groceries’ gravitational energy and kinetic energy are (a) both zero; (b) zero and 120 J, respectively; (c) 120 J and zero, respectively; (d) both 120 J; (e) none of the above. MAKI NG ESTI MATES Estimate your physics book’s energy, relative to the floor,

Figure 8

The total energy is conserved all the way down. The loss in gravitational energy between points 1 and 2 during the fall is precisely balanced by the gain in kinetic energy between these two points. This is true no matter where point 2 might be between the woman’s hands and the floor.

when lifted to arm’s length over your head. Assume the book’s weight is about 10 N. If you dropped it from this height, about how much kinetic energy would it have just before hitting the floor?

4 ENERGY: THE CAPACITY TO DO WORK Now let’s expand on the preceding two sections, extending these ideas to a wide variety of systems. This word system comes up a lot in science. It means a specific part of the universe, such as a particular collection of objects. Any system having the capacity to do work is said to have energy. Quantitatively, a system’s energy is the amount of work it can do. Although work and energy can both be measured in joules, work and energy are not the same thing. A system does

Suppose you can lift to about 2 m above the floor: GravE = wt * ht L 10 N * 2 m = 20 J. If you drop it, it will have nearly this entire 20 J of energy, in the form of kinetic energy, just before it hits the floor. The remaining small amount is converted to thermal energy, due to air resistance. SO LUTION TO MAKI NG ESTI MATES

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work, but it has energy. Work is a process, whereas energy is a property of a system. You can think of energy as stored work. A system’s energy is the amount of work the system could do, regardless of whether it ever actually does this work: A raised boulder has energy, even though it might be tied up and left that way forever and never do any work. The difference between energy and work is similar to the difference between money and spending. Just as energy is the capacity to do work, the money in your bank account represents your capacity to spend. Work is then similar to the act of spending some of that money. Notice that although your bank account and your spending are both measured in dollars, they are different things. There are many forms of energy, because there are many ways to do work. I’ll discuss eight of them, beginning with the two you already know something about. Kinetic energy (KinE) is energy due to motion. It’s the work a system could do while coming to rest. Gravitational energy2 (GravE) is energy due to gravitational forces. It’s the work a raised system could do while Earth (or any other object that can pull gravitationally) pulls it back to its initial position. There’s a quirk about gravitational energy: Its numerical value depends on the level chosen as the initial or reference level, simply because the amount of work you can get from a raised object depends on how far down it must go before you consider it no longer “raised.” For instance, your book’s gravitational energy is only a few joules relative to the floor of your room, but it may be thousands of joules relative to sea level. So we sometimes need to be explicit about the agreed-upon reference level when discussing gravitational energy. If you stretch a rubber band or bend a ruler, it can snap back when released. There’s energy in the deformed system because it can do work while snapping back. For instance, a stretched rubber band can do work in pulling your fingers together. This energy, resulting from the capacity of a deformed system to snap back, is called elastic energy (ElastE). A pot of hot water has more energy than does a pot of cold water of the same size. How do we know? Well, if the hot pot is boiling, it can rattle its lid, and this requires work, so boiling water has the capacity to do work. If the hot pot is below the boiling temperature, one way to get work from it would be to find another liquid that boils at a lower temperature and let the hot pot warm the other liquid to boiling so that this other liquid rattles its lid. This kind of energy that exhibits itself as warmth—as higher temperature—is called thermal energy (ThermE).3 It’s enlightening to look at thermal energy microscopically. As you know, temperature is associated with random microscopic motion, or thermal motion, that’s not visible macroscopically. For example, as water’s temperature rises, its molecules move faster, gaining kinetic energy. Thermal energy is this microscopic energy that cannot be directly observed macroscopically.4 To prevent confusion. I will reserve the term kinetic energy for macroscopic kinetic energy. Put one hand on a warm object and the other on a similar cool object. From a microscopic point of view, you are not really experiencing warmth and coolness, you

2

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4

Also known as “gravitational potential energy.” Some books define “potential energy” as energy resulting from a system’s position or configuration. Gravitational, elastic, and electromagnetic energy are all forms of potential energy. In the interest of brevity, we won’t use the word potential. More precisely, thermal energy (which is sometimes called “internal energy”) exhibits itself not only in a system’s temperature but also in its pressure and other so-called “thermodynamic variables.” More precisely, thermal energy includes all of the microscopic forms of energy that are not directly visible at the macroscopic level. It includes energy that results from the forces between molecules, a point that is important to understanding melting and other “phase transitions.”

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are only experiencing fast and slow molecules. Is that amazing or what? It amazes me. How could the mere motion of microscopic particles, that I can’t even see or feel individually, create the feeling of warmth in my hand? The idea of warmth has been replaced by, or “reduced to,” motion. In a way, the notion of warmth has vanished, a classic example of science’s reduction of a wide assortment of phenomena to a few basics. This reduction of sense impressions to the mechanical motion of atoms is precisely what Democritus was talking about when he proclaimed, “By convention hot is hot and cold is cold.... The objects of sense are supposed to be real—but in truth they are not. Only the atoms and the void are real.” Historically, thermal energy was confusing because it didn’t fit comfortably into the mechanical framework of Newtonian physics and because it is fundamentally different from the other energy forms. During the eighteenth and nineteenth centuries, Joule and others eventually demonstrated that what is experienced as warmth is in fact a form of energy. This was a key step in comprehending what energy really is. I’ll run quickly over the remaining four types of energy, returning to them in more depth later. The energy that results from electric and magnetic forces is called electromagnetic energy (ElectE), or sometimes simply “electric energy” or “magnetic energy.” There is energy in a light beam, as you can tell from the fact that light (sunlight, for instance) can warm things, and you can get work out of warm things. The energy carried by a light beam is one form of radiant energy (RadE). There are other forms of radiant energy, some of them familiar to you: radio, microwave, infrared, ultraviolet, X-ray, and gamma-ray energy. Chemical reactions can do work, as you can see from a wood fire used to boil water. This energy results from the molecular structure of the wood. The energy that results from a system’s molecular structure is called chemical energy (ChemE). Whereas chemical energy results from molecular structure, nuclear energy (NuclE) results from nuclear structure, from the way protons and neutrons are arranged into nuclei. One obtains nuclear energy from nuclear reactions, just as one obtains chemical energy from chemical reactions. CONCEPT CHECK 10 An operating lightbulb transforms ElectE into (a) KinE; (b) ElectE; (c) ThermE; (d) ChemE; (e) RadE. CONCEPT CHECK 11 In the operation of a hydroelectric power plant, the energy to generate the electricity can be traced to (a) GravE in the lake behind the plant’s dam; (b) ChemE in the lake behind the plant’s dam; (c) ThermE in the lake behind the plant’s dam;(d) RadE that comes from the sun; (e) ChemE that comes from the sun; (f) good vibes.

5 THE LAW OF ENERGY: ENERGY IS FOREVER You’ve seen that the gravitational energy lost during any portion of an object’s fall is exactly balanced by its kinetic energy gain, provided you neglect air resistance and observe the object only until just before it hits the floor. The object’s

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overall, or total, energy is conserved all the way down. Newton’s physics predicts this, and experiment confirms it. In fact, it’s possible to prove, still based on Newton’s laws, that any system that experiences only gravitational forces conserves its total energy, just as the falling object does. To a good approximation, our solar system is a system of this type that moves under the influence of gravity alone. It’s remarkable that there should be this rather abstract quantity, energy, that remains unchanged as the eight planets and their moons go through their complex motions. But far more remarkably, experiments show that the energy principle goes far beyond Newton’s physics. Energy is conserved in every physical process yet observed. We call this The Law of Conservation of Energy The total energy of all the participants in any process remains unchanged throughout that process. That is, energy cannot be created or destroyed. Energy can be transformed (changed from one form to another), and it can be transferred (moved from one place to another), but the total amount always stays the same.

This statement is as true as any general rule ever gets in science. It’s correct in every situation yet observed. It holds even when Newton’s physics is not remotely correct, such as near black holes, close to the speed of light, and for subatomic particles. It’s a useful principle, because once you have calculated or measured the total energy at one moment during some process, you automatically know it at any other moment without having to calculate or observe all the messy details of what happened between the two moments. For example, the number of joules of chemical energy consumed from a car’s fuel tank must equal the total number of joules appearing as the car’s kinetic and gravitational energy, exhausted thermal energy, chemical energy of pollutants, and so forth, during that time. The law of conservation of energy says that something, namely a system’s total capacity to do work, or its “total energy,” remains the same throughout any physical process. It’s similar to the law of conservation of momentum, which says that a system’s total motion through space or “total momentum” remains the same. You’ll encounter a third such conservation law: conservation of something called “net electric charge.” Another prominent conservation law, one that I won’t be discussing, states that any system’s total rotational motion or “total angular momentum” remains the same. And there are certain subatomic properties associated with microscopic interactions that are also conserved. Energy conservation is a kind of symmetry principle. Recall that a system has symmetry if it looks the same from various perspectives. Energy conservation says that a system’s energy remains the same no matter at what time you view it. In fact, all conservation principles can be traced to symmetries in nature. There’s a useful alternative way of stating conservation of energy. Whenever work is done, it’s done by some system on some other system. The system doing the work must lose some of its capacity to do work; in other words, it must lose energy. Since total energy is conserved, this energy cannot just vanish but must instead go

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into the system on which work is done. So work is an energy transfer from the system doing the work into the system having work done on it. I’ll call this The Work-Energy Principle Work is an energy transfer. Work reduces the energy of the system doing the work and increases the energy of the system on which work is done, both by an amount equal to the work done.5

How do we know that energy is conserved even in nuclear processes? Early in the twentieth century, nuclear physicists investigated a form of “radioactive decay” known as beta decay, a process in which a nucleus spontaneously creates an electron and spits it out of the nucleus. This alters the original nucleus. If energy is conserved, the nuclear energy of the original nucleus should equal the nuclear energy of the altered nucleus plus the energy of the ejected electron. But measurements showed that the energy was larger before than after! Being reluctant to conclude that energy was not conserved, physicists hypothesized that some undetected particle was also ejected along with the electron. It was thought that when this other particle’s energy was included, the energies would balance. Although the hypothesized particle had not been detected, it was thought that its energy could be directly measured by surrounding the nucleus with a large cylinder of lead. The unseen particle would surely be slowed down and stopped inside a sufficiently thick cylinder and so deposit its energy in the lead, causing a temperature rise in the lead. But there was no measurable temperature increase. Perhaps energy was not conserved in beta decay. This is where the matter stood from 1914 to 1930. By 1929, some physicists, such as Niels Bohr, were suggesting that energy conservation didn’t apply to the nucleus. But others didn’t accept this suggestion, and in 1930 Wolfgang Pauli hypothesized that the new particle was so penetrating that it could pass right through the thick lead without depositing any energy and that energy would be found to be conserved once the elusive particle was found. This set off a search for such a particle. Before long, physicists found other indirect evidence (other than beta decay), and they gave the hypothesized particle a name: “neutrino.” It was finally detected directly in 1956. Experiments showed that, as Pauli had predicted, energy was conserved once the neutrino was included in the balance.

It takes about 8 solid light-years of lead to stop half the neutrinos emitted in a typical nuclear decay. They move like “greased lightning” through matter.... If you make a fist, there are thousands of neutrinos flying through it right now, because the entire universe is filled with neutrinos.... Another proposal, made tongue-in-cheek, is for a neutrino bomb, a pacifist’s favorite weapon. Such a bomb would explode with a whimper and flood the target area with a high flux of neutrinos.... [T]he neutrinos would fly harmlessly through everything. Heinz Pagels, in The Cosmic Code

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x x

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CONCEPT CHECK 12 Farswell Slick (Figure 9) invites your investment in a business venture to manufacture his remarkable “supertranspropulsionizer.” His diagrams show a dazzling array of superconductors, lasers, liquid-helium coolants, and fancy computers. Slick informs you that this ultimate propulsion system will accelerate spaceships to nearly lightspeed for interstellar travel. Amazingly, no fuel supply is needed, either on board or outside the spaceship. The principle involved, he explains, is “bremsstrahlung superconduction” (BS). With BS, the device operates in a continuous cycle that both accelerates the spaceship and “feeds back” some of its laser light to maintain, for as long as may be desired, the operation of the transpropulsionizer itself. Should you invest?

Figure 9

“A remarkable device,” Farswell Slick remarks. Would you buy a supertranspropulsionizer from this man?

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There is another worklike process by which energy can be transferred, called “heating.” Heating is thermal energy transfer due to a temperature difference and can be thought of as microscopic work. When expanded to include not only ordinary work but also heating, the work–energy principle is called “the first law of thermodynamics.” We won’t need the first law of thermodynamics in what follows.

Conservation of Energy

6 TRANSFORMATIONS OF ENERGY Everything that happens can be described as an energy transformation. This section describes the energy transformations involved in some familiar processes. Once again, drop your book to the floor (it’s coming in for a lot of rough treatment in this chapter!). You’ve studied this process up until its impact with the floor. Where is the energy after impact? Conservation of energy says it can’t just vanish. Going through our eight forms of energy, there’s only one plausible candidate: thermal energy. The impact must warm the book or the floor. This temperature rise is hard to detect, but you can demonstrate the same effect by driving a nail into a board with a hard hammer blow. Feel the nail before and after the blow. Try several blows. We can summarize the energy transformations in the following way: GravE (at the top) : KinE (just before impact) : ThermE (after impact) Let’s add the effects of air resistance. Since air resistance slows the book, the falling book has less kinetic energy than it did before. But this energy is not lost— you can’t lose energy. It must be transformed into thermal energy. The air and book must warm a little as the book falls. Until the work of Joule and others around 1850, scientists had long believed that the work going into forces such as air resistance and friction, work that produces warming, was lost. Thus, it was believed that energy tended to decrease in most systems, rather than being conserved. The key to uncovering conservation of energy was discovering that warming represented an energy increase in a then-unknown form of energy, namely, thermal energy. How do we know that energy is conserved even when thermal energy is involved? I asserted above that air warms when you stir it with a falling object. James Prescott Joule (Figure 4) did an experiment like this in the 1840s, using water instead of air. He placed a paddle wheel in a tub of water, stirred the water with the paddle wheel, and measured the temperature rise in the water.6 He quantified the experiment by allowing a falling weight attached to a cord to turn the paddle wheel. The weight’s energy loss is then its weight multiplied by the distance fallen. Joule found that the water’s temperature rise was precisely proportional to the gravitational energy lost. This showed that the lost gravitational energy went directly into a temperature rise, in other words into thermal energy. Energy concepts were murky in Joule’s day because scientists didn’t understand that warmth (thermal energy) actually is a form of energy. Joule clarified matters by showing that work is precisely convertible to thermal energy. This breakthrough showed that the principle of energy conservation extends to processes involving thermal energy, a microscopic form of energy that lies outside of Newtonian physics.

Joule showed that a particular amount of work, about 4200 J, produces a 1°C rise in the temperature of 1 kilogram of water. This amount of energy is the dietitian’s Calorie.7 Although the Calorie is often used to measure thermal energy, Joule’s work showed that it is really a general energy unit, equivalent to 4200 joules.

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When you stir hot water in open air, the water cools because of evaporation. In Joule’s experiment the stirring occurred inside a closed container that prevented evaporation. The dietitian’s Calorie is always spelled with a capital C. Physicists use “calorie” (lowercase c) to denote the energy needed to raise 1 gram of water by 1°C.

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Conservation of Energy ThermE (air)

GravE Kin

E

ThermE (impact)

Figure 10

Energy flow diagram for a falling book, with air resistance. The “pipe” widths correspond to the amounts of energy involved in various parts of the process. Since energy is conserved, the pipe widths match up at each intersection.

Figure 11

What energy transformations occur when you briefly push a book and then let it slide?

ThermE (body) ChemE Ki

nE

ThermE (table and book)

Figure 12

Energy flow diagram for a book that is given a quick push and allowed to slide across a surface while coming to rest. The pushing process is very inefficient, with most of the initial chemical energy going into warming your body rather than into the book.

Back to the falling book (it’s remarkable what you can learn just by thinking carefully about a falling book): Just before impact, all the energy has been converted to kinetic energy of the book and thermal energy of the air and book. Since air resistance has only a small effect on the motion, thermal energy must form only a small fraction of the total. Finally, the impact converts the pre-impact kinetic energy to thermal energy of the floor and the book.8 As a helpful way to visualize energy transformations of all sorts, I’ll use energy flow diagrams. For example, Figure 10 shows the energy of the falling book transforming as though it were water flowing through pipes, beginning as gravitational energy, then transforming into kinetic energy and a little thermal energy of the air (note the smaller pipe), and finally transforming entirely to thermal energy. Since energy is conserved, the pipe widths match up at each intersection. Now give your book a quick hard push so that it slides across your tabletop, sliding to rest (Figure 11). Where does the energy come from for this process, and in what form is it? (...Time out, for thinking.) ... It comes from your body, in the form of chemical energy. Figure 12 shows the energy flow diagram for this process. Most of the initial chemical energy used to push the book turns into thermal energy in your body. The small amount that goes into the book then winds up as thermal energy produced while the book slides to rest. You might have noticed how frequently the various forms of energy transform into thermal energy. Energy transformations in animals provide many interesting examples. The energy that enables you to do useful work comes from foods and is stored in your body as chemical energy. Dietitians measure this stored chemical energy in Calories. For example, a 70 Calorie slice of bread gives you 70 Calories of stored chemical energy that can then provide 70 Calories of work and thermal energy. When animal chemical energy is used to do work, only a small fraction actually transforms into useful work. We say that such a process is “inefficient.” A “highly efficient” process, on the other hand, is one in which most of the initial, or “input,” energy is transformed into useful “output” energy and the wasted fraction is small. Quantitatively, the energy efficiency of any energy transformation is the fraction of the input that appears as useful output: useful output energy energy efficiency = total input energy It is usually expressed as a percentage. The energy efficiency of typical human muscular activities is only about 10%. Energy being one of this text’s four major themes, you will encounter many more energy transformations and energy flow diagrams in future texts. CONCEPT CHECK 13 The energy transformation during photosynthesis is (a) KinE : ThermE; (b) ThermE : KinE; (c) KinE : ChemE; (d) ElectE : ChemE; (e) RadE : ChemE; (f) ChemE : RadE.

8

156

And you can hear the impart. A small fraction of the energy is transformed into the energy of sound, a form of kinetic and elastic energy of the air.

Conservation of Energy

CONCEPT CHECK 14 While a wooden matchstick burns, the energy transformation is (a) ThermE : ElectE + RadE; (b) ElectE : ThermE + RadE; (c) KinE : ChemE + RadE; (d) ChemE : KinE + RadE; (e) ThermE : ChemE + RadE; (f) ChemE : ThermE + RadE. CONCEPT CHECK 15 Robin Hood shoots an arrow from his bow. Beginning just before he draws the bow, the energy transformation is (a) ChemE : ElastE : KinE; (b) ThermE : ElastE : KinE; (c) ElastE : ChemE : KinE; (d) ChemE : KinE : ElastE; (e) ElastE : KinE; (f) ThermE : ElastEly.

7 POWER: THE QUICKNESS OF ENERGY TRANSFORMATION What’s the difference between running and walking up a flight of stairs? Your gravitational energy increases by the same amount in both cases. So the work you do is the same. And yet your body knows there’s a difference between running and walking upstairs. The difference is that you do the work in less time when you run. There’s a word for this notion of how quickly work is done. It’s called power. Quantitatively, power is the work done per second—in other words, the work done divided by the time to do it: power =

work done time to do it

Because work is an energy transformation, power can be thought of as the rate of transforming energy. Suppose you run up one flight of stairs and then walk up a second, identical flight of stairs in twice the time it took to run up the first flight. You do the same work for each flight, but your power output during the first flight is double your power output during the second flight. The difference is a power difference, not an energy difference. The unit of power is the joule per second (J/s). It differs by an all-important “per second” from the unit of work or energy. Power is such a popular concept that its unit is given a special name. The joule per second is called the watt (W), in honor of the eighteenth-century developer of the steam engine, James Watt. The kilowatt (kW) is 1000 watts, and the megawatt (MW) is 1 million watts. Think of several everyday devices: automobile, lightbulb, electric blender, toaster, and so forth. These can be understood as energy transformers; they transform energy from one form to another form that you can use. An important feature is often the rate at which the energy is converted. For example, to get a certain lighting level from a lightbulb, the bulb must convert a certain number of joules per second to visible light. So lightbulbs and other devices must be rated in power units (watts) rather than energy units. A popular power unit for automobile engines and other heat engines is the horsepower, equal to about 750 watts. Table 1 gives the power transformed by typical household electrical appliances. The numbers give the power consumed only during the time that the appliance is turned on. Total electric energy consumption, perhaps over one day or over one year, often tells quite a different story. For example, one ordinarily uses a toaster for only a short time each day, so its daily energy consumption is low even though its 1200 W power consumption is high. And refrigerators, although their power consumption

157

Conservation of Energy MAKI NG ESTI MATES What’s your power output while running up a flight of stairs? If the energy efficiency of this process is 10%, what’s your (chemical) power input, in watts and in Calories/second?

can be as low as 300 W, are leading household energy consumers because they operate for so many hours every day. Although home energy use over the course of a year determines how much energy a power plant must deliver, energy use during so-called peak times has a special impact on the need for new plants. Each electric plant has a maximum power output, its power rating, usually one hundred or more megawatts. The plant’s actual power output is largest at times such as hot afternoons when many people are running air conditioners. If the power peak approaches the plant’s rating, the plant will cut its output by reducing the supply to all customers, causing lightbulbs and other appliances to dim in a “brownout.” Because industrial societies waste enormous amounts of energy, there are countless opportunities today for electric power companies to save customers’ money, enhance company profits, and protect the environment, all with no reduction in services, by finding ways to avoid building expensive new power plants. Pressures Table 1 Power consumption of household appliances while the appliance is turned on and consuming electric energy Power (W)

Appliance

Cooking range

12,000

Clothes dryer

5,000

Water heater

4,500

Air conditioner, window

1,600

Microwave oven

1,400

Dishwasher (incl. hot water)

1,200

Toaster

1,200

Hair dryer

1,000

Refrigerator, frostless

600

Refrigerator, not frostless

300

TV, color

350

Stereo set

100

SOLUTION TO MAKING ESTIMATES Suppose that you weigh 500 newtons (110 pounds), the vertical height of one flight of stairs is 4 meters (measure it!), and you run up one flight in 5 seconds (try it!). The work done to lift yourself and the power output are

work = weight * height = 500 N * 4 m = 2000 J power = work , time = 2000 J , 5 s = 400 W This is a large power output for a human being, as you will discover if you do the experiment. To produce this output at 10% efficiency, you must convert chemical energy at a rate of 4000 W, or 4000 J/s. In Cal>s (1 Cal = 4200 J), this is 4000>4200 L 0.95 Cal>s, your metabolic rate in this example. If you could maintain this rate for an hour (3600 s), you would “burn up” (transform) 3600 * 0.95 = 3400 Calories, the energy content of a big steak.

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Conservation of Energy

for new plants arise when existing plants can no longer provide the electricity needed during periods of peak demand. Energy-efficient devices can provide the same services (the same amount of light, for example) with less energy. Because such efficiency measures are usually far cheaper than the cost of building new plants, many power companies are actively seeking and providing new energyefficiency opportunities. For example, because it’s usually far cheaper to warm a house with additional insulation than with additional electricity, many power companies provide services and low-cost loans to encourage customers to insulate their homes. Everybody wins: the customer, who gets a warmer home cheaper; the power company, for which the insulation is cheaper than a new plant; and the environment, which benefits from reduced resource consumption and less pollution. Pricing is another way to reduce the need for new power plants. If electric companies charge higher rates at peak power times, balanced by reduced rates during offpeak periods, people have an incentive to switch their power use from peak to off-peak times. This reduces the need for new power plants, and the resulting financial savings can reduce customers’ electrical bills while increasing company profits. The most useful energy unit for measuring your home’s electric energy consumption is the kilowatt-hour, the amount of energy transformed when a power of 1 kilowatt operates for 1 hour. Since 1 kilowatt is 1000 joules/second and 1 hour is 3600 seconds, 1 kilowatt-hour = 1000 J>s * 3600 s = 3.6 * 106 J If a known power in kilowatts operates for a known number of hours, it’s easy to figure the number of kilowatt-hours of energy consumed: Just multiply the number of kilowatts by the number of hours. Electricity costs about 10 cents per kilowatt-hour. That sounds pretty cheap for 3,600,000 joules. How cheap? For instance, how far could 3,600,000 joules lift a 1000 newton (225 pound) person? Since the work done in lifting an object is the object’s weight times the distance through which it’s raised, the 3,600,000 J must equal 1000 N times the distance. So the distance is 3,600,000 J divided by 1000 N, or 3600 meters—nearly 12,000 feet! That’s a lot of lifting for just a dime. Electricity is phenomenally cheap, and we use a lot of it. The average U.S. household consumes about 1.4 kilowatt-hours of electric energy every hour! Society’s use of energy is a crucial topic today for many reasons, including global warming, pollution, national security, declining energy resources, nuclear power issues, and environmental destruction. CONCEPT CHECK 16 You press a 500 N weight from your shoulders up to arms’ length, a distance of 0.8 m, during a period of 2 seconds. How much work did you do? (a) 800 W. (b) 800 J. (c) 400 W. (d) 400 J. (e) 200 W. (f) 200 J. CONCEPT CHECK 17 In the preceding question, your power output is (a) 800 W; (b) 800 J; (c) 400 W; (d) 400 J; (e) 200 W; (f) 200 J.

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© Sidney Harris, used with permission.

Conservation of Energy

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Conservation of Energy Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions 1. What type of energy technology fueled the Industrial Revolution? 2. What is a fossil fuel? Name three kinds.

WORK 3. Is work done whenever a force is exerted? Explain. 4. Is work done whenever an object moves through a distance? Explain. 5. To what two quantities is work proportional? 6. You slowly lift a 3 N grapefruit by 2 m. How much work did you do and on what object? 7. A 3 N grapefruit falls 2 m to the floor. Was work done during the fall? By what object on what other object?

19. An apple in a tree has 90 J of gravitational energy (relative to the ground). It falls. If you neglect air resistance, what can you say about the amount of kinetic energy the apple has just before it hits the ground? What if you do not neglect air resistance?

POWER 20. Explain the difference between energy and power. 21. Choose the correct answer(s): The (watt, newton per second, joule, calorie, joule per second, meter per second, horsepower, kilowatt-hour) is a unit of power. Which are units of energy? 22. You lift a 2 N rock by 4 m in 3 s. What is your work output? Your power output? 23. Which do you pay for in your monthly electric bill, energy or power?

ENERGY 8. 9. 10. 11.

Explain the difference between energy and work. List eight physical types of energy. Explain thermal energy from a microscopic point of view. Give one example of each of these energy forms: elastic, thermal, chemical, kinetic, radiant, gravitational. 12. If you double the speed, how is the kinetic energy affected? If you double the height, how is the gravitational energy affected? 13. Choose the correct answer(s): One joule is the same as one (watt-meter, newton-meter, meter per second squared, newton-second, kilowatt-hour).

THE LAW OF ENERGY AND ENERGY TRANSFORMATIONS 14. Has the law of conservation of energy been found to be correct in all situations observed so far? Is the same true of Newton’s laws? Explain. 15. Choose the correct answer(s): For a system that returns to its initial state, during one complete cycle you can’t get more (acceleration, force, energy, power, speed) out of the system than was put in. 16. What energy transformations occur when this book falls to the floor? When you lift this book? 17. Give an example of each of these energy transformations: kinetic energy : thermal energy, kinetic energy : elastic energy, elastic energy : kinetic energy. 18. What do we mean when we say that the energy efficiency of a lightbulb is 10%?

Conceptual Exercises WORK 1. Does Earth do gravitational work on you as you walk downstairs? 2. In order for you to get out of bed with the least amount of work, would it be better for your bed to be on the floor or about a meter high? Explain. 3. Describe some work you could do that would produce elastic energy. Repeat for gravitational energy. For kinetic energy. 4. Describe some work you could do that would produce thermal energy. 5. Your left hand lifts a 2 N apple by 1.5 m, and your right hand lifts a 4 N grapefruit by 0.5 m. Which hand did the most work? Which hand exerted the largest force? 6. MAKING ESTIMATES About how much work would it take to lift the U.S. population by 1 km?

ENERGY 7. Which of the eight physical types of energy was the basis for the earliest human culture? Which was the basis for the industrial revolution? Which other types might have been used by early cultures, and which other types are used today? 8. Name the type of energy possessed by each of the following: Jill at rest at the top of a sliding board, Jill sliding off the bottom of the sliding board, sunlight, coal, hot air.

From Chapter 6 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Conservation of Energy: Problem Set 9. Name the main type of energy possessed by each of the following: dynamite, water at rest behind a high dam, a bow about to release an arrow, a wooden match, food. 10. Name the type of energy possessed by each of the following: a raised book, gasoline, a stretched spring, sunlight, a speeding train, hot steam. 11. Does your body contain any kinetic energy when you are sitting still? Explain. 12. Give an example of a system that has both kinetic and gravitational energy. 13. A rubber ball is thrown upward and bounced off a ceiling. What kinds of energy does it have at its highest point (when it hits the ceiling)? 14. Name two kinds of energy that are produced as a result of a typical explosion, such as exploding dynamite. What kind of energy is used (or transformed)? 15. You lift a brick and put it on top of a wall. What quantities could you measure in order to determine how much work you did? 16. You throw a baseball. What quantities could you measure in order to determine how much work you did during the throw? 17. Explain, in microscopic terms, why the air pressure inside a tire increases on a hot day. If the air in a balloon is warmed, will the balloon expand or contract? Why? 18. (a) Where would an apple have greater gravitational energy, at 100 km high or at 1000 km high? (b) Would the gravitational energy of an orbiting satellite be increased or decreased by moving it from an orbit that is 6000 km high up to an orbit that is 12,000 km high (see Figure 13)? (c) At which point, 6000 km high or 12,000 km high, does a satellite have the larger gravitational force on it?

6000 km Before

12,000 km After

THE LAW OF ENERGY AND ENERGY TRANSFORMATIONS 23. Give an example in which kinetic energy transforms into gravitational energy. 24. Give an example in which kinetic energy transforms into thermal energy. 25. Give an example in which chemical energy transforms into kinetic energy. 26. What is the main energy transformation (input and useful output) when an automobile speeds up? When a bicycle speeds up? 27. Neglecting air resistance, does the energy of a falling rock increase, decrease, or remain the same? What happens to its kinetic energy? Its gravitational energy? 28. Including air resistance, does the energy of a falling rock increase, decrease, or remain the same? What happens to its kinetic energy? Its thermal energy? 29. What is the main energy transformation (input and useful output) in the operation of an electric blender? A toaster? A lightbulb? 30. You squeeze an elastic spring and clamp it in the squeezed position. You then drop the clamped spring into acid, dissolving the spring. What happened to its elastic energy? 31. What energy transformation occurs when you climb a rope? 32. You throw a baseball horizontally, and Jill catches it. Neglect air resistance. Describe the energy transformation that occurs (a) during the throw (while the ball is in your hand) and (b) during the catch. 33. You throw a ball upward and then catch it at the same height. How does the ball’s final speed compare with its initial speed, (a) neglecting air resistance and (b) including air resistance? Defend your answers. 34. Does an automobile use more gasoline when its lights are on? When the air conditioner is on? (Note: The battery does not run these devices while the engine is running.) Defend your answer. 35. Imagine a 100% efficient automobile. Would it emit any exhaust? Would its engine be hot? 36. Figure 14 is a graph of a roller coaster’s height above the ground versus the length of track it covers. The coaster is powered up to its high point at 100 m from the starting point. From the high point, the coaster coasts freely all the way to the end. Assume that the coaster starts from rest at the high point and encounters no friction or air resistance. Between 200 m and the finish, where is it moving slowest? Fastest?

What happens to the gravitational energy of the satellite when it is moved to a higher orbit?

19. If you triple your altitude above the ground, how is your gravitational energy (relative to the ground) affected? 20. If you halve your altitude, how is your gravitational energy (relative to the ground) affected? 21. If you triple your speed, how is your kinetic energy affected? 22. If you halve your speed, how is your kinetic energy affected?

Elevation, meters

Figure 13 40 30 20 10 0

0

200

400 600 800 Track distance, meters

Figure 14

Elevation versus track distance for a roller coaster.

162

1000

1200

Conservation of Energy: Problem Set 37. Referring to the preceding exercise, is the roller coaster moving faster at 1000 m or at 1100 m? Describe how the coaster’s speed changes during the last 300 m (900 m to the end).

POWER 38. You start a bowling ball rolling by swinging it with your arm and releasing it. Then you start a second identical bowling ball rolling, at the same speed as the first, by hitting it sharply with a sledge hammer. Which process, the arm swing or the hammer blow, imparts more kinetic energy to the ball? Which process has the greater power output? 39. You lift bricks, one at a time, onto a table. After a while, you begin to lift bricks slower and slower. As you slow down, does the energy you put into lifting each brick increase, decrease, or remain the same? What about the power you put into lifting each brick? 40. What other unit(s) could automobile engines be rated in, instead of horsepower? 41. Why are electricity rates often higher in summer than in winter? 42. Which process has the largest power output: 2 J of work performed in 0.1 s, or 1000 J of work performed in an hour? Which has the largest energy output? 43. An automobile travels 60 km in 50 minutes, doing 30 × 106 J of work against outside forces (air resistance and rolling resistance) in the process. What is the automobile’s average power output in watts? 44. Referring to the previous question, if the auto’s energy efficiency is 10%, what is its power input (its rate of converting the gasoline’s chemical energy into other forms) in watts? How many 100 W lightbulbs could this light up? 45. A cyclist delivers 150 W of power to her bicycle, while her metabolic rate is 1000 W. What is her body’s bicycling energy efficiency? 46. How much does it cost to run a nonfrostless refrigerator for a month? Use Table 1. Assume the refrigerator consumes

power for 8 hours each day, and the electricity costs 10¢ per kilowatt-hour. What if it is frostless? 47. If one load takes 30 minutes to dry in an electric dryer and you dry 16 loads per month, how much does one month’s drying cost at 10¢ per kilowatt-hour? 48. A clothes dryer is equivalent to how many 100 W lightbulbs? Use Table 1. 49. MAKING ESTIMATES Use Table 1 to estimate the number of kilowatt-hours of electric energy a typical single-family home consumes in one month. Don’t forget lightbulbs (they aren’t in Table 1).

Problems WORK 1. Your gasoline engine has a limited supply of gasoline, able to do 5000 J of work. If you weigh 800 N, how high can this engine lift you? 2. A jumbo jet has four engines, each having a thrust of 30,000 N. How much work do the engines do during a 1500 m takeoff run? 3. If you do 20 J of work lifting a rock weighing 30 N, how far will you lift it? 4. If an airplane does 40 million joules of work during a takeoff run that is 1000 m long, what must be the total thrust of its engines?

ENERGY 5. You slam on your automobile brakes, sliding 40 feet with locked brakes. How much farther would you slide if you had been moving twice as fast? 6. You slam on your automobile brakes, sliding 40 feet with locked brakes. About how far would you have slid if you had been moving half as fast?

Table 1 Power consumption of household appliances while the appliance is turned on and consuming electric energy Appliance

Power (W)

Cooking range

12,000

Clothes dryer

5,000

Water heater

4,500

Air conditioner, window

1,600

Microwave oven

1,400

Dishwasher (incl. hot water)

1,200

Toaster

1,200

Hair dryer

1,000

Refrigerator, frostless

600

Refrigerator, not frostless

300

TV, color

350

Stereo set

100

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Conservation of Energy: Problem Set 7. Ned the skydiver weighs 600 N and is falling at terminal speed. That is, he has sped up until air resistance has built up so much that he has reached a final unchanging speed. How much work does Ned do on the air as he falls through 200 m at this terminal speed? 8. In the preceding question, into what type of energy does this work go? From what type of energy did it come? 9. How much more gravitational energy (relative to the water’s surface) does a diver have when she stands 7 m above the water, as compared with when she stands 2 m above the water? 10. How much more kinetic energy does a runner have when dashing at 7 m/s as compared with jogging at 2 m/s? 11. MAKING ESTIMATES Estimate the energy (relative to the water) of you standing on a high diving board, 3 m above the water. 12. MAKING ESTIMATES Estimate your jogging speed, in m/s (Hint: 1 mile = 8/5 km), and then estimate the kinetic energy (in joules) of you jogging. 13. Use your answer to the preceding question to estimate the kinetic energy of you walking, assuming that your walking speed is half of your jogging speed.

Answers to Concept Checks

THE LAW OF ENERGY AND ENERGY TRANSFORMATIONS

10. 11.

14. Jack, who has a mass of 30 kg and weighs 300 newtons, sits in a child’s swing. You pull the swing back so that it is 2 m above its low point, and release it. What form of energy, and how much energy, does Jack have when he is pulled back and held at rest? 15. In the preceding question, what form of energy, and how much energy, does Jack have as he swings through the low point (neglect air resistance and friction in the moving parts)? How fast is Jack moving at this point? 16. In a crash test, a 1000 kg automobile moving at 10 m/s crashes into a brick wall. How much energy goes into demolishing and warming the wall and the auto? 17. Referring to the previous question, from how high a cliff would the automobile need to fall in order to sustain the same amount of damage upon hitting the ground? (Note: A 1000 kg automobile weighs (on Earth) about 10,000 N.)

POWER 18. You do a pullup, lifting yourself by 0.5 m in 2 s. If your weight is 600 N, how much work did you do, and what was your power output during lifting? 19. How much energy does a 75 W lightbulb use while running for 30 minutes? 20. How long must a 100 W lightbulb run in order to use a million joules of electrical energy? 21. Find the power output of a 60 kg runner who accelerates from 0 to 10 m/s in 2 s. 22. Compare the amount of metabolic energy used by a typical person in running up a flight of stairs to the energy required to light a 100 watt bulb for 1 minute.

164

1. (a) 2. Neither Jed nor Ned is moving the wall, so the work done is

3. 4. 5. 6. 7. 8. 9.

12.

13. 14. 15. 16. 17.

zero, (c). However, at the microscopic level, Ned’s muscles do work on one another. This microscopic work is done only within Ned’s body. It causes Ned to sweat, but does not result in any work being done on the wall. (d) Except for starting and stopping the book, it moves at unchanging velocity (zero acceleration), so the net force is zero, (a). (b) (b) (e) (c) Its height above the floor is now zero, so there is no gravitational energy. Conservation of energy tells us that the total energy is still 120 J, so this must be the amount of kinetic energy (since no other kind of energy is produced during the fall), (b). (c) and (e) The high water level in the lake creates the water pressure that presses water through the turbines, (a). This water level can be further traced back to the evaporation of water that lifted it so that it could fall as rain. The sun’s radiation caused this evaporation, (d). Don’t invest. And don’t bother investigating his design. BS violates conservation of energy. Work must be done by the transpropulsionizer to accelerate the spaceship, so the device puts out energy. Conservation of energy then tells us that the device must also consume energy, so it needs a consumable fuel supply. You can’t get something for nothing. (e) (f) (a) work = force * distance = 500 N * 0.8 m = 400 J, (d). power = work>time = 400 J>2 s = 200 W, (e).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Yes, because Earth exerts a downward force on you as you walk downward. 3. Examples: Stretch a rubber band, lift a rock, throw a baseball. 5. Left hand does 2 * 1.5 = 3 joules of work, right hand does 4 * 0.5 = 2 joules of work. So the left hand does the most work, although the right hand exerts the largest force. 7. Possible energy forms used by early cultures: chemical (food), thermal (fire), gravitational (falling water), elastic (bow and arrow), radiant (warmth from sun). Used today: all of the eight types discussed in Section 4, prominently including chemical (fossil fuels). 9. Chemical, gravitational, elastic, chemical, chemical.

Conservation of Energy: Problem Set 11. Yes, it contains the kinetic energy of moving blood, a beating 13. 15. 17.

19. 21. 23. 25. 27. 29. 31. 33.

35. 37.

39. 41.

43. 45.

heart, moving lungs, etc. Elastic and gravitational (but not kinetic). The weight of the brick and the distance to the top of the wall. The air inside gets hotter, so the molecules move faster and hit the inside wall of the tire harder, so the pressure against the inside wall is larger. The balloon will expand because of the increased air pressure inside the balloon. Tripled, because gravitational energy is proportional to height. Multiplied by 9, because kinetic energy is proportional to the square of the speed. One example: A ball moving upward after being thrown upword. Examples: A bomb exploding, the operation of a gasolinefueled vehicle. It remains the same; its kinetic energy increases; its gravitational energy decreases. Electric to kinetic; electric to thermal; electric to radiant. Chemical energy (of human body) to gravitational energy. (a) The speed would have to be the same, since the ball’s energy has not changed. (b) The speed would have to be less, since the ball lost some of its energy in warming the surrounding air. No, it would not emit exhaust, and its engine would not be hot because no energy would go into heating anything. Faster at 1000 m, because its elevation is lower. During the last 300 meters: It speeds up and then slows down from 900 to 1000 m, it speeds up then slows down between 1000 to 1100 m, and it speeds up then slows down then travels a short distance at constant speed between 1100 to 1200 m. The energy remains the same; the power decreases. Because everybody runs their air conditioner in the summer, there is a larger total load on electric plants, so the electric company charges more in order to hold the load down (and also in order to pay for higher-cost “peaking power” that might need to be added). Fifty minutes is 3000 seconds. So the power output is 30 * 106 J>3000 s = 10,000 W. 150>1000 = 15%.

47. 5 kW * 8 hr = 40 kW # h

40 kW # h * $0.10>kW # h = $4

49. To answer this, perform a calculation similar to Exercise 47

for each appliance used in your home, getting the number of kW # h of electric energy consumed by each appliance during one month. Then add up all of the appliances. Problems 1. W = Fd. Solving for d, d = W>F = 5000 J>800 N = 6.25 m. 3. W = Fd. Solving for d, d = W>F = 20 J>30 N = 0.667 m. 5. At twice the speed, you would slide four times as far. Here’s why: Your car has four times as much kinetic energy, so it will do four times as much work in coming to rest, thus it must exert its sliding frictional force over four times as much distance (remember W = Fd) in coming to rest. 7. The force of air resistance on Ned must be 600 N, in order to maintain his unchanging speed. So the force by Ned on the air must be 600 N (law of force pairs). Thus, W = Fd = 600 N * 200 m = 120,000 J. 9. Since GravE is proportional to height, she has 7/2 (3.5) times as much. 11. My weight is about 160 pounds, or about 700 N. At 3 m high, my gravitational energy is wt * height = 700 N * 3 m = 2100 J. 13. At half the speed, you have 1/4th as much kinetic energy. So the preceding answer is divided by four. 15. All 600 J of the original gravitational energy is now kinetic energy. KinE = (1>2)ms2. Solving for s, s = 2(2 * KinE>m) = 2(2 * 600 J>30 kg) = 240 = 6.32 m>s. 17. The initial energy should be the same as the result found in the preceding question, namely 50,000 J. GravE = wt * ht. Solving for ht, ht = GravE>wt = 50,000 J>10,000 N = 5 m. 19. P = W>t. Solving for W, W = Pt = 75 W * (30 * 60 s) = 135,000 J. 21. Assume that all the work goes into speeding up the runner (i.e., into kinetic energy). KinE = (1>2)ms2 = (1>2) 60 kg * (10 m>s)2 = 3000 J P = W>t = 3000 J>2 s = 1500 W.

165

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Second Law of Thermodynamics

From Chapter 7 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

167

Second Law of Thermodynamics —And You Can’t Even Break Even

Many times I have been present at gatherings of people who . . . are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: “Have you read a work of Shakespeare’s?” C.P. Snow, British Scientist and Author

Y

ou might have noticed that the energy going into many processes eventually turns into thermal energy. This tendency of nonthermal forms of energy to end up as thermal energy is an important general feature of the universe, known as the second law of thermodynamics or “second law” for short. It’s our focus in this chapter. The big breakthrough in understanding energy was the discovery that “heat” (thermal energy) is a form of energy, in other words that thermal energy can do work, just like other forms of energy. This breakthrough showed the validity of the law of conservation of energy even in processes involving thermal energy. Because of the central role of thermal energy in understanding the general principles of energy, the study of energy is called thermodynamics, and a reformulated version of the law of conservation of energy is often called the first law of thermodynamics. These laws of thermodynamics have no known exceptions and are among the most general scientific principles known. There are three different ways of stating the second law. In its most straightforward form, it is a familiar observation about thermal energy flow (Section 1). Like many common observations, it has profound consequences. Section 2 discusses one of these, namely, another form of the second law that highlights the special nature of thermal energy. Unlike other energy forms, thermal energy can be transformed into other forms only with limited efficiency. This leads to discussion of a socially significant device: the heat engine (Sections 2 and 3). Section 4 presents the third way of stating the second law, known as the law of increasing entropy. Its intriguing philosophical implications include the direction of time, the ultimate fate of the universe, and why there is a second law of thermodynamics. Sections 5, 6, and 7 study the physics and social implications of two significant heat engines: the automobile and the steam–electric power plant. Because these topics bring up energy resource issues, it’s natural at this point to discuss exponential growth and its implications for resource depletion (Section 8).

168

Second Law of Thermodynamics

1 HEATING Touch a piece of ice (Figure 1). Energywise, what happens? Since your hand cools and the ice begins to melt, thermal energy must have flowed from your hand to the ice. Now touch a hot cup of coffee (Figure 2). Your hand warms while the coffee cools, so thermal energy must have flowed from the cup to your hand. Notice that in each case, thermal energy flowed from the high-temperature object to the low-temperature object. There is a general principle operating here, a principle that you experience whenever you touch an object that feels hot or cold: Thermal energy flows spontaneously (without external assistance) from hot to cold. Any such flow of thermal energy from a higher to a lower temperature is called heating. Heating is a one-way affair: Thermal energy flows spontaneously from higher to lower temperature, but not from lower to higher temperature. Like a lot of simple ideas, this one-wayness of heating has profound consequences. It’s one way of stating the second law of thermodynamics: The Second Law of Thermodynamics, Stated as the Law of Heating Thermal energy flows spontaneously from higher to lower temperature, but not from lower to higher temperature.

Higher temperature Low temperature Thermalenergy flow

Figure 1

When you touch a piece of ice, thermal energy flows from your higher-temperature hand to the lower-temperature ice, so the ice gets warmer and your finger gets colder.

Lower temperature

High temperature

Now we need to be more quantitative. Temperature is a quantitative measure of warmth. An object’s temperature is related to the microscopic motion of its molecules. Most materials expand as they warm, because more rapidly moving molecules take up more space than slow-moving molecules, for the same reason that jitterbugging couples need more space on a dance floor than slow-dancing couples. So it’s not surprising that most materials expand as they warm. Such an expansion can be used as the basis for a temperature-measuring device, or thermometer. One choice is liquid mercury, which expands inside a glass tube. The standard (metric) temperature unit is the degree Celsius (°C). The Celsius scale assigns 0°C and 100°C to the freezing and boiling points of water. The United States still uses the antiquated Fahrenheit scale, where water freezes at 32 and boils at 212 (Figure 3). Temperature and thermal energy are related but different. For instance, a cool lake contains far more thermal energy than does a hot cup of coffee, even though the lake has a lower temperature, because the lake is so much larger. A single cup of lake water has less thermal energy than a hot cup of coffee.

Thermalenergy flow

Figure 2

When you touch a hot cup of coffee, thermal energy flows from the high-temperature cup to your lower-temperature hand, so your finger gets warmer and the coffee cup cools.

CONCEPT CHECK 1 The temperature of a nice day is about (a) 10°C; (b) 75°C; (c) 40°C; (d) 55°C; (e) 25°C. (Hint: See Figure 3.) CONCEPT CHECK 2 Suppose you grasped a cold doorknob and found, surprisingly, that this warmed your hand and further cooled the doorknob. This would violate (a) conservation of energy; (b) the second law of thermodynamics; (c) both conservation of energy and the second law; (d) neither conservation of energy nor the second law although it would violate other physical laws; (e) no known physical laws.

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Second Law of Thermodynamics C

F

2 HEAT ENGINES: USING THERMAL ENERGY TO DO WORK

100 200

150 50 100

50 0

0

Drop a book on the floor. Slide it across a table. Smack it with your hand. Imagine tearing out a page and burning it up. Thermal energy is created during each of these processes! Creating thermal energy is easy—almost inevitable. What about processes or devices that convert thermal energy to other forms? Can you think of any? ———(Keep thinking.) One example is an automobile engine, which operates in regular, repeated cycles to use the thermal energy from burning gasoline to do work. Another would be a steam engine, which operates in repeated cycles to use hot steam to do work. Any such cyclic device that uses thermal energy to do work is called a heat engine.1 Most heat engines, for example the automobile engine, are based on the expansion of a gas when it’s heated. The expanding gas pushes against a movable surface, the “piston,” that causes a car or other device to move. One significant feature of an automobile engine is that, in addition to doing work, it ejects lots of unused thermal energy through its radiator and its tailpipe. So not all the thermal energy created in the engine is actually used to do work. This turns out to be true for every heat engine. A heat engine’s ejected thermal energy is called its exhaust. So the energy transformation for any heat engine is ThermE (input) ¡ Work (which could then produce any form of energy) + ThermE (exhaust)

Figure 3

The Celsius and Fahrenheit scales compared.

Heat engine Work output

See Figure 4. The energy efficiency of any device is its useful energy output divided by the total energy put into the device. Since we usually consider the work done by a heat engine to be “useful” and the exhaust to be “not useful,” the energy efficiency of any heat engine is energy efficiency =

ThermE input ThermE exhaust

Figure 4

Energy flow for a heat engine. Heat engines consume thermal energy and turn part of it into work, which could then produce any from of energy.

work output thermal energy input

As you can see from Figure 4, the energy efficiency of any heat engine must be less than 1, in other words less than 100%. This fact, that you cannot entirely consume (or use) thermal energy but must always have some left over as exhaust, has been found to be true every time anybody has checked. It is, in other words, a fundamental principle of nature. But as we will see, it turns out not to be another new principle of nature. It has a one-way quality about it that’s reminiscent of the law of heating. Perhaps it’s not surprising, then, that it turns out to be the second law of thermodynamics, only put into new words. I’ll call it The Second Law of Thermodynamics, Stated as the Law of Heat Engines Any cyclic process that uses thermal energy to do work must also have a thermal energy exhaust. In other words, heat engines are always less than 100% efficient at using thermal energy to do work.

1

170

Some noncyclic devices use thermal energy to do work. For example, a hot air balloon uses heated air to lift a balloon. I won’t call such devices heat engines.

Second Law of Thermodynamics

How do we know that no heat engine can be 100% efficient? One reason we accept the law of heat engines is that if it were not true, then it would be possible to make thermal energy flow from cold to hot, in violation of the law of heating. The following argument shows this by using an imagined “thought experiment”—a type of argument used frequently in science. Let’s temporarily suppose that (in violation of the law of heat engines) there is a heat engine that can convert thermal energy entirely to work. We could then use that heat engine to extract thermal energy from, say, a pot of warm water and convert this energy entirely to work. This work could then produce thermal energy (by frictional heating of a piece of metal, for example) at a higher temperature. The net result would be to transfer all of the thermal energy from a lower to a higher temperature, without any other change taking place. But this is exactly what the law of heating says we cannot do. In other words, any violation of the law of heat engines would imply that the law of heating can be violated. But we know directly from experiment that the law of heating cannot be violated. So it follows that the law of heat engines cannot be violated either.

2

3

High-temperature object

Heat engine

Thermal energy flow

Heat engines depend on the spontaneous flow of thermal energy from hot to cold. In fact, a heat engine may be described as a device that makes practical use of the natural hot-to-cold flow of thermal energy by shunting aside some of the flowing thermal energy to do work (Figure 5). Since heat engines are driven by thermal energy flowing from hot to cold, you must have a temperature difference before you can have a heat engine. The ocean, for example, contains a lot of thermal energy, but you can’t use it to do work unless you have a colder system into which the ocean’s thermal energy can flow.2 Heat engines always operate between two systems with different temperatures, as Figure 5 shows. How energy efficient can the very best heat engine be? It’s an important question, because most of the world’s energy passes through heat engines, mainly transportation vehicles and steam–electric power plants. Since a heat engine operates because of thermal energy flowing from hot to cold, we expect its energy efficiency to be influenced by both its hot input temperature at which thermal energy is put into the engine and its cooler exhaust temperature. Since temperature differences drive heat engines, we expect a higher efficiency for larger temperature differences between input and exhaust. Nineteenth-century physicists found a quantitative formula that predicts the best possible efficiency of a heat engine operating at any predetermined input and exhaust temperatures.3 As examples, Table 1 lists the best possible efficiencies predicted for several specific types of heat engines, along with the actual efficiencies obtained by these heat engines in practice. Table 1 shows how important the second law is to society. It says that, for practical heat engines, conversion efficiencies of thermal energy into other forms are only 60% even in the best, or “perfect,” case. Friction and other imperfections reduce this further, so that less than half the thermal energy fed into these heat engines goes into work. But it’s important, in these energy-conscious times, to note that the remaining thermal energy, the exhaust, needn’t be wasted. There’s a myriad of direct heating uses for this lower-temperature thermal energy. This dual use of thermal energy to simultaneously produce both work (usually in the form of electricity generation as

Work

Low-temperature object

Figure 5

Heat engines use a portion of the thermal energy that flows naturally from a high to a low temperature and convert it to work.

This means that temperature differences between different depths of ocean water could be used to run a heat engine. Here’s the formula: efficiency = (Tin - Tex)>Tin. In this formula, the temperatures must be measured in degrees Kelvin (K), a new temperature scale. The temperature in K is found by adding 273 to the temperature in °C. A temperature of 0 K (equal to −273°C) is known as absolute zero, because it is the lowest possible temperature—the temperature at which all microscopic motion is at its absolute minimum.

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Second Law of Thermodynamics Table 1 Heat engine efficiencies. Typical temperatures, best possible efficiencies, and actual efficiencies. Efficiency (%) Tin(°C)

Tex(°C)

Best possible

Actual

Gasoline automobile/truck

700

340

37

20

Diesel auto/truck/locomotive

900

340

48

30

Steam locomotive

180

100

20

10

Fossil fuel

550

40

60

40

Nuclear fuel

350

40

50

35

Solar powered

225

40

40

30

25

5

7

???

Engine type

Transportation

Steam-electric power plants

Ocean-thermal (solar)

described in Section 7) and useful heat is called co-generation. It can save society enormous amounts of fossil fuel and other energy resources. For example, many European, and a few American, communities locate electric power plants near large residential neighborhoods and use the plants’ “waste” thermal energy to heat their homes, saving enormous amounts of natural gas or electricity that would otherwise be used for home heating. Communities are beginning to install smaller electrical generation systems, running perhaps on burning trash from a housing development, and piping the “waste” thermal energy to the houses for home heating. Given the expense of transmitting and distributing electricity over large areas, there’s a lot to be said for such small, local electrical generation facilities. U.S. law allows co-generators at such community facilities to sell their excess electricity to electrical power companies at reasonable prices. For another example, steam heating plants at universities and other institutions often produce such high steam temperatures that the steam can be used to generate electricity at reasonable efficiencies. The “waste” thermal energy from electricity generation is then used to heat the university. Universities can often generate a significant fraction of their electricity consumption in this fashion, saving energy resources while getting electricity and heating for roughly the operating costs of the heating alone. If your college or university isn’t doing this, maybe it should. Table 1 shows the importance of “burning hot” and “exhausting cool.” For example, fossil, nuclear, and solar generating plants have progressively lower input temperatures. As you can see, efficiencies decline as the difference between Tin and Tex declines. Ocean-thermal generation of electric power uses some of the ocean’s thermal energy by exploiting temperature differences between different ocean depths. In the tropics, the ocean’s temperature drops from 25°C at the surface to 5°C at 300 m down. This small temperature difference could be used to run a heat engine with an efficiency of 7%. Because the energy resource would be free—sunlight falling on the ocean—the low energy efficiency would be of little concern. CONCEPT CHECK 3 Assuming that the energy flows in Figure 5 are proportional to the width of each “pipe,” this engine’s efficiency is closest to (a) 1/3; (b) 1/2; (c) 1/10; (d) 2/3; (e) 1; (f) 2.

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Second Law of Thermodynamics

CONCEPT CHECK 4 An engine that consumes 400 J of thermal energy while exhausting 300 J has an efficiency of (a) 133%; (b) 100%; (c) 75%; (d) 66%; (e) 33%; (f) 25%. CONCEPT CHECK 5 A typical large coal-fired electric-generating plant burns about 1 tonne (1000 kg) of coal every 10 seconds. According to Table 1, how much of the tonne actually goes into producing electric energy? (a) 600 kg. (b) 60 kg. (c) 500 kg. (d) 400 kg.

3 ENERGY QUALITY: THINGS RUN DOWN Thermal energy is special. A moving bullet or a raised rock can easily use nearly 100% of its kinetic or gravitational energy to do work, but the second law places strict limits on the percentage of thermal energy that can be converted to work. Thermal energy is thus less useful, or “of lower quality,” than other forms. Whenever you transform other energy forms into thermal energy—say by friction or combustion—you reduce the energy’s usefulness even though the total amount of energy is conserved. So there is a one-wayness, an irreversibility, about any process that creates thermal energy. Once a system creates thermal energy, that system will never by itself be able to return to its previous condition. To return, it would have to convert all the created thermal energy back to its original form, and the second law prohibits this. The system can return to its initial state only with outside help. Think of a rock swinging back and forth on a string tied to a hook (Figure 6). Air resistance and friction (between the string and the hook) gradually bring the rock to rest. Although the complete system (rock, string, hook, and surrounding air) loses no energy, it can’t return to its initial condition because thermal energy is created, and this cannot be entirely reconverted to kinetic or gravitational energy. Something is permanently lost when systems run down like this, but it cannot be energy because energy is conserved. Instead, energy quality is lost. When we use Earth’s energy resources, we don’t reduce Earth’s total energy. Instead, we degrade energy from highly useful forms such as the chemical energy of oil to less useful forms, usually thermal energy. Thus one of the two great laws of energy says that the quantity of energy is conserved, and the other says that the quality of energy runs down. You can’t get ahead, and you can’t even break even.

Figure 6

A rock swinging on a string tied to a fixed point overhead. The rock “dies down,” illustrating the irreversibility of natural processes implied by the second law.

4 THE LAW OF ENTROPY: WHY YOU CAN’T BREAK EVEN Suppose you put a box of hot gas and a box of cold gas into contact so that thermal energy (but not the gases themselves) can flow between them. The law of heating predicts that the hot box will heat the cold one, and that this will continue until there is no longer a temperature difference between the boxes. Figure 7 views this process microscopically, showing just a few molecules. The hot box’s molecules are moving faster on the average. The exchange of thermal energy causes the molecules of the hot gas to slow down and the molecules of the cold gas to speed up until both gases come to some intermediate temperature. Now the average speeds in the left- and right-hand boxes are the same, so the fast molecules and slow

173

Second Law of Thermodynamics High temperature Low temperature

(a)

Intermediate temperature

(b)

Figure 7

Microscopic view showing just a few molecules in a box of hot gas and a box of cold gas (a) at the instant they are put into contact and (b) after there has been time for the boxes to come to the same temperature. Figure (b) shows less organization than (a), because the faster molecules are no longer separated from the slower molecules.

molecules are no longer separated from each other.4 From the microscopic point of view, the system is less organized. Microscopic disorganization (a mouthful—sorry!) has increased. This turns out to be the general situation, no matter whether the materials are gases or anything else. When thermal energy flows from hot to cold, microscopic disorganization always increases. In fact, the universal increase of microscopic disorganization turns out (although we won’t prove it here) to be equivalent to thermal energy always flowing from hot to cold. In other words, this is another way of stating the second law. Physicists have found a quantitative measure of the microscopic disorganization of any system. It’s called entropy. For example, the entropy of 1 kg of water is greater than the entropy of 1 kg of ice, because the molecules of water are not organized into a regular crystal pattern as are the molecules of ice. We don’t need to delve into the precise definition of entropy here. Suffice it to say that entropy can be precisely defined and it can be measured entirely macroscopically by measurements of temperature, thermal energy, and a few other quantities such as volume. So we have yet a third way of stating the second law: The Second Law of Thermodynamics, Stated as the Law of Entropy The total entropy (or microscopic disorganization) of all the participants in any physical process cannot decrease during that process, but it can increase.

The law of entropy is similar to the law of conservation of energy. Both place restrictions on natural processes: The total energy of all the participants in any process must remain unchanged, and the total entropy must not decrease. The law of entropy predicts that most processes are irreversible—they cannot proceed in the opposite direction. For example, our hot and cold boxes of gas can 4

174

If the boxes contain different kinds of gases, then the average kinetic energies, rather than the average speeds, of the individual molecules of the two gases become equal when a common intermediate temperature is attained.

Second Law of Thermodynamics

come to the same temperature spontaneously, but they cannot start from the same temperature and evolve to different temperatures unless they have outside help (a heater on one side and a refrigerator on the other). Processes must go in the direction of increasing, not decreasing, entropy. In fact, except for a very subtle effect at the subatomic level,5 the second law is the only principle of physics that distinguishes between the forward and backward directions of time. So if it weren’t for the second law, everything could just as well run backward. For example, a book resting on a table could spontaneously leap into the air by converting some of its thermal energy into kinetic and gravitational energy. This is the reverse of a book falling onto a table. It might appear to violate such principles as Newton’s law of motion, but if viewed at the microscopic level, there is no violation: It is possible, although highly improbable, for the randomly moving molecules in the book to all just happen to be moving upward at the same instant, with sufficient speed to cause the book to leap from the table. Similarly, water could run uphill. Thermal energy could flow from cold to hot. And people could grow younger instead of older. Perhaps you have seen a movie run backwards. The only law of physics that would be violated if these backward events occurred in real time is the second law of thermodynamics. The law of entropy suggests a deeper reason behind the second law. As you can see from the cartoon at the end of this chapter, increased disorganization is common in everyday life. For example, if you start with a partly organized deck of cards having all the spades collected together and then shuffle the deck, you’ll almost certainly disorganize the deck further. This is simply because there are so many more ways to disorganize the deck than there are ways to further organize it. It’s easy to disorganize things but it takes effort—or lots of luck—to organize them. So the second law arises for simple statistical reasons. Like a deck of cards, molecular systems are much more likely to evolve toward greater disorganization than toward greater organization, simply because there are many more ways for a molecular system to become disorganized than to become organized. This leads to a fascinating point about the long-term fate of the universe. Applied to the universe as a whole, the second law says that its natural evolution must be toward greater disorganization. Its long-term fate would then be a state of maximum disorganization, in which no further macroscopic developments would occur. Such a state would be really boring. All the stars would have burned out and no new ones could form because all nuclear reactions would have run their course. Life could not exist because of the lack of sunlike stars and because all chemical reactions would have run their course. This has been called the “heat death” of the universe. Being hundreds of billions of years in the future, it’s not exactly our most pressing issue. More importantly, there is a huge speculative element here, because it’s always risky to assume that the principles of physics are so precisely understood that they can be applied to the entire universe for all time. Looking toward earlier instead of later times, the law of entropy implies that the universe must have had lower entropy—greater organization—in the past. In fact, physicists agree that the universe began in a highly organized, low-entropy state at the time of the big bang and that its entropy has been increasing ever since. The big bang

5

For some reason, the universe at one time had a very low entropy for its energy content, and since then the entropy has increased. So that is the way toward the future. That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in the history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future. Richard Feynman, Physicist

There is indirect but compelling evidence that certain types of subatomic particles distinguish between the forward and backward directions of time in processes involving the “weak force,” one of nature’s four fundamental forces. It’s not known whether this discovery is in any way related to the second law or to our sense of a forward direction in time.

175

Second Law of Thermodynamics A living organism . . . feeds upon negative entropy. Thus the device by which an organism maintains itself at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment. Erwin Schroedinger, Physicist, in What Is Life?

Radiant energy from sun at 5500

98% is reradiated at 25 : large increase in entropy

ThermE out

ThermE in

2% is converted to low-entropy chemical energy: smaller decrease in entropy

Figure 8

Energy flow through a leaf. The leaf is similar to a heat engine. A growing leaf illustrates how Earth has become more organized, despite the universe’s trend toward increased entropy.

was the source not only of energy and matter but also of the organization we see in the universe today. Biological systems provide interesting examples. For example, a growing leaf manufactures complex and highly organized glucose molecules out of less organized CO2 and H2O molecules. The leaf must create this organization. How does it manage to produce this decrease in entropy, in apparent violation of the second law? The answer is that the leaf had help. The second law says that the total entropy of all the participants in any process cannot decrease. In the growth of a leaf, the other vital participant is the sun. Solar radiation has a temperature, the 5500°C surface temperature of the sun. When this radiation is absorbed by a leaf, only about 2% of the energy is converted to chemical energy. The remaining solar energy is reradiated out into space, at the 25°C temperature of the leaf. So most of the solar energy flows from 5500°C to 25°C. The large entropy increase of this thermal energy flow allows the remaining solar energy to be organized into low-entropy chemical energy (Figure 8), without violating the second law, because the total entropy increases. The sun both energizes and organizes life on Earth! In view of the second law, it seems paradoxical that life on Earth could have evolved on its own from the simple organisms that existed shortly after Earth formed billions of years ago into the highly organized plants and animals of today. But like the leaf, biological evolution had help from the sun. Evolution is assisted by sunlight flowing through plants from higher to lower temperature, representing a great entropy increase that compensates for the decrease that occurs when plants evolve. And animals, which do not use solar energy directly, reduce their entropy by eating highly organized food—another form of outside help. Thus, biological evolution does not contradict the second law. Your brain is one result of this long evolution toward greater organization. As an information-storage device, the human brain is the most highly organized form of matter on Earth. It could even be the most organized form of matter in the Milky Way galaxy. It’s remarkable that, in the human brain, nature has finally created a self-aware collection of molecules, molecules so well organized that they are capable of knowing they are a collection of molecules! Nature has spent billions of years of evolution getting to this point. So please, my friend, take good care of yourself, and of all of us. CONCEPT CHECK 6 When a tablespoon of salt mixes with a quart of water, does entropy increase? (a) Yes. (b) No. (c) Sometimes. (d) Only on Fridays.

5 THE AUTOMOBILE You now have the physics background needed for four energy-related social topics that will occupy the remainder of this chapter. Few technologies shape our society as strongly as the automobile. It brings new freedom while affecting our quality of life, family structure, self-perceptions, physical environment, health, work, community structure, resource use, economy, and even war and peace. For most Americans, the environmental effects of their automobile use far outweigh the environmental effects of any other individual activity. Transportation consumes much of the USA’s energy (Figure 9) and most of its oil (Figure 10), most of it going into cars and trucks (Figure 11).

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Second Law of Thermodynamics Residential 22%

Industrial 32%

Transportation 28%

Commercial 18%

Figure 9

The fraction of total U.S. energy consumed by each economic sector. (U.S. Energy Information Administration, 2007)

Residential 4% Industrial 23%

Transportation 68%

Electricity generation 3% Commercial 2%

Water 5% Air 7%

Pipeline 2%

Rail and bus 3%

Autos 63%

Trucks 20%

Figure 10

Figure 11

The fraction of U.S. petroleum consumed by each economic sector. (U.S. Energy Information Administration, 2003)

The fraction of U.S. transportation energy consumed by each transportation mode. (U.S. Bureau of Transportation Statistics, 2007)

MAKI NG ESTI MATES Experiments show that upon combustion, 1 liter (0.26 gallons) of gasoline releases (converts to thermal energy) about 32 * 106 J of energy. Use this figure to estimate the rate, in watts, at which a typical car consumes chemical energy. (Hints: Typical gasoline consumption is 10 km/liter (25 miles/ gallon), and moderate highway speeds are about 80 km/hr (50 mi/hr).)

The preceding Making Estimates question shows that a typical car driven at moderate speed without acceleration consumes its gasoline’s chemical energy at a rate of 70 kW. This is equivalent to the electric power going into 700 continuously burning 100 W bulbs! As another comparison, 70 kW is about the average electric power consumption of 50 households. And if the car is accelerating, you can multiply these figures by about 5. Cars are powerful energy consumers. Most transportation fuel goes into heat engines, where it burns to produce thermal energy that is then partially transformed into useful work. Most cars and trucks are powered by internal combustion engines that burn a fuel–air mixture. The mixture’s high combustion temperature gives it a high pressure, so that the hot gases push strongly on a piston, a movable metal plate connected to a rod (Figure 12). The piston does the work that turns the drive wheels. Combustion is “internal” because it occurs directly inside the gases that do the work, in contrast to external combustion, which occurs in a fuel that then provides thermal energy to a second substance, such as steam, that does the actual work. Figure 13 shows the energy flows (measured in kW, or thousands of joules of energy transformed per second) in a typical gasoline-fueled automobile. An average of 1 kilowatt’s worth of fuel evaporates into the atmosphere, where it contributes to chemical pollution. The remaining 69 kW go to the engine, which produces about SO LU T I O N TO M A KI N G ESTI M ATES During 1 hour at 80 km/hr, a car travels 80 km and so consumes 8 liters. The chemical energy in 8 liters is 8 * 32 * 106 = 2.6 * 108 J. Since this is consumed in 1 hour (3600 s), the chemical energy consumed per second is

Cylinder walls

Piston Expanding gas Work

Figure 12

Cross-section of a single cylinder in an automobile’s engine, showing the conversion of thermal energy to useful work using a piston.

2.6 * 108 J>3600 s L 70,000 J>s, or 70,000 watts, or 70 kW

177

Second Law of Thermodynamics Evaporation

Thermal energy of exhaust, 55 kW

28 kW

Out of tailpipe

27 kW Water pump, etc. Friction, etc.

Figure 13

Typical energy flow rates in an unaccelerated gasoline-fueled car at a moderate highway speed.

Engine

1 kW

3 kW 5 kW Air resistance

Work, 14 kW Transmission and drive train

5 kW Rolling resistance

Waste, 60 kW

Into engine, 69 kW

Removed by radiator

Work, 10 kW

From fuel tank, 70 kW

1 kW

14 kW of work and exhausts the remaining 55 kW as thermal energy and unused chemical energy. About half of the exhaust energy is removed by the radiator, and the other half goes out through the exhaust pipe as polluting gases. Gasoline is a hydrocarbon, made of hydrogen (H) and carbon (C) atoms. Both H and C combust with oxygen from the atmosphere, so the exhaust gases are mostly CO2 and H2O. Although the H2O is harmless, CO2 from fossil fuel combustion is the main source of global warming. The tailpipe exhaust carries various other molecules, mainly CO, NO, NO2, and unburned hydrocarbons. These are toxic pollutants, and their unused chemical energy also represents an energy inefficiency. The carbon monoxide and unburned hydrocarbons are the result of incomplete combustion of the fuel. The two oxides of nitrogen—collectively called NOx—form from atmospheric oxygen and nitrogen, which combine under the influence of the engine’s high temperatures. Cars and trucks produce two-thirds of America’s CO pollution, one-third of its hydrocarbon pollution, and half of its NOx pollution. The automobile’s main loss of useful energy occurs in the engine, as a consequence of the second law. The engine’s theoretically ideal efficiency is 37% (Table 1), and its actual efficiency is 14 kW/69 kW = 20%. Several losses combine to bring the engine’s efficiency from the 37% allowable by the second law down to 20%: incomplete combustion, the formation of NOx, friction in the engine, and thermal losses through the engine’s wall. Of the 14 kW of work produced by the engine, 1 kW goes to internal devices like the water pump and air conditioner, and the rest goes to the transmission and drivetrain that couples the engine to the drive wheels. This coupling is about 75% efficient, so 10 kW finally arrive at the drive wheels. About half of this goes into overcoming air resistance, while the other half goes into overcoming rolling resistance. The overall energy efficiency of the entire automobile (not just the engine) is 10/70 = 14%, or one-seventh. Because the problems of scarce oil resources and dangerous global warming pollution loom ever larger, and because the automobile is a chief source of both, alternative transportation modes (next section) and alternative automobile fuels

178

Second Law of Thermodynamics

AP Photo/The Canadian Press, Jeff McIntosh

are increasingly important. Table 2 and Figures 14 through 17 present several alternative automobile fuels. Several alternatives to the standard internal combustion engine are now on the market or under development. Electric vehicles (EVs, Figure 15) are powered by large batteries that use stored chemical energy to create electricity. They are “zeroemission vehicles” because they have no tailpipes and emit no chemical pollutants

Figure 14

University of Michigan team members run with their solar car, driven by Brooke Bailey, as it crosses the finish line to win the 2008 North American Solar Challenge. Race drivers had to obey posted speed limits while driving 3800 km from Texas to Calgary, Canada, powered only by the sun and what could be stored in the car’s battery. The race has been described as the “Tour de France of engineering.” Table 2 Fuels for automobiles and trucks Fuel

Source of fuel

Description

For internal combustion Gasoline or diesel fuel

petroleum

liquid, widely used

Compressed natural gas

natural gas

high-pressure gas

Liquefied natural gas

natural gas

low-temperature liquid

Methanol (wood alcohol)

wood, natural gas, coal

liquid

Ethanol (grain alcohol)

grain, sugar, trash

liquid

any source of electricity

hydrogen produced from water

any source of electricity

recharge electrically

hydrogen, methane, other

hydrogen can be produced from water

Hydrogen

a

For noncombustion Storage batteriesa Fuel cell a

a

Since electricity for hydrogen production, for storage batteries, or for hydrogen fuel cells can come from any source, the ultimate energy resource can be wind, hydroelectric, nuclear, fossil fuel, photovoltaics, etc.

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Vince Bucci/Getty Images

Second Law of Thermodynamics

Figure 15

The Tesla Roadster, billed as the world’s first highway-capable all-electric car, runs on 900 pounds of rechargeable lithium ion batteries (shown). For safety, the car has a cooling system to prevent overheating the batteries. Its range is 380 km (240 miles) on one battery charge, a full recharge requires 3.5 hours, and its top speed is electronically limited to 200 km/h (125 mi/h). The high cost of the batteries makes it an expensive purchase. The company plans to produce 15,000 cars per year by 2011.

AP Photo/Atsushi Tsukada The Toyota Prius debuted in 2001. It’s a gasoline-electric hybrid vehicle that runs on a battery and on a small gasoline engine that energizes the battery and provides additional power when needed. Thus the car combines the convenience of gasoline with much of the environmental advantage of electric vehicles, while achieving 80 km (50 miles) per gallon. The front end is shown; the electric “inverter” that converts the battery’s DC to the engine’s AC and vice-versa is on the right, and the gasoline engine is on the left. The nickelmetal-hydride battery pack, warranted for 10 years or 240,000 km (150,000 miles), is in the back end.

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Chevrolet Corporation

Figure 16

Figure 17

The chassis of the Chevrolet Volt. A small gasoline engine-generator is on the far side (passenger side) of the front end, an electric motor is on the near side (steering wheel side) of the front end, and a long lithium-ion battery can be seen extending through the center of the car; the 180 kg (400 pound) battery then branches out in the rear end into a T shape (the top of the T is between the rear wheels and cannot be seen in the photo). The car should go on the market in 2011.

Second Law of Thermodynamics

while in operation. But the electricity to charge the battery must come from somewhere. If it comes from a fossil-fuel electric generating plant, then the vehicle causes plant emissions that create pollution and global warming. If the electricity comes from a less polluting source such as solar cells or wind, the vehicle becomes more environmentally benign. Typical EVs require several hours of recharging from a wall socket, the batteries are heavy, and EVs are expensive today. However, intense research is in progress to reduce these problems. Gasoline-electric hybrid vehicles (Figure 16) have recently achieved unprecedented energy efficiencies. “Hybrid” vehicles are fueled by gasoline, which runs a small gasoline engine that maintains a constant low power level. The engine does not directly drive the car, but instead drives an electric generator that provides electricity to energize a storage battery, which in turn drives the car just like an electric vehicle. Since the engine runs at a steady low power, it’s very energy efficient. Since the storage battery is continuously recharged, it needn’t store large amounts of energy, so it can be far smaller and lighter than an EV’s battery. Additional efficiencies are obtained by making the car of lightweight but strong (for crash safety) materials, streamlining (to reduce air resistance), and employing a braking mechanism that recovers kinetic energy losses during deceleration. Several hybrid passenger vehicles have entered the market. Because of recent and probable future rises in the price of oil, the Toyota Motor Corporation is betting that hybrids will become much more popular and has announced plans for all of its vehicles to eventually be run by hybrid engines. The plug-in hybrid car is an important newer variant. It’s a cross between the all-electric car (Figure 15) and the “conventional” hybrid vehicle (Figure 16). The Chevrolet Volt is a good example and will probably be the first plug-in hybrid on the market, in 2011. Figure 17 shows the Volt’s chassis, so you can see a little of how it works. While hybrids carry a battery that is continuously recharged on-board by a small gasoline engine, the Volt carries a battery that drives the car solely on electricity for the first 40 miles, after which the battery is assisted by a small gasoline engine for another several hundred miles. To re-charge the battery after use, it must be plugged in for several hours. So plug-in hybrids, like electric cars but unlike conventional hybrids, get energy for their battery from the electrical grid. The advantage of this is that no gasoline is needed for trips under 40 miles, so on average the car uses far less gasoline than other cars, replacing the gasoline with electricity and energy efficiency. This in turn reduces CO2 emissions, the main contributor to global warming, enormously: By year 2050, plug-in hybrids could reduce U.S. oil consumption by 4 million barrels a day (a 20% reduction), and reduce U.S. CO2 emissions by half a billions tons per year (a 33% reduction in vehicular emissions). Fuel cell vehicles are fueled by hydrogen obtained from fossil fuels or water. Even though the universe is made mostly of hydrogen, this light-weight element escaped from Earth’s gravitational hold long ago and is nearly absent on Earth in its free form (the H2 molecule), uncombined with other elements. It must be obtained from fossil fuels by chemical processes or from water by using electricity to split H2O molecules. It can be stored in the vehicle as a compressed gas, or as a liquid at extremely low temperature, or it can be chemically inserted into certain metals. Instead of being burned, the fuel is fed into a device called a fuel cell that converts the hydrogen’s chemical energy directly into electricity. It works by exploiting hydrogen’s tendency to combine chemically with oxygen—like a battery with hydrogen at one electrode (or pole) and oxygen at the other. The difference between

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a battery and a fuel cell is that batteries store chemical energy during the life of the battery, whereas fuel cells feed a chemical source through the cell when needed. So batteries must be recharged, while fuel cells must be refueled. Compared with batteries, fuel cells are less massive and operate continuously over longer times. But there are many scientific and practical barriers to the widespread use of fuel cells, and they are quite expensive today. Unlike gasoline engines, fuel cells convert chemical energy directly into electrical energy, so they are not heat engines and the second law does not affect the essentials of their operation. Thus, typical efficiencies of obtaining electrical energy from the hydrogen fuel’s chemical energy are 60% or more, far greater than the 20% that’s typical for gasoline engines. Environmental benefits depend on the source of the hydrogen. If the hydrogen is produced from water using solar-generated electricity, fuel cells are one of the most environmentally benign transportation technologies. Since the fuel cell combines the hydrogen fuel with oxygen to yield water as the only emission, there’s no pollution. There’s no fossil fuel consumption, and no global warming gas emissions. But there are several barriers to practical hydrogen fuel cells for cars: Today it’s expensive to produce the hydrogen from water, the fuel cells themselves are expensive, it’s not easy to store sufficient hydrogen in an automobile, and a new fuel distribution system will be needed for the hydrogen. Several companies have small numbers of experimental fuel cell vehicles on the road today. Hydrogen fuel cells might be on the market within ten years but if they are marketed that soon they’ll probably get their hydrogen from natural gas instead of from water and so they’ll lose two of their major advantages—they will consume fossil fuels, and they will emit global-warming gases. Some experts have dubbed the arrival of fuel cells in the marketplace—when and if it happens—as the dawning of a new energy age, the “Hydrogen Age.” CONCEPT CHECK 7 Which of the following uses a heat engine? (a) Gasolinefueled car. (b) Diesel-fueled car. (c) Electric car. (d) Fuel cell car running on methane. (e) Fuel cell car running on hydrogen. (f) Hybrid car.

6 TRANSPORTATION EFFICIENCY

Mary Ellen Scullen Figure 18

The two-person Smart Car. Its reduced size, weight, and engine give it a gasoline efficiency of 16 km/liter (37 mi/gal).

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My previous definition of energy efficiency—work output divided by total energy input—doesn’t really capture the automobile’s purpose. Although its purpose is to move people, its energy goes mostly into moving the car itself rather than people. Gasoline mileage, the common measure of automobile efficiency, suffers from the same defect. Neither of these measures captures people-moving efficiency, in other words, transportation efficiency. Gasoline mileage is, however, useful for comparing different cars with each other (Table 3). Most of the high-efficiency vehicles listed use hybrid engine technology, but the two-person Smart Car (Figure 18) instead achieves high efficiency by means of size and weight reductions. An appropriate measure of people-moving efficiency is passenger-kilometers per unit of energy. For example, if a bus moves 20 passengers a distance of 3 km, it has delivered 20 passengers * 3 km = 60 passenger-km. Similarly, the appropriate measure of freight-moving efficiency is the tonne-kilometer per unit of energy. For example, if a truck moves 5 tonnes a distance of 80 km, it has delivered 400 tonne-km. Table 4 compares passenger-moving efficiencies. For walking and bicycling, the table uses the “gasoline equivalent” of the required number of food calories.

Second Law of Thermodynamics Table 3 Fuel efficiencies of passenger vehicles km/liter

mi/gal

National averages: All U.S. passenger vehicles (cars, SUVs, pickups)

9

22

New U.S. passenger vehicles

12

27

New European Union passenger vehicles

14

34

New cars: Ford Expedition, SUV

6

16

Honda Accord

11

25

Ford Escape, SUV hybrid

13

32

Nissan Altima, hybrid

14

34

Smart Car

16

37

Honda Civic, hybrid

18

42

Toyota Prius, hybrid

21

50

Table 4 U.S. passenger-moving efficiencies of several human transportation modes passenger-km per liter

passenger-mi per gal

passenger-km per MJ

Human on bicycle

642*

1530*

18.0

Human walking

178*

425*

5.0

Intercity rail

60

144

1.7

Carpool auto (occupancy = 4)

36

88

1.0

Urban bus

33

80

0.9

Commercial airline

21

50

0.6

Commuting auto (occupancy = 1.15)

11

25

0.3

*For walking and bicycling, the table uses the “gasoline equivalent” of the required number of food calories.

Pierre Verdy/AFP/Getty Images

Walking and bicycling come out far ahead because no energy goes into moving a heavy vehicle, and because no heat engine is employed so there is no loss due to the second law of thermodynamics. Bicycling is more efficient than walking because wheels keep rolling and thus take maximum advantage of the law of inertia. Walking requires you to start and stop your legs with every step, and these accelerations require a force (Newton’s law of motion), which means that work is done. Trains (Figure 19) are far more energy efficient than other vehicles because they can more efficiently overcome air resistance and rolling resistance and because one train can carry many passengers. Because a train presents a small frontal area relative to its large load, its air resistance per kilogram of load is far below that of cars and trucks. And because a train rolls on inflexible steel wheels, there is little rolling resistance. Table 5 compares freight-moving efficiencies. Again, the advantage of rail is obvious. Since one freight train can carry the loads of 500 trucks, this is not surprising. You can see from Figures 9, 10, and 11 that transportation is a major consumer of energy in general and of oil in particular. This consumption poses huge problems

Figure 19

The French TGV (Train à Grande Vitesse or “train of great velocity”) has been in service since 1972. About 350 TGV “trainsets” are in service today. Like most of Europe’s high-speed trains, the TGV routinely travels at about 300 km/hr (186 mi/hr). Trains are far more energy efficient than other vehicles because they can carry several hundred passengers, because they present a small frontal area relative to their large load, and because they roll on inflexible steel wheels that experience little rolling resistance.

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Second Law of Thermodynamics Table 5 Freight-moving efficiencies of three transportation modes kg-km tonne-km per MJ per liter

2900

100

Truck (heavy)

720

25

Air (freight)

145

5

Rail (freight train)

Table 6 Mass-moving efficiencies of animals and machines, in kilogramkilometers per megajoule Human on bicycle

1100

Salmon

600

Horse

400

Human walking

300

Typical bird

200

Intercity rail

100

Urban bus

55

Hummingbird

50

Carpool auto

40

Commercial airline

25

Fly, bee

20

Commuting auto

12

Mouse

5

Adapted from S. Wilson, “Bicycle Technology,” Scientific American, March 1973.

for the United States: increasing energy costs, declining domestic and foreign sources of oil, and two Middle Eastern wars that were partly due to oil-related security problems. Tables 3, 4, and 5 suggest many ways to reduce oil consumption: • Enact automobile efficiency standards to bring new U.S. cars up to at least the efficiency of new European cars. • Use incentives to promote hybrid vehicles. • Promote carpooling. • Encourage mass transit while discouraging cars. • Move freight by train instead of by truck. • Plan cities that encourage walking, bicycling, and transit and discourage driving. For fun, let’s compare the entire realm of locomotion by animals and all forms of human technology. Which animal or human transportation mode is the most efficient transporter of mass: fruit flies? trains? horses? jet planes? humans walking? bicycling? To compare fruit flies, horses, and humans fairly, we must incorporate the fact that the horse’s energy goes into moving a lot more mass. So the useful output should be measured as the animal’s (or the human’s plus the machine’s) total mass times distance moved. Table 6 gives several such mass-moving efficiencies, in kilogram-kilometers per megajoule of energy. Again, bicycles come out far ahead, because animals don’t have wheels so they can’t take advantage of rolling and because bicycles are about the only major human transportation technology that is not a heat engine. In other words, bicycles come out on top because of the law of inertia and the second law of thermodynamics! As an avid bicycle commuter, I think that’s cool. This reasoning implies that animals with wheels would have a big energy advantage. In fact, some salamanders and other animals use this energy advantage by rolling their bodies into hoops and rolling down hills. One could speculate that on another planet with surfaces created by smooth lava flows, wheeled animals might evolve and be abundant! CONCEPT CHECK 8 You wish to move 125 tonnes of freight a distance of 200 km. How many liters of gasoline are needed to move it by truck, and by rail? (a) 125 liters by truck and 500 liters by rail. (b) 500 liters and 125 liters. (c) 250 liters and 1000 liters. (d) 1000 liters and 250 liters.

7 THE STEAM–ELECTRIC POWER PLANT

Every time I see an adult on a bicycle, I no longer despair for the human race. H. G. Wells, English Historian, Sociologist, Author of War of the Worlds and Other Novels.

184

Let’s turn now to another heat engine that has transformed modern society: the steam–electric power plant. Figure 20 is a schematic diagram of the operation of a coal-burning electric power plant. Coal is the most widely used energy source for electricity. Other plants that use oil, natural gas, nuclear energy, or solar energy to turn water into steam in a boiler operate much as a coal-burning plant does in producing electricity from steam. The coal combusts externally in a furnace, and its thermal energy is transferred to water inside a boiler. Most combustion products escape through the stack but some pollutants are removed first. The boiler produces high-pressure steam at over 500°C, far above the normal boiling temperature. The steam moves through pipes to a large rotating device called a steam turbine that turns when it feels a higher pressure on the front (upstream) side than on the back. Like a car’s piston, the steam

Second Law of Thermodynamics Electricity

Stack gases

Generator

Hot steam Turbine

Cooler steam

Hot steam Condenser

Cold water Hot water

Boiler Pump

Furnace

Water

Lake or cooling tower Fuel

Figure 20

A schematic diagram showing the operation of a coal-fueled steam–electric generating plant.

turbine is the key device that transforms thermal energy into work. The turbine turns an electric generator that creates electricity. The rotating turbine converts some of the hot steam’s thermal energy into work. The second law tells us that this is possible only if the remaining thermal energy flows to a cooler temperature. To maintain the required temperature difference, the exhaust side of the turbine is cooled by an external stream or lake or by evaporative cooling in the atmosphere. To obtain the greatest efficiency, the exhaust is cooled sufficiently to “condense” the steam back into liquid water, because this greatly reduces the pressure against the back side of the turbine. The steam is then sucked forcefully through the turbine, from very high pressure on one side to near-vacuum on the other. Once condensed, pumps move the water back around to the boiler, where the cycle begins again. As you can see from Figure 20, the plant is a heat engine. Thermal energy flows in at the boiler and out at the condenser, and work is done by the turbine (compare Figure 5). Figure 21 shows the energy flow (more precisely, the energy per second in megawatts). A large plant generates about 1000 MW of electric power, enough for a

185

Second Law of Thermodynamics Stack emissions, 300 MW

From coal, 2500 MW

To turbine, 2200 MW

Turbine exhaust, 1200 MW (removed by condenser) Work, 1000 MW

Electric energy, 1000 MW Turbine (heat engine)

Waste, 1600 MW

Lost in transmission, 100 MW

To user, 900 MW

Useful work, 900 MW

Figure 21

Energy flow in a typical 1000 MW coal-fueled electric generating plant.

large city. Because a typical plant’s efficiency is 40%, this electrical output requires 2500 MW, or 2500 million joules of energy input every second, requiring 100 kilograms of coal every second! Of the 2500 MW input, 300 MW go out through the stack, accompanied by oxides (oxygen compounds) of nitrogen, oxides of sulfur, carbon dioxide, and small incombustible particles called “ash.” Oxides of nitrogen and sulfur cause acid rain, and carbon dioxide is the main source of global warming. Modern plants remove most of the sulfur oxides, some of the nitrogen oxides, and nearly all of the ash, which then presents a significant solid-waste disposal problem. Since coal is made mainly of carbon, CO2 is by far the predominant stack gas. None of it is removed today, although in the future it may be possible to remove it and inject it in gaseous form into the ground. The turbine converts the thermal energy of steam to useful work, which in turn drives a generator that creates 1000 MW of electric power. The plant’s biggest loss in useful energy, the 1200 MW exhausted (Figure 21), is an unavoidable consequence of the second law. This exhaust goes into the condenser’s cooling water. If the cooling water comes from a lake or river, the exhaust warms the water, an effect called thermal pollution. Many plants use the atmosphere as the coolant by employing large evaporative cooling towers (Figure 22). Finally, an average 100 MW of the generated electricity is lost as thermal energy during transmission over electric power lines, and 900 MW gets to the user. Grapes/Michaud/Photo Researchers, Inc. Figure 22

Cooling towers (on the right) and stacks at a coal-fueled generating plant. Cool air is sucked into the bottom of the cooling towers, where it cools hot water from the plant. The tower’s shape promotes a rapidly rising hot-air column.

186

CONCEPT CHECK 9 Judging from Figures 20 and 21, the efficiency of the boiler in converting the coal’s chemical energy into steam is (a) 100%; (b) 12%; (c) 88%; (d) 36%; (e) 10%. CONCEPT CHECK 10 A particular coal-burning generating plant consumes 8000 tonnes of coal per day. Assuming that the coal is pure carbon, which of the following is closest to the amount of carbon dioxide that this plant injects into the atmosphere every day? (a) 8000 tonnes. (b) 3200 tonnes. (c) 4800 tonnes. (d) 24,000 tonnes. (e) 16,000 tonnes. (f) 48,000 tonnes.

Second Law of Thermodynamics M A K I N G EST I M AT ES At 100 kg/s, estimate the amount of coal (in tonnes) that

a typical plant uses in one day. How many traincars full of coal is this, at about 100 tonnes per traincar?

8 RESOURCE USE AND EXPONENTIAL GROWTH6

Value of account in dollars

The social implications of energy raise many growth-related issues. As our growing numbers and environmental impact begin to affect the entire natural world, it is important to understand the long-term effects of growth. Suppose you invest $100 at a rate of return or growth rate of 10% per year. When will you double your money? You earn $10 during the first year, so you have $110. In the second year you earn 10% of $110, or $11. Now you have $121, so you earn $12.10 during the next year. Each year you earn more than you did the previous year. Figure 23 graphs your account and compares it with a second graph that increases by a fixed $10 every year. The second graph illustrates linear (straightline) growth. As you can see, there’s a big difference between $10 per year and 10% per year. When a quantity grows by a fixed percentage in each unit of time, its growth is said to be exponential.7 If you continue adding 10% each year, your account will about double to $200 after 7 years. What will happen after another 7 years? Since the same arithmetic applies, it will double again, to $400. In the next 7 years it will double again, to $800. And so forth. Exponential growth has an unchanging doubling time.

2000 1800 1600 1400 1200 1000 800 600 400 200

The arithmetic of growth is the forgotten fundamental of the energy crisis. Albert Bartlett

Growth at 10% per year: exponential growth

Growth at $10 per year: linear growth

0

2

4

6

8

10

12

14 16 Years

18

20

22

24

26

28

30

Figure 23

The 10% investment account. The initial investment is $100. Would you rather have exponential growth at 10% per year or linear growth at $10 per year?

6 7

This section draws on the work of University of Colorado physicist Albert A. Bartlett. It is called “exponential” because the account is worth 100 * 1.1 after 1 year, 100 * 1.12 after 2 years, 100 * 1.13 after 3 years, and so forth. The number of years is in the exponent.

The number of seconds in a day is 60 s>min * 60 min>hr * 24 hr>day ' 105 s>day. 100 kg enter the plant every second, so the amount entering in a day is 105 * 100 = 107 kg, or 10,000 tonnes. This is 10,000/100 = 100 traincars every day! SO LUTION TO MAKI NG ESTI MATES

187

Second Law of Thermodynamics MAKI NG ESTI MATES You take a job requiring you to work every day for 30 days and your employer offers you just one cent for the first day and then a doubled salary every day after that. Will this be a good salary for the month? Pressures resulting from unrestrained population growth put demands on the natural world that can overwhelm any efforts to achieve a sustainable future. If we are to halt the destruction of our environment, we must accept limits to that growth. From World Scientists Warning to Humanity, a Declaration Signed by Nearly 1700 Leading Scientists from 71 Countries, Including 104 Nobel Laureates

In a population of animals, the number of newborns each year is roughly proportional to the number of potential parents in the population that year. So if the population doubles, the number of newborns should also double. So the percentage increase—the number of newborns divided by the total population—should be roughly the same from year to year. This unchanging percentage increase means that population growth is roughly exponential. CONCEPT CHECK 11 Bacteria reproduce themselves by simply dividing. If you start with 1 bacterium, it will divide into 2; they will divide into 4, then into 8, and so forth. Since each population doubling occurs in the same time interval, this is an exponential process. Suppose that some strain of bacteria has a dividing time of 1 minute. You put 1 bacterium into a bottle at 11 A.M., and at noon you note that the bottle is full of bacteria. The bottle was half full at (a) 11:30; (b) 11:40; (c) 11:50; (d) 11:55; (e) 11:58; (f) 11:59.

As Concept Check 11 shows, when you consume a finite resource exponentially, it’s easy to use nearly all of it before you realize there’s a problem (Figure 24). Continuing with Concept Check 11, suppose that at 11:56 A.M. (when the bottle was only 1/16 full, or 94% empty!), some visionary bacteria, realizing they have a problem, launch an all-out search for new bottles. By 11:58 A.M., this program has been successful in discovering a vast new reserve: three new bottles! It took the bacteria an entire hour to fill the first 1

Fraction of jar that is filled with bacteria

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 Number of minutes past 11 A.M.

Figure 24

Bacterial growth in a jar. A finite resource, consumed exponentially, runs out surprisingly rapidly toward the end. On the scale of this graph, growth is imperceptible until 11:53 A.M. when the bottle is 1% full. You will earn $5.12 on day 10. To simplify matters, round this to just $5. Now continue doubling. On day 20, your earnings will be $5120. Round this to $5000, and continue. On day 30 alone, your earnings are more than $5 million!

SO LUTION TO MAKI NG ESTI MATES

188

Second Law of Thermodynamics

bottle. When will the new bottles be full? The answer is at 2 minutes past noon. Continued exponential growth eventually overwhelms all attempts to expand the resource base. There is a simple and useful quantitative relation for exponential growth. Any increase in the growth rate must decrease the doubling time, so we might expect to find a relation between these two. It turns out that they are inversely proportional. The relation is, approximately, doubling time = T =

70 growth rate 70 P

where T stands for the doubling time and P is the growth rate (the percentage growth per unit time, expressed in percent). This can be turned around to read 70 P = T Either quantity, the doubling time or the growth rate, is equal to 70 divided by the other quantity. For instance, the 10% savings account has a doubling time of T = 70>P = 70>10 = 7 years For a historical example, consider the growth of U.S. electric power. As you can see by examining Figure 25, production grew exponentially between 1935 and 1975, doubling about every 10 years for a percentage growth rate of P L 70>T = 70>10 = 7% per year. What if this growth rate had continued past 1975? In 1975, all electric energy could have been provided by about 400 large plants. If the 10-year doubling time had continued, 800 plants would have been needed in 1985, 1600 in 1995, 3200 in 2005, and 6400 in 2015. Sixty-four hundred power plants would mean some 125 in every U.S. state, with everybody living within a few miles of a large power plant! Obviously, expansion at a fixed growth rate is unsustainable. In fact electric power production increased by only 3% per year during 1973 to 1988, by 2% per year during 1988 to 2000, and by 1% per year during 2000 to 2010. U.S. oil production illustrates what happens when a finite resource is consumed exponentially. Like many industries, oil production grew exponentially during its early years, maintaining 8% annual growth during 1870–1930. But this could not be maintained, because recoverable oil resources would be gone by now. The growth 4000 Electricity generated in one year, in billions of kilowatt-hours

3500 3000

Figure 25

2500 2000 1500 1000 500 0 1900

10

20

30

40

50

60

Year

70

80

90

2000 2010

The history of electric power production. The annual electric energy produced, in billions of kilowatt-hours, is graphed from 1900 through 2010. The growth was roughly exponential between 1935 and 1975. (U.S. Energy Information Administration)

189

Second Law of Thermodynamics

rate declined, and then around 1970 U.S. oil production in the 48 contiguous states began to drop, as in Figure 26. This bell-shaped curve is typical for a nonrenewable resource—a resource that cannot be readily replaced within a human lifetime. U.S. oil production is following this pattern and is in region C on the graph. World oil production is probably in region B. Resource depletion is inevitably driving the world toward the end of the oil age, although other problems such as global warming might end it even sooner. Renewable resources, such as wood or solar energy, follow a different history (Figure 27). In their early stages, renewable and nonrenewable resource use rises exponentially. But renewable resources can be sustained indefinitely, assuming they are consumed at less than the replacement rate, so the graph levels off as shown. Finally, consider world population growth (Figure 28). It took 6 million years for the human population to grow to its first billion in 1825. It reached its next billion only a century later in 1930, and its third billion in 1960. The sixth billion was reached in 1999. Population experts estimate that the population in 2050 will be around 9 billion. The actual outcome will be strongly dependent on human fertility between now and then. We can find the approximate current rate of growth from the population doubling during 1960 to 2000: P = 70>T = 70>40 = 1.75%. As you can see from the graph, this is a large—in fact explosive—rate.

Region C: exhaustion and decline Region A: exponential growth

Region B: reduced growth, leveling off

Yearly consumption

Yearly consumption

CONCEPT CHECK 12 U.S. oil production grew at 8% per year during 1870–1930. Its doubling time was roughly (a) 6 years; (b) 9 years; (c) 12 years; (d) 15 years; (e) 30 years.

Years

190

Region C: no growth, sustainable level

Region A: exponential growth

Region B: reduced growth, leveling off

Years

Figure 26

Figure 27

A typical bell-shaped curve showing the life history of consumption of a nonrenewable resource. Exponential growth must slow as the resource is depleted. Consumption eventually levels off and declines as the resource nears exhaustion.

A typical life history of a renewable resource such as hydroelectric power. Exponential growth slows as consumption reaches its natural limits. Consumption eventually levels off at some sustainable value.

Second Law of Thermodynamics 9

About 9 billion in 2050

8

6

6 billion in A.D. 1999

5

4 Third billion in 1960 3 Second billion in 1930 2 First billion in 1825 1

Figure 28 0 ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ 200 180 160 140 120 100 800 600 400 200 0 200 400 600 800 100 120 140 160 180 200 0 0 0 0 0 0 0 0 0 0 0 0 Year

The population explosion: faster than exponential. Note the resemblance to Figure 24.

© Sidney Harris, used with permission.

World population, in billions

7

191

192

Second Law of Thermodynamics Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions HEATING 1. What is heating? 2. In your own words, state the law of heating. 3. Give an example showing that thermal energy and temperature are really two different things.

HEAT ENGINES AND ENERGY QUALITY 4. Give an example of each of these energy transformations: kinetic to thermal, gravitational to thermal, thermal to kinetic. 5. In your own words, state the law of heat engines. 6. What properties of the input and the exhaust are the most important to determining a heat engine’s efficiency? Describe the manner in which the efficiency depends on these properties. 7. Is the actual overall energy efficiency of an automobile closest to 98%, 90%, 40%, 10%, or 2%? What about a steam–electric power plant? 8. If a heat engine operated entirely without friction, would it then be 100% efficient? Explain. 9. In terms of energy, what happens when the motion of a rock swinging from a string “dies down”? In what sense is this behavior irreversible?

THE LAW OF ENTROPY 10. What is entropy? 11. In your own words, state the entropy form of the second law. 12. Which law or laws of physics distinguish between forward and backward in time? 13. When a growing leaf increases its organization, does it violate the second law?

THE AUTOMOBILE AND TRANSPORTATION 14. Name two general types of heat engines of major social importance. 15. Why do we call it an internal combustion engine? Describe in your own words how it works. 16. Name two alternative fuels (not gasoline or diesel fuel) for the automobile. 17. What is the source of the largest inefficiency in an automobile’s operation?

18. Describe two different ways of measuring a transportation mode’s efficiency and give an appropriate measurement unit for each. 19. Why are trains more efficient than other transportation vehicles?

THE STEAM–ELECTRIC POWER PLANT 20. In a steam–electric power plant, what is the purpose of the turbine? Generator? Condenser? Cooling tower? Stack? 21. What is thermal pollution? 22. What is the source of the most important inefficiency in a steam–electric power plant’s operation? 23. What part of a steam–electric power plant is analogous to the piston in an automobile?

EXPONENTIAL GROWTH 24. What is the difference between exponential and linear growth? 25. Your savings account grows at 7% per year. What is its doubling time? 26. Draw a typical life-history graph for a nonrenewable resource. Is any part approximately exponential? 27. Repeat the previous question, but for a renewable resource.

Conceptual Exercises HEATING 1. How would you describe the weather on a day when the temperature was –3°C? +3°C? 22°C? 35°C? 2. Give the approximate temperature, in °C, of each of the following: your body, water boiling in an open pot, ice water, a nice day. 3. Which is larger, a Celsius degree or a Fahrenheit degree? 4. How does the flow of thermal energy through a closed window illustrate the second law? Which direction is this flow when it is cold outside? Hot outside? 5. Try to think of at least one technological device that causes thermal energy to flow “uphill,” from colder to hotter. Does this device violate the law of heating? Explain. 6. In the operation of a refrigerator, does thermal energy flow from hot to cold, or is it from cold to hot? Does this happen spontaneously, or is outside assistance required?

From Chapter 7 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

193

Second Law of Thermodynamics: Problem Set

HEAT ENGINES 7. Is it possible to convert a given quantity of kinetic energy entirely into thermal energy? Is it possible to convert a given quantity of thermal energy entirely into kinetic energy? In each case, either give an example or explain why it is impossible. 8. Is it possible to convert a given quantity of chemical energy entirely into thermal energy? Is it possible to convert a given quantity of thermal energy entirely into chemical energy? In each case, either give an example or explain why it is impossible. 9. Which are not heat engines: natural-gas-burning power plant, hydroelectric power plant, ethanol-fueled automobile, bicycle, solar–thermal electric power plant, steam locomotive? 10. Which of the following are heat engines: nuclear power plant, diesel locomotive, electric locomotive, geothermal power plant, wind turbine (windmill for generating electricity), solar hot water heater? 11. What does the second law tell us about the efficiency of heat engines? 12. Can you think of any way to drive a ship across the ocean by using the ocean’s thermal energy without violating the second law? 13. Farswell Slick approaches you with plans for a revolutionary transportation system. He has noticed that when he drives an automobile without accelerating, all the input energy eventually shows up as thermal energy. Slick proposes to use this thermal energy to drive the car at a constant speed. The car will still need fuel, but only for accelerating. It will be possible to travel cross-country on only a few gallons of gasoline. He describes his scheme as a “computerized advanced-technology exhaust feedback afterburner.” Should you invest in Slick’s scheme? Explain. 14. On the Fahrenheit scale, what are the freezing and boiling points? Use your answer to calculate the number of Fahrenheit degrees in one Celsius degree. 15. Use the result of the preceding question to convert 10°C to Fahrenheit. Convert 30°C to Fahrenheit. 16. In one cycle of its operation, a heat engine does 100 J of work while exhausting 400 J of thermal energy. What is its energy input? Its efficiency?

Residential 22%

Industrial 32%

Transportation 28%

Commercial 18%

Figure 9

The fraction of total U.S. energy consumed by each economic sector. (U.S. Energy Information Administration, 2007)

194

17. In one cycle of its operation, a heat engine consumes 1500 J of thermal energy while performing 300 J of work. What is its efficiency? How much energy is exhausted in each cycle?

ENERGY QUALITY AND THE LAW OF ENTROPY 18. When your book falls to the floor, is this a thermodynamically irreversible process? Is energy conserved? Does entropy increase? 19. When we say that the motion of a rock swinging on a string is irreversible, do we really mean that it is impossible to get the rock back to its starting condition? Explain. 20. When a block of wood slides down a sliding board, is this a thermodynamically irreversible process? Does this mean that it is impossible to make a block of wood slide up a sliding board? Explain. 21. As an egg develops into a chicken, its contents become more ordered. In light of what you have learned about the second law of thermodynamics, do you expect that this process violates the law of increasing entropy? Explain. 22. A pan of liquid water freezes when you place it outside on a cold day. Liquid water has greater molecular disorder than ice does. Is the freezing process then an exception to the law of entropy? Explain. 23. When orange juice and grapefruit juice are mixed, does entropy increase?

THE AUTOMOBILE AND TRANSPORTATION 24. Describe the energy input for walking and bicycling. How do walking and bicycling illustrate the second law? 25. Suppose an automobile’s fuel could be made to burn hotter without harming the engine’s operation (for instance, without cracking the engine). Would you still get the same amount of useful work from each gallon of gasoline? 26. Suppose an automobile could run on hard wheels that were not squeezed by the weight of the car on the road. Would this alter the car’s efficiency? How might this affect the gas mileage? What kind of wheels and road might you suggest? 27. According to Figures 9, 10, and 11, which of the three main sectors of the U.S. economy (industry, residential– commercial, transportation) consumes the most oil?

Residential 4% Industrial 23%

Transportation 68%

Electricity generation 3% Commercial 2%

Water 5% Air 7% Rail and bus 3%

Pipeline 2% Autos 63%

Trucks 20%

Figure 10

Figure 11

The fraction of U.S. petroleum consumed by each economic sector. (U.S. Energy Information Administration, 2003)

The fraction of U.S. transportation energy consumed by each transportation mode. (U.S. Bureau of Transportation Statistics, 2007)

Second Law of Thermodynamics: Problem Set 28. One car has twice the gasoline mileage efficiency of a second car. Compare the amounts of pollution they produce when they both travel the same distance. 29. Out of every 100 barrels of gasoline, about how many actually go into driving a typical car down the road? 30. A bus carries 30 people 200 km using 300 liters of gasoline. Find its passenger-moving efficiency.

THE STEAM–ELECTRIC POWER PLANT 31. Which type of generating plant would you expect to be more energy efficient, steam–electric or hydroelectric? Defend your answer. 32. Would it be more energy efficient to heat your home electrically or to heat it directly using a natural gas heater, assuming that the electricity comes from a steam–electric plant? 33. Which method of fueling your car is likely to be more energy efficient, and why: gasoline used in a standard car engine or electricity taken from a coal-fueled generating plant and stored in lightweight car batteries? Assume that the batteries convert electricity to work at 100% efficiency. 34. Out of every 100 tons of coal fed into an electric generating plant, roughly how many tons produce the electricity you can use at your home and how many go into waste energy? Use the approximate energy flows indicated in Figure 21. 35. For every 100 kilograms of coal entering a generating plant (recall that this much enters every second), about 15 kilograms of sulfur oxides and ash are removed, producing a significant solid-waste disposal problem. For a typical 1000 MW plant, how much of this solid waste is produced every day? Express your answer in tonnes (1 tonne = 1000 kg). 36. How would the annual pollution from two coal plants compare if the first plant is twice as energy efficient as the second? Assume that they both produce the same amount of electric power.

EXPONENTIAL GROWTH AND RESOURCE USE 37. A lily pond doubles its number of lilies every month. One day, you notice that 2% of the pond is covered by lilies. About how long will it be before the pond is entirely covered? 38. On June 1 there are a few water lilies in a pond, and they then double daily. By June 30 they cover the entire pond. On what day was the pond still 50% uncovered? 39. Company X increases its profits every year by $50 million. Is its growth in profits exponential? Company Y increases its profits by 1% every year. Is its growth in profits exponential? 40. According to Figure 25, did electric power production grow exponentially between 1910 and 1935? Estimate the number of kilowatt-hours produced in 1935, 1945, 1955, 1965, and 1975, and verify that production grew approximately exponentially between 1935 and 1975. 41. Which of the following are renewable energy resources: coal, firewood, nuclear power, wind, water behind a dam. 42. What is the original source of energy in each of the following energy resources: oil, firewood, wind, water behind a dam, geothermal, ocean-thermal electricity? Which of these are renewable resources? 43. The most recent world population doubling, to a total population of about 6 billion, has occurred in about 40 years. Making the (unrealistic!) assumption that this rate of population will continue for two centuries, what would the world’s population be two centuries from now? Such unrealistic assumptions are often useful in projecting future trends because they give us a sense of what is likely or unlikely. For example, this exercise shows us that it is very unlikely that our present population growth will continue for two more centuries. 44. The most recent world population doubling has occurred in about 40 years. Suppose that the next doubling occurs also in 40 years, but that a new agricultural “green revolution” manages to also double food production. Then how many people will be starving 40 years from now, as compared to the number starving now?

Stack emissions, 300 MW

From coal, 2500 MW

To turbine, 2200 MW

Turbine exhaust, 1200 MW (removed by condenser) Work, 1000 MW

Electric energy, 1000 MW Turbine (heat engine)

Waste, 1600 MW

Lost in transmission, 100 MW

To user, 900 MW

Useful work, 900 MW

Figure 21

Energy flow in a typical 1000 MW coal-fueled electric generating plant.

195

Second Law of Thermodynamics: Problem Set 4000

Figure 25

The history of electric power production. The annual electric energy produced, in billions of kilowatt-hours, is graphed from 1900 through 2010. The growth was roughly exponential between 1935 and 1975. (U.S. Energy Information Administration)

Electricity generated in one year, in billions of kilowatt-hours

3500 3000 2500 2000 1500 1000 500 0 1900

10

20

30

40

50

60

70

80

90

2000 2010

Year

45. Is the graph of Figure 29 an exponential curve? Explain.

Time

Figure 29

Is this an exponential curve?

Problems HEAT ENGINES (You will need footnote 3 to solve some of these problems.) 1. If a heat engine’s efficiency is 30% and its work output is 2000 J, how much thermal energy must have been put into it? 2. If a heat engine’s efficiency is 20% and 1.5 million joules of energy are put into it, how much work does it do? 3. The steam entering the turbine in a coal-burning power plant is heated to 500°C. The steam is cooled and condensed to water at 80°C. Find the best possible efficiency of the power plant. Remember that you must convert Celsius temperatures to degrees Kelvin before using the formula. 4. A solar-heated steam–electric generating plant heats steam to 250°C. After passing through the turbine, cooling towers cool the steam to 30°C. Calculate the best possible efficiency of this power plant. Remember that you must convert Celsius temperatures to Kelvins before using the formula in footnote 3. 5. In the preceding question, suppose that for every 1000 J of thermal energy going into this plant, the cooling towers remove 750 J as exhaust. What is the actual efficiency of this power plant? 6. A coal-burning steam locomotive heats steam to 180°C and exhausts it at 100°C. During 1 s of operation, it consumes 500 million J of energy from the burning coal. According to

196

Table 1, how much work can be obtained from this locomotive during 1 s of operation under ideal conditions (no friction or other imperfections)? 7. In the preceding question, how much work can be obtained under actual conditions?

THE AUTOMOBILE AND TRANSPORTATION 8. You travel alone from New York to Los Angeles, about 2800 miles. Working from Tables 3 and 4, how many gallons of gasoline will you use if you travel by car (assuming your car gets average gasoline mileage for U.S. automobiles)? How many gallons if you travel by air? By bus? By train? 9. A 100-car freight train hauls 16,000 metric tonnes of freight from New York to Los Angeles, about 5000 km. How many trucks would be needed for this load, assuming that each truck carries 32 tonnes of freight? Working from Table 5, how many liters of gasoline are saved if this load is carried by train rather than by truck?

THE STEAM–ELECTRIC POWER PLANT 10.

MAKING ESTIMATES. In the United States, solar energy strikes a single square meter of ground at an average rate (averaged over day and night and over the different seasons) of 200 watts (200 joules/second). At what average rate does solar energy strike a football field (about 100 m by 30 m)? 11. Continuing the preceding question, a typical U.S. home consumes electricity at an average rate of 1 kW. How much surface area would be needed to provide this electric power, assuming a 10% conversion efficiency? What dimensions would a squareshaped photovoltaic collector need to cover this area?

EXPONENTIAL GROWTH 12. How much electric energy would have been produced in 1985 if the exponential growth of 1935–1975 had continued for another 10 years beyond 1975? If this growth had contin-

Second Law of Thermodynamics: Problem Set Table 3 Fuel efficiencies of passenger vehicles km/liter

mi/gal

National averages: All U.S. passenger vehicles (cars, SUVs, pickups)

9

22

New U.S. passenger vehicles

12

27

New European Union passenger vehicles

14

34

New cars: Ford Expedition, SUV

6

16

Honda Accord

11

25

Ford Escape, SUV hybrid

13

32

Nissan Altima, hybrid

14

34

Smart Car

16

37

Honda Civic, hybrid

18

42

Toyota Prius, hybrid

21

50

Table 4 U.S. passenger-moving efficiencies of several human transportation modes passenger-km per liter

passenger-mi per gal

passenger-km per MJ

Human on bicycle

642*

1530*

18.0

Human walking

178*

425*

5.0

Intercity rail

60

144

1.7

Carpool auto (occupancy = 4)

36

88

1.0

Urban bus

33

80

0.9

Commercial airline

21

50

0.6

Commuting auto (occupancy = 1.15)

11

25

0.3

*For walking and bicycling, the table uses the “gasoline equivalent” of the required number of food calories.

Table 5 Freight-moving efficiencies of three transportation modes kg-km tonne-km per MJ per liter

2900

100

Truck (heavy)

720

25

Air (freight)

145

5

Rail (freight train)

ued, roughly how many power plants would have been needed in 1985, as compared with 1975? 13. During 1985–1990, annual U.S. population growth was 0.8% per year, for Mexico it was 2.2%, and for Kenya (the highest) it was 4.2%. At these rates, how long does it take for the populations of each of these countries to double?

14. World population is now about 7 billion. The growth rate has been roughly 2% per year since the end of World War II (1945). If a 2% per year growth rate continued, when would world population be 14 billion? 15. Centerville, with a growth rate of 7% annually, is using its only sewage treatment plant at maximum capacity. If it continues its present growth rate, how many sewage treatment plants will it need 40 years from now? 16. During the 1980s, U.S. car and truck miles traveled increased by 4% per year, but the length of highway increased by only 0.1% per year. Find the doubling time for vehicle miles traveled and for miles of highway. 17. Continuing the preceding problem, suppose that these rates are maintained in the future. While vehicle miles double (a 100% increase), by roughly what percentage will the amount of highway increase? Roughly, how much worse will traffic congestion be at that time?

197

Second Law of Thermodynamics: Problem Set

Answers to Concept Checks 1. (e) 2. (b) 3. The “work” pipe appears to be about 1/3 as wide as the “ther4. 5. 6. 7. 8.

9. 10.

11. 12.

mal energy flow” pipe coming out of the high-temperature source, (a). The work done must be 400 J - 300 J = 100 J, so the efficiency is 100 J/400 J, (f). Table 1 tells us that the actual efficiency is about 40%, so the amount that goes into producing electricity is 0.4 * 1000 kg = 400 kg, (d). Salt and water molecules are randomly mixed together, so microscopic disorganization (entropy) increases, (a). (a), (b), and (f ) 125 tonnes * 200 km = 25,000 tonne-km. Table 5 tells us that a truck can transport 25 tonne-km on 1 liter of gasoline, so the number of liters needed for 25,000 tonne-km is 25,000>25 = 1000 liters. The number of liters needed for a train is 25,000>100 = 250 liters, (d). 2200>2500 = 88%, (c) According to the periodic table, carbon and oxygen atoms have roughly equal masses (oxygen is actually 33% more massive). Thus the CO2 molecule is roughly three times as massive as the C atom, so the CO2 emitted is roughly three times as massive as the coal. 3 * 8000 tonnes = 24,000 tonnes, (d). (f ) T = 70>P = 70>8 L 9, (b)

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Cold, below freezing; cold, above freezing; a nice day; a hot day. 3. A Celsius degree. 5. Refrigerator; it moves thermal energy from inside the refrigerator to outside. It does not violate the second law, because the second law states that thermal energy cannot spontaneously flow from cold to hot. In a refrigerator, the flow is not spontaneous (it is assisted by the operation of the refrigerator, which draws thermal energy out of the inside). Another example: air conditioner. 7. Yes; an example is dropping a book onto a table. No, because the second law prohibits it. 9. Hydroelectric power plant, bicycle. 11. The efficiency must be less than 100%. 13. Don’t invest. Slick’s scheme violates the second law of thermodynamics, because it purports to convert thermal energy entirely into the work needed to drive the automobile. 15. According to the preceding question, there are 1.8 Fahrenheit degrees in each Celsius degree. 10°C is 10 Celsius degrees above freezing, which is 10 * 1.8 = 18 Fahrenheit degrees above freezing, or 32°F + 18°F = 50°F. Similarly, 30°C is 30 * 1.8 = 54 Fahrenheit degrees above freezing, or 32°F + 54°F = 88°F. 17. Efficiency = 300 J>1500 J = 20%. 1200 J are exhausted in each cycle. 19. No. We can push the rock back to its starting condition. The precise process (without the push) cannot be reversed.

198

21. This does not violate the law of increasing entropy,

23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43.

45.

because the egg is not an isolated system; it has outside help in the form of energy (thermal energy that is transferred into the egg). Microscopic disorganization increases, so entropy increases. You should get more useful work, because the efficiency would tend to be higher due to the higher input temperature. Transportation. Assuming an efficiency of 13%, about 13 barrels go into getting the car down the road. Hydroelectric, because it is not a heat engine and so is not subject to the inefficiency implied by the second law of thermodynamics. Electricity from a coal-fired generating plant, because such a plant is about 40% efficient while a car engine is only 10%–15% efficient (Table 1). (15 kg>s) * (3600 s>hour) * (24 hr>day) = 1,300,000 kg>day = 1300 tonnes per day. Between 5 and 6 months: 4% in 1 month, 8% in 2 months, etc. No; yes. Firewood, wind, water behind a dam, ocean thermal. World population is about 6 billion now. 200 years is 5 doubling times, so the population would have increased by a factor of 2 * 2 * 2 * 2 * 2 = 32. So the population would be 32 * 6 billion = 192 billion (of course, this will not happen because the doubling time will not be maintained). No, because part of it is a straight line.

Problems 1. eff = Work output>ThermE input, so ThermE input = Work>eff = 2000 J>0.3 = 6670 J. 3. Input temp = (500 + 273) K = 773 K, eff = (input temp - exhaust temp)>input temp = 420 K>773 K = 54%. 5. The actual efficiency is (work output)>(total energy input) = (1000 J - 750 J)>1000 J = 250 J>1000 J = 25%. 7. From Table 1, actual eff = 0.1. eff = Work out>ThermE in, so Work = ThermE in * eff = (500 * 106 J) * 0.1 = 50 * 106 J. 9. Number of trucks = 16,000 tons>32 tons = 500 trucks. The number of tonne-km is 16,000 tonnes * 5000 km = 8 * 107 tonne-km. By truck, the gallons of gasoline required is 8 * 107 tonne-km>25 tonne-km>liter = 3.2 * 106 liters. By train, the gallons of gasoline required is only 1/4 as much (because it’s four times more efficient, according to Table 5), or 0.8 * 106 liter. 11. To receive 1 kW, a home would need to use all of the solar energy striking an area of 5 m2. But since the conversion efficiency is only 10%, the receiving area would need to be 10 times larger, or 50 m2. A square-shaped collector would need to be about 7 m on a side. 13. T = 70>P = 70>0.8 = 80 yr (U.S.), T = 70>2.2 = 32 yr (Mexico), T = 70>4.2 = 17 yr (Kenya). 15. T = 70>P = 70>7 = 10 yr. So 40 years is 4 doubling times. Centerville’s population will increase by a factor of 16 during this time. It will need 16 treatment plants. 17. At a 4% rate of increase, the number of vehicle miles traveled per year will double in T = 70>4 = 18 yrs. During this time, the number of miles of highway will increase by about (0.1%>yr) * 18 yrs = 1.8%, a very small increase. Thus, congestion will be about twice as bad.

Electromagnetism

One day, Sir, you may tax it. Michael Faraday, Co-Discoverer of Electromagnetism, When asked by the Chancellor of the Exchequer about the Practical Worth of Electricity

I

n this chapter, we are on the trail of light: What is light? How does it behave? How is it related to the basic physical forces such as electricity? Are phenomena such as “X-rays” and “infrared rays” related to light, and if so, how? How do these various kinds of rays affect our planet? Light is all around us, yet it’s not easy to say what light is. How are you able to see this page? Do your eyes emit invisible rays that then move toward the page, as Plato and Euclid thought? Does the page send out or reflect a stream of particles that is received by your eyes, as the Pythagoreans and Isaac Newton thought? Is light a wave, as Newton’s contemporary Christian Huygens thought? The nature of light is one of science’s oldest questions, a question that led to both of the great modern (post-1900) theories, namely relativity theory and quantum theory. Light and other “electromagnetic radiations” are also crucial for understanding social topics like solar energy and global warming. This chapter studies electromagnetism, meaning the combined effects of electric and magnetic forces. It’s a topic that’s essential for understanding light, for understanding modern physics, and for discussing ozone depletion and global warming. Sections 1 and 2 study the electric force and the electric, or planetary, model of the atom. Section 3 looks at electric current and other implications of the electric atom. Section 4 studies electric circuits. In Section 5, you’ll meet a radically new concept: force fields or simply “fields.” “Radical” is not too strong a term, for this text has so far been based on the Newtonian view of a universe made of particles moving mechanically in empty space, and fields are in many ways the opposite of particles. Physicist Michael Faraday first conceived of force fields in 1831 in connection with magnetism, and they soon became essential for understanding electromagnetic phenomena. Today, fields are essential for understanding most of modern physics, especially electromagnetism, gravity, and quantum physics. Section 6 uses fields to present the full electromagnetic force.

From Chapter 8 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

199

Electromagnetism

1 THE ELECTRIC FORCE

Figure 1

Two rubbed transparencies exert electric forces on each other.

Gordon R. Gore Figure 2

A really bad hair day: electric hair. The source of this effect is the “charged” metal sphere.

Find a couple of plastic transparencies that teachers sometimes use on overhead projectors. Rub them vigorously with tissue paper and hold them from one edge in separate hands, parallel and just a few centimeters apart (Figure 1). They should repel each other. The force weakens at larger separations, but careful observation would show that this force still exists even when the transparencies are far apart. Now spread out the tissue on a level surface and hold a rubbed transparency directly above it. The tissue is pulled to the transparency. You may experience similar forces when you take clothes from a dryer or brush your hair. Figure 2 shows an extreme example. This force is a little like gravity: It can act across a distance, and it weakens as the separation widens. But there are reasons why it cannot be gravity: The transparencies repel each other, whereas gravity attracts: this new force is far stronger than gravity could possibly be between relatively low-mass objects such as transparencies and tissues; and this force depends on whether the transparencies are rubbed, and it’s hard to see how rubbing could affect gravity. This force is called the electric force. An “electrified” object such as the rubbed transparency or tissue is said to be electrically charged or just “charged,” and any process that produces this state is called charging. The experiments show that when we electrically charge two identical objects in identical ways, they repel each other. But the charged transparency and the charged tissue attract each other. So the transparency must be charged differently from the tissue. After experimenting with lots of charged objects, one finds that they all fall into just two categories: those that repel the transparency but attract the tissue, and those that attract the transparency but repel the tissue. These two categories are named positive and negative. Don’t attach much significance to the names—they could just as well be called red and blue, or charming and revolting. During the eighteenth century, French physicist Charles Coulomb measured the changes in the electric force between two objects (that is, the force by either object on the other) as he varied the amount of charge on them and the distance between them. He found that the force is proportional to the amount of charge on either object: If you double the charge on the first object, the force doubles; if you triple the charge on the second object, the force triples, etc. This is pretty much what you’d expect. But the way the force varies with distance is more interesting. As the transparency experiment shows, the force gets smaller as the distance gets larger. Working with charged objects that were small compared to the distance between them, Coulomb found that if the distance doubles, the force falls to one-fourth the initial value; if the distance triples, the force falls to one-ninth; if the distance quadruples, the force falls to one-sixteenth. Any guesses as to the relationship between distance and force? ——— Time out, for guessing. We found precisely the same relationship between force and distance when we studied gravitational force. The electric force is proportional to the inverse of the square of the distance, just as is the gravitational force. I’ll summarize all this as

200

Electromagnetism

Coulomb’s Law of the Electric Force Between any two small charged objects there is a force that is repulsive if both objects have positive charge or if both have negative charge, and is attractive if one has positive and the other has negative charge. This force is proportional to the amount of charge on each object, and proportional to the inverse of the square of the distance between them: electric force r

(charge on 1st object) * (charge on 2nd object) square of the distance between them

Using abbreviated symbols, F r

q1 * q2 d2

If electric charge is measured in “coulombs” (see below), distance in meters, and force in newtons, then this proportionality becomes1 F = 9 * 109

q1 * q2 d2

The definition of the measurement unit for electric charge, the coulomb (abbreviated C), was chosen for convenience of use in electrical circuits. It turns out that it’s the total charge of 6.25 billion billion electrons. That sounds like a lot of charge. CONCEPT CHECK 1 Two objects each carry a charge of 1 C. How much force do they exert on each other at a distance of 1 meter? (a) 1 N. (b) 9 N. (c) 9 million N. (d) 9 billion N. (e) about 10–10 N.

Concept Check 1 reveals one way of defining the “coulomb”: It’s the amount of charge that causes an electric force of 9 * 109 N on an identical charge at a distance of 1 m. This is about the weight of 25,000 fully loaded highway trucks! Clearly, 1 C is a lot of charge. Nevertheless, 1 C is only the amount of charge that passes through an ordinary (incandescent) 100-watt lightbulb in a little over a second. This seems paradoxical: Lightbulbs don’t exert forces equal to the weight of all those trucks! The resolution (see Section 3 for more on this) is that the electrons that flow through wires and bulbs are always surrounded by an equal number of stationary protons, so that the wire and the bulb are actually electrically neutral (no net charge) and exert no electrical force on surrounding objects.2 Coulomb’s law refers to two small objects (much smaller than the distance between them) having net charges q1 and q2, unbalanced by other charges of the opposite sign. The charges on most such objects are usually measured in millionths of a coulomb (10 –6 C). Although Coulomb’s law looks a whole lot like Newton’s law of gravity, there are differences. For one thing, the electric force can be either attractive or repulsive, but the gravitational force can be only attractive. “Negative mass”—mass that repels ordinary mass—has never been observed, but both positive and negative electric charge is all around us. 1 2

More precisely, the number on the right-hand side is 8.988 * 109. For reasons described in Section 6, they can, however, exert magnetic forces on surrounding objects.

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Electromagnetism

For another thing, the electric force between any two charged particles is generally vastly larger than the gravitational force between them. For example, the electric force between the electron and the proton in a hydrogen atom is more than 1000 trillion trillion trillion (or 1039) times larger than the gravitational force between them. This is why scientists can ignore the effects of gravity within an atom. Comparison of the huge “proportionality constant” 9 * 109 in Coulomb’s law with the tiny proportionality constant 6.7 * 10 - 11 in Newton’s law of gravity also indicates that, at the macroscopic level in ordinary units, electric forces tend to be much larger. This is why it’s so easy to demonstrate electrical forces between ordinary charged objects (Figures 1 and 2) but challenging to demonstrate gravitational forces between ordinary objects. Finally, the electric and gravitational forces arise from different sources: one from charge, the other from mass. You can, for example, add additional charge to a charged object without appreciably changing its mass, perhaps greatly increasing the electric force on the object but without noticeably changing the gravitational force. So these are fundamentally different forces. Nevertheless, their similarities encouraged Albert Einstein to spend the latter part of his life searching unsuccessfully for a “unified field theory” that would unify these two forces into a single force. More recently we’ve begun to realize Einstein’s dream, but at the microscopic level. We’ve learned that there seem to be four fundamental forces—gravitational, electromagnetic, strong, and weak. Using quantum physics, the weak and electromagnetic forces have been unified and the unification of these two forces with the strong force appears near at hand, but the ultimate unification of these three forces with gravity looks far more challenging.

2 THE ELECTRIC ATOM

The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine. Ernest Rutherford, discoverer of the atomic nucleus, made this famous wrong prediction in 1933.

Although thermal energy, chemical reactions, and much more are comprehensible in terms of the Greek model of the atom as a single tiny rigid object, it’s difficult to fit electromagnetic phenomena into this indivisible-particle picture of the atom. Where does electric charge come from? How can rubbing produce it? Why are there two kinds of charge? These and other questions led, early in the twentieth century, to the planetary model of the atom.3 According to this theory, the atom is not a solid, indivisible object. To the contrary, the planetary model of the atom is almost entirely empty, is divisible, and is made of many parts. As its name implies, the planetary model of the atom resembles a miniature solar system. Figure 3 portrays single atoms of two different elements, helium and carbon. The defining feature of the planetary model of the atom is the tiny nucleus (greatly enlarged in the figure) at the center, surrounded by a number of even tinier electrons (“electrified ones”) that orbit the nucleus at a distance much greater than the size of the nucleus itself. The overall size of an atom, the distance across its electron orbits, is typically 10–10 m. This is roughly the distance between the centers of adjoining atoms in solid materials. But a typical nucleus is 10,000 times smaller, on the order of 10–14 m in size. To put this into perspective, if we built a scaled-up atom in which the nucleus were represented by a soccer ball, the orbiting electrons would be dust specks several kilometers away! An atom is nearly totally empty. 3

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It’s sad but true that the widely used term “planetary model of the atom” is self-contradictory. “A-tom” means indivisible, but “planetary” refers to the parts into which the atom can be divided! The old Greek name, atom, has stuck, but not its essence.

Electromagnetism

You can add or remove charge from macroscopic objects such as transparencies and tissues, but you can’t remove the charge from an electron—it’s permanently negatively charged. Furthermore, to as high a precision as we can measure, all electrons have precisely the same amount of charge and the same mass. The electron’s mass is about 2000 times smaller than the mass of even the least massive atom. Nobody has any idea of why any of this is so. The nucleus is itself made of several subatomic particles of two types, called protons and neutrons. A proton (“positive one”) is another permanently charged particle, charged precisely as strongly as the electron, but positively instead of negatively. When we say that electrons and protons are charged “equally strongly,” we mean that when they are placed near some other charged object, both exert the same amount of force (but in opposite directions) at the same distance away. But they don’t have equal masses. The proton is about 2000 times more massive than an electron. The neutron (“neutral one”) is an uncharged, or neutral, particle whose mass is nearly the same as the proton’s mass. Between one and a few hundred protons and neutrons form the nucleus of any atom. The “glue” that holds electrons into their orbits around the nucleus is the electric attraction between electrons and protons. The glue that holds the nucleus together, however, must be some nonelectric force, because the electric force between the positively charged protons is repulsive and neutrons do not exert an electric force. Since an atom’s electrons are relatively distant from the nucleus, it’s not surprising to learn that it’s easy to remove electrons from atoms. But on Earth, most atoms have just as many electrons as protons, because any atom having a deficiency of electrons carries a net positive charge and quickly attracts electrons from its environment, while any atom having an excess of electrons quickly loses its outermost electrons to its environment. That’s why it took so long to discover many electrical phenomena: Individual atoms are normally electrically neutral and exhibit no obvious electrical effects. An atom that does have an excess or deficiency of electrons is called an ion.

How do we know that electrons exist? In 1897, English physicist J. J. Thomson (Figure 4) was investigating a type of invisible beam known as a cathode ray. Cathode rays were produced in a nearly evacuated (emptied of air) glass tube whose two ends were attached by metal wires to a source of electric power. When the power was switched on, rays of unknown composition streamed along the length of the tube, as could be observed by the flashes of light where they hit one end of the tube. Suspecting that these rays were electrically charged, Thomson placed electric charges and magnets around them. The flashes of light shifted in position, which meant that the rays had to be charged. The only charged microscopic objects then known were ions, observed in certain chemical experiments. So Thomson hypothesized that the electrically charged cathode rays were streams of such ions. He then measured the deflections of the rays. Using the known electric and magnetic force laws, he deduced from these measurements that these rays were streams of charged particles whose charge was the same as the charge of typical ions but whose mass was far smaller, only about 1/2000th of an ion’s mass.4 These, then, were not ions. This was revolutionary. It established that atoms had parts. According to Thomson, “At first there were very few who believed in the existence of these bodies smaller than atoms.... It was only after I was convinced that the experiments left no escape from it that

Helium

Carbon

Figure 3

Two examples of the planetary model of the atom. Protons are green, neutrons are white, and electrons are black. The diagrams are not drawn to scale! If they were drawn to scale, the nuclei and the electrons would be too small to be seen.

American Institute of Physics/ Emilio Segre Visual Archives Figure 4

4

More precisely, he found that the ratio of the mass to the charge was 1/2000th of the ratio of mass to charge for any known ion.

J.J. Thomson, discoverer of the electron. He was the first to show that atoms are made of smaller, electrically charged parts.

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Electromagnetism I published my belief in the existence of bodies smaller than atoms.” Thomson had discovered the electron. Today, Thomson’s rays, now known as electron beams, are used in TV tubes, fluorescent bulbs, computer screens, and much more.

CONCEPT CHECK 2 Which one of the following has the smallest mass, and which one has the largest mass? (a) Proton. (b) Electron. (c) Helium nucleus. (d) Neutron. (e) Water molecule. (f) Oxygen atom.

C.E.Wynn-Williams/American Institute of Physics/Emilio Segre Visual Archives Figure 5

Ernest Rutherford, codiscoverer of the nucleus and one of the greatest experimental physicists of the twentieth century, talks with a colleague. Because Rutherford’s resounding voice could upset delicate experimental apparatus, the sign overhead was playfully aimed at him. His research on radioactivity and nuclear physics influenced a generation of experimental physicists early in the twentieth century. Not exist—not exist! Why I can see the little beggars there in front of me as plainly as I can see that spoon! Rutherford, When Asked over a Dinner Table Whether He Believed That Atomic Nuclei Really Existed

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How do we know that every atom has a nucleus? Like others around 1910, New Zealander Ernest Rutherford (Figure 5) was trying to determine the atom’s internal structure. He knew that atoms contained electrons, so a positive charge must be present too. It was known that atoms are pressed right up against one another in solid materials and that huge forces are required to compress solids into smaller volumes. This suggested to scientists that atoms must be filled with matter throughout most of their volume. To test this hypothesis, Rutherford used what has become a traditional physics technique: He threw tiny things at other tiny things in order to see what would happen. He “threw” a recently discovered ray known as an alpha ray at the atoms residing in a thin metal foil, similar to aluminum foil. The alpha ray was a high-energy stream of positively charged and fairly massive “alpha particles” (helium nuclei, made of two protons and two neutrons) that emerged from certain “radioactive” substances. The idea was to observe how far the foil deflected the fast-moving alpha particles from their original directions and, from this, to deduce how matter must be distributed within the foil’s atoms (Figure 6). The deflection was measured by observing flashes of light where the alpha particles hit a screen placed partially around the foil, as shown in the figure. Similar experiments had been done before, and it had been found that the foil had surprisingly little effect on the motion of the alpha particles. Most deflections were less than 1 angular degree, as shown in the two “magnified” portions of the diagram. Since the foils were about 500 atoms thick, alpha particles apparently passed straight through most atoms without deflection. Apparently, atoms were fairly porous, open structures. Then in 1911, Rutherford decided to see whether any alpha particles were deflected through very large angles, greater than 90 degrees. He studied this by nearly surrounding the foil with the detection screen. He expected to see no large deflections, because a fast-moving and massive alpha particle was thought to pass through an atom like a cannonball through pudding and would have to experience an enormous force to be deflected by very much. His coworkers came to Rutherford a few days later with the news that a few alpha particles had been deflected backward. In Rutherford’s words, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch [artillery] shell at a piece of tissue paper and it came back and hit you.” Apparently, nearly all of the atom’s material was concentrated at its center. The cannonball had struck another cannonball and bounced back. Rutherford and his colleagues had discovered the atomic nucleus.

CONCEPT CHECK 3 Which of the following objects has an overall, or “net,” charge? (a) Proton. (b) Electron. (c) Helium nucleus. (d) Neutron. (e) Ionized oxygen atom. (f) Nonionized hydrogen atom.

3 ELECTRIC CURRENT AND OTHER APPLICATIONS OF THE ELECTRIC ATOM Like all good theories, the planetary model of the atom explains many things. It explains our experiments with charged objects. When you rub a transparency with tissue, some of the loosely attached outermost electrons in the transparency’s

Electromagnetism

Metal foil (target) Part of metal foil, magnified Alpha ray

Source of alpha ray Receiving screen to detect alpha particles

An occasional alpha particle is bounced back by a close encounter with a nucleus

Single atom, magnified

Most alpha particles pass straight through

Figure 6

Rutherford’s alpha-scattering experiment.

atoms are rubbed off and transferred to the tissue’s atoms, charging the transparency positively and the tissue negatively. That’s why the two attract each other after rubbing. The two rubbed transparencies repel each other because both have a deficiency of electrons. The planetary model provides a microscopic explanation of many chemical phenomena, including why all atoms of a single element have identical chemical behaviors and why different elements are chemically different. An element’s chemical behavior results from the behavior of its orbital electrons. Table salt, NaCl, makes a good example. Sodium (Na) combines readily with chlorine (Cl) because the Cl atom has a stronger attraction for electrons than does Na, so one electron from Na is attracted to Cl, leaving an overall positive charge on the Na and a negative charge on the Cl. The electric force between opposite charges then attracts and holds the Na and the Cl atoms together. The property that really defines an element is the number of protons in the atomic nuclei of that element, because the number of electrons in the neutral (nonionized) atom must equal the number of protons, and the number of electrons in turn determines the chemical properties of the atom. Two neutral atoms with the same number of electrons have the same chemical properties because their electron orbits have the same shapes. So it makes sense to number the different elements according to the number of protons in an atom of the element. This number is called the element’s atomic number.

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Since an atom is mostly empty space, what keeps solid matter solid? The answer is that the repulsion of electrons by other electrons keeps atoms from penetrating one another. All contact forces, such as your hand slapping a table, can be interpreted microscopically as forces by the orbital electrons in atoms (in your hand, for instance) on the orbital electrons in other atoms (in the table). Every time you touch something, you experience the force between orbiting electrons! In fact, all the forces in your daily environment come down to just two kinds: The gravitational force explains weight, while the electromagnetic force explains all the contact forces and also the forces between charged objects and, as we’ll see, magnetized objects. That’s some unification! When you electrically charge an object, electrons (or it could be protons, which are also moveable in some situations) are merely moved onto or off of the object. No electrons are created or destroyed. Charge is “conserved.” In fact, careful measurements have verified to high precision that the net (positives minus negatives) amount of charge is conserved in every process. Even in high-energy physics processes where charged particles such as electrons are actually created rather than merely transferred, equal numbers of oppositely-charged particles such as “antielectrons” are always created. This is another conservation law, similar to, and as fundamentally important as, conservation of momentum and conservation of energy: The Law of Conservation of Charge Although charge can be moved around and although charged particles can be created or destroyed, no net charge (positives minus negatives) can be created or destroyed.

Nobody has ever figured out how to split an electron into parts. So when you charge an object, it always gains or loses some whole number multiple of the electron’s charge. An object can have a charge of 1 electron, 2 electrons, 3 electrons, etc., but it cannot have a charge of 1.6 or 2.9 electrons. We call this quantization of charge, with the smallest quantity or “quantum” of charge being the electron’s (or proton’s) charge.5 Another way to say this is that charge is a discontinuous (computer buffs might say “digital”) quantity rather than a continuous (or “analogue”) quantity: It increases or decreases in steps that are whole number multiples of the electron’s charge. This is our first example of a quantized aspect of nature. The planetary atom underlies many electrical devices, such as batteries. Any battery has two “terminals,” one positively charged and the other negatively charged. Chemical processes within the battery maintain these charges by removing electrons from one terminal and depositing them on the other. If we attach the two ends of a single copper (or other metal) wire to the terminals, every charged particle in the wire instantly feels an electric force. These forces produce practically no disturbance of the positively charged copper nuclei, which are fixed in position. But in copper or any other metal, each atom’s outermost electrons are only loosely held to

5

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We’ve discovered that protons are made of smaller particles called “quarks,” and quarks carry charges having one-third and two-thirds the magnitude of the electron’s charge. However, quarks have never been found in isolation—they’re always combined into particles such as the proton carrying a whole number multiple of the electron’s charge.

Electromagnetism

their parent atom. As soon as these conduction electrons feel the electric forces established by a battery, they all simultaneously begin to move along the wire, through the body of the metal. As they move, they constantly bump into atoms, slowing the electrons and causing the atoms to vibrate, warming the wire. Such a flow of charged particles is called an electric current (Figure 7). Such a battery with a simple wire attached to the terminals forms an electric circuit: a closed loop around which electric current can flow. But try the experiment shown in Figure 7 carefully and only with a small flashlight battery. The problem is that electrons flow so easily through ordinary wires that the electric current is large, so the warming effect described above can burn out either the battery or a portion of the wire. Materials such as copper and other metals through which electric current can easily flow are called electrical conductors; they have atoms whose outermost electrons are only loosely attached. Materials such as rubber and dry wood whose outermost electrons are more firmly attached don’t permit the easy flow of electric current and are called insulators. If, as shown in Figure 8, we insert a lightbulb into the circuit of Figure 7, electrons will flow through the bulb’s thin filament and heat it by simply bumping into atoms, causing them to vibrate energetically. As compared with the circuit of Figure 7, the insertion of the narrow filament causes the flow of current in the circuit to decrease, for the same reason that the flow of water in a garden hose is reduced if you squeeze the hose at one point to make the cross-sectional area smaller: Conduction electrons can’t get through the narrow part (the filament) in such large numbers. We say that the filament creates electrical resistance in the circuit, by which we mean that the filament reduces the overall flow of current throughout the entire circuit. This is why you can easily burn out the battery of a circuit like Figure 7, while a circuit like Figure 8 doesn’t burn out quickly. The filament, on the other hand, is made of a heat-resistant material such as tungsten and is designed to heat up until it glows. It heats up because conduction electrons move faster through the thin filament than through the fatter wire, much as water “spouts” more rapidly out Figure 7 Short length of wire, magnified Electrons move through wire

–

+

Wire loop

A battery produces electrical forces that cause conduction electrons (black dots in the magnified view) to move through the volume of the metal wire (the green circles are the wire’s atoms). Electrons flow around the wire circuit, repelled by the battery’s negative terminal and attracted toward the positive terminal. Chemical forces within the battery then push the electrons through the battery from the positive electrode back to the negative electrode. Note that electrons within the battery feel electric forces toward the positive terminal, while leftward chemical forces push them toward the negative terminal.

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Electromagnetism Figure 8

Because electrons flow so easily through ordinary wires, the circuit of Figure 7 would soon burn out the wire or battery. Inserting an incandescent lightbulb or other “circuit element” reduces the flow to safe levels. This happens because the lightbulb’s glowing filament is very thin and thus restricts or “resists” the current, much as a squeezed garden hose restricts the flow of water.

– +

–

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of a garden hose when you narrow the nozzle. These faster electrons collide more violently with the atoms of the filament, heating the filament to high temperatures. The average forward speed of electrons in typical electrical circuits is surprisingly slow because they constantly run into atoms and bounce in all directions, enormously slowing their forward motion. A conduction electron’s average forward speed along a wire, called its drift velocity, is typically less than one millimeter per second! You might wonder, then, how the lightbulb in your room lights up so quickly after the switch is turned on, since it’s at least a few meters from the switch to the bulb and a conduction electron would take about an hour to cross this distance. The answer is that the electric force is not transmitted by the motions of the conduction electrons. Instead, the light switch connects a wire containing the bulb’s filament to a power source such as a battery, and electric forces and energy spreading outward from the power source at the speed of light exert forces on all the electrons in the circuit, causing them all to move at practically the same instant. All the standard electrical appliances—toasters, lightbulbs, electric motors, and so forth—are based on a similar flow of the electrons that ordinarily orbit within atoms, and they all create electrical resistance in the circuit that powers them. Figure 8 shows how the process works when a battery causes the electric force. Electrical outlets in your home work in a similar way, except that the current reverses its direction of flow many times every second (Figure 9). Such a current is called alternating current or AC, while current that always flows in the same direction is called direct current or DC. In any battery, one terminal remains negative and the other remains positive because the chemical reactions inside continue operating in the same direction, so batteries produce DC. Although devices exist that can transform DC into AC and vice-versa, AC typically arises from an entirely different process. This different process is the rotation of a loop of wire in a magnetic field. Commercial electric power plants in the United States use a rotational frequency of 60 cycles per second. So when you plug your lamp into a wall outlet, the conduction electrons in the electric cord and in the lamp instantly (well, with a slight delay determined by the speed of light) begin moving back and forth 60 times per second, moving forward and then backward at a drift speed of less than 1 mm per second. Think of electrons jiggling back and forth over tiny distances while bouncing rapidly in all directions.

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Electromagnetism Figure 9

Electrical appliances are based on the motion of unseen electrons that move back and forth in the appliances. A wall socket (more precisely, a generating station connected by wires to a wall socket) is the electrical equivalent of a water pump. It “pumps” (energizes) the electrons so that they can move back and forth in the circuit.

Wall socket

When the plug is plugged in, electrons flow first in the direction of the black arrows, and then in the Plug direction of the green arrows, reversing directions many times every second. Normally, the two wires shown stretching from the plug to the bulb are both placed inside a single electrical cord.

4 ELECTRIC CIRCUITS Electricity, in the form of electrons flowing through all sorts of devices, is so pervasive today that it’s a defining feature of modern life. Many poorer regions of the planet have little or no electricity and so live very different lives from you and me. Think of how your life—the past 24 hours for example—would be different if you’d lived two centuries ago when there was no electricity! To understand in more detail how electricity works, look again at Figure 8. This simple electric circuit has three essential electrical elements: a battery, a metal wire that conducts electric current, and a light bulb. The battery moves electrons from the positive to the negative terminal by means of chemical reactions that we won’t further delve into here. Even without the wire, an isolated battery has electrons piled on the negative terminal and excess protons (a deficiency of electrons, really) on the positive terminal. Since there’s nowhere for these electrons to go, nothing happens: The battery just sits there with charge piled on both terminals and no current flowing. But once you attach the wire and bulb, electrons have someplace to go: from the negative terminal onto the wire, and from the wire onto the positive terminal. As described in the previous section, conduction electrons immediately start flowing everywhere in the circuit. Let’s look at this in terms of energy. With the disconnected battery (no wire), excess electrons are more or less at rest on the negative terminal. Nevertheless, they have energy. The reason is that energy is the capacity to do work, and these electrons could do work if you connected the external circuit to the terminals and allowed the electrons on the terminal to flow through the circuit. For this circuit, the work would be done within the lightbulb filament as electrons heat the filament. What do you suppose we call the form of energy that the electrons have when they’re at rest on the negative terminal? ——— (Pause, for supposing)

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The answer is electrical (or electromagnetic) energy; it could be defined as “the energy that an electrically charged object has due to electrical (or electromagnetic) forces on it.” A useful analogy: The electrical energy of an electron on the negative terminal is analogous to the gravitational energy of a rock at the top of a hill. Just as the rock can give up its gravitational energy (while creating kinetic and thermal energy) by sliding down the hill, the electron can give up its electrical energy (while creating radiant and thermal energy) by flowing around the external circuit (the wire and bulb) to the positive terminal. Electrons arriving at the positive terminal are like the rock arriving at the bottom of the hill. They’ve lost their electrical energy. The purpose of the battery is then to “pick up” these electrons from the positive terminal and push them back “up” to the negative terminal, against the electrical attraction of the positive terminal and the repulsion of the negative terminal, so that they can again flow around the external circuit. The battery re-energizes the electrons. Quantitatively, a battery’s voltage is a measure of the amount of energy it gives to each electron. More precisely, a battery’s voltage is the number of joules of electric energy that the battery provides to each coulomb of electrons (some 1019 electrons) flowing through the battery. More generally, the voltage between (the official term is “across”) any two points A and B along an electrical circuit is the amount of electrical energy that a coulomb of charge would lose (or gain) in moving from A to B. For example, the voltage across a lightbulb is the number of joules of electrical energy lost by one coulomb of electrons in flowing from the negative side to the positive side of the bulb (Figure 8). Note that electrons lose energy in flowing “downhill” across a circuit element such as a lightbulb, and they gain energy when they are pushed “uphill” across a battery. From its definition, voltage is measured in joules/coulomb. But we have an abbreviation for this: the joule/coulomb is called—you guessed it (perhaps)—the volt. CONCEPT CHECK 4 As electrons move around the circuit of Figure 8, the energy transformations first in the battery and then in the bulb are (a) ChemE ¡ ElectE and then ThermE ¡ ElectE; (b) ElectE ¡ ChemE and then ThermE ¡ ElectE; (c) ChemE ¡ ElectE and then ElectE ¡ ThermE + RadE; (d) ElectE ¡ ChemE and then ElectE ¡ ThermE + RadE; (e) ThermE ¡ ElectE and then ElectE ¡ ThermE + RadE. CONCEPT CHECK 5 Suppose the battery of Figure 8 has a voltage of 2 volts, and that the battery sends 3 coulombs of electrons from the negative terminal and through the bulb to the positive terminal. The energy of these 3 coulombs of electrons as they leave the negative terminal, as compared with their energy upon arriving at the positive terminal, is (a) –6 joules; (b) +2 joules; (c) +6 volts; (d) +2 volts; (e) +6 joules.

Now let’s look more closely at the wire carrying current. I described this process microscopically in the previous section. The amount of current flowing in the wire could be quantitatively measured in electrons per second flowing into, out of, or across any cross-section of, the wire. This would be a huge number in most circuits, something like 1019 electrons per second. A more practical (because it’s a smaller, less cumbersome number) measure is the number of coulombs flowing, measured in coulombs/second. There’s an abbreviation for the coulomb/second: It’s called the ampere, or amp. The amount of current flowing out of the battery, into the bulb, out

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of the bulb, or in fact across any cross-section of the wire, filament, or battery, is the same everywhere along the circuit of either Figure 7 or 8. If this weren’t true, for instance if there were more electrons (per second) coming out of the small magnified segment of wire in Figure 7 than were going into it, then electrons would have to be created inside the small segment, which would violate conservation of charge. Finally, let’s look at the bulb. I explained in the previous section that the bulb’s filament slows or “resists” the flow of electrons mainly because the filament is narrow. The filament’s length and the material of which it’s made also help determine its resistance to the flow of electrons. Unsurprisingly, a battery of higher voltage causes a larger electric current to flow in the circuit of Figure 8 because the higher voltage provides more energy to each electron. But how much larger? Measurements show that, in most circuits, the current through any circuit element is proportional to the voltage across the element. For instance, if you double the voltage of the battery in Figure 8, you’ll double the current through the bulb. This proportionality is called Ohm’s law, although it’s just a practical rule that holds for most circuit elements in most circuits rather than a basic physical law comparable to Newton’s law or conservation of momentum. Maybe we should call it “Ohm’s rule of thumb.” Ohm’s law says that current is proportional to voltage. Equivalently, voltage must be proportional to current: voltage r current, or voltage = R * current where R is some fixed number for any particular circuit element. The standard symbols for voltage and current are V and I in which case V = RI or, equivalently, V = IR. Summing up: Ohm’s Law V = IR where V is the voltage across any circuit element and I is the current through it. Although V and I may vary, R is a fixed number for any particular circuit element. R is called the circuit element’s resistance.

“Resistance” is the right word for R because small R means that only a small voltage is needed get 1 amp (say) of current to flow in the element, while large R means a large voltage is needed to get 1 amp to flow. According to Ohm’s law, R is measured in volts/ampere. But we have an abbreviation for this combination, called the ohm. V = IR can be rearranged into two other useful forms: I = V>R,

and R = V>I

Example: Returning to the circuit of Figure 8, a resistance of 200 ohms is typical for an incandescent bulb filament. In this case, a 10-volt battery would create an electric current of I = V>R = 10 volt > 200 ohm = 0.05 amp. Every wire has a certain amount of electrical resistance. For example, the resistance of a 1-meter length of copper wire having a cross-sectional diameter of 1 millimeter is about 0.02 ohms. As we saw in the preceding section, a thinner wire (such

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as a lightbulb filament) would have a larger resistance. A longer wire should also have a larger resistance because the conduction electrons bump into more atoms as they more down a longer wire as compared with a shorter wire. So it’s not surprising that the resistance of 100 m of 1 mm diameter copper wire is 100 times the resistance of a 1 m length, or 2 ohms. From the preceding two paragraphs, you can see that in a circuit like Figure 8, each of the two strands of wire usually have a far smaller resistance than the circuit element. From an energy point of view, as electrons pass through the external circuit they lose a little energy in each strand of wire, but they lose most of their energy in the circuit element. CONCEPT CHECK 6 Suppose a 1 m strand of 1 mm diameter copper wire is attached directly from the negative to the positive terminal of a 6-volt battery, as in Figure 7. The current in the wire is then (a) 3000 amp; (b) 300 amp; (c) 30 amp; (d) 3 amp; (e) 0.3 amp.

Don’t try this at home. The current found in concept check 6 is large enough to raise the copper wire to its melting point within a few seconds! This is why you don’t want to attach a low resistance device such as a simple strand of wire across a battery, or worse yet (because the voltage is larger) a wall outlet. Such a situation is called a short circuit.

Fields are conditions of space itself, considered apart from any matter that may be in it. Fields can change from moment to moment and from point to point in space, in something like the way that temperature and wind velocity are conditions of the air that can vary with time and position in the atmosphere.... In the modern theory of elementary particles known as the Standard Model, a theory that has been well verified experimentally, the fundamental components of nature are a few dozen different kinds of fields. Steven Weinberg, Co-Inventor of the Standard Model of Elementary Particles

5 FORCE FIELDS: A DISTURBANCE OF SPACE To some people, it seems unbelievable that Earth could exert a force on the moon across 400,000 km of nearly empty space. After all, when you push a box across the floor, you exert a force on the box by actually touching or “contacting” it. How might you push a box without contacting it? Well, you could put another box between your hand and the box you want to push, and push on this other box (Figure 10). But it’s hard to see how you could push on box 2 in the figure without box 1 or something else to fill the space between your hands and box 2. By the same token, many nineteenth-century physicists felt that if Earth exerts a gravitational force on the moon, then something must fill the space between Earth and the moon to transmit the force. They called this “something” a gravitational field. It’s not really a “thing” in any ordinary sense—not material, not made of atoms. It’s one example of a “force field” (or simply “field”), a concept that lies at the heart of most new fundamental physics since 1900. Although physicists invented this idea in order to understand forces like gravity that act across empty space, we’ll discover that force fields are not imaginary but are physically quite real.

Figure 10

Could you push on box 2 from some distance away without having box 1 or some other object between you and box 2?

2 1

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Earth’s gravitational field fills the space around Earth, out to far beyond the moon. Think of this and other force fields as the effect that the source of a force (Earth, in this case) has on the surrounding space: not on the things in the space, but on the space itself. Think of a field as a distortion or disturbance of space. Earth’s gravity disturbs the space between Earth and the moon, and this disturbance—this gravitational field—pulls on the moon. So the gravitational field transmits Earth’s gravitational force to the moon. Earth’s gravitational field exists everywhere around Earth, even in places where there is nothing to feel any gravitational force. It would exist even if the moon weren’t there. The field fills the surrounding space in the way that smoke can fill a room. Earth’s gravitational field exists everywhere that a material object would feel Earth’s gravitational pull if such a material object were present. More generally: A gravitational field exists throughout any region of space where an object would feel a gravitational force if an object were placed there. Please ponder that sentence. A gravitational field is “the possibility of a gravitational force.” Every material object can exert gravitational forces and so is surrounded by its own gravitational field. We can speak of the gravitational field of the sun, the moon, a rock, your body, and so forth. Strictly speaking, each object’s gravitational field fills all space, but from a practical point of view, most fields can be neglected at large distances from the objects that create them. This force field concept applies to every force that can act across empty space, so it applies to the electric force. Just as a gravitational field surrounds every object possessing mass, an electric field surrounds every charged object. An electric field exists wherever any other charged object would (if it were present) feel an electric force; it is “the possibility of an electric force.” It fills the space between two or more separate charged objects and causes them to exert forces on each other. Force fields might seem abstract at first, but they are a simple and natural concept. Every mass, and every electric charge, is surrounded by a force field that you can’t see but that you can feel when the field exerts a force on other masses or other charges. For instance, an electrically charged transparency creates an electric field around itself, and this field exists even in the absence of other material objects around the transparency. Even if the transparency is isolated in outer space, it still creates an electric field throughout the space around it. You can demonstrate the existence of this electric field by holding a second charged transparency in the vicinity of the first transparency and finding that this second transparency feels an electric force. To visualize fields, we represent them by “field lines.” For an electric field, the field lines are in the direction of the force that would be exerted on a positive charge. For two examples, Figure 11(a) and (b) show some of the electric field lines surrounding a small positive charge and a small negative charge, respectively. In Figure 11(b), the lines point inward toward the negative charge since this is the direction of the force that would be exerted on a positive charge placed anywhere near the negative charge. For two more examples, Figure 12(a) shows some of the electric field lines surrounding two small equal (the same number of coulombs) but opposite (one positive and one negative) charges, while Figure 12(b) shows the electric fields lines surrounding two small equal positive charges. CONCEPT CHECK 7 The direction of the force on a positive charge placed at point A in Figure 11 would be (a) upward (toward the top of the page); (b) downward; (c) leftward; (d) rightward. What would be the direction of the force on a negative charge placed at point A?

⫹

A

(a) B ⫺

(b)

Figure 11

Electric field lines (a) near a small positive charge and (b) near a small negative charge.

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Electromagnetism Figure 12

C

Electric field lines surrounding (a) two small equal but opposite charges and (b) two small equal positive charges.

D ⫹

⫺

(a)

⫹

⫹

(b)

CONCEPT CHECK 8 The direction of the force on a negative charge placed at point B in Figure 11 would be (a) upward; (b) downward; (c) leftward; (d) rightward. CONCEPT CHECK 9 The direction of the force on a positive charge placed at point C in Figure 12 would be be (a) upward; (b) downward; (c) leftward; (d) rightward. What if the positive charge were instead placed at point D?

During the nineteenth century, scientists began using electric fields and also magnetic fields to help them understand and visualize electric and magnetic forces. In fact, it’s possible to state the basic laws of electricity and magnetism entirely in terms of force fields. Written in terms of the electric field, but leaving out the quantitative details, we can restate the electric force law (Coulomb’s law) this way: The Electric Force Law, Stated in Terms of Fields6 An electric field surrounds every charged object. Furthermore, any charged object that happens to be located at a point in space where an electric field exists will feel an electric force due to that field. Briefly, charged objects create electric fields and feel forces due to the electric fields of other objects.

6 ELECTROMAGNETISM Have you ever played with magnets? Everyone should have the opportunity to experience these intriguing toys. You can buy some at a toy store. If you bring two bar 6

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If you really want to know the quantitative details, here they are: The “electric field strength” at a distance d from a small charge q1 is E = (9 × 109) q1/d2, and the force on any charge q 2 placed at any point in an electric field E is F = q2 E. Putting the two formulas together, we recover Coulomb’s law.

Electromagnetism

magnets near each other, you will discover that their ends either attract or repel each other even when they are not touching. The ends of a magnet are called its north and south magnetic poles. Experiment shows that similar poles repel each other and dissimilar poles attract each other. This reminds us of the forces between electric charges: Likes repel, and unlikes attract. It’s plausible that the force acting between magnets actually is the electric force. This hypothesis is easy to check, for it predicts that magnets should exert forces on electrically charged objects such as a rubbed transparency or tissue. If you try this, you’ll find that the magnets do not exert forces on a rubbed transparency or tissue.7 So our hypothesis is false. The force between bar magnets is not the electric force, and the two ends of a magnet are not electrically charged. There are other big differences between magnetism and electricity. First, a bar magnet’s magnetism is permanent and has nothing to do with rubbing. Second, every magnet has both a north and a south pole. Nobody has found an object that possessed either kind of pole without the other kind, despite serious searches for such “monopoles.” On the other hand, it’s easy to find objects such as a rubbed transparency that possess only one kind of electric charge. We call this new type of force the magnetic force. The similarities between the electric and magnetic force suggest that they might be related. One of the great triumphs of nineteenth-century physics was the demonstration that this is in fact the case. The most concrete evidence was an experiment, first conducted in 1820, in which electrically charged particles that were in motion exerted a measurable force on a small magnet. Note that it is only moving charged objects that can exert forces on magnets. As we have seen, stationary charged objects do not exert forces on magnets. Further experiments during the nineteenth century showed that all magnetic forces can be traced to the motion of charged objects. Moving charged objects exert and feel magnetic forces over and above whatever purely electric forces they would feel if they were at rest. This additional force, due to the motion, is the magnetic force. This means that the separate concept of magnetic poles is not needed, so we can drop the idea of magnetic poles and just think of moving charges instead. For example, Earth’s magnetic effects are due to electrically charged material flowing within Earth. This is a good thing, because it permits the operation of magnetic compasses so that Boy Scouts and Girl Scouts can find each other. But if all magnetic forces can be traced to the motion of charged objects, where are the moving charges responsible for permanent magnets? The answer is that the moving charges are found at the subatomic level, in both the orbiting and spinning motions of electrons in atoms. Because of these motions, each electron in a bar magnet exerts its own tiny magnetic force on each electron in another bar magnet. In most materials, these tiny magnetic forces cancel one another because all the electron motions have different orientations. But the treatment of the iron when a magnet is manufactured locks many electron orbits into similar orientations, causing the many microscopic magnetic forces to add up to a large macroscopic effect. Permanent magnets can temporarily magnetize objects such as nails by forcing many of the nail’s electrons to orient themselves in similar directions. This is why non-magnetized nails are attracted to permanent magnets. 7

A small attractive force is sometimes obtained with the transparency, due to an electric effect called “electrical polarization.” This force occurs equally strongly even if an unmagnetized piece of metal is used in place of the magnet, so it is not caused by the magnetic poles. Rather, it is caused by redistribution of the highly mobile electrons within a metal when a charged object is brought near it. A similar electrical polarization occurs quite dramatically when a charged transparency is brought near an empty aluminum can that is free to roll. Try this!

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Electromagnetism

Summarizing: The Magnetic Force Law Charged objects that are moving exert and feel an additional force beyond the electric force that exists when they are at rest. This additional force is called the magnetic force. All magnetic forces are caused by the motion of charged objects.

How do we know that moving charges act like magnets? With the help of a D cell, a short length of insulated copper wire, and a sensitive magnetic compass with a well-balanced needle, you can demonstrate the magnetic force law. When the compass is placed on a level surface and the wire connected to the poles of the battery in such a way that the wire runs north-south (parallel to the needle) and is above or below the compass, the needle should rotate to a new position. Explanation: The battery causes electrons to flow along the wire, and the flowing electrons exert a magnetic force on the magnet. Caution: Connect the wire for only a few seconds to prevent the battery from quickly burning out. Use insulated wire because the wire might get hot.

CONCEPT CHECK 10 The force between two bar magnets cannot be due to gravity because (a) it’s far too strong to be caused by gravity; (b) it’s far too weak to be caused by gravity; (c) it can be attractive, while gravity is always repulsive; (d) it can be repulsive, while gravity is always attractive; (e) gravity acts even over large distances, while magnetism acts only over short distances. CONCEPT CHECK 11 If you rub a transparency with a tissue to charge both objects and then hold them at rest several meters apart, the forces they exert on each other will be (a) zero; (b) electrical repulsion only; (c) electrical attraction only; (d) electrical repulsion, plus a magnetic force; (e) electrical attraction, plus a magnetic force; (f ) a magnetic force only. CONCEPT CHECK 12 If you saw off one end of a magnet, you will have (a) two nonmagnetized pieces of metal; (b) two magnets; (c) two magnets that have magnetic poles on only one end; (d) none of the above.

N

S

Figure 13

A representation of the magnetic field of a bar magnet.

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Just as charged objects create electric fields in their vicinity, moving charged objects create magnetic fields; they also feel forces arising from the magnetic fields created by other moving charged objects. Like electric fields, magnetic fields can exist in a vacuum—in a region of space that contains no material particles. Just as an electric field exists wherever any charged object would (if it were present) feel an electric force, a magnetic field exists wherever any moving charged object would (if it were present) feel a magnetic force. Like electric fields, we can visually represent magnetic fields by “magnetic field lines.” For example, Figure 13 shows the magnetic field lines in the vicinity of a bar magnet. They point in the direction along which a small compass needle would orient itself. Just as electric field lines point outward from positive charges and inward toward negative charges (Figure 11), magnetic field lines point outward from north poles and inward toward south poles (Figure 13). Figure 14 is an experimental demonstration that a bar magnet’s field actually does have the shape drawn in Figure 13. Figure 14 is made by sprinkling small iron filings in the vicinity of a bar magnet. The long slender filings are temporarily

Electromagnetism

magnetized by the magnetic field, and the magnetic forces on their north and south poles then cause the filings to line up parallel to the field of the bar magnet. Summarizing: The Magnetic Force Law, Stated in Terms of Fields A magnetic field surrounds every moving charged object. Furthermore, any moving charged object that happens to be located at a point in space where a magnetic field exists will feel a magnetic force due to that field. Briefly, moving charged objects create magnetic fields and feel forces due to the magnetic fields of other moving charged objects.

As you’ve seen, electric and magnetic forces both arise from electric charge, so we think of them as different aspects of a single electromagnetic force. Similarly, both electric and magnetic fields arise from electric charge; we think of them as different aspects of a single electromagnetic field. English physicist Michael Faraday (Figure 15) was the first scientist to take electromagnetic fields seriously. Partly because of his ability to visualize electromagnetic phenomena in terms of fields, he was one of history’s greatest experimental scientists. During the mid-nineteenth century, he carried out a wide variety of experiments involving electromagnetic forces and fields. In the course of these experiments, he investigated what happens when a magnet is brought close to a simple circular loop of wire. He found that nothing at all happens so long as both the magnet and the wire loop are stationary. But when he moved either the wire loop or the magnet, an electric current was created in the wire. As soon as the motion of the wire loop or the magnet ceased, the electric current ceased. Apparently, the moving magnet exerted a force on the electrons within the wire loop, even in the case when the wire loop was stationary. Visualizing this in terms of fields, Faraday realized that moving either the loop or the magnet caused the magnetic field in the vicinity of the wire loop to change and that this changing magnetic field must in turn create an electric field in the vicinity of the loop because it takes an electric field to cause electrons to begin flowing in a stationary metal wire. This was something new. Today it is called

Figure 14

An experimental demonstration, using iron filings, that the field of a bar magnet actually does have the shape drawn in Figure 13.

Faraday’s Law When a wire loop is placed in the vicinity of a magnet and when either the loop or the magnet is moved, an electric current is created within the loop for as long as the motion continues. Stated in terms of fields: A changing magnetic field creates an electric field.

Like the electric and magnetic force laws, Faraday’s law has enormous social consequences. It is behind large-scale electric power generation in steam–electric (fossil-fueled or nuclear-fueled) power plants, hydroelectric power plants, and wind turbines (windmills that generate electricity). These power plants are based on machinery that is caused to rotate by either high-pressure steam, high-pressure water, or wind. Once you have rotating machinery, you can use Faraday’s law to generate electric current by wrapping many loops of wire around the machinery and allowing it to rotate in the presence of magnetic fields created by powerful magnets.

American Institue of Physics Emilio Segre Archives Figure 15

Michael Faraday was reared in a nineteenth-century British working class family, and had little formal schooling. He entered science at age 21 when he applied for a job as technical assistant to a well-known chemist, Humphry Davy, whose public lectures he had attended. Faraday’s enthusiasm and talent for science soon established him as an independent researcher who, at age 34, succeeded Davy as director of the Royal Institution of Great Britain.

217

Electromagnetism

Each loop generates additional electricity, so large amounts of electric energy can be supplied in this way. The basic principle, showing only a single loop, is illustrated in Figure 16. CONCEPT CHECK 13 A proton is placed at rest in the middle of a “vacuum chamber,” an enclosure that has been emptied of all matter. Consider some point X near a particular corner of the chamber. Neglect all influences other than the proton. Then at point X there is (a) an electric field; (b) an electric force; (c) a magnetic field; (d) a magnetic force; (e) none of the above, because there is nothing at point X. CONCEPT CHECK 14 In the preceding question, suppose that the proton is made to shake back and forth. Then at point X there is (a) an electric field; (b) an electric force; (c) a magnetic field; (d) a magnetic force; (e) none of the above, because there is nothing at point X. CONCEPT CHECK 15 Suppose that, as in Concept Check 13, a proton is placed at rest in the middle of a vacuum chamber, and also that an electron is placed at rest at point X. Then the electron (a) feels an electric force due to the electric field created by the proton; (b) feels a magnetic force due to the magnetic field created by the proton; (c) feels no electromagnetic force.

Shaft from power source

N

Moving (slip) rings

S Stationary conducting brushes

Figure 16

The principle of electric power generation, showing only a single rectangular loop of wire. A power source such as wind or steam causes the shaft to rotate, which rotates the loop. Stationary magnetic north and south poles are placed above and below the loop, so that their magnetic field passes through the loop as the loop is rotated. As Faraday’s law predicts, this generates an electric current that flows around the loop and onto the moving metal “slip rings” that are rigidly attached to the loop. This current then flows onto the stationary metallic brushes that are in electrical contact with the moving rings. The current from the brushes can then flow to an external consumer of electricity such as the lightbulb shown.

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© Sidney Harris, used with permission.

Electromagnetism

219

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Electromagnetism Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions

22. State Ohm’s law. 23. What is a short circuit?

ELECTRIC FORCE

FORCE FIELDS AND ELECTROMAGNETISM

1. When you rub two transparencies with tissue and hold them close together, they stand apart. Give two reasons that the force causing this cannot be gravity. 2. Cite the evidence supporting the claim that there are two, and only two, types of electric charge. 3. Suppose that the electric force between two objects is 2 N and that you then double the distance between the objects. What is the new force? 4. Suppose that the electric force between two objects is 2 N and that you then double the electric charge on each object. What is the new force? 5. Describe at least two ways in which the gravitational force and the electric force differ. 6. In what ways are the electric and gravitational force laws similar?

THE ELECTRIC ATOM 7. List the types of particles that are found within the atom. 8. Which types of particles within the atom are electrically charged? 9. What holds, or binds, an atom’s orbiting electrons to the nucleus? 10. What is an ion? 11. What is an electric current? 12. List several phenomena that require the planetary model of the atom, rather than the Greek atom, for their explanation. 13. Name and briefly describe the three kinds of subatomic particles found in atoms. 14. Give evidence supporting the claim that most of an atom’s mass is concentrated in a tiny nucleus at the center. 15. Explain what happens at the microscopic level in a wire when a battery creates an electric current in the wire. 16. What is an atomic number, and how is it related to the chemical elements?

ELECTRIC CIRCUITS 17. 18. 19. 20. 21.

What is an electric circuit? Give an example of electric energy. What is the meaning of a battery’s “voltage”? What is an ampere? How does AC differ from DC?

24. Name two kinds of force fields. 25. Which force fields would be felt by a stationary charged object: gravitational, electric, or magnetic? 26. Which force fields would be felt by a moving uncharged object: gravitational, electric, or magnetic? 27. Which force fields would be felt by a moving charged object: gravitational, electric, or magnetic? 28. What does it mean to say that there is an electric field throughout this room? 29. What does Faraday’s law say about magnets and wires? 30. What does Faraday’s law say about magnetic fields and electric fields? 31. Give two reasons that the force between bar magnets cannot be the electric force. 32. Magnetic forces are always caused by what types of objects?

Conceptual Exercises ELECTRIC FORCE 1. Suppose that you rub a transparency with a tissue to charge both objects and then hold them several meters apart and shake both of them back and forth. Name the forces that they exert on each other. 2. Since matter is made of electrically charged particles, why don’t we and the objects around us feel electric forces all the time? 3. When you remove a wool dress from a garment bag, the sides of the bag might tend to stick to the dress. Explain. 4. Figure 17 shows an electroscope. The leaves (made of metal foil) normally hang down, but they spread apart when the metal sphere on top touches a charged object. Explain. 5. How does the operation of the electroscope (previous exercise) demonstrate electric current? 6. When tiny scraps of paper are placed between two flat metal plates that have been oppositely charged (one plate charged positively and the other charged negatively), they bounce back and forth between the plates. Explain this phenomenon. 7. Highway trucks can become electrically charged as they travel. How can this happen? This can be dangerous, especially for gasoline tank trucks. How can it be prevented? 8. What happens to the electric force between two charged objects if the charge on one of them is reversed in sign?

From Chapter 8 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Electromagnetism: Problem Set Metal sphere

Helium

Wire

Leaves of thin metal foil

Figure 17

Why do the leaves stand apart? 9. What happens to the electric force between two charged objects if the charges on both of them are reversed in sign? 10. Ping pong ball A has an electric charge that is 10 times larger than the charge on ping pong ball B. When placed sufficiently close together to exert measurable electric forces on each other, how does the force by A on B compare with the force by B on A? 11. Objects A and B are both electrically charged. If the distance between them is halved while the charge on A is also halved, what happens to the force between them? 12. If the distance between two charged objects is reduced to one-fourth of its original value, what happens to the electric force between them? 13. If the distance between two charged objects and the charge on each of them are all doubled, what happens to the electric force between them?

THE ELECTRIC ATOM 14. While brushing your hair, you find that the hairs tend to stand apart from one another and that they are attracted toward the brush. Explain this in microscopic terms. 15. A covered mystery shoebox is placed on a table. What are a few ways that you could learn something about its contents without directly touching it or having it lifted? 16. After you walk across a rug and scuff electrons off the rug, are you positively or negatively charged? 17. According to Figure 3, what are the atomic numbers of carbon and helium? Roughly how much more massive is the carbon atom than the helium atom? 18. Some science fiction stories portray atoms as true miniature solar systems populated by tiny creatures. What are some differences, other than size, between our solar system and the planetary model of an atom? 19. An atom loses its two outermost electrons. How does the resulting ion behave when it is near a positively charged transparency? A negatively charged tissue?

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Carbon

Figure 3

Two examples of the planetary model of the atom. Protons are green, neutrons are white, and electrons are black. The diagrams are not drawn to scale! If they were drawn to scale, the nuclei and the electrons would be too small to be seen.

20. In the preceding question, would anything be different if it lost only one electron? 21. MAKING ESTIMATES About how many atoms thick is a sheet of paper? 22. MAKING ESTIMATES Which is bigger, an atom or a wavelength of light? Roughly how much bigger?

ELECTRIC CIRCUITS 23. Is a wire that carries current electrically charged? 24. At what point or points in the circuit of Figure 8 do electrons have the least energy? What kind of energy? 25. Does more current flow out of a battery than into it? 26. Only a small fraction of the electric energy that is used up in an incandescent lightbulb is transformed into light. What happens to the remaining energy? 27. In the circuit of Figure 8, would a thicker lightbulb filament produce a larger current, smaller current, or neither? Explain. 28. Do the headlights of an automobile carry AC or DC? What about a toaster in your kitchen? 29. The filament of a lightbulb glows, while the connecting wires do not. Why?

Electromagnetism: Problem Set Figure 8

Because electrons flow so easily through ordinary wires, the circuit of Figure 7 would soon burn out the wire or battery. Inserting an incandescent lightbulb or other “circuit element” reduces the flow to safe levels. This happens because the lightbulb’s glowing filament is very thin and thus restricts or “resists” the current, much as a squeezed garden hose restricts the flow of water.

– +

–

+

FORCE FIELDS 30. Do the electric circuits in your home produce magnetic fields? Suggest a measurement that might check your answer. 31. Is an electric field a form of matter? Explain. What about a gravitational field? 32. A proton is placed, at rest, at some point A within a room that is otherwise devoid of all matter. At some other point B within the room is there an electric field? An electric force? A magnetic field? A magnetic force? Is there energy at point B? 33. Suppose that, in the preceding exercise, the proton is oscillating back and forth. Is there an electric field at point B? An electric force? A magnetic field? A magnetic force? Energy? 34. Suppose you have a piece of metal wire and a bar magnet. Describe two ways in which you could create an electric current. What law of physics is involved here?

ELECTROMAGNETISM 35. You have three iron bars, only two of which are permanent magnets. Because of temporary magnetization, all three bars at first appear to be magnetized. How can you determine which one is not magnetized, without using any other objects? 36. Suppose you have two iron bars (see the previous exercise), one magnetized and one not magnetized. Can you then determine which one is magnetized, without using any other objects? 37. If you place a proton at some point in an electric field and then release it, what will happen? 38. How would a proton’s motion differ from the motion of an electron placed at the same point in the same electric field? 39. How would a proton’s motion differ from the motion of an electron placed at the same point in the same gravitational field?

Problems THE ELECTRIC FORCE 1. Two small electrically charged objects are placed 8 cm apart, where they exert an electric force F on each other. How far apart must they be in order to exert an electric force of (1/4) F on each other?

2. Referring to Problem 1, how far apart must the objects be in order to exert an electric force of 4F on each other? 3. Two small electrically charged objects are placed a certain distance apart, where they exert an electric force of 4 N on each other. Suppose the charge on object #1 is doubled. What happens to the force? What if the charge on both objects is doubled? 4. Two small electrically charged objects are placed a certain distance apart, where they exert an electric force of 4 N on each other. Suppose the charge on object #1 is halved. What happens to the force? What if the charge on both objects is halved? 5. Two small objects, each containing an electric charge q, are placed a certain distance apart, producing an electric force F by each object on the other. Suppose half of the first object’s charge is transferred to the second object. What happens to the force? 6. How does the electric force between two helium nuclei placed a certain distance apart compare with the force between two hydrogen nuclei placed the same distance apart? 7. How does the electric force between a helium nucleus and a lithium nucleus placed a certain distance apart compare with the force between two hydrogen nuclei placed the same distance apart? 8. How does the electric force between two hydrogen nuclei placed a certain distance apart compare with the force between two helium nuclei placed twice as far apart? 9. What is the electric force between two pellets that each have a charge of 10–6 C placed 1 cm apart? 10. A dust particle carrying a charge of -3 * 10 - 10 C is 2 mm to the left of another dust particle carrying a charge of +4 * 10 - 10 C. Find the magnitude and direction of the electric force on the first particle. 11. Two objects carrying equal amounts of charge are placed 10 cm apart, where the force between them is found to be 0.9 N. Find the charge on each of the objects. 12. How far should an object carrying a charge of 2 * 10 - 6 C be from another object carrying a charge of 4 * 10 - 6 C in order for them to exert a force of 6 N on each other?

ELECTRIC CIRCUITS 13. What should be the resistance of a lightbulb in order for it to draw a current of 2 amp when plugged into a 120-volt outlet?

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Electromagnetism: Problem Set 14. A blow dryer with a resistance of 6 ohms is plugged into a 120-volt outlet. How much current does it draw from the outlet? 15. If the coils of a heater have a resistance of 12 ohm, how much current does it draw when plugged into a 120-volt outlet? 16. An 0.5 amp current runs through a lamp whose resistance is 150 ohm. What is the voltage across the lamp? 17. If a lightbulb has a resistance of 40 ohm and a current of 2 amp, at what voltage is it operating? 18. A 1.5-volt battery is short-circuited by a 1-meter length of wire having a resistance of only 0.02 ohm. How large is the current flowing through the wire (before the wire or the battery burn out)?

13. The force is unchanged. 15. Roll a ball so that it collides with the box to see whether the

17. 19.

21.

Answers to Concept Checks 1. If you set q1 = 1 C, q2 = 1 C, and d = 1 m, Coulomb’s law 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15.

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tells you that F = 9 * 109 N, (d). Smallest mass (b), largest mass (e). (a), (b), (c), and (e) (c) (e) I = V>R = 6 volts>0.02 ohm = 300 amps, (b). (c). The force on a negative charge placed at A would be in the opposite direction, (d). The field points downward at point B, so the force on a small negative charge placed at point B would be upward, (a). The direction of the field at point C is rightward, so the force on a positive charge placed at point C would be rightward, (d). If the charge were instead placed at point D, the force on it would be downward, (b). (a) and (d) (c) (b) (a). Note that (b) is incorrect because there is no material object at point X to feel a force; (c) is incorrect because the proton is stationary, so it doesn’t create a magnetic field. (a) and (c) (a)

23. 25.

27. 29. 31. 33.

35.

contents have high mass or low mass. Tie a string around the box and pull it; the box’s mass can be determined by measuring the pulling and the acceleration. Fire bullets into the box from all directions. Hit the box with a hammer to see if anything inside rolls around. 6 and 2. The ratio is about 12 to 4, which is the same as 3 to 1. The ion will carry a positive charge, so it will be repelled by a positively charged transparency, and attracted to a negatively charged tissue. A 500-sheet stack of typing paper is about 5 cm thick, so the thickness of one sheet of paper is about 5 cm>500 = 0.01 cm = 10 - 4 m. An atom is about 10 - 10 m across, so a piece of paper is about 10 - 4>10 - 10 = 106 times bigger. No, the number of protons in any segment equals the number of electrons. But the protons remain at rest while the electrons move along the wire. The amount of current flowing out always equals the amount flowing in. For instance, if more electrons were flowing out than in, electrons would have to pile up someplace along the circuit. A thicker filament would allow electrons to flow through more easily, so it would produce a larger current. The filament gets a lot hotter because, due to the thinness of the filament, the moving electrons bump into so many of the filament’s atoms. An electric field is not made of atoms or of other material particles, so it is not a form of matter. The same goes for a gravitational field. At B there is an electric field (because of the charge at A), there is no electric force (because there is no charge at B), there is a magnetic field (because the charge at A is moving), there is no magnetic force (because there is no charge at B), and there is energy (because of the presence of an electromagnetic field). The two permanent magnets will be able to both attract and repel each other, depending on which ends are put together. The non-magnetized bar will only be attracted to (and not repelled by) the other two bars. It will start to move in the direction of the field. They wouldn’t differ. They would both move at the same acceleration and the same speed, just like two falling objects having different masses (Galileo’s principle of falling).

Answers to Odd-Numbered Conceptual Exercises and Problems

37. 39.

Conceptual Exercises 1. Both an electric force and a magnetic force will be exerted. (There will also be a tiny gravitational force.) 3. The bag and the dress become oppositely charged, due to friction, causing them to attract each other and cling together. 5. Charge must have flowed, or moved, from the metal sphere down to the leaves; this motion of charge is electrical current. 7. The truck picks up charge from the road by friction (the tires rubbing against the road). It can be prevented by providing an easy pathway for charge back to the road—a chain hanging from the truck to the road, for example. 9. The forces on each charge are unchanged. 11. The force is doubled.

Problems 1. Because of the inverse-square nature of the force, placing them twice as far apart (16 cm) will cause the force to be 1/4 as strong. 3. With doubled charge on #1, the force will double to 8 N. If both charges are doubled, the force will be 16 N. 5. #1 now contains a charge of q/2, while #2 contains (3/2)q. Thus q1q2 = (1>2)q * (3>2)q = 3>4q2. So the force is reduced to 3/4 of its previous value. 7. Lithium has three protons, helium has two protons, and hydrogen has one proton. So the force between a lithium and helium nucleus is 3 * 2 = 6 times larger than that between two hydrogen nuclei.

Electromagnetism: Problem Set 9. From Coulomb’s law,

F = 9 * 109 *

(10 - 6) * (10 - 6)

= 90 N. (0.01)2 11. Coulomb’s law tells us that F = 9 * 109 q2>d2, from which 0.9 = 9 * 109 q2>(0.01)2. q2 = 0.9 * (0.01)2> Thus 9 - 14 9 * 10 = 10 . Taking the square root, q = 10 - 7 C.

13. R = V>I = 120>2 = 60 ohm. 15. I = V>R = 120>12 = 10 amp. 17. V = IR = 2 * 40 = 80 volt.

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Waves, Light, and Climate Change Quite simply, I think it is no exaggeration to say that climate change is the biggest problem our civilization has ever had to face up to in its 12,000 years, because it requires a collective response. David King, Chief Science Adviser to the British Government, 2001–2007

T

his chapter continues our quest to grasp the nature of light, and looks at the planetary consequences of recent human interference with the radiations (including light) that arrive from the sun. In the first two sections, you’ll learn about waves, a topic that we’ll also need for studying quantum physics. In Section 3, you’ll see what waves have to do with light. Section 4 explains light in terms of electromagnetic fields. Section 5 makes the important, even revolutionary, point that electromagnetic fields are physically real and looks ahead to the modern view that, at the most fundamental level, the universe is made of fields. The electromagnetic field theory of light leads to an understanding of several other lightlike “radiations” (Section 6) and of sunlight (Section 7). In line with my goal of presenting important physics-related social implications as soon as the physics background is prepared, I’ll describe in Sections 8 and 9 two ways in which humans have significantly altered the interaction of our planet with the sun: (1) alteration in the planetary impact of the sun’s ultraviolet radiation, caused by human depletion of atmospheric ozone, and (2) alteration of the planetary impact of the sun’s infrared radiation, caused by human emissions of carbon-dioxide and other gases. The two problems have a lot in common. Encouragingly, humans have solved the first of these, but the second looms ever larger.

1 WAVES: SOMETHING ELSE THAT TRAVELS You’re probably familiar with some kinds of waves (Figure 1). Stretch a few meters of flexible rope along the floor, fix one end (perhaps under a friend’s foot), and give the free end a single shake. Something travels down the rope. Figure 2 is a series of pictures taken with a movie camera, showing a similar “something” traveling down a long spring that has been given a single up-and-down shake at the right-hand end. As another example, imagine (better yet, try it!) stretching a Slinky™ toy between your two hands along a tabletop. Quickly move the left end a short distance toward the right and then back to the left, holding the right end fixed. Something travels along the Slinky from your left to your right hand (Figure 3). This “something”

From Chapter 9 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Jeff Greenberg/Omni-Photo Communications, Inc. Figure 1

Water waves.

that travels across the water, along the rope, and along the Slinky is called a wave. As another example, the continued shaking of one end of a rope causes a long continuous wave to travel along the rope (Figure 4). But wave is just a word that names the behavior without telling us what it really is. What actually happens here? In Figure 2, how do the individual parts of the spring actually move? As you can see from the motion of the small ribbon tied to the spring, each loop just moves up and then back down. How does a particular part of the water move in Figure 1? Fill a bowl with water, float a small cork in it, and drop a small pebble in, several centimeters from the cork, to create ripples. Observe the cork as ripples pass by. If the ripples are small, the cork will move up and down, not outward along with the ripples. Each portion of the water just shakes or “vibrates” up and down, but does not travel along the water surface. The Slinky wave is similar, except that the vibrations are parallel instead of perpendicular to the Slinky. One thing that is traveling with each of these waves is energy. You can verify this for yourself by holding the fixed end of a rope while a friend shakes the other end. Your hand vibrates as the pulse arrives. It takes work to force your hand back and forth this way, and we know that work requires energy. So waves transfer energy. On the other hand, no material substance is transferred by waves: No water is transferred outward in Figure 1, no part of the spring is transferred from right to left in Figure 2, and no part of the Slinky is transferred from left to right in Figure 3. This type of motion is unlike any motion we have examined before. Previously we studied balls, books, molecules, and other material objects actually moving from one place to another. What do we see traveling along the spring in Figure 2? Well, we see a bump traveling along the otherwise straight spring! In Figure 3 we see a compression, a squeezed region, traveling along the Slinky. We could describe both as “disturbances” that travel along the otherwise undisturbed spring or Slinky. The situation Compression

Compression moves toward the right

Figure 3

With the right-hand end of the Slinky held fixed, a quick motion of the left-hand end to the right and back again to the left creates a pulse that travels down the Slinky. Uri Haber-Schaim Figure 2

A series of pictures taken with a movie camera, showing a wave moving along a spring. A ribbon is tied to the spring at the point marked by the arrow. The ribbon moves up and down as the wave goes by, but it does not move in the direction of the wave.

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Direction of wave motion

Figure 4

Continued shaking of the end of a rope creates a continuous wave that travels down the rope.

Waves, Light, and Climate Change

is similar for water waves. The material through which the disturbance travels—the spring or Slinky or water—is called the medium for the wave. So a wave is a disturbance that travels through a medium in such a way that energy travels through the medium but matter does not. A “sports wave” in a large stadium filled with people is an instructive example. It begins when all the people at one end of the stadium stand up briefly with their hands in the air. As they sit down, the people in the adjoining part of the stadium stand up briefly with their hands in the air, and so forth all around the arena. Although this gives the appearance of something traveling around the stadium, this “something” is not any single thing. The people who are momentarily standing constitute a disturbance of the otherwise-seated crowd, and it is this disturbance that travels through the crowd. This is precisely the sort of situation we have in mind when we use the word wave. We need some quantitative terms. The wavelength of a continuous, repeated wave is the distance from any point along the wave to the next similar point, for example, from crest to crest or from trough to trough in Figure 5. A wave’s frequency is the number of vibrations that any particular part of the medium completes in each second. Waves are usually sent out by a vibrating source of some kind, in which case the wave’s frequency must be the same as the source’s frequency. The frequency could also be defined as the number of waves that the source sends out during each second. The unit for measuring frequency is the vibration per second, also called a hertz (Hz). A wave’s amplitude is its maximum height or depth (Figure 5), in other words, its maximum disturbance from the “neutral” or undisturbed situation. The wavespeed is the speed at which the disturbance moves through the medium.1 In most waves, disturbances are able to travel through a medium because of the connections between the parts of the medium. (In the sports wave, this connection is mental rather than directly physical.) For example, when you shake one end of a rope, this disturbance moves down the rope because the different parts of the rope are connected, so that when one part is lifted, its neighbor is soon lifted also. So it’s reasonable to suppose that the wavespeed is determined mainly by the medium and is roughly the same for differently shaped disturbances in the same medium. Experiments confirm this notion that differently shaped disturbances all travel through any particular medium at roughly the same wavespeed. Wavelength Amplitude

Wavespeed

Figure 5

The meaning of wavelength and amplitude. The wavespeed is the speed at which a crest or a trough moves down the rope.

1

Quantitatively, a wave’s wavelength l, frequency f, and wavespeed s are related by s = f l. For example, if three waves are sent out by the wave source every second ( f = 3 vib>s) and each wave has a length of 2 meters (l = 2 m), then it seems reasonable that the wavespeed should be 3 * 2 = 6 m>s. Extending this argument, you can see that the general relation is s = f l.

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CONCEPT CHECK 1 Which of the following is a true wave? (a) A row of falling dominoes. (b) Ripples on the surface of a pond, extending outward from a pebble dropped in the water. (c) A large water wave coming into the beach, one that surfers can ride on. (d) Water rushing downstream.

Figure 6

Which wave has the higher (larger) frequency, assuming that both have the same wavespeed?

CONCEPT CHECK 2 In Figure 6, which wave has the larger or “higher” frequency, and which carries more energy? (a) The top wave has higher frequency and carries more energy. (b) The top wave has higher frequency but the bottom wave carries more energy. (c) The bottom wave has higher frequency and carries more energy. (d) The bottom wave has higher frequency but the top wave carries more energy.

From Concept Check 2, note these useful rules: Shorter wavelength means higher frequency and, if the amplitude remains unchanged, then higher frequency means higher energy.

2 INTERFERENCE: A BEHAVIOR UNIQUE TO WAVES Before meeting

Figure 7

Two waves travel in opposite directions along a rope. What happens when they meet?

Before

During

After

Figure 8

Two waves meeting: interference.

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How do different waves traveling through the same medium interact with one another? For example, what happens when the large upward wave in Figure 7 meets the small downward wave? Experiment shows that they just pass through each other without distortion (Figure 8). You might have expected this, because each wave simply lifts or lowers the rope as it travels, so when the two waves meet, the rope is raised a lot by the large wave and simultaneously lowered a little by the small wave. Effects such as this, occurring when two waves are present at the same time and place, are called wave interference, or just “interference.” CONCEPT CHECK 3 Suppose that the two waves in Figure 7 had the same size and shape, with the wave on the right being inverted as shown, and that the wave on the left is a 2 cm crest (high point). The resulting interference would be (a) a 4 cm crest; (b) a 2 cm crest; (c) flat; (d) a 4 cm trough (low point); (e) a 2 cm trough.

Two equal waves of opposite orientation interfere by canceling each other (Figure 9), and two equal waves of the same orientation interfere by reinforcing each other (Figure 10). These two cases, cancellation and reinforcement, are called destructive interference and constructive interference. Wave interference shows, once again, the stark difference between the motion of a material object and wave motion. Two moving material objects—say, two freight trains—don’t pass through each other undisturbed! This distinction will be significant later in this text. Interference gets more interesting when it happens in two or three dimensions. An undisturbed rope has only one significant dimension, length. The surface of a lake is “two-dimensional” because it has length and width; the space in a room is “three-dimensional” because it has length, width, and height. In a two- or threedimensional medium, the waves created by a small source are outward-spreading circles (Figure 1) or spheres, respectively. As a two-dimensional example, suppose you fill a rectangular pan with water and tap your fingers at the same steady rate on the surface at two points along one side of the pan. Continuous waves will spread out from each of the two sources and soon cover the water surface. With the help of Figure 11, you can predict the interference effects. The figure shows the water as viewed from above. The two

Waves, Light, and Climate Change

sources are marked A and B. The solid circles represent crests from source A acting alone, and the dashed circles represent crests from source B acting alone. The troughs, not drawn, lie midway between the crests. To predict the interference pattern, work through Concept Check 4. CONCEPT CHECK 4 In Figure 11, draw an “x” (a color enhances the effect) at every point of constructive interference. (Hint: These are places where crest meets crest, and where trough meets trough.) Can you see a pattern? Next, draw an “o” (in a different color) at every point of destructive interference. (Hint: These are places where crest meets trough.) Now can you see a pattern?

Before Before

During During After After

Figure 9

Figure 10

Two waves meet and interfere destructively.

Two waves meet and interfere constructively.

Figure 11

Continuous surface waves spreading out from two sources. What will the interference effects look like?

A

B

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Uri Haber-Schaim Figure 12

Interference between continuous surface waves spreading out from two sources: experimental results. Crests (constructive interference) are bright, troughs (also constructive interference) are dark, and flat places (destructive interference) are gray.

Figure 12 is a photograph of this experiment, looking down onto the water’s surface. The photographic technique causes crests to appear bright, troughs to appear dark, and flat places to appear gray. As you can see, the interference pattern has lines of undisturbed water radiating outward as though they came from a point somewhere between the two sources. The interference is destructive along these lines. Between these undisturbed lines are other lines of constructive interference, with large crests and troughs. Just what Concept Check 4 predicted, right? Our analysis so far has been at one instant in time. Now “turn on time” by imagining a moving picture that begins with the snapshot in Figure 12. Since the individual circular waves move outward from A and B, the entire pattern must move outward also; in other words, the “rays” of destructive and constructive interference remain fixed in place, while the large waves within the constructive rays move outward, as shown by the arrows in Figure 13. Finally, imagine that the water is a rectangular swimming pool and that you examine the waves as they slosh against the right-hand wall of the pool. What would you observe? You can predict the answer using Figure 13. The observer should find some points where large waves pound against the wall, marked with large Xs in Figure 14, and other points, marked with large Os, where no waves roll in. The difference between the pattern from a single source and from two sources is striking. Waves from a single source, say source A operating alone, roll into all parts of the bordering wall (Figure 15). If we also turn on the second source, B, the pattern along the wall shifts to an interference pattern (Figure 14). The most dra-

X x

A

Uri Haber-Schaim Figure 13

Lines of constructive and destructive interference remain fixed in place, and constructive (large) waves move outward within the constructive regions in the directions indicated by the arrows.

B

x

x

x

x x o o x x o o o x x oo x x o o o x x x x xo o x x x x o x x o x x x o o o o ox x x o o o o o o x o o o o o x x x x x x x x x x x x x x o o o x x xo o o o o o o o o o o o x x o o o x x x x x x o x x x x o o x x o o x x x o o x x o o x x o o x o x x x x x

O X O X O

Observer stands on this side and looks down at pool, observing large waves rolling into points marked X at side of pool, and no waves rolling into points marked O. Small x’s and o’s are places on surface of pool where interference is constructive (x’s) and destructive (o’s).

X O

X

Figure 14

An observer scanning a wall at the far border of the pool finds points where large waves come into the wall, interspersed with points where no waves come in.

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Waves, Light, and Climate Change Figure 15

If one of the two wave sources shuts off, an observer scanning the wall will find that waves arrive at all points. Since waves now spread out from only a single source, there is no longer any interference. A

matic change is that now no waves come into the points marked O, even though they did come into these points when only one source was operating. It seems paradoxical: When you add a second source you get a reduced (in fact, zero) effect at the points marked O. Now let’s look at light.

3 LIGHT: PARTICLES OR WAVE? When you turn off the lightbulb at night, it gets dark. So the light in your room must have come from the lightbulb and not, for example, from your eyes. When you look at a luminous (light-emitting) object like a lightbulb, light goes from the bulb to your eyes. In order for you to see a nonluminous object, such as the wall of your room, light from the lightbulb must bounce (reflect) off the wall and then into your eyes. The light reflecting from the wall does not give you a nice mirror reflection, however, because the rough surface of most walls scatters the incoming light in many different directions. But what enters your eyes when you see light? This has been debated for centuries, with most of the suggested answers falling into either the “particle” or “wave” category. Experiment is the ultimate judge. We need an experimental test that distinguishes between the particle and wave models of light. The preceding section suggests a good candidate: wave interference. Particles might interact in various ways, but they do not interfere in the way that waves do. What does light do? To answer this, we need an experiment like the water–wave interference experiment, but with light. The first experiment you might think of is to simply shine two flashlights on a flat surface. But if you try this (do it!), you’ll find that it gives no observable interference effects—no alternating regions of constructive (brightly lit) and destructive (darker) regions. So maybe light is a stream of particles.

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Waves, Light, and Climate Change Figure 16

The double-slit experiment with light. What will we see on the screen? A B

Partition with two very small thin slits (shown here greatly enlarged) to let light through

?

Screen

But in our discussion of water–wave interference, we assumed that the two wave sources had identical vibrations. For example, if the two sources in Figure 12 were changing their frequency all the time and in different ways, we would not expect to see a recognizable interference pattern. A flashlight bulb’s light is produced by heating up the bulb’s thin wire, or filament, until it glows. The microscopic thermal motions that make the filament hot enough to glow are highly random, so we wouldn’t expect two different bulbs to have identical vibrations, so they wouldn’t show interference even if light were a wave. How do we know whether light is a wave, or particles? In 1801, Thomas Young solved the problem of finding two sources with identical vibrations by using a single light source that he split into two parts. He then recombined these parts to see whether they interfered. Figure 16 shows how to do this. A single light source sends light through two very small and narrow parallel slits (shown greatly enlarged) in a partition that blocks all the light except that going through the slits. The two slits act as two new sources of light. If light is a wave, these two sources should have synchronized vibrations, because the light from each slit originates in the same filament.2 Young found an experimental result like that shown in Figure 17. This photograph was made by placing photographic film at the position of the receiving screen as shown in Figure 18. To interpret Figure 17, let’s compare it with water–wave interference. The receiving screen of Figure 16 is similar to the right-hand wall in Figure 14. But water waves occur on the two-dimensional surface of water, while light fills three-dimensional space. The two sources of light are not tiny points like A and B in Figure 14 but instead are slits that extend into the third dimension. If these slits send out light waves, we would expect the interference pattern on the receiving screen to be alternating lines of constructive and destructive interference running parallel to the slits, not small points like those marked X and O in Figure 14. In other words, we would expect alternating bright (lit) and dark lines—precisely the outcome in Figure 17. Conclusion of this double-slit interference experiment with light: light is a wave.

Figure 17

The double-slit experiment with light: experimental result.

A B

Very narrow slits, shown here greatly enlarged.

What happens if we close one of the slits, leaving only one slit open? If light is a wave, we would expect waves to spread out from the open slit, without interference, just like the water waves in Figure 15. A broad band of light should then cover a large area of the receiving screen (Figure 19). This is, in fact, what happens. The clearest evidence that the flashlight is sending out waves and not particles can be found at the positions of the dark lines in the double-slit experiment, the points 2

Figure 18

The double-slit experiment with light: the experimental setup and result.

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More precisely, the light must first be filtered so that it is all of one color (one frequency), and it must first come through a single narrow slit so the vibrations at slit A are synchronized with those at slit B. This makes Young’s experiment exactly analogous to Figures 13 and 14. In those figures, the waves from A and B have the same frequency and they are synchronized.

Waves, Light, and Climate Change

where no light arrives. With only one slit open, light spreads out over the entire receiving screen. How is it, then, that if we simply open a second slit, no light arrives at these particular positions? It’s difficult to see how particles coming through the two slits could cancel one another in this way, but it’s just what we expect of waves. By measuring the distance from one bright constructive-interference line to the next such line in a pattern such as Figure 17 and using a little geometry, it’s possible to calculate the wavelength of the light that created the pattern. Measurements of interference patterns like this are the usual method of measuring the wavelength of light. This wavelength turns out to be very small. Light sources have wavelengths ranging from about 0.4 * 10-6 m to 0.7 * 10-6 m (less than a millionth of a meter, or less than one-thousandth of a millimeter). How do we know that light is a wave? You can easily demonstrate light-wave interference yourself, using a single-slit wave-interference effect that occurs when the slit is hundreds of times larger than the wavelength of the light. With such a wide slit, the light coming through the slit acts like hundreds of tiny sources. If light is a wave, then all the individual waves from these hundreds of sources should interfere with one another to form an interference pattern. Here’s the experiment: Focus your eyes on a well-lit wall or other surface. Make a slit by holding your thumb and forefinger about a millimeter apart and several centimeters in front of your eye. Focus on the light source (the wall), not on your fingers, so that your fingers look blurred. Where the blurs overlap, you should see narrow bright and dark lines running parallel to your fingers. These lines are constructive and destructive interference regions, formed at the position of your eye.

A

Extremely narrow single slit, shown here greatly enlarged. To get the noninterference pattern shown, the slit’s width must be less than the wavelength of the light!

Figure 19

If one of the two slits is closed, light will arrive at all points along the receiving screen. The white screen indicates that there is no interference pattern—that light arrives everywhere on the screen, in contrast to the pattern that emerged in Figure 18.

CONCEPT CHECK 5 If water waves of longer wavelength were used in the experiment shown in Figure 14, the Xs and Os along the right-hand side of the figure would be (a) farther apart; (b) closer together; (c) unchanged. CONCEPT CHECK 6 If shorter-wavelength light were used in the experiment whose result is shown in Figure 17, the alternating bright and dark lines in the figure would be (a) unchanged; (b) greater in number, but unchanged in length or width; (c) wider; (d) narrower; (e) longer; (f) shorter.

MAKI NG ESTI MATES Roughly, how does a typical light wavelength compare with the thickness of a piece of paper?

4 THE ELECTROMAGNETIC WAVE THEORY OF LIGHT Water waves, rope waves, and Slinky waves are waves in water, ropes, and Slinkies. But what medium vibrates when light waves travel? Hmm... It’s not an easy question. We don’t see light beams directly the way we see water waves (Figure 20). It is as though we could see the impact of water waves against the edge of a swimming pool, without being able to see the water. We can see light beams in dusty air

Choose a typical wavelength of light, say 5 * 10-7 m (in making estimates, choose simple but reasonable numbers). To estimate the thickness of a sheet of paper, estimate the thickness of, say, 500 sheets (about 5 cm) and divide by 500 (5 cm>500 = 0.1 cm = 10-4 m). The number of wavelengths in this thickness is 10-4>(5 * 10-7) = 10-4 + 7>5 = 103>5 = 1000>5 = 200. SO LUTION TO MAKI NG ESTI MATES

Figure 20

Light beams cannot be seen from the side. What invisible medium is carrying these waves?

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Waves, Light, and Climate Change

Uri Haber-Schaim Figure 21

You can see a light beam by allowing it to reflect off dust particles in the air.

Figure 22

If you shake a charged object such as a charged comb, other charged objects will shake in response.

(Figure 21), but only because the light is reflected off the dust particles. The medium for light waves is itself invisible. Could the medium be air? Sounds plausible. But what about light traveling here from the sun, moon, and stars? Air extends, in any appreciable amounts, only a few miles above Earth’s surface, so air cannot be the medium for light waves.3 One odd thing about light is that it moves through outer space where there is essentially no matter at all. But something must be out there in so-called empty space, because without a medium to do the waving, you can’t have a wave. The medium for light, then, must be nonmaterial—not made of atoms or other forms of matter. Nineteenth-century scientists devoted lots of effort to learning what kind of wave light is. It turns out, as we’ll see, that the answer is bound up with electricity. Suppose you pull a rubber comb through your hair, scuffing electrons from your hair onto the comb. The charged comb then creates an electric field in the surrounding space, a field that can be detected by a rubbed (and hence electrically charged) transparency held near the comb. If you quickly shake the comb once, up and back down, the electric field in the surrounding space will shake too. This can be detected by the transparency, which will shake in response to the comb’s motion. The comb also creates a magnetic field during the brief time that it’s moving. This temporary magnetic field could in principle (the force would be very small) be detected as a brief shake of a magnet placed near the comb. In summary, the comb’s motion causes changes in the electromagnetic field around the comb, changes that can be detected by other charged objects and magnets (Figure 22). There is an interesting question about this experiment, a question that many nineteenth-century scientists asked: When will a distant detector feel the changes in the field? Is the effect instantaneous? Suppose you shake the comb precisely at noon. Does the transparency shake precisely at noon, too, or a little later? During the 1860s, British physicist James Clerk Maxwell (Figure 23) did some hard thinking about electromagnetism, putting all that was then known about the subject together into a single theory. Maxwell’s theory emphasized fields and described how electrically charged objects create electromagnetic fields. Three basic principles of the electromagnetic force were known at that time. Stating these three principles in terms of fields, the electric force law says that charged objects create electric fields, the magnetic force law says that moving charged objects create magnetic fields, and Faraday’s law says that any change in a magnetic field must create an electric field. Maxwell, like most theoretical physicists, felt that a correct and fundamental description of the natural world should also be fitting, balanced, symmetric, or, in a word, beautiful. It seemed to him that the laws of electricity and magnetism should treat electricity on the one hand, and magnetism on the other, symmetrically. The three basic laws (electric force law, magnetic force law, Faraday’s law) seemed to be missing something in this regard. The first two state that electric fields and magnetic fields arise from charged objects and from moving charged objects, respectively. Faraday’s law then states that electric fields can be created in a second way, namely by a changing magnetic field. It seemed to Maxwell that there should then be a fourth law, one that would balance Faraday’s law by providing a second way to create magnetic fields. Such a fourth law should be symmetric to Faraday’s law; in other words, it should state that magnetic fields can be created by a changing electric field. 3

236

Air is the medium for sound waves rather than for light waves. Since sound does not bear directly on the major purposes of this text, we won’t discuss it further here.

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Then the theory would treat electric and magnetic fields symmetrically: Changes in one field always create the other field. Maxwell’s invention, when combined with the other three laws, led him to predict the existence of so-called “electromagnetic waves” (see below) and to predict that light is a wave of this sort—predictions that are now amply verified and that represent a stunning success for theoretical reasoning. Once again we see the importance of beauty and symmetry in science.4 Maxwell’s theory, which he formulated in precise mathematical language, predicted a time delay for electromagnetic forces. The key ingredient was the way that changes in one field created the other field. This meant that electric and magnetic fields can create and re-create each other. Once the fields at one point in space are changed—for instance, by giving a charged comb a single shake—Maxwell’s theory implied that the change is transmitted outward as a change in the nearby fields a short time later, and these changing fields in turn transmit the change farther outward, and so forth. It follows from this that electric and magnetic forces are not transmitted instantaneously. Maxwell’s analysis showed that if you disturb an electromagnetic field at one point, the disturbance will move outward through the field. This is exactly the kind of behavior that we called “wave motion” in Section 1. But this new type of wave is not a wave in a material (made of matter) medium such as water. Rather, the medium is the electromagnetic field itself. Any such disturbance that moves through an electromagnetic field is called an electromagnetic wave. You can’t directly see electromagnetic waves in the way that you can see water waves, because the medium for electromagnetic waves is a nonmaterial electromagnetic field instead of a material substance such as water. Nevertheless, electromagnetic waves can be detected by other charged or magnetized objects at some distance from the source of the wave and at some later time after the wave was sent out. Figure 24 pictures these invisible waves. This was all worked out quantitatively in Maxwell’s theory. The theory predicted not only a delay in the transmission of electromagnetic forces but also the speed of transmission. The predicted speed was about 300,000 km/s or 3 * 108 m>s. This particular speed had come up before, in experiments performed nearly two centuries before Maxwell invented his theory. But these previous experiments seemed entirely unrelated to the electromagnetic effects that Maxwell was studying. This speed, 300,000 km/s, was the known speed at which light travels!

American Institute of Physics/ Emilio Segre Visual Archives Figure 23

James Clerk Maxwell, the “Isaac Newton of electromagnetism.” He cast the principles of electricity and magnetism into the form of four equations involving the electric and magnetic fields created by electric charges and electric currents. The theory led to a unification of the electric with the magnetic force and to understanding electromagnetic radiation, which underlies much modern technology including radio, television, and lasers.

How do we know the speed of light? People once thought that light requires no travel time—that its speed was infinite. Light certainly travels much faster than sound, as you verify whenever you see lightning before you hear thunder. Galileo was one of the first to try to measure the speed of light, or “lightspeed” as I will call it, by measuring the total round-trip time for light to travel to a distant mountain and back. His experiment didn’t work because the time turned out to be far too short to measure using Galileo’s timing methods. Either greater timing accuracy or a greater travel distance was needed. The first evidence for a finite, and not infinite, speed of light came from astronomical observations several decades later. Pointing telescopes at a moon of Jupiter, astronomers

4

In 1894, physicist Pierre Curie suggested that the symmetry between electricity and magnetism exhibited by Maxwell’s four laws would be complete if, in addition to electric charge, there existed in nature a pure “magnetic charge” called a “monopole.” Every magnet ever observed has two poles, north and south. You can’t isolate one from the other. A monopole would be a pure north, or pure south, pole, and would create a magnetic field even when it was not moving. Although monopoles have never been observed, theorists have never discarded the idea. Today, theorists searching for a “grand unified theory” of the fundamental particles suggest that monopoles exist or at least that they once existed, during the early stages of the big bang.

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Figure 24

When you shake a charged object, it sends out an electromagnetic wave in all directions. This invisible wave is a disturbance in the charged object’s electromagnetic field.

found that the time they measured for this moon to orbit Jupiter didn’t remain constant. This was weird. Why should a moon take longer for some orbits than for others? Earth’s moon takes 27.3 days, every time. The astronomers found that these variations were not caused by Jupiter’s moon at all but were instead related to Earth’s motion around the sun. The variations were just what would be expected if the light from Jupiter’s moon traveled at a finite, and not infinite, speed (see Figure 25 for the explanation). From the measured variations in orbital time, lightspeed could be estimated.

Maxwell hypothesized that light might actually be an electromagnetic wave. But scientists knew of no way to verify this tantalizing suggestion until two decades later, when it became possible to check Maxwell’s theory directly by causing charged objects to oscillate and observing the effects some distance away. How do we know that electromagnetic waves exist? One way to verify Maxwell’s theory would be to shake a charged object at the frequency of visible light, about a thousand trillion Hz, to see whether the shaking created light. You’d have a hard time shaking your hand that fast! Such high frequencies are hard to achieve in the laboratory, even today. German physicist Heinrich Hertz (Figure 26)—the hertz is named for him—figured out how to do an experiment of this sort, but at a frequency of “only” about a billion Hz. He constructed an electric circuit that contained a small open gap. Ordinarily, such a gap stops the flow of electric charge, but Hertz built the endpoints of the gap in such a way that large amounts of charge (excess electrons on one side, excess protons on the other) could build up on them. After enough buildup, electrons were forced to jump across the gap. We observe such charge jumping as a spark. Lightning is a spark of this sort. In Hertz’s circuit, a jump of charge triggered a brief series of such jumps back and forth across the gap, at a rate of a billion back-and-forths per second. If Maxwell was correct, these oscillations should create electromagnetic waves with a frequency of a billion Hz.

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Waves, Light, and Climate Change Earth, at two different points in its orbit B Jupiter’s moon, on two successive orbits A Sun

Jupiter

Figure 25

It takes light from Jupiter’s moon about 35 minutes to reach point A, and 43 minutes to reach point B. Thus, if Earth moves from point A to point B while Jupiter’s moon is orbiting Jupiter one time, the orbital time as measured on Earth will be 8 minutes longer than the true orbital time, because of the extra 8 minutes that it takes light to reach point B. This effect creates a variation in the measured orbital time that can be explained by assuming that light has a finite, not infinite, speed. At some distance from this predicted source of electromagnetic waves, Hertz placed a second circuit. This circuit was entirely passive, with no battery or other internal source of electric current. If Maxwell’s theory was correct, electromagnetic waves from the first circuit should cause an electric current to oscillate in the second circuit, also at a billion hertz. The transmission from one circuit to the other should occur at lightspeed. Hertz’s results entirely confirmed these predictions. Although Hertz’s waves were not light waves, his work convinced scientists that electromagnetic waves really existed and that light is actually an electromagnetic wave. As a by-product, Hertz’s work came to the attention of an ingenious Italian inventor named Guglielmo Marconi, launching the radio and television revolution. Today, we know Hertz’s waves as radio waves.

Hulton-Deutsch Collection/ CORBIS Figure 26

Two decades after Maxwell predicted the existence of electromagnetic waves, German physicist Heinrich Hertz discovered them experimentally. Hertz’s waves were in the radio region of the electromagnetic spectrum, and provided the scientific basis for the radio and television revolution.

It’s a stunning unification: Maxwell’s theory correctly describes electricity, magnetism, light, and radio. All these are different manifestations of one underlying reality: electric charge. Summarizing: Electromagnetic Wave Theory of Light Every vibrating charged object creates a disturbance (wave) in its own electromagnetic field. This disturbance spreads outward through the field at lightspeed, 300,000 km/s, or 3 * 108 m>s. Light is just such an electromagnetic wave.5

CONCEPT CHECK 7 Suppose you electrically charge a comb by running it through your hair and then shake it back and forth at a frequency of 1 Hz. This will produce (a) a sound wave having a frequency of 1 Hz and a speed of 300,000 km/s; (b) a sound wave having a wavelength of 300,000 km and a speed of 300,000 km/s; (c) an electromagnetic field that vibrates at a frequency of 1 Hz, but no electromagnetic wave; (d) an electromagnetic wave having a frequency of 1 Hz and a speed of 300,000 km/s. 5

More precisely, the speed of light, and all electromagnetic waves, is 299,792.458 km/s in a vacuum. When traveling through matter, however, light is slower than this because it is continually absorbed and re-emitted by atoms.

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Hertz’s waves had a frequency of 109 hertz. Could a normal home radio receive waves of this type and frequency? (a) No, because radios receive only sound waves, and Hertz created only electromagnetic waves. (b) No, because these waves are neither in the AM radio frequency range nor the FM radio frequency range. (c) Yes, these waves could be received by an AM radio. (d) Yes, these waves could be received by an FM radio. CONCEPT CHECK 8

MAKI NG ESTI MATES About how long does it take light to get to your eyes from a lightbulb in your room?

5 FIELDS ARE REAL

We now think of electric and magnetic and gravitational fields as being as real as rocks and people. Normally we are not aware of those fields, but you can confirm that they are all around you by turning on a radio. Gordon Kane, Particle Physicist, in His Book Supersymmetry

Since ancient Greek times, scientists have generally thought that the universe was made of tiny material particles, atoms. As Democritus put it, there are only atoms and empty space. It’s a view that is remarkably compatible with Newton’s physics, which was once thought of as the rules according to which atoms move. This worldview— atomic materialism coupled with Newtonian physics—dominated science during the eighteenth and nineteenth centuries. When Faraday first proposed electromagnetic fields around 1830, most scientists thought of them as only a useful way to picture electromagnetic forces and not as real physical objects. Then Maxwell and Hertz showed that waves can travel in electromagnetic fields and that light is one example of these waves. So electromagnetic fields were not just a useful fiction; they were physically real, as real as light. The most convincing argument for the reality of electromagnetic fields comes from conservation of energy. Suppose a radio transmitter sends a message (an electromagnetic wave) to a receiver on Mars and that the message’s travel time is 20 minutes. Energy must travel from the sender to the receiver because it takes energy to cause the receiver to respond. Where is this energy during the 20 minutes between sending and receiving? Not in the sender. Not in the receiver. And energy never just vanishes. So it must be in the space between sender and receiver, in the electromagnetic field. So electromagnetic fields contain energy. Philosophers might disagree about what is “real,” but to a physicist nothing is more real than energy. Today we know that the universe is filled with gravitational, electromagnetic, and other kinds of invisible, but physically real, fields that are smoothly spread out in space and not made of tiny particles. This represents a real break with the Newtonian worldview. As Einstein put it, We may say that, before Maxwell, Physical Reality, in so far as it was to represent the processes of nature, was thought of as consisting in material particles. . . . Since Maxwell’s time, Physical Reality has been thought of as represented by continuous fields, . . . and not capable of any mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton.6 6

A. Einstein, in James Clerk Maxwell, A Commemoration Volume. (The Macmillan Company, New York, 1931).

SO LUTION TO MAKI NG ESTI MATES The travel time for light is the distance to the lightbulb divided by lightspeed, 3 * 108 m>s. To make the arithmetic easy (remember that in estimates you want to choose approximate numbers that make the arithmetic easy), suppose the distance is 3 m: 3 m>(3 * 108 m>s) = 10-8 s, or a hundredth of a millionth of a second.

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This is quite a far-reaching statement. Einstein is not saying that the universe is made of some combination of material particles and fields, but rather that it’s made only of fields. Einstein’s view is beautifully confirmed by the development of physics since about 1950, when a theory based on quantum physics and known as “quantum field theory” came to dominate the way that physicists think about the structure of matter and energy. According to this extremely well-confirmed theory, the universe is made entirely of fields. Atoms, for example, are made of several kinds of fields known collectively as “matter fields,” and also of electromagnetic fields spread out smoothly over distances the size of an atom or smaller. Nineteenth-century physicists resisted giving up the Newtonian clockwork universe. So ingrained was the Newtonian worldview that scientists could not imagine that energy might exist apart from tiny material particles. They developed the idea that an extremely light gaslike material substance called ether filled all space. Ether was assumed to be a form of matter but made of some unknown substance rather than of the atoms that are familiar to us. Electromagnetic forces and other forces that act at a distance were assumed to be transmitted by ether. Light and other electromagnetic waves could then be explained mechanically, in terms of the motions of the material ether and in keeping with the Newtonian tradition. Maxwell, Hertz, and others accepted this ether theory of the electromagnetic force. After two centuries of the Newtonian worldview, it was difficult to think in any other way. Albert Einstein, early in the twentieth century, was one of the first to break out of this mold. He showed that the ether theory had to be rejected. But surprisingly, this had no effect on Maxwell’s theory or on the interpretation of light and radio as electromagnetic waves. It only affected the mechanistic interpretation of the electromagnetic field. After Einstein’s work, electromagnetic fields could no longer be interpreted as properties of a material substance. So the electromagnetic field turned out to be philosophically revolutionary, the first of many post-Newtonian physical ideas. Apparently the universe is not made entirely of atoms, not made like a mechanical clock. There is something else: fields. Although the Newtonian worldview still dominates much popular culture and even lies behind many scientists’ intuitive view of nature, the mechanical universe began to unravel around 1900 and is by now seriously out of tune with much of contemporary physics. The two major modern theories, relativity theory and quantum theory, contradict both the specific predictions and the conceptual underpinnings of Newtonian physics. Physics is still in the middle of the post-Newtonian revolution, and it is not clear what new scientific worldview will emerge.

6 THE COMPLETE SPECTRUM The possible frequencies of light lie in a narrow range near 1015 Hz. We have seen that Heinrich Hertz produced electromagnetic waves, now called radio waves, having a frequency around 109 Hz. These are only two examples of the huge range or “spectrum” of electromagnetic waves now known. We call this range the electromagnetic spectrum (Figure 27). In the figure, wavelengths are arranged from the longest at the bottom to the shortest at the top, with typical objects having the size of these wavelengths listed for comparison. Frequencies are shown from the lowest (smallest) at the bottom to the highest at the top, with typical sources of these frequencies listed. In order to display a large range, Figure 27 shows wavelengths and

241

Waves, Light, and Climate Change Typical Sources That Send out Waves at This Frequency:

Typical Object Whose Size Is the Same as This Wavelength:

Frequency, Hz

1022 Processes by protons and neutrons in atomic nuclei

Electrons in atoms, high-energy processes Electrons in atoms, low-energy processes

Gamma ray

X-ray

1018

Ultraviolet

1016 1014

Microwave oven

1012

Radar antenna

violet green yellow red

Cell phone

Infrared

108

TV, FM radio

AM radio antenna

106

AM radio

Atom

108

DNA molecule Amoeba

106

Fine dust particle

104 Millimeter

Radar

FM radio, TV antenna

1010

Visible

Microwave 1010

102

Centimeter

1

Meter

102

Soccer field Kilometer

Radio

60 Hz power-line radiation

Nucleus

1012

1020

Thermal vibrations of molecules

1014

104

104

102

106

1

108

Earth

Wavelength, m

Figure 27

The electromagnetic spectrum. There are no definite ends to the spectrum and no sharp boundaries between the regions.

frequencies on a so-called “logarithmic scale” in which each increment is a factor of 10: 1, 10, 100, 1000, and so forth. A “linear scale”—such as 10, 20, 30, 40, and so forth—could not do justice to the entire range. All these waves are the same phenomenon, namely, an electromagnetic field disturbance that is created by a vibrating charged object and that travels at lightspeed outward through the field. Energy from all these waves can be received by other charged objects that the wave moves as the wave passes by. All can travel through empty space. And all carry energy, known as radiant energy. Electromagnetic waves are often called electromagnetic radiation because they “radiate” out in all directions from charged objects. Since higher frequency means higher energy (Section 1), energies increase as we move up the scale from bottom to top. Let’s tour the electromagnetic spectrum. It’s useful to arrange it into the six regions shown in Figure 27, regions that correspond to different ways of either sending or receiving electromagnetic radiation. The longest wavelengths, down to about a millimeter, form the radio waves, comprising AM and FM radio, TV, and microwaves.

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Humans can create and control these waves electronically by causing electrons to vibrate in human-made electric circuits. Hertz’s waves fall into this category, and so does a lot of modern technology. AM radio waves at around 1000 kilohertz (106 Hz), FM radio and TV waves at around 100 megahertz (108 Hz), and cell phone transmission waves at around 1 gigahertz (109 Hz) are created by electrons moving back and forth along a metal antenna that is part of an electric circuit. Radar and microwaves, with frequencies up to a trillion (1012 ) hertz, also are created electronically. Many natural processes also create radio waves. Radio astronomers use radio receivers or “radio telescopes” pointed at stars or other astronomical objects to learn about the universe. In fact, astronomical objects produce electromagnetic radiation in all parts of the spectrum. During the past few decades, many new sorts of receivers, stationed on or above Earth, have produced an explosion of astronomical knowledge. Infrared radiation has wavelengths ranging from 1 millimeter to below 1/1000 of a millimeter—the size of a fine particle of baby powder. Infrared is typically created by the random thermal motion of molecules due to their thermal energy. Since all objects have thermal energy, all objects produce infrared and hotter objects produce more of it. Infrared detectors, such as certain infrared-sensitive chemicals, can detect warmer objects against a cooler background, which is the basis for night-vision devices and infrared photography. You cannot see infrared radiation but you can feel it. Since it’s created by thermal motion, it’s not surprising that it has the proper frequency to shake molecules into thermal motion—so it warms the objects it hits. When you feel the warmth of a fire or a hot plate at some distance away, you are using your skin as an infrared detector, “seeing” with your skin. Some animals have evolved highly developed infrared sensors for nocturnal vision. Many animals, including humans, have sensors that detect a narrow range of frequencies just above infrared. This range of visible radiation or “light” has wavelengths centering on 5 * 107 m. This is smaller than the finest dust particles and 5000 times larger than an atom. Light is typically created by electrons moving within individual atoms. The visible region’s defining characteristic is simply that the human eye is sensitive to it. Light waves entering the pupil of the eye strike the retina at the back (Figure 28). The retina is covered with light-sensitive cells that act like tiny antennae to receive electromagnetic waves in the visible range. Some cells respond differently to different wavelengths, and the brain interprets these as different colors. Suppose that you have a variable-frequency source of electromagnetic waves and that you set it to 6 * 1014 Hz—the frequency of green light. If you gradually decrease the frequency, this green light will change to yellow, then orange, and finally red. As you continue decreasing the frequency, the red becomes deeper and darker until, at about 4 * 1014 Hz, the frequency is so low that your retina can no longer respond to it. The source no longer emits visible light. The waves have crossed the boundary into infra- (below) red. The source still radiates, but your eye cannot detect it. Now go in the other direction. Beginning with 6 * 1014 Hz, increase the frequency. The color changes from green to blue to violet. The violet light darkens until, around 8 * 1014 Hz, your eye can no longer detect it. The waves have crossed into the ultra- (above) violet region. Ultraviolet radiation is created in the same way that light is created, by electrons moving within individual atoms. Although similar to light, ultraviolet’s higher energy has important consequences. Ultraviolet radiation has the proper frequency to shake many biological molecules, so it is readily absorbed by living things. And it has enough energy to split molecules, which can disrupt or kill living cells. If absorbed by a cell’s DNA, this can lead to cancerous growth.

Light beam focused on retina

Lens Light beam entering eye

Retina Optic nerve

Figure 28

The human eye.

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Waves, Light, and Climate Change Heater X-rays

Electrons   High voltage

Collision with metal plate creates X-rays

Figure 29

The operation of an X-ray tube. Electrons are boiled off a thin, heated wire filament and are accelerated toward a positively charged metal plate at the other end of the vacuum tube. When the electrons smash into this plate, their rapid deceleration causes them to emit X-rays, and the collision also causes the plate’s atoms to emit X-rays.

X-ray radiation also comes from electrons in individual atoms, but only from the highest-energy electron activities within atoms. X-ray wavelengths span a range around 10–10 m—about the size of an individual atom. Humans make X-rays in highenergy X-ray tubes, as described in the caption of Figure 29. X-rays have important interactions with biological matter. They have enough energy to ionize molecules within biological cells, that is, to knock the electrons right out of some molecules. Like ultraviolet, this radiation can cause cancers. Radiation energetic enough to ionize biological matter is called ionizing radiation. X-rays and gamma rays are ionizing radiations, and so is the higher energy (higher frequency) portion of the ultraviolet region. Because X-rays are able to penetrate deeply into biological matter, they can be put to the useful cause of examining the interior of the human body without surgery. There is a certain logic to our tour through the electromagnetic spectrum. As we move to smaller wavelengths, we move toward higher frequencies and hence higherenergy radiation, which in turn implies higher-energy processes to create the radiation. We also have progressed toward processes that occur in smaller and smaller regions of space: Radio waves are created in macroscopic electric circuits, infrared is created in molecules, and the next three (visible, ultraviolet, and X-ray) are created in atoms. It should come as no surprise then that the shortest-wavelength radiation, gamma radiation, carries the highest frequency and highest energy and comes from the highest-energy processes in the smallest regions of space. Gamma rays are created within atomic nuclei by high-energy nuclear processes involving the strong forces that hold the nucleus together. Gamma rays are created in radioactive materials and in the nuclear reactions known as “fission” and “fusion.” Like X-rays, gamma rays are a form of ionizing radiation and can damage biological matter. But this very feature is often put to use to destroy diseased cells and so cure some cancers. Since gamma ray wavelengths are much smaller than individual atoms, atoms cannot readily respond to them, and so they penetrate deeply into matter. The room you are in is full of electromagnetic waves. Hundreds of television and radio broadcasts, radio pulsations from neutron stars, radio noise from millions of normal stars, the faint background radiation from the big bang, possibly communications from extraterrestrial life, radiations from the sun and the center of our galaxy, and much more are passing through your room right now. Your body is equipped to receive directly only the tiny visible portion of the complete spectrum of these waves. With the proper receiver, you could sense any of the other frequencies. The universe would appear far different in other wavelength ranges and would appear complex indeed if you could directly receive the entire spectrum. The reality that meets your eye is only a tiny fraction of nature’s reality. CONCEPT CHECK 9 When your radio is tuned to 100 on the FM dial, it is receiving (a) a 100 Hz sound wave; (b) a 108 Hz sound wave; (c) a 100 Hz electromagnetic wave with a wavelength about the size of Earth; (d) a 106 Hz electromagnetic wave with a wavelength of around 100 m; (e) a 108 Hz electromagnetic wave with a wavelength of around 100 m; (f) a 108 Hz electromagnetic wave with a wavelength of around 1 m. CONCEPT CHECK 10 In the preceding question, the sound coming from the radio is (a) an electromagnetic wave traveling at 300,000 km/s; (b) an electromagnetic wave that travels far more slowly than 300,000 km/s; (c) not an electromagnetic wave of any kind, and travels far more slowly than 300,000 km/s.

244

Waves, Light, and Climate Change MAKI NG ESTI MATES In the following list, which of these waves have wavelengths much bigger than your room (a few meters), which have wavelengths between a millimeter and a few meters, and which have wavelengths of less than a millimeter: AM radio, light, electromagnetic waves from the alternating current that oscillates 60 times each second in your house circuits, warming rays from a fire, rays from a microwave oven, radar, electromagnetic radiation from shaking an electrically charged blouse that you remove from the dryer?

7 SOLAR RADIATION: THE LIGHT FROM OUR STAR The sun, “Sol,” transmits electromagnetic waves in every region of the spectrum. Most of this solar radiation is in the visible, infrared, and ultraviolet parts of the spectrum and is created at the sun’s visible surface. Other solar radiation is created in the rarefied, very hot gas that surrounds the sun in the same way that Earth’s atmosphere surrounds Earth. Processes within the sun’s atmosphere create high-energy X-rays and some gamma rays, along with radio waves. The intense radiation created by high-energy processes deep within the sun is absorbed and altered within the sun, and little of it escapes directly. Figure 30 graphs the relative amounts of radiant energy emitted by the sun at different wavelengths. When you sit in the sunlight, your eyes detect the sun’s visible radiation and your skin detects its infrared as warmth. Your skin also detects ultraviolet but you don’t notice it until a little later, as the cellular damage known as “sunburning.” The amount of solar energy reaching Earth is different at different locations, in different seasons, in different weather conditions, and at different times of the day. In the United States, an average 200 watts (200 joules every second) strikes every square meter of the ground.

Relative amount of energy

Figure 30

Ultraviolet Visible

0

500

The relative amounts of energy at different wavelengths in the solar spectrum. Most of the sun’s radiant energy is in the ultraviolet, visible, and infrared portions of the electromagnetic spectrum.

Infrared

1000 1500 2000 2500 Wavelength, in nanometers (109m)

3000

SO LUTION TO MAKI NG ESTI MATES Use Figure 27. Much bigger than a few meters: AM radio, waves from alternating current, waves from the blouse. One millimeter up to a few meters: microwaves, radar. Less than 1 mm: warming rays, light.

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Waves, Light, and Climate Change MAKI NG ESTI MATES Photovoltaic cells are devices that transform solar energy into electric current. If such devices were 100% efficient, about how much area would need to be covered by these cells in order to provide the average 1.3 kilowatts of electric power that a typical family home uses? Actual photovoltaic cells are only about 15% (one-seventh) efficient. At this efficiency, how much area must be covered? Could you put this on your roof ?

CONCEPT CHECK 11 When energy from the sun is absorbed by your skin (a) it remains there as electromagnetic energy; (b) it remains there as radiant energy; (c) it transforms into nuclear energy; (d) it transforms into kinetic energy; (e) it transforms into thermal energy; (f ) it gives you the heebie-jeebies.

8 GLOBAL OZONE DEPLETION: A VULNERABLE PLANET7

High-temperature object such as your kitchen

ThermE out Cooling system

Work ThermE in

From electric company

Low-temperature object such as the inside of your refrigerator

This and the next section apply our knowledge of molecules, energy, and electromagnetic radiation to discuss two environmental issues: ozone depletion and global warming. These represent a new kind of social issue: environmental effects that cannot be contained locally and are truly global. As part of the dues that we all must pay if Earth is to pull through its current experiment with powerful new technologies, we’d better think seriously about such issues. An invisible trace of gas drifting 10 to 50 kilometers overhead protects life on Earth from the sun’s ultraviolet radiation. This wispy “ozone layer” would be only 2 millimeters thick if compressed to normal atmospheric pressure, but without it most life on Earth would soon cease. During the past century, humans using common household chemicals destroyed a large portion of this ozone. Belatedly realizing what we had wrought, we all came together in the nick of time to agree to ban the offending chemicals. The story of ozone depletion demonstrates the threat of global environmental destruction, shows that strong collective counter-action is possible, and offers an encouraging lesson for these times. The story begins in 1928 when the General Motors Corporation first synthesized chlorofluorocarbons (CFCs), molecules made from atoms of chlorine, fluorine, and carbon, for its Frigidaire refrigerators. CFCs are chemically inert, meaning that they do not readily react with other substances. They normally form a gas but become liquid when put under high pressure. Being inert, they are nontoxic to humans, noncorrosive in mechanical devices, and nonflammable. Such a chemical can have many uses, one of which is as a coolant. Refrigerators and air conditioners operate like heat engines in reverse (Figure 31). Just as heat engines use hot gases as the “working fluid” that does work while exhausting thermal energy, so refrigerators and air conditioners use a “coolant” that has work done on it while extracting thermal energy from a refrigerator or house.

Figure 31

Energy flow diagram for a refrigerator. Refrigerators operate like heat engines in reverse. An outside energy source does work to push thermal energy “uphill,” from a low to a high temperature.

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7

The U.S. government maintains an informative Web page on this topic, at http://www.epa.gov. Click on “index” and find “ozone.”

SO LUTION TO MAKI NG ESTI MATES 1.3 kilowatts (1300 watts) of solar energy falls on 6.5 square meters (1300/200) of surface. At an efficiency of one-seventh, it would take seven times this much area: 45 square meters. If square-shaped, this would be about 7 m on a side and might fit on your roof.

Waves, Light, and Climate Change

CFCs soon became a universal coolant. Production soared. In the 1940s, CFCs were found to be useful as pressurized gases to propel aerosol sprays. In the 1950s, they created the air-conditioning revolution that facilitated America’s shopping malls, summer automobiling odysseys, and population shifts to Southwestern cities. CFCs created lots of business and little fuss until 1974 when scientists began to ask where all these inert gas molecules might be drifting. After all, being inert they were nearly indestructible, so essentially all the CFCs manufactured since 1930 should still be in the atmosphere. But where? And what became of them there? During the previous four decades of profitable production, nobody had bothered to ask. In 1974, two university chemists suggested an alarming possibility. Mario Molina and Sherwood Rowland (Figure 32) discovered that because CFC molecules are inert and gaseous, they are not chemically broken down or rained out in the lower atmosphere. Instead, they drift slowly into the upper atmosphere or stratosphere, 10 to 50 kilometers overhead, where they may remain intact for decades or centuries. Molina and Rowland theorized that high-energy solar ultraviolet radiation should eventually split CFC molecules apart, releasing large quantities of chlorine. This was alarming because chlorine reacts strongly with O3, known as ozone. Ozone is one of a long list of trace gases in the atmosphere—gases that, all together, make up far less than 1% of the atmosphere. Table 1 shows only a few of these trace gases, namely those whose concentrations are one part per million (that is, one molecule per million atmospheric molecules) or larger. The list would be far longer if it were extended down to one part per billion! Here’s how chlorine destroys atmospheric ozone: Ozone is produced naturally in the stratosphere from O2 when high-energy radiation from the sun breaks up O2 molecules and the resulting oxygen atoms then combine with O2 to create O3. But ozone can be easily broken down by this reaction with chlorine:

Nobelstiftelsen/The Nobel Foundation Figure 32

Paul Crutzen, Mario Molina, F. Sherwood Rowland. The theory of stratospheric ozone depletion by means of human-made compounds was recognized by the awarding of the 1995 Nobel Prize in Chemistry to the three scientists who discovered it. Crutzen’s work involved nitrogen compounds, while Molina and Rowland’s work involved chlorine compounds. The Nobel Committee commended them for having “contributed to our salvation from a global environmental problem that could have catastrophic consequences.” Table 1 Composition of the atmosphere Molecule

Major constituents

Cl + O3 : ClO + O2 Under bombardment by the ultraviolet radiation at that altitude, a second reaction then occurs:

78.084 %

O2

20.946 % 00.934 % Total

99.964 %

Trace gasesa (in ppmb)

This second reaction releases the chlorine, which is then free to destroy more ozone. Scientists found that a single Cl atom destroyed about 100,000 ozone molecules. A little chlorine goes a long way. But stratospheric ozone is essential to most life on Earth.8 Because ozone molecules vibrate naturally at ultraviolet frequencies and so absorb much of the sun’s ultraviolet radiation, they protect us from this biologically harmful radiation. Unfortunately, ozone is easily altered by human activities because there is so little of it in the atmosphere. Out of every 10 million atmospheric molecules, only 3 are ozone! To get a feel for this, imagine a huge city of 10 million, in which just 3 people are labeled “ozone.” We see in ozone the potential importance of each of the many atmospheric trace gases (Table 1). In 1974, most people regarded it as absurd to think that coolants and spray cans could cause a catastrophe, because it violated the intuitive notion that human activities were far too puny to alter the global environment. But some were alarmed. A debate, of Ground-level ozone, on the other hand, is a toxic pollutant. It is a consequence of automobile exhaust and is the primary component of urban smog.

N2 Ar

ClO + ClO + sunlight : Cl + Cl + O2

8

Concentration

CO2

377

H2O

20–20,000

Ne

12

He

5

NO2

2

CH4

2

Xe

2

Kr

1

O3

3 waves>s = 1>3 Hz. 7. Solving s = fl for l, l = s>f = 2 m>s > 3 Hz = 0.67 m. 9. Solving s = fl for l, l = s>f = 3 * 108 m>s > 108 Hz = 3 m. 11. (5000 km)>(300,000 km>s) = 0.017 s. 13. 3 * 105 km>s * 8.3 min * 60 s>min = 1.5 * 108 km = 150 million km. 15. Solving s = fl for l, we get l = s>f = (3 * 108 m>s)>60 = 5 * 106 m = 5000 km. 17. Solving s = lf for f, we get f = s>l = (3 * 108 m>s)> 589 * 10 - 9 m = 5.09 * 1014 Hz. 19. 2.7 * 1019>106 = 2.7 * 1013 = 27 trillion. Even at “only” 1 ppm, there are still a lot of Krypton atoms in a cubic centimeter of air!

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The Special Theory of Relativity

From Chapter 10 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Special Theory of Relativity

Nature and Nature’s laws lay hid in night: God said, “Let Newton be” and all was light. Alexander Pope

It did not last: the Devil, shouting “Ho Let Einstein be” restored the status quo. Sir John Collings Squire

P

hysics changed around 1900. Physicists began investigating phenomena farremoved from the normal range of human experience, things like the structure of atoms and the precise speed of a light beam. They found that Newtonian physics and nineteenth-century electricity and magnetism were far off the mark in phenomena involving very high speeds, very strong gravitational forces, large astronomical regions, and the microscopic world. To deal with these new realms, they invented new theories called special relativity (this chapter), general relativity, and quantum physics. All of these new theories reproduce, nearly exactly, the standard Newtonian predictions within the normal range of human perceptions. For example, special relativity correctly predicts new, non-Newtonian results for objects moving at speeds comparable to lightspeed, but also correctly predicts the normal Newtonian results for slower-moving objects such as cars and speeding bullets. But despite this similarity within the normal range of human perception, the concepts behind these new theories are quite unlike the concepts behind Newtonian physics. For example, Newtonian physics describes the universe as a kind of giant predictable clockwork mechanism. But you’ll find that, according to quantum physics, the universe is nothing like a clock, quite non-mechanical, and far from predictable. The new theories represent the most accurate knowledge known about the real physical universe, and they describe a different universe from what you would have expected on the basis of Newtonian or pre-Newtonian concepts. So expect your preconceptions about space, time, motion, gravity, matter, energy, and physical reality to be assaulted. Each of these new theories has a non-intuitive oddness about it, as might be expected since they deal with phenomena beyond your normal range of perception. In this chapter you’ll learn about some unexpected effects that happen when objects move at high speeds, speeds comparable to lightspeed. You’ll also learn that space and time aren’t quite what you thought they were, and you’ll learn something new and, for most people, amazing about energy. Einstein’s “special theory of relativity” is based on

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two simple ideas and all of its odd conclusions are off-shoots of these. This theory has a reputation for being difficult, but this comes really from its strangeness rather than any inherent difficulty. Its conclusions violate common sense. The main requirement for understanding this theory is not intelligence but mental flexibility. Einstein created two related theories of relativity. The “special” theory of relativity, discussed in this chapter, revolutionizes the way we think about space and time, and this leads to a further revolution in our concepts of mass and energy. The “general” theory of relativity revolutionizes our concepts of space and time even further, and radically reformulates the way we look at gravity. Following some historical context in Section 1, Section 2 discusses the older “Galilean” way of viewing the phenomena with which Einstein was concerned. Sections 3 and 4 cover the theory’s two key laws: the principle of relativity and the principle of the constancy of lightspeed. Sections 5 and 6 present Einstein’s prediction of the relativity of time. Section 7 presents two more predictions: the relativity of space and the relativity of mass. Section 8 presents Einstein’s famous prediction of the equivalence of energy and mass, the aspect of special relativity that Einstein himself thought was most important, and discusses its profound significance.

1 EINSTEIN: REBEL WITH A CAUSE The Scottish mathematician and physicist Lord William Thomson Kelvin stated in an address to physicists at the British Association for the Advancement of Science in 1900 that “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” Many scientists1 of that day shared Kelvin’s confidence that the known “grand unifying principles”—Newton’s laws and the laws of thermodynamics and electromagnetism—were complete and permanent. But the world soon changed. In 1900, Max Planck introduced a revolutionary new principle, the quantum of energy. And a scant five years later, in 1905, a quite different but equally revolutionary theory was hatched in the brain of an obscure patent clerk in Bern, Switzerland: Albert Einstein (Figures 1 and 2). Einstein was a rebel in more ways than one. In his midteens he got fed up with high school and dropped out. This surprised no one, for he had been a mediocre student and a daydreamer since beginning elementary school. Before that he had been a slow child, learning to speak only at 3 years of age. His high school teachers were glad to see him go, one of them informing Einstein that he would “never amount to anything” and another suggesting that he leave school because his presence destroyed student discipline. Einstein was delighted to comply. He spent the next few months as a model dropout, hiking and loafing around the Italian Alps. After deciding to study engineering, he applied for admission to the Swiss Federal Polytechnic University in Zurich, but he failed his entrance exams. It seems he had problems with biology and French. To prepare for another try, he spent a year at a Swiss high school, where he flourished in this particular school’s progressive and democratic atmosphere. He recalled later that it was here that he had his first ideas leading to the theory of relativity. The university now admitted Einstein. He was known as a charming but indifferent university student who attended cafes regularly (where he enjoyed discussing philosophy and science) and lectures sporadically (because he preferred to spend time in physics laboratories). He managed to 1

I thought of that while riding my bicycle. Einstein, on the Theory of Relativity, in the Quotable Cyclist.

Common sense is nothing more than a deposit of prejudices laid down by the mind before you reach eighteen. Einstein

My intellectual development was retarded, as a result of which I began to wonder about space and time (things which a normal adult has thought of as a child) only when I had grown up. Einstein

If I were a young man again and had to decide how to make a living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler, in the hope of finding that modest degree of independence still available under present circumstances. Einstein, in a remark made near the end of his life.

But perhaps not most scientists. Many physicists were dissatisfied with the theoretical foundations of physics and rejected Newtonian mechanics as the basis for physics in favor of electromagnetism.

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Were I wrong, one professor would have been quite enough. Einstein, when asked about a book in which 100 Nazi professors charged him with scientific error.

Figure 1

Figure 2

Never one to take himself too seriously, Einstein stuck his tongue out when asked to smile on his seventysecond birthday.

Albert Einstein during his student days in Zurich, a few years before he created his special theory of relativity.

pass the necessary exams and eventually graduate with the help of friends who shared their systematic class notes with the nonconforming Einstein. Following his graduation in 1900, Einstein applied for an assistantship to do graduate study, but it went to someone else. After looking unsuccessfully for a teaching position, in 1902 a friend helped him land a job as a patent examiner. Einstein often referred to his seven years at this job as “a kind of salvation” that paid the rent and occupied only 8 hours a day, leaving him the rest of the day to ponder nature. And ponder he did. One of the many remarkable aspects of the theory of relativity is that it was invented nearly single-handedly.

2 GALILEAN RELATIVITY: RELATIVITY ACCORDING TO NEWTONIAN PHYSICS Here is a typical relativity question: Suppose that a train passenger, call her Velma, throws a baseball toward the front of the train. Both she and Mortimer, who is standing on the ground watching the passing train, measure the baseball’s speed (Figure 3). Will they get the same answer? If not, how will their answers differ? Think about it. This question concerns two observers who are moving differently. We say that Velma and Mort are in relative motion whenever they are moving at different speeds or in different directions. A theory of relativity is any theory that works out answers to questions concerning observers who are in relative motion. You can think of the train as being Velma’s laboratory, or her reference frame, within which Velma measures things like the speed of the ball. You can think of the ground beside the tracks as a second reference frame, Mort’s reference frame, for his measurements. The standard question that any theory of relativity asks is how measurements made in one reference frame compare with those made in another. Scientists have thought about questions like this since at least the time of Galileo.

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Figure 3

Velma throwing a ball, observed by Mort.

To be more specific, suppose that the train moves at 70 meters per second (150 miles per hour, a typical modern train speed). Suppose that Velma throws the baseball toward the front of the train at 20 m/s “relative to Velma” (as measured on the train, using meter sticks and clocks that are on the train). How fast does the baseball move “relative to Mort” (as measured on the ground)? …Think about that. Well, during each second, the baseball moves 20 meters toward the front of the train as measured by Velma. But as observed by Mort, the baseball moves an additional 70 meters during that same second, because the train itself moves 70 meters. So the ball must move at 90 m/s relative to Mort. Right? Because Galileo would have given the same answer four centuries ago, this straightforward and fairly intuitive form of relativity is called Galilean relativity. CONCEPT CHECK 1 Velma’s normal ball-throwing speed is 20 m/s. She is in a train moving eastward at 70 m/s and throws a ball toward the rear of the train. The velocity of the ball relative to Velma is (a) 50 m/s eastward; (b) 50 m/s westward; (c) 20 m/s eastward; (d) 20 m/s westward; (e) 70 m/s eastward; (f) 70 m/s westward. CONCEPT CHECK 2 In the preceding question, the velocity of the ball relative to Mort, who is standing beside the tracks, is (a) 50 m/s eastward; (b) 50 m/s westward; (c) 20 m/s eastward; (d) 20 m/s westward; (e) 70 m/s eastward; (f) 70 m/s westward.

Let’s turn to a similar example involving light beams instead of baseballs. Light is an electromagnetic wave moving at 300,000 km/s, a speed that I will symbolize by the letter c. It’s difficult to imagine such a high speed. A light beam travels from New York to Los Angeles in a hundredth of a second. Trains, jet planes, and even Earth satellites moving at 8 km/s are slowpokes by comparison. Imagine that Velma pilots a really fast rocket ship past Earth at 75,000 km/s, or 0.25c (25% of lightspeed), and that she holds a source of light—a flashlight or a laser—pointed forward. Mort stands on Earth. What would be the speed of the light

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Velma’s spaceship moves past Mort at a speed of 0.25c

Velma’s light beam moves away from Velma at speed c

Figure 4

How fast is Velma’s light beam moving, as observed by Mort?

beam—the moving tip of the beam—relative to Velma and relative to Mort? It seems plausible that Velma measures the light beam to move at speed c, since she’s holding the light source. In fact, experiments with light beams emitted by moving sources show this to be true: Any light beam from a moving source moves at speed c relative to the source.2 What speed would Mort measure for the same light beam (Figure 4)? Following the logic of the baseball example, the sensible answer would seem to be 1.25c. After all, the light beam travels 300,000 km in each second as measured by Velma, and Velma travels 75,000 km in each second as measured by Mort, so it seems sensible that the light beam would travel 300,000 km + 75,000 km in each second, or 375,000 km/s, as measured by Mort. This is the answer Galileo would have given, the answer given by Galilean relativity. It is the answer that all scientists would have given up through the end of the nineteenth century. It is indeed a most sensible answer. Nevertheless, it’s experimentally wrong. Nature does not always comply with our notion of what is sensible! To see why there might be something wrong with this answer and to learn nature’s answer, let’s turn in the next two sections to Einstein’s thoughts.

3 THE PRINCIPLE OF RELATIVITY You ride in a smoothly moving unaccelerated jet airplane in level flight at unchanging velocity. The flight attendant pours you a cup of coffee. Where should you hold your cup: directly under the spout, or someplace else to take into account the motion of the airplane? In other words, does the coffee pour straight downward relative to the airplane? Try it sometime and see. Or try dropping a coin from one hand to the other in a moving vehicle (but not when you are driving): Is the catching hand directly beneath the dropping hand? The answer is that the coffee pours straight downward relative to the plane. You could experiment with many things, all within a smoothly moving reference frame: a falling ball, frictionless air coasters, electric currents, magnets, and more.

2

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Provided the source is not accelerating; see Section 4.

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Just as for the poured coffee, you would find that the results are the same as when the experiments are performed in a reference frame at rest on Earth. Suppose you are a passenger on an airplane with no windows in the passenger compartment. You fall asleep and awaken later to find yourself alone in the compartment. Can you tell, without receiving information from the outside world,3 whether your airplane is in level flight at unchanging velocity or parked on the ground? The answer is no. You could throw a ball, do handstands, pick up nails with magnets, and the like, and everything would be the same, regardless of whether your plane was in flight or parked. This is another example of a symmetry principle. It says that, no matter from what nonaccelerating reference frame you view the universe, the laws of physics are the same. I’ll summarize this as: The Principle of Relativity Every nonaccelerated observer observes the same laws of nature. In other words, no experiment performed within a sealed room moving at an unchanging velocity can tell you whether you are standing still or moving.

Unless you look outside, you can’t tell how fast you’re going. It’s a plausible idea and was the key to Einstein’s thinking about relativity. It’s called the “principle of relativity” because it says that all motion is just relative motion. When you say “the car moves at 25 km/hr westward,” you really mean that “the car moves westward at 25 km/hr relative to the ground” or that “the car and the ground are in relative motion at 25 km/hr.” You could just as well say that the car is standing still and the ground is moving eastward at 25 km/hr. You could even say that the ground is moving eastward at 1600 km/hr (which it is, relative to Earth’s center, due to Earth’s spin) and that the car is moving eastward at only 1575 km/hr. It is only the relative speed, the 25 km/hr, that really counts. CONCEPT CHECK 3 What about acceleration—can this be detected without looking outside? (a) Yes, you can do simple experiments to tell you whether you are accelerating. (b) Yes, but the experiments must involve light beams. (c) No.

4 THE CONSTANCY OF LIGHTSPEED: STRANGE BUT TRUE Have you ever asked yourself what it would be like if you could keep up with a light beam? Some people do. The 16-year-old Einstein did, and his reflections on this question helped lead him to his theory of relativity. To Einstein, the possibility of moving along with a light beam seemed paradoxical, contradictory. The reason is that, to an observer moving along with a light beam, the light beam itself would be at rest. To this observer, the light beam would appear as an electromagnetic “wave” that was standing still! To Einstein, this seemed absurd. Here’s why.

3

The Lord is subtle, but He is not malicious. Einstein

Information from the pilot would be from the outside world, because the pilot’s information enters through the cockpit window and through radio receivers.

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The Special Theory of Relativity You could see that Einstein was motivated not by logic in the narrow sense of the word but by a sense of beauty. He was always looking for beauty in his work. Equally he was moved by a profound religious sense fulfilled in finding wonderful laws, simple laws in the universe. It was really a religious experience for him, of the most profound sort, even though he did not believe in a personal god. Banesh Hoffmann, Mathematician and Author, in Some Strangeness in the Proportion

Our understanding of electromagnetic waves, such as light, is based on Maxwell’s theory of electromagnetic fields. Recall that Maxwell’s theory predicts that any disturbance in an electromagnetic field, such as a disturbance caused by the motion of an electrically charged object, must propagate as a wave moving outward through the field at speed c. This particular speed, 300,000 km/s, is built into Maxwell’s theory. Einstein believed that Maxwell’s theory should, like all other laws of nature, obey the principle of relativity. So Maxwell’s predictions should be correct within every moving reference frame. Since speed c is built into Maxwell’s theory, Einstein concluded that every observer ought to observe every light beam to move at speed c, regardless of the observer’s motion. No matter how fast you move, a light beam should always pass you at speed c, relative to you. If every observer sees every light beam move at speed c, then nobody can even begin to catch up with a light beam, much less move along with a light beam. It’s a simple idea. But it’s also pretty crazy, which is why it took Einstein to think of it. After all, if you run after a departing light beam, common sense tells you that from your perspective the speed of the departing light must be less than 300,000 km/s. And if you run toward an approaching light beam, common sense says that the speed of the approaching light must be greater than 300,000 km/s. Einstein’s idea is so odd that other turn-of-the-century physicists who might have discovered it did not. It’s the second important principle underlying Einstein’s theory. I’ll summarize it as: The Principle of the Constancy of Lightspeed The speed of light (and of other electromagnetic radiation) in empty space is the same for all nonaccelerated observers, regardless of the motion of the light source or of the observer.

I don’t try to imagine a personal God; it suffices to stand in awe at the structure of the world, insofar as it allows our inadequate senses to appreciate it. Einstein

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Like the principle of relativity, this principle is valid only for nonaccelerated observers. The reason is that Maxwell’s theory, like most laws of physics, is valid only for nonaccelerated observers. To get a feel for it, we’ll apply this principle to several “thought experiments,” impractical experiments that could in principle be performed. Each experiment involves a light beam, which we take to be a laser beam but which could just as well be a flashlight beam. Suppose Velma moves away from Mort at a quarter of lightspeed and holds a laser pointed forward, as in Figure 4. As noted in Section 2, she observes the beam to move away from her at speed c. What speed does Mort observe for the laser beam? Galilean relativity and our intuitions answer 1.25c, or 375,000 km/s. But Einstein’s relativity predicts that the answer is c, or 300,000 km/s! Another example: Mort has the laser and he shines it in the direction of Velma who is departing from him at a quarter of lightspeed (Figure 5). Mort observes the beam to move away from him at speed c, but what does Velma observe? Galileo, and common sense, now predict 0.75c, but Einstein predicts c. To dramatize the oddness of this, imagine that Velma is moving away from Mort at a speed of 0.999 999c, just a hair slower than lightspeed (Figure 6). Mort switches on his laser and sees the light beam depart from him at speed c. As

The Special Theory of Relativity Velma’s spaceship moves away from Mort at a speed of 0.25c

Mort’s light beam moves away from Mort at speed c

Figure 5

What is the speed of Mort’s light beam relative to Velma?

Velma’s spaceship moves past Mort at a speed of 0.999,999c

Mort’s light beam moves away from Mort at speed c. According to Mort, Velma is moving only 0.000,001c, or 300 m/s, slower than his light beam

Figure 6

Now how fast is Mort’s light beam moving, as observed by Velma?

observed by Mort, Velma moves only slightly slower than the light beam—he says that she nearly keeps up with the light beam. Galilean relativity predicts that Velma observes the light beam passing her at only 0.000 001c. This is just 300 m/s—the speed of fast jet airplanes. But Einstein’s relativity says that she sees the light beam pass her at precisely 300,000 km/s, despite the fact that she is moving away from the light source at nearly lightspeed! Maybe you’ve noticed that we don’t allow Velma to have precisely speed c. If we imagined that she moves right at speed c, we’d get into the difficulty that Einstein noted: She would observe the light beam to be at rest. So an observer can move at nearly, but not precisely, speed c relative to another observer. Later, we’ll see why. How do we know that light goes the same speed for all observers? Strange though the constancy of lightspeed may seem, it’s verified daily. However, most experiments involve fast-moving microscopic particles rather than spaceships. In one especially striking experiment in 1964, a subatomic particle moving at nearly lightspeed emitted

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The Special Theory of Relativity electromagnetic radiation both forward and backward. Galilean relativity predicts that the forward-moving radiation should move much faster than c while the backward-moving radiation should move much slower than c, as measured in the laboratory. But measurement showed that both radiation beams move at speed c relative to the laboratory.

Maxwell and other nineteenth-century scientists had a more conventional view of light beams. They believed that light was a wave in a material medium, just as water waves are waves in water. They called this medium ether. Nobody had observed ether. It couldn’t be made of ordinary atoms, because light waves travel through outer space where there are essentially no atoms. Instead, ether was thought to be a continuous material substance filling the entire universe and made of some unknown nonatomic form of matter. The ether theory assumes that the “natural” speed of light, 300,000 km/s, is light’s speed relative to the ether. Observers moving through the ether should then measure other speeds for light beams, speeds that should depend on the observer’s speed through the ether. But as the principle of the constancy of lightspeed states, and as experiment shows, all observers measure the same speed for all lightbeams, so the ether theory must be wrong. Since Einstein, electromagnetic waves have been viewed as the vibrations of an electromagnetic field, which itself is not made of any material substance. This contrasts sharply with the materialist worldview of Newtonian physics. The constancy of lightspeed is the key principle that gives the theory of relativity its odd quality. It’s natural to question this principle. How do we know it’s true? The answer is simple but profound: It’s true because nature says so. Numerous experiments show that every light beam moves at speed c, regardless of the motion of the source or observer. Although this odd notion violates our preconceived beliefs, it is observation of nature, rather than preconceived beliefs, that determines truth in science. Our preconceived beliefs about motion are based on observations of objects moving far slower than lightspeed and are very nearly correct at such speeds. But at higher speeds, our preconceptions are radically incorrect. The foundations of Einstein’s theory are the principle of relativity and the constancy of lightspeed. Their role in the theory of relativity is identical to the role of Newton’s laws in Newton’s theory of force and motion: They form the logical basis of the theory, from which everything else is derived and which are themselves justified directly by observation. Physicists call this theory the special theory of relativity. The word special distinguishes this theory from another, related theory of Einstein’s called the general theory of relativity. The distinguishing feature of the general theory of relativity is that it allows accelerated observers, while the special theory allows only nonaccelerated observers, so the general theory is a more general—broader—theory than the special theory. Strictly speaking, Earth itself is an accelerated reference frame, because it spins on its axis and because it rotates around the sun. But these accelerations are so small that the predictions of the special theory are excellent approximations for any Earth-based observer. The remainder of this chapter explores five of special relativity’s most important predictions: the relativity of time, the relativity of space, the relativity of mass, c as the speed limit, and E = mc2. CONCEPT CHECK 4 Velma moves away from Mort at 0.75c. She turns on two lasers, one pointed forward and the other backward. According to Galilean relativity, how fast should the forward and backward beams move, as observed by Mort? (a) 0.25c and 1.75c. (b) 1.75c and 0.25c. (c) 0.25c and 0.75c. (d) 0.75c and 0.25c. (e) c and c.

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CONCEPT CHECK 5 In the preceding question, Mort actually observes (a) 0.25c and 1.75c; (b) 1.75c and 0.25c; (c) 0.25c and 0.75c; (d) 0.75c and 0.25c; (e) c and c.

5 THE RELATIVITY OF TIME The constancy of lightspeed suggests something is amiss in our intuitive conceptions of space and time. After all, speed measures how far an object moves through space divided by the time to move, so speed is intimately tied to space and time. We feel that we understand what “time” is, but its meaning fades when we ponder it. Being enmeshed in time, we cannot study it from a distance, so our attempts to define it are usually circular, implicitly using the concept of time in order to define time. Einstein’s insight into time was that it’s physical—part of the physical universe. Just as one can measure the properties of a stone or of a light beam, one can measure the properties of time. And how should we measure the properties of time? With clocks! This reply is more profound than it appears. The only way we can measure time is with real, physical “clocks,” by which we mean any phenomenon—a swinging pendulum, Earth’s rotation around the sun—that goes through identical repetitions. Physically, the concept of a clock really defines time. So to investigate the properties of time, we must investigate clocks. How do clocks really behave? Einstein managed to predict the properties of clocks using as his starting point only the two principles of the special theory of relativity. An ordinary spring-wound or battery-driven clock would be hard to study based only on Einstein’s two principles because these clocks are so complex, involving springs, electric current, gears, and so forth. So Einstein invented a simple kind of clock, a simple thought experiment, really. His light clock (Figure 7) involves no mechanically moving parts; its only motion is the motion of a light beam. Two parallel mirrors face each other, one above the other, and a light beam bounces up and down (reflects) between them. Although it’s not terribly practical for the clock maker, it’s convenient to imagine that the mirrors are separated by 150,000 kilometers, because then the time for one complete round trip of the light beam is just 1 second. You know it’s 1 second because the constancy of lightspeed says all light beams travel 300,000 kilometers in 1 second. We’ll assume this light clock ticks at the end of each round-trip. We begin investigating the properties of time by installing one light clock in Velma’s spaceship moving eastward past Earth, and another in Mort’s laboratory on Earth. Let’s think about Velma’s light clock. She sees her light beam bouncing straight up and down, covering 300,000 km per tick [Figure 8(a)]. Simple enough. But from Mort’s point of view, the tip of Velma’s light beam is not only moving up and down, it’s also moving eastward because of Velma’s eastward motion. So the tip of Velma’s light beam, as seen by Mort, moves along diagonal paths. Figure 8b shows Mort’s observations of Velma’s spaceship at three instants: when the tip of her light beam is at the bottom mirror, when it has moved up to the top mirror, and when it is back at the bottom mirror. Since the distance between the mirrors is 150,000 km, you can see from the figure that the distance along one of the two diagonals is greater than 150,000 km. This means that the total round-trip distance traveled by Velma’s light beam, as measured by Mort, is greater than 300,000 km. There is nothing surprising or subtle about this; Galileo would have said the same thing. Now comes the part that Galileo (and our intuitions) wouldn’t agree with: The constancy of lightspeed says that Mort observes

Mirrored faces

Tip of light beam

150,000 kilometers

Figure 7

A light clock. A light beam bounces up and down between two mirrors. If the distance between mirrors is 150,000 km, then 1 second will elapse during one complete round-trip up and back down.

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(a)

(b)

Mort’s light clock

Figure 8

(a) Velma in her spaceship, observing her light clock. (b) Velma’s spaceship and the light beam on Velma’s light clock as observed by Mort using his own light clock. According to Mort’s observations, the tip of Velma’s light beam moves along the diagonal path shown by the dashed arrows.

Velma’s light beam to move at just 300,000 km/s (Galileo would say that Mort observes Velma’s light beam to move faster than 300,000 km/s, because of Velma’s motion). Since Mort observes the round-trip distance to be greater than 300,000 km, it follows that according to Mort it takes more than 1 second for Velma’s light beam to make the round-trip! So, as measured by Mort using his clock, more than 1 second elapses between Velma’s ticks. According to Mort, Velma’s clock runs slow. Velma’s second is different from Mort’s second. The two observers measure different time intervals for the same event (one round-trip of Velma’s light beam). Time is relative to the observer. It’s simple, but hard to believe. Let’s turn things around. How does Mort’s clock appear to the two observers? To Mort, his own clock’s light beam travels 300,000 km in one round-trip and requires 1 second to do so. But from Velma’s viewpoint, Mort’s clock is moving westward, so the tip of Mort’s light beam is moving along a diagonal and therefore the total round-trip distance traveled by Mort’s light beam as observed by Velma is greater than 300,000 km. But because Velma observes Mort’s light beam to move at 300,000 km/s, she must observe that more than 1 second elapses between Mort’s ticks. According to Velma, it’s Mort’s clock that runs slow. The rule is moving clocks run slow: Mort and Velma both observe that the other person’s clock runs slow. This is not your normal situation caused by an inaccurate clock, in which if my clock runs slow according to your clock, then your clock must run fast according to my clock. This raises an interesting question: Whose clock is really running slow, and whose is really accurate? The answer is that Velma and Mort are both right! Velma observes that Mort’s clock is slow, and Mort observes that Velma’s clock is slow, and both observations are correct. This situation is not caused by inaccurate clocks; it is instead a property of time itself. There is no single “real” time in the universe, no “universal time”; there is only Mort’s time and Velma’s time and all the other possible observers’ times.

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As you might expect, there is a formula that quantitatively describes the relativity of time.4 Table 1 gives a few of the numerical results that can be calculated from this formula, and Figure 9 is a graph based on the same formula. As you can see from the table, the effect is negligible even at orbiting satellite speeds (10 to 20 km/s). It’s not until speeds of 0.1c—a speed that would get you around the world in 1 second—that the effect amounts to even a half of 1%. But at large fractions of lightspeed, the effect becomes quite large: At 99.9% of lightspeed (not shown on the graph), Mort and Velma’s seconds will be more than 22 seconds long as measured by the other observer. The relativity of time is also called time dilation, because a time interval of 1 second on a moving clock is expanded, or dilated, to more than 1 second as measured by an observer past whom the clock is moving. Although we investigated the relativity of time by studying light clocks, the conclusion holds for every type of clock—every regularly repeating phenomenon. Einstein thought about light clocks only in order to learn what the two principles of his theory implied about time. Every clock must behave the way a light clock behaves because they all measure the same thing: time. And every phenomenon that occurs during an interval of time must also behave in this way. Think, for example, of an ice-cream cone melting. Suppose you can make ice-cream cones that melt in exactly 10 minutes and that both Velma and Mort have one of these cones. These cones are a kind of clock, a clock that ticks in 10 minutes.

It requires a very unusual mind to undertake the analysis of the obvious. Alfred North Whitehead, TwentiethCentury Philosopher

Time in seconds

CONCEPT CHECK 6 Mort and Velma have identical 10-minute ice-cream cones. Velma passes Mort at 75% of lightspeed. Use Table 1 to predict the times measured by Mort for his and Velma’s cone to melt. (a) 10 minutes for Mort’s cone, 10 minutes for Velma’s cone. (b) 10.5 minutes and 10 minutes. (c) 10 minutes and 10.5 minutes. (d) 15 minutes and 10 minutes. (e) 10 minutes and 15 minutes.

4

3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0

Figure 9

0

0.1c

0.2c

0.3c

0.4c

0.5c 0.6c Speed

0.7c

0.8c

0.9c

c

The relativity of time. The graph shows the duration of one clock tick (representing 1 second in the clock’s reference frame) on a moving clock, for various speeds of the clock relative to the observer.

This formula can be derived from Figure 8 by using the Pythagorean theorem, which states that a right triangle’s short side lengths a and b are related to its diagonal length c by c2 = a2 + b2. The formula is T = To> 2(1 - y2>c2), where y is the relative speed, To is the time between two of Velma’s ticks as observed by Velma (To = 1 second), and T is the time between two of Velma’s ticks as observed by Mort.

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The Special Theory of Relativity Table 1 The relativity of time: some quantitative predictions To give you a feel for these speeds: 0.3 km/s is a typical subsonic jet plane speed, 3 km/s is twice the speed of a high-powered rifle bullet, at 3000 km/s you could cross the United States in 1 second, and at 30,000 km/s you could circle the globe in 1 second. Clearly, relativistic effects are small until the speed becomes very large! Relative speed (km/s) 0.3 3 30

Relative speed as a fraction of lightspeed (c)

Duration of one “tick” on a moving clock, as measured by an observer past whom the clock is moving (s)

10–6

1.000 000 000 000 5

10

–5

10–4

1.000 000 000 5 1.000 000 005

300

0.001

1.000 000 5

3000

0.01

1.000 05

30,000

0.1

1.005

75,000

0.25

1.03

150,000

0.5

1.15

225,000

0.75

1.5

270,000

0.9

2.3

297,000

0.99

7.1

299,700

0.999

22.4

Instead of ice-cream cones, they could have frogs. Suppose your local biology department hatches guaranteed 10-day frogs, having a 10-day lifetime. Biological life occurs in time, too, so these frogs can be thought of as a kind of clock. So if Velma passes Mort at 75% of lightspeed, he says that her frog lives 15 days but that his frog lives only 10 days (see Concept Check 6). And she says that his frog lives 15 days but that her frog lives only 10 days. So each observes their own frog to die first. And both observations are correct! Fantastic. “But,” you may ask, “whose frog really dies first?” If you are tempted to ask this, your unspoken belief is that there is one single, universal, “real” time. But there isn’t. There is only Mort’s time, and Velma’s time, and every other individual observer’s time. How do we know that time flows differently for different observers? The relativity of time has been verified repeatedly in laboratories, by observing fast-moving subatomic particles. One experiment, similar to the frog example, involved a type of subatomic particle known as a “muon.” Muons, unlike most ordinary matter, are not permanent objects. Instead, they have a “lifetime” after which they disintegrate spontaneously into other particles. The lifetime of a muon is only 2.2 microseconds (2.2 millionths of a second), as measured by you if the muon is at rest relative to you. But a muon moving rapidly past you lives much longer as measured by you, because of time dilation. For example, at 99% of lightspeed (muons often move this fast in high-energy physics labs), Table 1 says that its lifetime will be lengthened by a factor of 7.1, so it will not disintegrate until 7.1 * 2.2 = 15.6 microseconds have passed. This experiment has been done, and the moving muons were observed to have lifetimes that were lengthened by just the predicted amount.

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6 TIME TRAVEL: YOU CAN’T GO HOME AGAIN As you might have suspected, the next step is to investigate the life spans of Velma and Mort themselves. Suppose they are born at the same time5 and that they have 80-year lifetimes. In other words, Velma observes her lifetime to be 80 years and Mort observes his lifetime to be 80 years. If Velma and Mort spend their lives moving at 75% of lightspeed relative to each other, then Table 1 informs us that Mort’s descendants observe that Velma lives for 120 years, as measured by Mort’s clocks. And Velma’s descendants observe that Mort lives for 120 years, as measured by Velma’s clocks. From Mort’s viewpoint, Velma ages slowly; she ages by just a year during each of Mort’s 1.5 years; he dies after 80 of his years; and she dies after 120 of Mort’s years but having the physical appearance of a person who is only 80. According to Velma, all of this is reversed. And both of them are correct. Incredible. CONCEPT CHECK 7 When Velma observes herself to be 60 years old, she will observe Mort to be (a) 30; (b) 40; (c) 60; (d) 80; (e) 90.

This suggests a perplexing question. Suppose that Velma and Mort are born at the same time on Earth, as twins perhaps, and Velma then boards a spaceship, takes a fast trip to a far star, and returns to Earth. This scenario is different from the scenario in the preceding paragraph, because now Velma and Mort begin and end in the same reference frame. Once they are back together they must agree on who is older, because there is only a single time in any single reference frame. Which twin will be older, or will they be the same age? Let’s think about that. Recall that the special theory of relativity applies only to nonaccelerated observers. But in the scenario for the two twins, Velma leaves Earth, speeds up enormously, turns around to get back to Earth, and then comes to rest on Earth. Since this trip necessarily involves three enormous accelerations, the special theory of relativity does not apply to Velma’s observations. But the special theory does apply to Mort’s observations, since he didn’t accelerate. As you have seen, the theory predicts that he observes Velma to age slowly during her entire trip, because she is moving relative to him. For example, if she moves at 0.75c, he should observe that 1.5 of his years elapse for every 1 of hers (Table 1). If Velma’s trip takes 60 years as measured by Mort, he observes that only 40 of her years elapse. So he observes that when they get back together on Earth, he is 60 and she is 40! Her observations must agree with this, since the two are now in the same reference frame. This is how you can get to be 20 years younger than your twin brother.

The testimony of our common sense is suspect at high velocities. Carl Sagan, Astronomer and Author

How do we know that time travel is possible? This conclusion has been experimentally verified, but in a less dramatic fashion. Atomic clocks were flown around the world on commercial jet flights and compared to clocks that remained at rest on Earth. Although the predicted time difference was only a fraction of a second, it was measurable using highaccuracy clocks. As predicted, the clock that went on the trip came back younger (it hadn’t ticked as many times) than the clock that stayed home. And the quantitative difference in elapsed time was precisely as predicted. As you will see in a moment, such experiments demonstrate that time travel is possible, but only into the future. 5

You might wonder what “at the same time” means, since we are assuming that Mort and Velma are in different reference frames. To simplify matters, suppose that Mort and Velma are just passing each other. Then “at the same time” means that as either one comes into the world, he or she observes that the other is coming into the world too.

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This suggests some astonishing possibilities. Suppose your mother leaves Earth for the star Vega, a sunlike star lying relatively close to our sun and a possible candidate for a planetary system. The distance to Vega is 26 light-years, meaning that it takes light 26 years to reach Vega from here. A light-year is the distance light travels in 1 year. Suppose mom’s spaceship averages a colossal 0.999c. She spends 3 years on a planet that is orbiting Vega and returns home. Since she travels at nearly lightspeed, each one-way trip takes slightly more than 26 years, as measured on Earth. So she is gone for slightly more than 26 + 3 + 26 = 55 years, as measured on Earth. If you were 5 and mom was 30 when she departed, you would be 60 when she returned. But mom would no longer be 25 years older than you! Table 1 informs us that during the 52 “Earth-years” of space travel at 0.999c, she aged by only 1 year for every 22.4 years of “Earth time.” So she aged by only 52>22.4 = 2.3 years during the 52 Earth-years. Including the 3 years spent on Vega, she aged by only 5.3 years during the entire trip. So mom is 35.3 years old when she returns, and you are 60! This is how you can get to be older than your mother. It’s a form of time travel. Your mother took a trip to Earth’s future. She could travel much further into the future, hundreds or thousands of years into the future, by moving faster, say at 0.9999c. But it’s a one-way trip. You can’t go home again to the past from which you departed. Time dilation suggests that humans might travel to distant stars within a human lifetime. Suppose you travel to a star 200 light-years away, at 0.999c relative to Earth. Even though the trip takes a little over 200 years as measured on Earth clocks, it takes you only 200>22.4 = 9 years as measured in your spaceship. When you arrive at the star, two centuries have elapsed on Earth. Even if you immediately hurry back to Earth, you time-travel four Earth centuries into the future during the round-trip but you age by only 18 years. On Earth, you will be a relic from four centuries earlier. CONCEPT CHECK 8 It is physically possible for your mother to leave Earth after you were born and return (a) before you were born; (b) before she was born; (c) younger than you; (d) older than you; (e) younger than she was when she left; (f) older than she was when she left.

7 THE RELATIVITY OF SPACE AND MASS What is space? Just as time means “what is measured by clocks” (Section 5), space means “what is measured by rulers.” What operations should Mort perform to measure, say, the width of a window? For a window at rest relative to Mort, the prescription is to place a measuring rod along the window and compare the ends of the window with the marks on the rod. If the window is moving past Mort, he should continue using a measuring rod that is fixed in his own reference frame, because he wants to know the width of the moving window as measured in his own reference frame. If the width being measured lies along the direction of motion, Mort must measure the positions of the two ends simultaneously because otherwise the window will shift positions during the lag between measurements and Mort won’t measure the true width. In order to ensure that the front-end and back-end measurements are simultaneous, Mort must use two clocks—one at each end. This means that the measurement of the width of a moving object is mixed up with the measurement of time; time and space are tangled up with each other! Since time is relative, it then comes as no surprise to

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learn that space is relative too. I won’t go through the argument that proves this result; it’s similar to the argument in Section 5 showing that moving clocks run slowly. More specifically, Einstein’s theory predicts that Mort observes the window’s width along its direction of motion to be shorter than does Velma who is traveling along with the window (Figure 10). This effect is called length contraction. There is no length contraction along directions perpendicular to the window’s direction of motion. As with time dilation, length contraction works both ways: Just as Mort finds that Velma’s window is contracted, Velma finds that Mort’s window is contracted. A quantitative analysis leads to a formula, graphed in Figure 11.6 The figure graphs the predicted length of a 1-meter-long object such as a meter stick, held parallel to its motion, for various speeds of the object. Like time dilation, length contraction is barely detectable for speeds below about 0.1c but becomes large at higher speeds. Length contraction is not simply something that happens to meter sticks. Since space is defined by meter sticks, it is space itself that is contracted. Just as Velma’s time flow is different from Mort’s time flow, we must speak of “Velma’s space” and “Mort’s space” rather than a single, universal space. Space is different for different observers. Space is relative. CONCEPT CHECK 9 Velma measures her spaceship to be 100 m long and 10 m high. Is it possible for her spaceship to move fast enough past Mort for its length to be equal to its height, as observed by Mort? (a) Yes, by moving at about 0.9c. (b) Yes, by moving at about 0.99c. (c) Yes, by moving at about 0.1c. (d) No, because she would have to move at precisely lightspeed to accomplish this. (e) No, because objects do not change their shapes.

1m

1m

(a) Less than 1 m

1m

(b)

Figure 10

The window in Velma’s spaceship as measured by (a) Velma and (b) Mort.

Einstein’s new principle, the constancy of lightspeed, affects nearly everything in physics: time, space, and more, including Newton’s law of motion. This law states that an object’s acceleration is equal to the net force exerted on the object divided by the object’s mass, or in symbols a = F>m

Length, m

This implies that if you exert an unchanging force on an object, the object maintains an unchanging acceleration. Eventually, the object will be going at lightspeed and still accelerating. An observer riding on such an object could catch up with and pass a light beam.

6

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Figure 11

The relativity of space. The predicted length of a meter stick for various speeds of the meter stick relative to the observer. 0

0.1c

0.2c

0.3c

0.4c

0.5c 0.6c Speed

0.7c

0.8c

0.9c

c

The formula is L = L0 2(1 - y2>c2) where L0 is the object’s rest length (the length as measured by an observer for whom the object is at rest), and L is the length of the object when it is moving at speed y.

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So Newton’s law of motion is not consistent with the theory of relativity! Apparently, relativity alters Newton’s law in such a way as to prevent objects from accelerating up to lightspeed. To describe this alteration of Newton’s law of motion, let’s imagine that Mort and Velma (who is moving past Mort) have identical 1 kilogram objects, 1 kilogram melons perhaps. If Mort pushes on his melon with, say, a 1 newton force, he will find that it accelerates at 1 m/s2, just as Newton’s law of motion predicts. If he now pushes on Velma’s melon (which is moving past him) with a 1 newton force, Newton’s law of motion predicts that Velma’s melon accelerates at 1 m/s2, but relativity theory predicts7that Velma’s melon accelerates at less than 1 m/s2. As was the case for other relativistic effects, this effect is negligibly small at normal speeds but large at speeds comparable to lightspeed. From Mort’s point of view, a 1 newton force applied to both melons produces a smaller acceleration in Velma’s melon than in his own melon. From Mort’s point of view, Velma’s melon has more inertia than does his own melon (recall that a body’s inertia is its resistance to acceleration). But this is the same as saying that Velma’s melon has more mass, because the fundamental meaning of mass is “amount of inertia.” In other words, Mort measures Velma’s melon to have a larger mass than his own melon, even though they are identical melons. As usual, the effect works the other way around: Relative to Velma, her melon has a mass of 1 kg, but Mort’s melon has a mass of more than 1 kg. Thus, mass is relative: An object’s mass increases with its speed, so different observers measure different masses for the same object. A quantitative analysis leads to a formula that predicts an object’s mass for various speeds.8 Figure 12 is a graph of this formula, along with the previous graphs for time dilation and length contraction. The formulas for mass increase and time dilation have identical forms, so their graphs have identical shapes. In Newtonian physics, “mass” (or inertia) means the same thing as “quantity of matter.” But in relativity, an object’s mass increases with its speed while its quantity of matter does not increase because it still contains the same atoms. So mass no longer means “quantity of matter.” But we need a word for an object’s quantity of matter. That word is rest-mass, the mass of an object as measured by an observer in a frame of reference in which the object is at rest. For example, Velma’s and Mort’s melons both have rest-masses of 1 kg, regardless of who observes them. This number, 1 kg, is a measure of its quantity of matter. An object’s mass, however, is the amount of inertia it possesses and is different for different observers. The mass and rest-mass of a slow-moving object are essentially the same, but the mass of a high-speed object is significantly greater than its rest-mass. How do we know that mass increases with speed? Relativistic mass increase is an everyday fact of life in high-energy physics labs. A subatomic particle can be accelerated to speeds so close to lightspeed that its mass is thousands of times greater than its rest-mass. One way to check this prediction is to bend a high-speed particle’s path by applying electric or magnetic forces and measure the curvature of the resulting path. If high-speed particles really do have larger masses, their paths should curve less than they otherwise would, because their larger inertia tends to keep them moving straight ahead. Measurements show that such paths are less curved than they would be in the absence of relativistic mass increase and that the amount of curvature agrees with Einstein’s predictions. 7

8

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The reason is that accelerations of Velma’s melon, as viewed by Mort, are reduced because distances are contracted and time intervals are expanded. The formula is m = m0> 2(1 - y2>c2), where m0 is the object’s rest-mass (the mass as measured by an observer for whom the object is at rest), and m is the mass of the object when it is moving at speed y.

Time in seconds, length in meters, or mass in kilograms

The Special Theory of Relativity 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Time dilation and mass increase

Figure 12

Length contraction

0

0.1c

0.2c

0.3c

0.4c

0.5c 0.6c Speed

0.7c

0.8c

0.9c

c

Relativistic mass increase, length contraction, and time dilation. The graph shows the duration of one clock tick (representing 1 second in the clock’s reference frame) on a moving clock, the length of a moving meter stick, and the mass of a moving standard kilogram, for various speeds of the clock, meter stick, and kilogram relative to the observer.

Time, space, and mass are relative, but not everything is relative. In fact, the two basic principles of Einstein’s theory tell us that the speed of any light beam is the same for every observer, and the same goes for the laws of physics. Relativistic mass increase explains why you cannot accelerate objects up to lightspeed. At high speeds, an object’s mass becomes very large, increasing without limit as the speed approaches c (Figure 12). Eventually, the force needed for further acceleration becomes so large that the object’s surroundings cannot provide it. But there is something that moves as fast as lightspeed: light itself. In fact, light never moves slower than 300,000 km/s.9 When you turn on a lightbulb, the light does not accelerate from zero up to lightspeed; instead, it moves at precisely lightspeed from the instant it is created. Light is quite different from any material object. When you put a material object down in front of you, it has rest-mass. Light beams must not have rest-mass, because if they did, then relativistic mass increase would make their mass infinite while moving at lightspeed. Anything that has no rest-mass and always moves at lightspeed, such as light and other forms of electromagnetic radiation, is classified as radiation. It’s a useful distinction: Matter has rest-mass and always moves slower than lightspeed, while radiation has no rest-mass and always moves at lightspeed. 9

However, light travels through material substances such as water or glass at an average speed that is sometimes far less than lightspeed. When moving through matter, light momentarily vanishes when absorbed by an atom and is re-created when emitted by the atom. Whenever the light actually exists as light, it moves at 300,000 km/s.

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CONCEPT CHECK 10 Which is a form of matter? (a) Red light. (b) invisible waves drawn (c) The invisible carbon dioxide gas emitted by automobiles. (d) The electron beam that creates the picture on a TV tube. (e) A gamma ray.

8 E = mc2: ENERGY HAS MASS, AND MASS HAS ENERGY As an object speeds up, its kinetic energy increases and, as you have just learned, its mass increases. So, at least in the case of kinetic energy, energy increase and mass increase go hand in hand. Working from the theory of relativity and the law of conservation of energy, Einstein found that mass is connected to every form of energy in this fashion. You can increase a system’s mass by simply lifting it (giving it gravitational energy), warming it (giving it thermal energy), stretching it (giving it elastic energy), or giving it any other form of energy. Does that surprise you? It surprises me. If you stretch a rubber band, you don’t expect its mass to increase. It’s still the same rubber band, after all. This is a new and surprising prediction: Any increase in a system’s energy increases its mass, regardless of what form that energy increase might take. Einstein’s analysis yields a simple formula that quantitatively relates the change in mass to the change in energy. The formula states that the change in mass equals the change in energy divided by the square of lightspeed:

S

N S

N

(a) Less energy

change in mass =

S

N

S

N

(b) More energy

Figure 13

The separated magnets of (b) have more energy, and hence more mass, than do the two joined magnets of (a). The excess energy and mass in (b) reside in the invisible and nonmaterial magnetic field, indicated by dashed lines.

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change in energy square of lightspeed

In the standard metric units, mass and energy are in kilograms and joules, and c = 3 * 108 m>s, so c2 = 9 * 1016 m2>s2. Note that, since the standard metric unit for use in physics formulas is meters rather than kilometers, you need to use 3 * 108 m>s for “c” rather than 300,000 km/s. Here’s an example. Suppose you stretch a large, strong rubber band by exerting an average force of 300 N through a distance of 0.6 m. Since work equals force times distance, you’ve done 300 N * 0.6 m = 180 J of work on the band. So the work–energy principle says you’ve added 180 J of energy to the band. This increases the band’s mass by 180 > 9 * 1016 = 2 * 10 - 15 kg = 0.000 000 000 000 002 kg. Not much. The increase is small because c2 is so large. This is why relativistic mass increase wasn’t noticed before Einstein: In ordinary situations, it’s too small to notice. As a second example, suppose you have two bar magnets and that the north pole of one is joined to the south pole of the other so that they cling together [Figure 13(a)]. Since it takes work to pull them apart, the separated magnets of Figure 13b must have more energy than do the joined magnets. But more energy means more mass. So the total mass of the two combined magnets increases simply by pulling them apart! The separation process creates a magnetic field in the space between the two magnets [Figure 13(b)]. The excess energy in the separated magnets resides in this invisible and nonmaterial magnetic field. You encountered such “field energy” before, in the energy of electromagnetic radiation. But now you can see that fields also have mass. This mass is in the “empty” space between the magnets. The work done in separating the two magnets is only a few joules, so the mass difference is again tiny. Nevertheless, it’s extraordinary that nonmaterial fields in empty space have mass.

The Special Theory of Relativity

Turning to more dramatic examples, nuclear reactions entail nature’s strongest forces, the forces acting within the atomic nucleus. For now, all you need to know about nuclear reactions is that they are analogous to chemical reactions but they involve changes in nuclear structure rather than changes in electron orbits. For example, in nuclear power reactors and nuclear weapons, the element uranium undergoes a nuclear reaction known as nuclear fission in which the nucleus of each uranium atom is altered.10 Fission is a little like combustion, but the forces involved are so strong that the thermal energy created is far larger than in any chemical reaction. So the rest-mass loss, after removing the thermal energy, is far larger. If a kilogram of uranium is fissioned, the rest-mass loss is about 0.001 kg (1 g), which is a 0.1% mass decrease and easily detected. This can be checked experimentally, and the results agree with Einstein’s predictions. Nineteenth-century scientists believed matter was indestructible, in other words, that rest-mass was conserved in every physical process. This is certainly plausible. Since the days of the early Greek materialists, most scientists have felt that matter is indestructible—that although its form might change, its total amount cannot change. Nineteenth-century chemists performing high-precision mass measurements concluded that rest-mass is conserved even in highly energetic chemical reactions. But Einstein’s relativity contradicts the conservation of matter. Matter—that is, rest-mass— is not conserved in chemical reactions, in stretching a rubber band, and so forth. But these changes in rest-mass are so small that they are experimentally undetectable. In high-energy processes such as nuclear fission, however, the changes are easily detected, and the results show clearly that matter is not conserved. Now take this reasoning one step further: Einstein believed that this result extended not just to changes in mass but to all of the mass of any system. In other words,

total mass of any system =

When I think of matter, I like to think mostly of fields. We are fields rather than particles. Freeman Dyson, Physicist

total energy of that system c2

or, in symbols, m =

E c2

This implies Einstein’s famous formula, total energy of any system = (system’s total mass) * (c2) E = mc2 So all energy has mass, and all mass has energy. Since energy means the capacity to do work, and mass means inertia, the practical meaning of E = mc2 is that any system of mass m should be able to do mc2 units of work, and any system of energy E has an inertia E/c2. How do we know that E = mc2? If Einstein is right, there should be some physical process by which mc2 units of work can be obtained from any object of mass m. Such processes, known as matter–antimatter annihilation, have been discovered. Here’s how they work. In addition to the protons, neutrons, and electrons that form ordinary matter, physicists have discovered three other material particles, known as “antiprotons,” “antineutrons,” and 10

If matter turns out in the end to be altogether ephemeral, what difference can that make in the pain you feel when you kick a rock? John A. Wheeler, Physicist

Each uranium nucleus splits to form two nuclei of various lighter-weight elements.

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The visible world is neither matter nor spirit but the invisible organization of energy. Heinz Pagels, Physicist

Science has found no “things,” only events. The universe has no nouns, only verbs. R. Buckminster Fuller, Architect and Futurist

There are no things, only processes. David Bohm, Physicist

“antielectrons.” If one of these “antiparticles” is brought close to its corresponding particle, the two particles vanish entirely, and high-energy radiation is created. It’s an extreme example of the nonconservation of matter: Matter entirely vanishes, to be replaced by radiation. So any material object can be turned into radiation by annihilating all its protons, neutrons, and electrons—although it would be difficult to collect enough antiparticles to annihilate a macroscopic object. The energy of this radiation can then be used to do work. Furthermore, when the radiation’s energy is measured, it is found to equal the total mass of the particles times c2.

E = mc2 is simple but subtle, and easy to misinterpret. Most of the confusion arises from confusion between mass (inertia) and rest-mass (matter). Following are two common misconceptions about E = mc2. It is sometimes said, incorrectly, that Einstein’s relation means that “mass is not always conserved.” It is true that matter (rest-mass) is not always conserved. But mass (inertia) is always conserved, because mass equals energy divided by c2, and energy is always conserved. It is sometimes said, incorrectly, that Einstein’s relation means that “mass can be converted to energy.” It’s true that rest-mass—matter—can be converted to nonmaterial forms of energy such as radiation. But you just saw that mass is always conserved, so mass can never be converted to anything else! In proton-antiproton annihilation, for example, the mass of the pair is precisely equal to the mass of the created radiation. But rest-mass, or matter, is destroyed, and is converted to radiation. One must be careful with the word mass. To summarize: The Principle of Mass–Energy Equivalence Energy has mass; that is, energy has inertia. And mass has energy; that is, mass has the ability to do work. The quantitative relation between the energy of any system and the mass of that system is E = mc2.

Mass–energy equivalence represents another sharp break with the Newtonian worldview, which follows the Greek materialists in believing that interactions between indestructible atoms moving in empty space determine everything that happens in the physical universe. Let’s think about the mass–energy relationship at the atomic level. Since all energy has mass, some of an atom’s mass must be due simply to the kinetic energy of its parts (electrons, protons, and neutrons) and to the energy of its various electromagnetic and nuclear force fields. This suggests an intriguing question: Is that all there is? Are atoms made only of fields and motion? If so, atoms are not only mostly empty space, they are entirely empty space, made only of fields similar to the magnetic fields in Figure 13, and the motion of those fields! High-energy physics has already provided part of the answer. It is now known that protons and neutrons are made of three smaller particles called “quarks.” Because quarks exert enormous forces on each other, the energy in their force fields is enormous. In fact, calculations show that the energy of these fields is sufficient to explain 90% of the mass of the proton (or neutron)! Since essentially all of the mass of ordinary matter comes from protons and neutrons, this result implies that some 90% of the mass of ordinary matter comes from the nonmaterial energy of fields and motion! The remaining 10% might arise in a similar way, although this is not yet confirmed. Our most accurate theory of physics (the “standard model”) suggests the existence

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throughout the universe of a field called the “Higgs field.” If verified, the Higgs field will explain the still-unexplained 10%. The fundamental theories of contemporary physics known as “quantum field theories” also suggest that all mass arises solely from nonmaterial fields. For example, Steven Weinberg, a leading high-energy theorist, states the following: [According to the physical theories developed during the 1920s] there was supposed to be one field for each type of elementary particle. The inhabitants of the universe were conceived to be a set of fields—an electron field, a proton field, an electromagnetic field—and particles were reduced to mere epiphenomena. In its essentials, this point of view has survived to the present day, and forms the central dogma of quantum field theory: the essential reality is a set of fields [Weinberg’s emphasis] subject to the rules of special relativity and quantum mechanics; all else is derived as a consequence of the quantum dynamics of these fields.

In this field view of reality, there is no “there” there (to quote the poet Gertrude Stein), no “things” at all. Electrons and other material particles are only non-material fields in space, similar to the magnetic field in the space between the poles of a magnet. All mass is due only to the energy of fields. Since fields are “possible forces,” and forces are interactions, this view implies that every “thing,” everything, is interactions and motion. It’s the interactions and motion themselves that are fundamental rather than the material particles that we had always supposed were doing the interacting and the moving. It’s a view that stands Newtonian materialism on its head.

We are such stuff As dreams are made on Shakespeare, The Tempest

CONCEPT CHECK 11 In which of the following processes does the system’s mass change? (a) A bullet that speeds up while moving down a gun barrel. (b) A rubber band that is being stretched around a package. (c) Two positively charged objects that are moved closer to each other and placed at rest. (d) An electron and an antielectron, at rest, that spontaneously annihilate each other.

© Sidney Harris, used with permission.

CONCEPT CHECK 12 In the preceding question, in which processes does the system’s rest-mass change?

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The Special Theory of Relativity Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions GALILEAN RELATIVITY 1. What is meant by relative motion, reference frame, a theory of relativity? 2. A train moves at 70 m/s. A ball is thrown toward the front of the train at 20 m/s relative to the train. How fast does the ball move relative to the tracks? What if the ball had instead been thrown toward the rear of the train? 3. A spaceship moves at 0.25c relative to Earth. A light beam passes the spaceship, in the forward direction, at speed c relative to Earth. According to Galilean relativity, how fast does the light beam move relative to the spaceship? Is this answer experimentally correct? If not, then what answer is correct?

THE PRINCIPLES OF RELATIVITY AND CONSTANCY OF LIGHTSPEED 4. How does travel in a jet airplane illustrate the principle of relativity? How must the airplane be moving in order to illustrate this principle? 5. State the principle of relativity in your own words. Does it apply to every observer? Explain. 6. State the principle of the constancy of lightspeed in your own words. Does it apply to every observer? Explain. 7. Use the principle of the constancy of lightspeed to explain why no observer can move at precisely speed c relative to any other observer. 8. What is the ether theory, and why did physicists ultimately reject it? 9. In Galilean relativity, space and time are absolute and lightspeed is relative. What is the situation in Einstein’s relativity? 10. What distinguishes the special from the general theory of relativity? 11. List the basic “laws” of the special theory of relativity.

THE RELATIVITY OF TIME 12. How is time defined in physics? 13. Describe the light clock. 14. Velma passes Mort at a high speed. Both observers have clocks. What does each observer say about Velma’s clock? What do they each say about Mort’s clock?

15. One twin goes on a fast trip and returns. Does the special theory of relativity apply to the observations of both twins? Why, or why not? 16. One twin goes on a fast trip and returns. Have the two twins aged differently during the trip? If so, how do their ages differ? 17. Explain how you can travel to the future.

THE RELATIVITY OF SPACE AND MASS 18. What do we mean by “space” or “distance”? 19. What does “space is relative” mean? 20. Velma passes Mort at a high speed. Each of them holds a meter stick parallel to the direction of motion. What does each observer say about Velma’s meter stick? What does each say about Mort’s meter stick? 21. According to Einstein’s theory, which of these are relative: time, lightspeed, rest-mass, length, mass? 22. Velma passes Mort at a high speed. Both observers carry a standard kilogram. What does Mort say about the mass of each of the standard kilograms? What does Velma say? 23. Mort exerts a 1 newton force on his standard kilogram. What acceleration does this give to the kilogram? What will he find if he exerts the same force on Velma’s standard kilogram while Velma is passing him at a high speed? 24. What is the distinction, if any, between rest-mass, mass, and matter? Which ones increase with speed? 25. What is the distinction between matter and radiation? 26. Why can’t material objects be sped up to lightspeed? Does anything move at lightspeed?

E = mc 2 27. What does E = mc2 mean? Does it mean that mass can be converted to energy? Explain. 28. Is matter always conserved? Is mass always conserved? Is rest-mass always conserved? Is energy always conserved? 29. According to Einstein’s relativity, is rest-mass precisely conserved in chemical reactions? 30. Describe an experiment in which a system’s entire rest-mass vanishes. Is matter conserved here? Mass? Energy?

Conceptual Exercises GALILEAN RELATIVITY 1. Two bicyclers, on different streets in the same city, are both moving directly north at 15 km/hr. Are they in relative motion?

From Chapter 10 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Special Theory of Relativity: Problem Set 2. According to the Galilean theory of relativity, does every observer measure the same speed for a light beam? 3. Velma moves toward Mort at half of lightspeed. Mort shines a searchlight toward Velma. What does Galilean relativity predict about the speed of the searchlight beam as observed by Velma? 4. Velma bicycles northward at 4 m/s. Mort, standing by the side of the road, throws a ball northward at 10 m/s. What is the ball’s speed and direction of motion, relative to Velma? What if Mort had instead thrown the ball southward at 10 m/s? 5. A desperado riding on top of a train car fires a gun toward the front of the train. The gun’s muzzle speed (speed of the bullet relative to the gun) is 500 m/s, and the train’s speed is 40 m/s. What is the bullet’s speed and direction of motion as observed by the sheriff standing beside the tracks? What does a passenger on the train say about the bullet’s speed? What if the desperado had instead pointed his gun toward the rear of the train? 6. Velma is in a train moving eastward at 70 m/s. Mort, standing beside the tracks, throws a ball at 20 m/s eastward. What is the ball’s speed and direction relative to Velma? 7. Velma is in a train moving eastward at 70 m/s. Mort, standing beside the tracks, throws a ball at 20 m/s westward. What is the ball’s speed and direction relative to Velma?

THE PRINCIPLE OF RELATIVITY 8. Does the principle of relativity require that every observer observe the same laws of physics? Explain. 9. If you were riding on a train moving at constant speed along a straight track and you dropped a ball directly over a white dot on the floor, where would the ball land relative to the dot? 10. Suppose that you drop a ball while riding on a train moving at constant speed along a straight track. If you measure the ball’s acceleration, will your result be greater than, less than, or equal to, the usual acceleration due to gravity? 11. Think of several ways that you could determine from inside an airplane whether the plane was flying smoothly or parked on the runway. Do each of these ways involve some direct or indirect contact with the world outside the airplane? 12. How fast are you moving right now? What meaning does this question have? 13. If you drop a coin inside a car that is turning a corner to the right, where will the coin land? 14. If you drop a coin inside a car that is slowing down, where will the coin land?

THE CONSTANCY OF LIGHTSPEED 15. Does every observer measure the same speed for a light beam? Explain. 16. A star headed toward Earth at 20% of lightspeed suddenly explodes as a bright supernova. With what speed does the light from the explosion leave the star? With what speed (as measured on Earth) does it approach Earth? 17. Is it physically possible for a person to move past Earth at exactly lightspeed? Explain. 18. Velma’s spaceship approaches Earth at 0.75c. She turns on a laser and beams it toward Earth. How fast does she see the

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beam move away from her? How fast does an Earth-based observer see the beam approach Earth? 19. A desperado riding on top of a freight-train car fires a laser gun pointed forward. What is this gun’s “muzzle velocity”? Suppose the train is moving at 40 m/s (0.04 km/s). How fast does the tip of the laser beam move relative to the sheriff, who is standing on the ground beside the train? What answer would the Galilean theory of relativity have given to this question?

THE RELATIVITY OF TIME 20. Velma passes you at a high speed. According to you, she ages slowly. How does she age according to her own observations? How do you age according to her? 21. Suppose you have a twin brother. What could be done to make him older than you? 22. The center of our galaxy is about 26,000 light-years away. Could a person possibly travel there in less than 26,000 years as measured on Earth? Could a person possibly travel there in less than 26,000 years of his or her own time? Explain. 23. A woman conceives a child while on a fast-moving space colony moving toward a distant planetary system. How long should it take before the baby is born, as measured by the woman? Would an Earth observer measure the same amount of time? 24. A certain fast-moving particle is observed to have a lifetime of 2 seconds. If the same particle was at rest in the laboratory, would its lifetime still be 2 seconds, or would it be more, or less, than 2 seconds? 25. Does the special theory of relativity allow you to go on a trip and return older than your father? 26. Does the special theory of relativity allow your father to go on a trip and return younger than you? 27. Does the special theory of relativity allow you to go on a trip and return younger than you were when you left? 28. When you go on a very fast trip, must you always return older than you were when you left? 29. A satellite orbits Earth at 8 km/s. Find its speed as a fraction of lightspeed. Would an orbiting astronaut directly notice the effects of time dilation without using sophisticated measurement techniques? 30. Velma passes Earth at 50% of lightspeed. On her video player, she watches a taped video program that runs 1 hour. How long does the program run as measured by an Earthbased observer? 31. Your fantastic rocketship moves at 30,000 km/s. If you took off, moved at this speed for 24 hours as measured by you, and returned to Earth, by how much time would your clock differ from Earth-based clocks? Would you have aged more than, or less than, people on Earth? By how much? 32. Answer the preceding question assuming that your extraordinarily fantastic rocketship moves at 99% of lightspeed. 33. Mort and Velma have identical 10-minute ice-cream cones. Velma passes Mort at 75% of lightspeed. How long does Mort’s cone take to melt as measured by Velma? 34. How fast must Velma move in order for her 10-minute icecream cone to melt in 30 minutes as measured by Mort?

The Special Theory of Relativity: Problem Set

THE RELATIVITY OF SPACE AND MASS 35. How fast must Velma move past Mort if Mort is to observe her spaceship’s length to be reduced by 50%? If Velma is flying east to west across the United States (about 5000 km wide) at this speed, how wide will she observe the United States to be? 36. Mort’s swimming pool is 20 m long and 10 m wide. If Velma flies lengthwise over the pool at 60% of lightspeed, how long and how wide will she observe it to be? 37. Mort’s automobile is 4 m long as measured by Mort. What length does Velma measure for Mort’s auto, as she passes him at 90% of lightspeed? 38. Velma, who is carrying a clock and a meter stick, passes Mort. Is it possible that Mort could observe length contraction of Velma’s meter stick but observe no time dilation of her clock? If so, how? 39. Velma, who is carrying a clock and a meter stick, passes Mort. Is it possible that Mort could observe time dilation of Velma’s clock but observe no length contraction of her meter stick? If so, how? 40. Velma drives a really fast rocket train northward past Mort, who is standing beside the tracks. Two posts are driven into the ground along the tracks. How does Mort’s measurement of the distance between the posts compare with Velma’s: longer, shorter, or the same? 41. If Velma passes Mort at a high speed, Mort will find her mass to be larger than normal. Will he also find her to be larger in size? 42. Velma’s spaceship has a rest-mass of 10,000 kg, and she measures its length to be 100 m. She moves past Mort at 0.8c. According to Mort’s measurements, what are the mass and the length of her spaceship? 43. How fast must Velma move past Mort if Mort is to observe her spaceship’s mass to be increased by 50%? How fast must she move if Mort is to observe her spaceship’s length to be reduced by 50%? 44. A meter stick with a rest-mass of 1 kg moves past you. Your measurements show it to have a mass of 2 kg and a length of 1 m. What is the orientation of the stick, and how fast is it moving? 45. Use Figure 12 to estimate how fast Velma must move, relative to Mort, for Mort to observe that her body’s mass is 50% larger than normal.

E = mc 2 46. When you throw a stone, does its mass increase, decrease, or neither? Can this effect be detected? 47. A red-hot chunk of coal is placed in a large air-filled container where it completely burns up. The container is a perfect thermal insulator—in other words, thermal energy is unable to pass through the container’s walls. According to E = mc2, does the total mass of the container and its contents change during the burning process? If so, does the mass increase, or decrease? 48. Referring to the previous question: Suppose that the container is not a thermal insulator—in other words, thermal energy passes through the walls. In this case, does the total mass of the container and its contents change during the burning process? If so, does the mass increase, or decrease?

49. An electron and an antielectron annihilate each other. In this process, is energy conserved? Is mass conserved? Is restmass conserved? 50. Two mousetraps are identical except that one of them is set to spring shut when the trigger is released, and the other is not set. They are placed in identical vats of acid. After they are completely dissolved, what, if any, are the differences between the two vats? Will the masses differ? 51. In a physics laboratory, an electron is accelerated to nearly lightspeed. If you were riding on the electron, would you notice that the electron’s mass had increased? If you were standing in the laboratory, what would you notice concerning the electron’s mass and energy?

Problems Use the time-dilation formula T = T0 > 2(1 - y2>c2) (explained in footnote 4) to answer questions 1–6. 1. Time dilation depends on the quantity 2(1 - y2>c2), which in turn depends on the fraction y2>c2. Evaluate the fraction y2>c2 for each of the following speeds: 3 km/s (high-powered rifle bullet), 30 km/s (speed of Earth in its orbit around the sun), 3000 km/s (fast enough to cross the United States in about 1 second). Is time dilation a very significant, noticeable effect at these speeds? 2. Time dilation depends on the factor 2(1 - y2>c2), Evaluate this factor for each of the following speeds: 30,000 km/s (fast enough to circle the globe in 1 second), 150,000 km/s. 3. Velma passes Mort at 30,000 km/s. What fraction of lightspeed is this? What is the duration of one of Velma’s seconds (a time interval that Velma observes to be 1 second in duration) as observed by Mort? 4. Velma passes Mort at 150,000 km/s. What fraction of lightspeed is this? What is the duration of one of Mort’s seconds (a time interval that Mort observes to be 1 second in duration) as observed by Velma? 5. Velma passes Mort at a high speed. His clock, as observed by her, runs at half of its normal speed—for example, his clock advances by only 30 minutes during a time of 1 hour as recorded on her own clock. What must be the value of the quantity 2(1 - y2>c2)? Find Velma’s speed relative to Mort. 6. Velma passes Mort at a high speed. Her clock, as observed by him, runs at 25% of its normal speed—for example, her clock advances by only 15 minutes during a time of 1 hour as recorded on his own clock. What must be the value of the quantity 2(1 - y2>c2)? Find Velma’s speed relative to Mort. 7. You give 90 J of kinetic energy to a 1 kg stone when you throw it. By how much do you increase its mass? 8. A large nuclear power plant generates electric energy at the rate of 1000 MW. How many joules of electricity does the plant generate in one day? What is the mass of this much energy? 9. If you had two shoes, an ordinary shoe and an “antishoe” made of antiparticles, and you annihilated them together, by how far could you lift the U.S. population? Assume that each person weighs 600 N, that each shoe’s rest-mass is 0.5 kg, and that all the energy goes into lifting.

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The Special Theory of Relativity: Problem Set 10.

Show that, if all the energy released (transformed) in fissioning 1 kg of uranium were used to heat water, about 2 billion kg of water could be heated from freezing up to boiling. (Assume that the uranium’s rest-mass is reduced by about 0.1%. Roughly 4 J of thermal energy is needed to raise the temperature of 1 gram of water by 1°C.) How many tonnes of water is this (a tonne is 1000 kg)? How many large highway trucks, each loaded to about 30 tonnes, would be needed to carry this much water? 11. Solar radiation reaches Earth at the rate of 1400 watts for every square meter directly facing the sun. Using the formula pR2 for the area of a circle of radius R, find the amount of solar energy entering Earth’s atmosphere every second. Earth’s radius is 6400 km. 12. Use the answer to the preceding question to find how many kilograms of sunlight hit Earth every second. MAKING ESTIMATES

Answers to Concept Checks 1. (d) 2. During every second, the ball moves 20 m closer to the rear

3. 4. 5. 6. 7. 8.

9. 10. 11.

12.

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of the train, while the train moves 70 m eastward. The net result of these two motions is that the ball moves 50 m eastward (relative to the ground). So the velocity observed by Mort is 50 m/s eastward, (a). (a). For instance, you could pour a cup of coffee. If your vehicle is speeding up, the coffee won’t pour straight down. (b) (e) Mort observes his own cone to melt in 10 minutes. Table 1 says that when he observes Velma’s cone, the time dilation factor is 1.5, so he observes Velma’s cone to melt in 15 minutes, (e). She observes him to be younger, in the same ratio as in the other examples (1.5 to 1), so when she has aged by 60 years, she observes him to have aged only by 40 years, (b). She cannot go into the past, which rules out answers (a), (b), and (e). She can accomplish (c) by moving sufficiently fast. She can accomplish (d) by moving slowly. Finally, (f) will be true regardless of how fast or how slow she moves. (c), (d), and (f). In order for 100 m to contract to 10 m, 1 m must contract to 0.1 m. Figure 11 tells us that this happens when the relative speed is about 99% of lightspeed, (b). (c), (d) Mass increases whenever energy increases. The bullet’s energy increases as it moves faster. The rubber band’s energy increases (because work must be done to stretch it). The two charged objects have more electrical energy after the move (because work must be done to move them closer). However, the electron–antielectron pair do not gain or lose energy (even though they are annihilated), because of conservation of energy, (a), (b), (c). The bullet’s rest-mass is unchanged. The rubber band and the two charged objects are left at rest, with greater energy and hence greater mass, so the rest-mass of these two systems increases. The electron–antielectron pair lose all their rest mass when they annihilate to create gamma radiation (which has zero rest mass), (b), (c), (d).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. No. 3. According to Galilean relativity, she observes the light beam to move at 1.5c. 5. 540 m/s as observed by the sheriff. 500 m/s as observed by the passenger. With the gun pointed toward the rear, the bullet moves at 460 m/s as observed by the sheriff, 500 m/s as observed by the passenger. 7. 90 m/s west. 9. The ball would land on the dot. 11. Look out the window, radio to the outside, ask the pilot to look out of the window and tell you what he sees, stick your hand out of the airplane, etc. All of these involve contact with the outside world. 13. To your left. 15. No. Only non-accelerated observers measure the same speed for a light beam. 17. No. All material objects move slower than lightspeed. 19. 300,000 km/s. 300,000 km/s. 300,000.04 km/s. 21. If you go on a sufficiently long and fast trip and return, he will then be older than you. 23. Nine months. An Earth observer would measure a longer time. 25. No, because you will age less than your father. 27. No. Time always goes forward, never backward. 29. (8 km>s)>300,000 km>s = 2.67 * 10 - 5. No. 31. The speed is 0.1c, so Table 1 says that one of your seconds is observed on Earth as 1.005 s. So when you return you will have aged by 24 hours while people on Earth have aged by 1.005 * 24 = 24.12 hr = 24 hr and 7.2 min. You have aged less than people on Earth, by 7.2 minutes. 33. Table 1 says that the time-dilation factor is 1.5, so Velma observes Mort’s cone to melt in 1.5 * 10 min = 15 min. (Note that Mort moves at 75% of lightspeed relative to Velma.) 35. According to Figure 12, the required speed is about 0.86c. She will observe the United States to be 0.5 * 5000 km = 2500 km wide. 37. 0.43 * 4 m = 1.8 m. 39. Yes. Velma could be holding her meter stick perpendicular to the direction of motion. 41. No, in fact he observes her to be shorter as measured along her direction of motion. 43. Using Figure 12, Mort observes her spaceship’s mass to be increased by 50% when she moves past him at a speed of 0.75c. Mort observes the length to be reduced by 50% when she moves past him at 0.86c. 45. About 0.75 c. 47. No; since the total energy is unchanged, the total mass is also unchanged. 49. Yes. Yes. No; in fact, rest-mass is entirely destroyed. 51. No. If you were standing in the laboratory, you would notice that the electron’s mass and energy had both increased.

The Special Theory of Relativity: Problem Set Problems 1. y>c = (3 km>s)>300,000 km>s = 10 - 5, y2>c2 = 10 - 10. 2 2 -8 Similarly, y >c = 10 when s = 30 km>s. y2>c2 = 10 - 4 when y = 3000 km>s. Time dilation is not very significant at these speeds. 3. This is 0.1 (or 10%) of lightspeed. y2>c2 = 0.01. 2(1 - y2>c2) = 2(1 - 0.01) = 20.99 = 0.995 T = T0> 2(1 - y2>c2) = 1 s>0.995 = 1.005 s. 5. From the given information, the time-dilation factor is 2, i.e., T = 2T0. Thus, 1> 2(1 - y2>c2) = 2. 2(1 - y2>c2) = 1>2 1 - y2>c2 = 1>4 y2>c2 = 3>4, so y>c = 20.75 = 0.87. Velma moves at 87% of lightspeed. Note that this answer agrees with Figure 10. 7. 90 J>c2 = 90 J>9 * 1016 m2>s2 = 10 - 15 kg, or 0.000,000,000,000,001 kg.

9. mc2 = (1 kg) * (9 * 1016 m2>s2) = 9 * 1016 J. This much

energy goes into lifting. The energy needed to lift a weight through a height is weight * height. The weight of the U.S. population is about (300 * 106 people) * (600 N>person) = 1.8 * 1011 N. The height through which this mass could be lifted is 9 * 1016 J>1.8 * 1011 N = 5 * 105 m = 500 kilometers! 11. Since 1 watt = 1 joule/second, 1400 joules hit each square meter in each second. Earth’s area facing the sun (the cross-sectional area facing the sun) is pR2 = 3.14 * (6.4 * 106 m)2 = 1.3 * 1014 m2. The energy hitting Earth each second is thus 1400 J>m2 * 1.3 * 1014 m2 = 1.8 * 1017 J.

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Einstein’s Universe and the New Cosmology Einstein’s Pegasus There’s Einstein riding on a ray of light, In which he cannot see his face in flight Because his jesting image, I now understand, Won’t ever reach the mirror since its speed, Too, is the speed of light. He rides, this fleeting day, As if on Pegasus, immortal steed Of bridled meditation, past the Milky Way, Out to my mind’s Andromeda, where I, Also transported, staring at a windless pool, Watch his repaired reflection whizzing by. Though he can’t see himself, this self-effacing fool Who holds all motion steady in his head, I won’t forget his facing what he cannot see In thought that binds the living and the dead, And ride with him, outfacing fixed eternity. Robert Pack, Middlebury College, 1991

T

he special theory of relativity describes the observations of nonaccelerated observers. What about accelerated observers? Einstein found a surprising connection between acceleration and gravity, and between gravity and a feature best described as “warps in spacetime.” Section 1 presents these key ideas. I’ve devoted the remainder of the chapter to cosmology: the study of the origin, structure, and evolution of the large-scale universe. The general theory of relativity is science’s basic tool for such matters. You are living in the golden age of cosmology. It started in 1992 when microwave receivers on orbiting satellites gathered the first detailed image of the “cosmic microwave background” showing the earliest light from the creation of the universe. It continues today with the search for dark matter, dark energy, and an elusive microscopic particle known as the “Higgs boson.” Cosmology is inspired by some of the oldest questions ever asked, and is perhaps the oldest story ever told. For thousands and probably millions of years, humans have looked for answers to questions such as: How did all this come to be? Where did Earth come from? What is the layout of the universe? Where do humans fit in? There’s been plenty of speculation about all this, but now for the first time we are finding evidence-based answers, answers that have at least as much to do with physics as with astronomy. I hope you’ll share in the excitement by pondering the discoveries and concepts in this chapter.

From Chapter 11 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Einstein’s Universe and the New Cosmology

Section 2 presents the “big bang” that created our universe and evidence that it actually occurred. Einstein’s connection between gravity and warped spacetime leads to a new way of viewing, in Section 3, the overall structure and expansion of the universe. Section 4 presents the recent microwave image of the big bang shortly after it occurred and its implications for the overall shape of the universe. Section 5 presents a surprising and exciting development: The universe is filled with enormous amounts of “dark matter” that doesn’t interact with light and so has not yet been directly observed. Section 6 describes two additional completely unexpected developments: the accelerating universe and the mysterious “dark energy” pushing this acceleration. Section 7 presents a recent hypothesis on how, and perhaps even why, the big bang banged. Because these results aren’t easy to believe, I’ve included quite a few “How Do We Know” subsections.

A rocket ship in outer space accelerates at 9.8 m/s2 in this direction

Due to the acceleration, this occupant feels a force by the floor against his shoes.

(a)

Due to gravity, this occupant at rest on the ground feels a force by the floor against his shoes.

(b)

Figure 1

Acceleration is indistinguishable from gravity. The occupant cannot tell the difference.

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1 EINSTEIN’S GRAVITY: THE GENERAL THEORY OF RELATIVITY The special theory of relativity begins with the principle that the laws of physics are the same for all unaccelerated observers. What about accelerated observers? This is the starting point for the general theory of relativity. You’ve probably noticed, when riding in an elevator accelerating upward from a building’s ground floor, that you felt squashed down, heavy, as though there were more gravitational pull on you than usual. This connection between acceleration and “apparent gravity” runs deeper than you might think. For example, imagine being inside an accelerating rocket ship in outer space, far from all planets and stars so that there are no gravitational forces [Figure 1(a)]. If the rocket’s acceleration is 9.8 m/s2 or 1g (“one gee”), you will feel the same as you do when you are stationary on Earth [Figure 1(b)]. The reason is that, according to Newton’s law of motion, the rocket’s floor must push upward on the bottoms of your shoes in order to accelerate you at 1g. Because this push is quantitatively equal to your weight on Earth, you feel the same force against your feet as you do at rest on Earth. So accelerations mimic the effects of gravity. If you were in a rocket accelerating smoothly at 1g through outer space, could you tell, without communicating with the world outside the rocket, that you were actually in space and not at rest on Earth’s surface? Think about it. You might try dropping a stone to see how it falls (Figure 2). But your rocket is accelerating at 1g so the floor accelerates upward to meet the stone. From your point of view inside the rocket, the stone “falls” down to the floor with an acceleration of 1g. Furthermore, Galileo’s law of falling is valid: A large-mass stone and a small-mass stone, released together, reach the floor (or rather, the floor reaches them) at the same time. You also could throw a stone horizontally (Figure 3). Because of the rocket’s upward acceleration, the stone gets closer to the floor as it moves across the rocket. As you view it, the stone “falls” to the floor exactly as though it were thrown horizontally on Earth. It seems it’s not easy to perform an experiment inside your rocket ship that can tell you whether you’re at rest on Earth’s surface or moving through space with a 1g acceleration. Einstein made this reasoning into a fundamental principle that’s similar to the principle of relativity. The principle of relativity says that there is no way, from within your own laboratory, to distinguish a state of rest from motion at constant

Einstein’s Universe and the New Cosmology Figure 2

Rocket ship accelerates at 1g

Floor accelerates upward and hits the stone

If you release a stone inside an accelerating rocket in outer space, it will appear to you that the stone falls “down” to the floor, just as though you were on Earth and feeling the effects of gravity.

Observer releases stone

Stone’s path relative to you

Rocket ship accelerates at 1g

Figure 3

If you throw a stone inside an accelerating rocket in outer space, it will appear to you that the stone falls to the floor as though you were on Earth and feeling the effects of gravity.

Floor accelerates upward to meet the stone Observer throws stone horizontally

velocity. The new principle states that there is no way, from within your own laboratory, to distinguish the effects of gravity from the effects of acceleration. Because it says that gravity is equivalent to acceleration, we call this The Equivalence Principle No experiment performed inside a closed room can tell you whether you are at rest in the presence of gravity or accelerating in the absence of gravity.

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Einstein’s Universe and the New Cosmology

Rocket ship accelerates at 1g

Observer points flashlight horizontally

Light beam’s path relative to you

Floor accelerates upward toward the flashlight beam

Figure 4

If you turn on a flashlight inside an accelerating rocket in outer space, the light beam bends relative to you.

Distant star

Star’s apparent position as seen from Earth

Starlight bent by sun’s gravity

From Earth, the star appears to lie in this direction Sun

Earth

Figure 5

Because the sun bends light beams, we can (during a total eclipse) see stars that are behind the sun.

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Light beams play a central role in the general theory just as they do in the special theory. How do accelerations affect light beams? If you accelerate through outer space and you turn on a flashlight horizontally, the light beam must bend downward relative to you (Figure 4), just like the path of a horizontally thrown stone (Figure 3). The equivalence principle implies that this experiment must come out the same way if performed in a stationary room in the presence of gravity. So gravity must bend light. How do we know that gravity bends light? Earth’s gravity is too weak to bend light very much. But the sun is massive enough to measurably bend the light from distant stars as the light passes close to the sun. The first measurement of this effect was made during a total eclipse of the sun in 1919, when astronomers could photograph the stars that appear near the edge of the sun (Figure 5). Measurements of these stars’ positions showed that the starlight does bend as it passes the sun and that the amount of curvature agrees with Einstein’s predictions.

Recall that the constancy of lightspeed led Einstein to the surprising discovery that time is relative. Similarly, the gravitational bending of light implies a surprising property of space, related to the concept of straightness. Just as time is a physical property of the universe that can be measured by a light clock, straightness is a physical property that can be defined as the path followed by a light beam. In fact, surveyors often use laser beams to determine straightness, and you use light beams to determine straightness when you aim a gun by sighting along its barrel. But what can it mean to say that gravity bends light beams, when light beams themselves are the definition of straightness? Just as the slowed ticking of moving light clocks implies that time itself slows down, Einstein saw that the bending of light beams

means that space itself is bent, or curved, or warped, by gravity. The path of a light beam is best described as the “straightest possible” path. In a curved space, even the straightest possible path must be curved. Space is warped. It’s an odd concept. It took an Einstein to think of it, but it’s not something that Einstein, or you or anybody else, can visualize. As Stephen Hawking (Figure 6) remarked, “It is hard enough to visualize ordinary three-dimensional space, let alone warped three-dimensional space.” The difficulty is that space has only three dimensions (length, width, and height), so there is no higher dimensionality from which to view the curvature of our three-dimensional space the way you can view, from your three-dimensional perspective, the bending of a twodimensional sheet of paper. The best anybody can do is visualize analogies to this important idea of curved space. For example, a flat tabletop is two-dimensional (the surface has length and width only) and can be considered to be a “flat two-dimensional space” (Figure 7). If we put a warp in it, a depression perhaps (Figure 8), the surface becomes a warped two-dimensional space. For another example, the surface (not the inside) of a sphere is a curved two-dimensional space. The two standard dimensions on the surface of a globe, for example, are called longitude (angular distance east or west of a circle running through the two poles and through Greenwich, England) and latitude (angular distance north or south of the equator). In this curved two-dimensional space, the straightest possible lines (analogous to the paths of light beams in curved threedimensional space) are the “great circles,” such as the equator and the circles of longitude running through the poles. Suppose you were a two-dimensional creature inhabiting a two-dimensional spherical space, something like a flat ant crawling on the surface of a large globe. How could you tell that your space was curved? You couldn’t stand outside or inside the globe’s surface, in the third dimension, to see that you are on a spherical surface, because there is no such third dimension in this two-dimensional analogy. One way you could learn that your space is curved is by performing geometry experiments. For instance, two lines, beginning parallel and extending as straight lines (or straightest lines, as perceived from our three-dimensional vantage point), should eventually meet (Figure 9). Similarly, you cannot directly see the curvature of three-dimensional space, but you can perform experiments to determine whether our space is curved. The 1919 experiment that measured the curvature of light near the sun was just such a geometry experiment. It found that even the straightest path, the path of a light beam, bends near the sun. We conclude that three-dimensional space itself is curved.

Figure 7

A flat tabletop is a flat twodimensional space.

UPI/M. Manni/Corbis/Bettmann

Einstein’s Universe and the New Cosmology

Figure 6

Stephen Hawking has made remarkable contributions to astrophysics and cosmology. Then I would have felt sorry for the dear Lord, for the theory is correct. Einstein’s reply when asked how he would have felt if the 1919 Solar Eclipse observations had disagreed with his General Theory of Relativity.

Figure 9 Figure 8

If you warp a flat two-dimensional space, it becomes a curved twodimensional space.

In a two-dimensional spherical space, two lines that start out parallel and extend as “straight” (or straightest) lines will eventually meet.

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At this point, many students develop the misconception that there must be a fourth spatial dimension into which three-dimensional space is curving. This is wrong. Our two-dimensional analogy is meant to be imagined with no reference to any “embedding” of those two dimensions in a third dimension; the real threedimensional space is curved despite the absence of a fourth spatial dimension into which three-dimensional space is curving. How do we know that space is curved? But does the bending of light really show space to be curved or does it merely show that light beams bend in ordinary or “flat” threedimensional space? The latter possibility was ruled out by an experiment in 1972 in which a spacecraft orbiting Mars beamed back radar signals sent from Earth (Figure 10). The radar beam’s travel time was measured at a time of year when the line of sight from Earth to Mars passed near the sun. This travel-time measurement can tell whether the bent light beam travels through a flat space or through a warped space. Here’s how. It’s easy to use the observed curved path to predict the travel time in a flat space by making a scaled-down drawing of the curved path on a flat sheet of paper and seeing how much longer it is than a straight line. In the experiment, the answer was about 10 m, so if the radar beam was merely bending in a flat space, it should have been delayed by about 30 billionths of a second, the time taken by light (and radar) to travel 10 m. But you can’t use a flat sheet of paper to measure distances in a warped space, for the same reason that you can’t determine the distance from Los Angeles to London by making measurements on a flat map: The “scale” keeps changing because of the curvature. Einstein’s formulas predict a delay of 200 millionths of a second, 7000 times longer than the predicted delay in a flat space. The experiment confirmed Einstein’s prediction.

Spacecraft in orbit around Mars

Radar beam from Earth is reflected back by spacecraft

Sun

Earth

Figure 10

An experiment to measure the total travel time for a radar beam to get to Mars and back.

Figure 11

Masses such as the sun cause space to curve.

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I have so far ignored one fact that I now must mention. Space and time are tangled up with each other. For example, to measure the width of a moving window, you need at least two clocks to ensure that you measure the two sides of the window at precisely the same instant. So distance measurements involve time measurements. In general relativity, this tangling of space and time means that any warping of space must also distort time, causing clocks (in other words, time) to go slower in stronger gravitational fields. It’s really space and time together, or spacetime, that is distorted by masses. Spacetime is not an especially subtle or difficult idea. It’s not hard to imagine two or three of its dimensions, but impossible to imagine all four at once. For example, if you’ve ever graphed the position “x” of an object moving along a straight line versus the object’s time of travel “t,” you’ve graphed the motion of an object in spacetime. The general theory of relativity revolutionized our view of gravity and of space and time. Newtonian physics viewed space and time as a passive, unchanging background against which events unfolded, while modern physics views spacetime as an active and changing physical participant in events. Spacetime forms a kind of fabric that can be molded by masses (Figure 11), much as a hammer can bend a sheet of metal. Spacetime has a shape, a shape that is molded by matter and that affects the motion of matter and radiation through space. For familiar situations on Earth such as the fall of a stone, general relativity’s predictions are nearly identical to Newton’s.1 For exotic situations such as near a 1

Even on Earth, the small differences from Newtonian predictions are important for practical applications requiring extreme accuracy. For example, the global positioning system (GPS) depends on satellites to provide an accurate determination of the position of any GPS receiver on Earth. It’s crucial that all 24 GPS satellites use the same time to a high degree of accuracy. For this, scientists must take the effects of both special and general relativity into account.

Einstein’s Universe and the New Cosmology

black hole or during the creation of the universe, general relativity’s predictions differ enormously from Newton’s. Conceptually, the two theories differ radically. In Einstein’s theory, gravitational effects such as Earth’s circular motion around the sun are not caused by forces at all but are instead due entirely to the curvature of spacetime. Earth’s orbit is pulled into a circle not by the force of gravity, but rather because the sun warps spacetime and Earth simply “falls” freely (experiencing no force at all) along those warps. Earth must move along a curved path in spacetime, because spacetime is curved. To ward off a common misconception, I’m not saying here that space is curved into a circle around the sun and that Earth follows these circles. Instead, spacetime is curved in such a way that Earth moves in a circle in the spatial dimensions while moving toward increasing time in the time dimension, producing a spiral in spacetime. How do we know that general relativity is accurate? What with curved space, bending lightbeams, and spacetime, this theory introduces some unusual concepts. It would be natural for you to question its validity. So it’s reassuring to know that scientists have checked the theory frequently and carefully and it has not yet failed a single test. The most demanding test was reported in 2006, and involved a pair of pulsating neutron stars that orbit each other in our own galaxy at 2000 light-years from Earth. Imagine two stars, each more massive than the sun yet squeezed down by gravity to a diameter of only a few kilometers, each containing a billion tonnes of material in every cubic centimeter, one star spinning an incredible 44 times per second and the other at 3 seconds per revolution, each sending out with each revolution a radio beep similar to a rotating lighthouse beacon, and separated from each other by only about 3 times the distance from Earth to the moon—close enough that each star affects the pulses of the other. The stars are converging at 7 mm per day, and will merge in a galaxy-shaking collision in 85 million years. The enormous gravitational fields created near these tiny but massive stars, the regularity of the stars’ motions and their clocklike radio signals make this system a perfect “laboratory” for testing many quantitative details of general relativity in a situation where spacetime is predicted to be strongly bent by gravity, and where Newtonian gravity is far wrong. According to Ingrid Stairs, a member of the team who reported the first measurements, “general relativity does a perfect job of describing what we know of the system so far.” The results showed that, despite the extreme gravity, the theory of general relativity is accurate to within the team’s measurement uncertainty of 0.05%. A similar but even more mind-blowing observation was reported in 2008 when scientists discovered the largest known black hole at the center of a galaxy 3.5 billion light-years from Earth. This black hole has the mass of 18 billion suns. To make matters even more interesting, they found a smaller 100-million-sun black hole orbiting the larger black hole every 12 years. Again, this system is a perfect laboratory to observe general relativistic effects. These observations have been done, and they fully agree with general relativity while ruling out several competing theories that had been proposed as alternative theories of gravity. Like the neutron stars, the two black holes are converging and will merge in about 10,000 years, a collision that will literally shake spacetime in a manner that should be detectable here on Earth, across 25% of the observable universe.

CONCEPT CHECK 1 Since accelerations can mimic the effects of gravity, accelerations should be able to cancel gravity. Thus, a person could experience weightlessness by (a) blasting off from Earth, straight upward, at an acceleration of 1g; (b) falling from a high place such as a diving board or airplane (skydiving); (c) orbiting Earth; (d) standing on the surface of the moon.

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CONCEPT CHECK 2 The equator is a “straightest possible” line on the surface of a globe. Are the other east-west circles of latitude “straightest possible” lines? (a) Yes. (b) No, they curve more than the equator’s curvature. (c) No, they curve less than the equator’s curvature. (d) No, despite the fact that their curvature is the same as the equator’s curvature.

2 THE BIG BANG You don’t have to search far to locate where the big bang occurred, for it took place where you are now as well as everywhere else; in the beginning, all locations we now see as separate were the same location. String Theorist Brian Greene in The Elegant Universe

You are living in the golden age of cosmology: the study of the origin, structure, and evolution of the large-scale universe. I will take full advantage of that fact by presenting some of the mind-blowing recent cosmological discoveries. The golden age began in 1992 when an observing satellite charted the first detailed map of the early universe. The keys to the new cosmological discoveries are the wonderful new observing instruments such as the Hubble Space Telescope. The key to understanding these discoveries is the general theory of relativity. When applied to the universe as a whole, general relativity predicts the possible ways our three-dimensional universe could evolve throughout past and future time. When supplemented with certain astronomical observations (described in the following discussion), general relativity leads to a striking description of the origin and evolution of the universe: About 14 billion years ago,2 the universe began in a single event called the big bang that created the different forms of energy and matter, causing the “observable” universe (the portion that can be observed with telescopes) to expand from a much smaller initial size. The reality of the big bang is strongly confirmed by serval independent lines of observational evidence, but the theoretical understanding of how and why this event occurred is just beginning (Section 7). How do we know there was a big bang? Four independent lines of evidence support the big bang theory:

1. Astronomers first hypothesized the big bang in 1929 because they discovered evidence that all the galaxies throughout the universe are receding from one another just as if they had been driven apart by an explosion. Extrapolating backwards in time from the speeds and distances we see today, the galaxies should have all been together 14 billion years ago. 2. In 1964, radio astronomers first detected the cosmic microwave background, the faint afterglow that still fills the universe from the hot initial explosion. The radiation has now cooled all the way down to –270°C.3 This cold radiation has too little energy to be visible and is observable today only as faint radio static in the microwave and radio regions of the spectrum. Its observed characteristics, such as its temperature, agree with the big bang theory’s predictions. 3. In 1992 and again in 2003, observing satellites mapped the cosmic microwave background arriving at Earth from all directions in space (Figure 12). The results (Figure 13) showed that this radiation contains subtle and highly complex “ripples” of precisely the sort expected if the initial big bang did indeed develop into the structured universe of galaxies and clusters of galaxies that we see today. The existence of the radiation mapped in Figure 13, and the close relationship between that radiation and the universe we see around us today, are strong evidence for the big bang theory.

NASA Earth Observing System Figure 12

The Wilkinson Microwave Anisotropy Probe (WMAP) leaving the Earth/moon system, headed for a gravitational blance point in space known as “L2.” In 2003, this satellite looked nearly 14 billion years back in time to observe our universe when it was in its infancy—about 400,000 years old. This is comparable to viewing a baby picture of an 80-year-old man taken when he was less than one day old. WMAP used the moon to gain velocity for a slingshot to L2.

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2 3

More precisely, 13.73 billion years with a surprisingly small 1% margin of error. This is just 3 degrees above absolute zero, the lowest possible temperature, the temperature at which all microscopic motion is the least it can be without violating the quantum uncertainty principle.

The Wilkinson Microwave Anisotropy Probe/NASA

Einstein’s Universe and the New Cosmology

Figure 13

First light: A “fossil” of the creation of the universe. This map, a portrait of the 14-billion-year-old microwave whisper that now remains from the mighty flash of radiation that was released a mere 380,000 years after the big bang, shows the temperature differences in the universe as it existed at the time the radiation was released; darker regions are slightly cooler, lighter regions are warmer. The map shows every direction in space; think of horizontal and vertical axes going through the map’s center, with units in angular degrees extending 360° along the horizontal axis and 180° along the vertical axis. Although the expansion of the universe has by now stretched the fabric of space so much that the radiation has stretched into the microwave region of the spectrum, you are looking at a photograph (“microwave-graph” actually) of the first light that traveled through the universe. Before this time, the universe was so hot that its atoms were electrically charged, which prevented light from traveling through space. Thus, the cosmic microwave background acts like a lightemitting curtain, beyond which we cannot see. It is the oldest, largest, and furthest observable structure known to science.

4. The fourth line of evidence concerns the creation of the universe’s first chemical elements. The earliest kinds of ordinary matter, formed during the first thousandth of a second of the big bang, were protons, neutrons, and electrons. Conditions during just the next 3 minutes were right for protons and neutrons to “fuse” together into more complex nuclei. After these 3 minutes, the universe was too cool and too dilute for protons and neutrons to continue fusing. Well-developed and highly reliable nuclear physics calculations predict that at the end of these 3 minutes, 75% of the original protons still remained, while 25% of the original protons had fused with neutrons to form four other types of nuclei, labeled 21H, 32He, 42He, and 73Li . The remaining single protons are ordinary hydrogen nuclei, labeled 11H. The universe was then made of two different types of hydrogen, two types of helium, and one type of lithium, in the proportions stated in Table 1. Astronomers have made measurements of the light or “spectra” from the oldest stars, stars that presumably formed from the original material created in the big bang and that have changed little since that time. These measurements show relative amounts of the five isotopes that are in excellent agreement with the theoretically predicted amounts of Table 1. This detailed quantitative agreement between observations and the big bang theory’s predictions for five different nuclear types is strong evidence for the theory. The prediction and confirmation of 21H is especially compelling, because nuclear physics predicts that there is essentially no process anywhere in the universe, other than the big bang, that could have made this material. The big bang is as real as the “snow,” or interference, that you can see on an old analog (pre-digital) TV screen when the power is on with no station tuned in. Cosmic microwave background radiation causes some of this interference. The echo of the big bang is all around you!

Table 1 Predicted nuclear composition of universe at about 3 minutes after start of big bang. Current observations of the oldest material in the universe agree well with these predictions. Nuclear type

Relative concentration by mass

1 1H 2 1H 3 2He 4 2He 7 3Li

75% 5–10 parts in 100,000 2–5 parts in 100,000 25% 2–5 parts in 10 billion

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Einstein’s Universe and the New Cosmology In the patterns of the subtle temperature differences in the cosmic microwave background in different directions we are learning to read the Genesis story of the expanding universe. The resulting origin story will be the first ever based on scientific evidence and created by a collaboration of people from different religions and races all around the world, all of whose contributions are subjected to the same standards of verifiability. Nancy Ellen Abrams, Lawyer and Writer, and Joel Primack, Astrophysical Theorist, Writing in the Journal Science

Figure 14

The two-dimensional surface of an expanding balloon is a twodimensional representation of the expansion of the three-dimensional universe. As space, represented by the balloon’s surface, expands, the galaxies, represented by flat raisins glued to the balloon, move farther apart. Although this twodimensional analogy has the universe expanding into the empty space outside the balloon, there is no space outside the real threedimensional universe.

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The universe is still made mostly of hydrogen and helium, although heavier elements created since the big bang now contribute a small percentage. Nearly all the hydrogen and helium can be traced back to the big bang. Although our bodies contain no helium, the hydrogen forged 14 billion years ago in the big bang is one of the most prevalent elements in your body and in all living organisms. CONCEPT CHECK 3 The gold nuclei in the universe were (a) all created in the big bang; (b) all created sometime after the big bang; (c) created partly during the big bang, and partly after.

3 THE POSSIBLE GEOMETRIES OF THE UNIVERSE The expansion of the universe may be the most important fact ever discovered about our origins. The key to understanding it is to not take the term “big bang” too seriously. It was not like the explosion of a bomb that happened in time and space. Rather, the big bang created time and space. Time and space are part of the universe, not the other way around. As the universe expands, it makes its own time and space. The universe is expanding, but it is not expanding into anything because there is no space “outside” of the universe. So space started small and has been geting bigger ever since. One of the predictions of general relativity is that three-dimensional space can’t remain static but must always either expand or contract. It’s remarkable that even space itself must continually change. Everything, it seems, is active and changing: The stars are born and die, life on Earth evolves, you and I are born and will die, and even space itself must always expand or contract. Direct evidence for the expansion of the universe comes from astronomical observations of other galaxies outside our Milky Way galaxy. Distant galaxies are moving away from us, and the more distant galaxies move away faster. But the galaxies are not just moving away from our particular galaxy; they are all moving away from one another. Regardless of which galaxy you live in, you will observe the other galaxies moving away from you. It’s like a loaf of raisin bread expanding as it bakes: If you were standing on any one of the raisins observing the other raisins, you would observe all of them moving away from you, and more distant raisins would move away from you faster. To visualize the expansion of our entire curved three-dimensional universe, we must imagine a two-dimensional analogy as in Section 1. Imagine that the surface of a partially inflated balloon is a two-dimensional universe, similar to the ant and globe analogy of Section 1. To represent the galaxies, imagine two-dimensional (flat) raisins glued to the surface. Remember that, in this two-dimensional analogy, you must imagine that the inside and outside of the balloon don’t exist; only the twodimensional surface of the balloon is supposed to exist. Now imagine that the balloon inflates (Figure 14), representing the expansion of the universe. Note that, as the balloon expands, the distance between all the raisins increases. No matter which raisin you are standing on, all the other raisins move away from you. No raisin is at the center of this balloon universe, in fact the surface of the balloon has no center. In agreement with the philosophy of the Copernican revolution, this universe is, on average, the same all over. Note that the galaxies are at rest relative to the balloon’s surface. It’s not really the raisins that are moving; instead, the space between the raisins is expanding. In

Einstein’s Universe and the New Cosmology

the real three-dimensional universe, gravity holds each galaxy (also each star and each planet) together in a relatively fixed size and shape, while the space between the galaxies expands. Note also that no galaxy is at the edge of the balloon universe, because the balloon universe has no edge. And neither does the real three-dimensional universe. According to general relativity, the possible shapes or geometries for the largescale structure of the three-dimensional universe fall into three categories. Figure 15 shows the two-dimensional analogs of these three-dimensional geometries. A closed universe bends back on itself to form a sphere. If you lived in a closed universe, you could detect this from the fact that straight (that is, straightest) lines that start out parallel eventually meet (Figure 9), and the angles of a triangle add up to more than the normal 180°, as you can see from Figure 15. Although a closed universe has only a finite extent, the other two geometries have infinite total extents and so only a portion of these surfaces can be shown in the figure. A flat universe has no overall large-scale curvature (in all three geometries there will be smaller-scale warps caused by stars, black holes, galaxies, and other objects) and has the normal Euclidean geometry with which you are familiar—parallel lines remain parallel, and the angles of a triangle add up to 180°. An open universe is analogous to a saddle-shaped surface; in such a universe, straight lines that start out parallel eventually diverge from each other, and the angles of a triangle add up to less than 180°. Regardless of which of the three geometries our actual universe might have, if you follow a straight (straightest) path, you will never come to an edge or to the center of the universe. In the open and flat universes, this is because the universe is infinite in extent. In the closed universe, it is because straight (straightest) lines simply curve back to where they started. In such a universe, if you head in an absolutely straight line for many billions of light-years, you will reach your starting point. CONCEPT CHECK 4 The universe is expanding. Is everything in the universe expanding? (a) Yes. (b) No, the distances between the galaxies are not expanding. (c) No, the Milky Way galaxy is not expanding. (d) No, our solar system is not expanding. (e) No, Earth is not expanding.

4 THE SHAPE OF THE UNIVERSE The revolution in cosmology has been driven by a revolution in observational techniques. Until 1992, observations having cosmological significance were few and far between and highly imprecise. Cosmology was of necessity highly theoretical and conjectural. The age of precision cosmology began in 1992 with the first observation of the details of the cosmic microwave background, similar to the far more detailed Figure 13. Figure 13 is a “microwave photograph,” similar to an infrared photograph, showing the temperature variations in the background radiation emitted by the big bang. The light regions are slightly warmer than the dark regions. This radiation was emitted just 400,000 years after the big bang. Before that time, the temperature of the universe was so high that protons and electrons moved too rapidly to stick together to form hydrogen atoms. The resulting mix of electrically charged protons and electrons immediately absorbed any radiation present. At 400,000 years, the universe had cooled enough for electrons to combine with protons to form neutral hydrogen atoms, and radiation propagated through space for the first time. The microwaves

(a) Closed geometry

(b) Flat geometry

(c) Open geometry

Figure 15

Two-dimensional analogs of the possible large-scale geometries of the three-dimensional universe, as predicted by general relativity. A closed universe bends back on itself to form a three-dimensional spherical space; in such a universe, the angles of a triangle add up to more than the normal 180° and the total volume is finite. A flat universe has no overall largescale curvature; it has the normal Euclidean geometry where the angles of a triangle add up to 180°, and an infinite total volume. An open universe is analogous to a saddle-shaped surface; in such a universe, the angles of a triangle add up to less than 180° and the total volume is infinite.

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that made Figure 13 traveled through nearly empty space for 14 billion years before entering the microwave detectors that created this map. You are looking at the image of the earliest light in the universe, a 14-billion-year-old “fossil.” From this map, showing details of the waves of matter and energy (similar to sound waves in air) that sloshed around in the early universe, scientists conclude that the large-scale geometry of the universe is flat rather than closed or open (Figure 15). Here’s how we know.

If you’re religious, it’s like looking at God. George Smoot, Leader of the Team That Announced in 1992 the Discovery of the Ripples in the Cosmic Microwave Background

How do we know the shape of the universe? With their knowledge of the physical nature of the hot, dense, and electrically charged early universe, scientists can predict the maximum distance that wavelike disturbances in this material could travel during the 400,000 years between the big bang and the release of the light seen in this map. Astronomers can also directly observe this distance in the cosmic microwave background, based on the average size of the observed hot or cool regions seen in the map (Figure 16). However, such observations are distorted by the geometry of the space through which the microwave radiation travels on its long journey to Earth, and this distortion enabled scientists to determine that geometry. As shown in Figure 16, a typical wavelike disturbance, as observed today from Earth, should make an angle of about 1° if the universe is flat, while a closed universe would warp the radiation into an angle larger than 1° and an open universe would warp it into an angle smaller than 1°. The observed angle was about 1°—fairly conclusive evidence that the overall geometry of the universe is flat or at least very close to it.

CONCEPT CHECK 5 Since there is evidence that the universe is flat, does this mean that there is no such thing as curved or warped space? Defend your answer. (a) Yes. (b) No. Figure 16

A single typical disturbance—a region of hotter or cooler temperature—in the nearly uniform early universe

A typical wavelike disturbance in the material of the early universe, as observed today from Earth, should make an angle of about 1° if the universe is flat. A closed universe would warp the radiation into an angle larger than 1°, while an open universe would warp it into an angle smaller than 1°. The observed angle was about 1°— strong evidence that the overall geometry is flat.

Hot, dense, charged material prior to 400,000 years after the big bang

Distance that any single disturbance could spread during 400,000 years following the big bang

14 billion light-years

Angle of less than 1 (open geometry)

Angle of 1 (flat geometry)

Angle of more than 1 (closed geometry) Observer

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11.5 DARK MATTER We’re accustomed to thinking that the universe is made mostly of the visibly luminous (shining) stars and a few nonluminous objects such as planets. But we’ve learned during the past 20 years that the universe is made of many more kinds of things than this. First, an enormous amount of the hydrogen and helium created in the big bang has neither gathered into stars nor collected within the visible galaxies but instead lies in the vast regions between the galaxies where it is invisible and nearly undetectable. Astronomers first detected it by observing how the light traveling to Earth from distant objects is partly absorbed as it passes through intergalactic space. The mass of this invisible intergalactic gas is now known to be 10 times larger than the mass of all the stars, planets, and luminous gas in the universe! Stars, planets, and intergalactic gas are made of atoms of ordinary matter, just like your chair. But there are other kinds of matter, matter that is not formed into atoms. One example is the neutrino. There are a vast number of individual neutrinos flying through the universe with a total mass estimated at one-quarter of the total mass of all the stars. Another kind of nonatomic matter is the black hole. Judging from what’s known about the massive black holes at the centers of galaxies, these are estimated to contribute a total mass about one-tenth as large as the mass of all the stars. That’s pretty fantastic, in my opinion. But there’s more. During the past few decades, scientists have learned that there is another kind of matter, matter not made of protons, neutrons, electrons, neutrinos, or any of the other particles currently known. Nobody knows what it’s made of, although there are several hypotheses. It doesn’t interact with electromagnetic radiation, so it can’t be detected by emitted light (like stars) or reflected light (like planets) or absorbed light (like intergalactic gas), and nobody has yet detected it in the laboratory. But we know it’s there because of its gravitational effects on the stars in galaxies, and we know there’s a lot of it. The total mass of this so-called dark matter is 60 times larger than the mass of all the stars!

How do we know that dark matter exists? Several independent methods of observation show that most galaxies, including our own, are made mostly of dark matter. One method is based on the fact that galaxies are rotating structures, with stars and gas orbiting the center. Like planets orbiting the sun, the stars and gas are held into their roughly circular orbits by the gravitational pull of the massive center of the galaxy. When astronomers observe stars and gas clouds orbiting the centers of their galaxies, their speeds turn out to be so high that the galaxies would fly apart unless held together by the gravitational pull of many times more matter than we actually see. So galaxies must contain invisible matter. But how can astronomers measure orbital speeds around distant galaxies where it’s difficult to pick out individual stars let alone measure their speeds? Looking at galaxies that could be seen “edge on” (Figure 17) from Earth, Vera Rubin (Figure 18) compared the light coming from points on one side of the galaxy’s bright center with the light coming from points on the other side. Since the galaxy is rotating, the stars on one side were moving toward Rubin’s telescope, and the stars on the other side were moving away. The frequency of the light coming from the stars moving toward the telescope was higher than the frequency of the light moving away, for the same reason a police siren shifts to a higher pitch as the police car approaches you and then to a lower pitch as it recedes from you while you listen from the sidewalk. From the difference between the two frequencies, Rubin was able to calculate the speeds of the stars.

California Inst. of Technology/ Palomar/Hale Observatory Figure 17

A galaxy, full of stars and gas and dust, viewed “edge on.”

John Irwin collection/AIP/Photo Researchers, Inc. Figure 18

Vera Rubin. She made pioneering discoveries that contributed to understanding the existence and amount of dark matter by observing frequency shifts of stars in galaxies.

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Einstein’s Universe and the New Cosmology In a second method of observation, light reaching Earth from distant galaxies is warped as it passes through the gravitational fields of galaxies that lie in the path of the light. By analyzing this bending, called “gravitational lensing” (Figure 19), astronomers can deduce that the intervening galaxies contain far more matter than can be seen. By the time you read these words, dark matter might be discovered in the laboratory. The biggest particle accelerator in history is coming online in 2009 or 2010 at the European Organization for Nuclear Research, or “CERN,” near Geneva, and physicists believe that it will be able to spot the predicted candidates for dark matter, if they exist.

W. Couch/R. Ellis/NASA Headquarters Figure 19

Warped light. To make this photograph, the Hubble Space Telescope peered straight through the center of a distant cluster of galaxies. The rounded objects in the photo are galaxies in this cluster. The stretched-looking objects are other galaxies lying at great distances behind the “foreground” cluster of galaxies. The light from these more distant galaxies is gravitationally warped as it passes through the foreground cluster. The warped light in this photograph comes from galaxies lying many billions of light-years away; some of this light originated when the universe was barely a quarter of its present age! A photograph such as this is direct visual evidence for the general theory of relativity.

From such observations, we know that our galaxy, and most other galaxies, is immersed in a giant spherical cloud of dark matter whose diameter is many times the diameter of the visible galaxy (Figure 20). What, then, is this dark matter? No known form of matter can account for it. Scientists expect that entirely new forms of matter will be discovered, and there have been several theoretical suggestions about what form it might take. It must interact only weakly with ordinary matter, or we would have discovered it by now. Whatever it is, it’s all around us: There are probably billions of dark matter particles passing through your body every second, but leaving no effect on your body. Dark matter has inspired many searches among cosmic rays (particles from space) and in high-energy physics experiments. A parallel situation existed during 1914 to 1955 when theory suggested that an unobserved particle was created during beta-decay, but no such particle could be detected until 1955, when physicists discovered the neutrino. The laboratory discovery of dark matter would be momentous.

Luminous matter Dark matter

Figure 20

Dark matter forms a giant invisible spherical “cloud” around each visible galaxy. The small object at the center of the figure is a spiral galaxy, like our Milky Way galaxy, seen edge-on (compare Figure 17).

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Einstein’s Universe and the New Cosmology

CONCEPT CHECK 6 What’s so unusual about dark matter? (a) It exerts no gravitational force. (b) Its gravitational force pushes (or repels) instead of pulling. (c) It is made of material that has never been observed in our laboratories. (d) It moves faster than lightspeed. (e) It does not interact with electromagnetic radiation.

6 THE ACCELERATING UNIVERSE AND DARK ENERGY Will the universe expand forever, or will it eventually collapse back inward on itself? This is similar to asking what happens to an object that is thrown upward from Earth’s surface. If you throw a ball upward, it slows as it comes to a momentary stop at its maximum height and then immediately accelerates downward to the ground. But if NASA “throws” a space vehicle upward faster than 11 km/s (25,000 mph), it slows as it rises but instead of returning to the ground it keeps rising and escapes from Earth. Like the rising ball and the space vehicle, it stands to reason that the universe’s expansion should be slowing down. Just as the ball and the space vehicle are slowed by the backward pull of Earth’s gravity, the universe’s expansion should be slowed by the inward gravitational pull of all the matter in the universe. It’s important to quantitatively measure this deacceleration of the universe, because a sufficiently large deacceleration would imply that the universe is like the upward-thrown ball in that it will eventually stop expanding and then immediately begin collapsing on itself in an ultimate “big crunch.” On the other hand, if the deacceleration is sufficiently small, then the universe is like the upward-thrown space vehicle and will continue expanding forever. But it’s difficult enough to measure the expansion rate of the universe, let alone the rate at which that expansion rate is slowing down, so for many decades cosmologists didn’t know whether the universe would eventually collapse or would continue expanding forever. During the 1990s, cosmologists managed to measure that deacceleration. The result, in 1998, was a shocker: The universe’s expansion isn’t slowing at all. It’s speeding up.

Not only are we not at the center of the universe, we aren’t even made of the same stuff the universe is. Joel Primack, Astrophysical Theorist, University of California

How do we know the universe is accelerating? First, let’s see how scientists measure the speeds at which the galaxies are moving apart. Light waves stretch as they travel through the universe, because of the stretching of space during the time of travel. Thus, light from distant galaxies arrives at Earth with a longer wavelength than it had when it left its home galaxy; it is shifted toward the long wavelength or red end of the electromagnetic spectrum. This redshift of the light from distant galaxies, first discovered during the 1920s, was the earliest evidence of the big bang and the expansion of the universe. Scientists can measure the amount by which a galaxy’s light is redshifted and from this deduce the galaxy’s speed. But in order to use redshifts to confirm that the universe is expanding, one needs to know that it actually is the more distant galaxies that are redshifted the most. Such distances are not easy to determine. You can’t just stretch a tape measure out to a distant galaxy! Nevertheless, astronomers have for many years had methods for determining such distances and have amply confirmed that more distant galaxies are more redshifted in just the way expected in an expanding universe. Recently, astronomers developed an especially powerful method of determining such distances, along with speeds. Large modern telescopes can detect a particular type of supernova explosion (an explosion of a star) in far-distant galaxies. These “Type 1a supernovas” are bright enough to be seen even at distances greater than halfway across the observable universe. Also, it’s known that all Type 1a supernovas are nearly identical, and all shine with the same brightness during their roughly one-month period of maximum

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Einstein’s Universe and the New Cosmology intensity following the explosion. Since they all have the same actual brightness, more distant ones always appear dimmer from Earth, and from their observed brightness one can deduce how far away they must be. Thus, Type 1a supernovas are our most accurate markers for determining expansion speeds and distances across most of the universe. They’re sufficiently accurate to determine not only the speeds but also the rate of change of the speeds—the accelerations—of distant parts of the universe. In 1998, these observations revealed that the expansion of the universe is actually speeding up.

This was not expected. If you threw a silver dollar up into the air and, instead of slowing and coming back down, it sped up until it rose out of sight, you’d say that’s a pretty mysterious way to lose a dollar. You’d probably want to know what pushed it into outer space. In the same way, the gravitational pull of all the matter in the universe should slow the universe’s expansion. But it’s speeding up. What’s pushing on it? Recall that the receding galaxies are not really moving at all, but are simply remaining roughly at rest in space while space itself expands, like the raisins in our expanding balloon analogy in Section 3. Since accelerations are caused by forces, the accelerating expansion means that something is pushing outward on the fabric of space. What can it be? It’s certainly not matter of either the ordinary or the dark type, because the force of gravity from both ordinary and dark matter can only pull, not push. Scientists believe that all of space, including even “empty” space or vacuum, must contain some new form of nonmaterial energy that pushes outward. It’s called dark energy. This astonishing new concept burst upon the physics community in 1998 with the discovery of the acceleration of the universe. Nobody knows what dark energy is, although some theories relate it to the energy of the field that “inflated” the universe during the early moments of the big bang (next section). Dark energy is more mysterious than dark matter: We have evidence that it’s there, but little idea what it is. Dark energy must influence the shape of the universe, because Einstein says that all forms of energy have mass and because mass affects the curvature of space. It happens that it’s possible to infer the amount of dark energy present in the universe from the details of the cosmic microwave background. When the mass of this dark energy is added to the masses of the luminous matter, nonluminous ordinary matter, and dark matter in the universe, the total comes out to be precisely the amount needed to flatten the overall geometry of the universe! Thus, the flatness of the universe, dark matter, the acceleration of the universe, and dark energy all fit together in a beautifully consistent but totally unexpected picture of the universe. All of this provides a new answer to the ancient question “What is the universe made of?” Observations of the cosmic microwave background, and of the universe’s acceleration show that it’s made mostly of dark energy! The other ingredient is matter, the great bulk of which is dark matter. In more detail, the universe is 73% dark energy, 23% dark matter, nearly 4% nonluminous “ordinary” matter (including intergalactic gas, neutrinos, and black holes), and only 0.4% (less than half a percent) ordinary visible matter (Figure 21). The universe is stranger than you or I could have imagined: 96% of it is made of completely unknown matter and energy, most of the remaining 4% is invisible, and only a fraction of 1% is normal visible matter. The universe we can see is only a tiny fraction of all that is! To return to the question that began this section: If the universe continues its accerating expansion, it will not only expand forever but will expand faster and faster forever. But this assumes that the universe does keep accelerating, and, given the surprises of the past few years, few cosmologists would bet much on any particular long-term scenario.

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Einstein’s Universe and the New Cosmology Figure 21

Dark energy (identity unknown): 73%

Dark matter (identity unknown): 23%

Luminous matter: stars and luminous gas 0.4%

What is the universe made of? These numbers show that, whatever may be the nature of the unknown dark energy and dark matter, the universe is not made primarily of the same stuff that we are made of!

Other nonluminous components: intergalactic gas 3.6% neutrinos 0.1% Supermassive BHs 0.04%

CONCEPT CHECK 7 Type 1a supernova explosions make excellent markers for measuring the universe’s acceleration because (a) they all emit about the same amount of light; (b) they are all the same distance away from us; (c) they can be seen from immense distances; (d) they are all moving away from us at the same speed. CONCEPT CHECK 8 Dark energy (a) is made of some unknown form of matter; (b) has mass; (c) is made of invisible electromagnetic radiation; (d) pushes on space.

7 COSMIC INFLATION AND A BRIEF HISTORY OF THE UNIVERSE Alan Guth (Figure 22) bicycled hurriedly to the Stanford Linear Accelerator Laboratory (SLAC) to start work on the morning of December 7, 1979, breaking his personal speed record with a time of 9 minutes and 32 seconds. Working late the previous night, he had begun to understand a new and extraordinary cosmological phenomenon, and he was anxious to get back to thinking about it. He checked his calculations from the night before and found them exactly on target. Several weeks later the young physicist apprehensively presented his new idea to a packed audience at SLAC. The response was overwhelmingly favorable, exceeding Guth’s wildest expectations. The hypothesis of cosmic inflation was born. Guth had combined ideas from general relativity, quantum physics, and highenergy physics to explain how the matter and energy in the universe could have been created from nearly nothing by a high-energy submicroscopic event occurring in nearly empty space. Guth’s hypothesis does not explain how the universe actually got started, but it does explain how, starting from a tiny fragment of spacetime containing a minuscule amount of matter and energy, the universe expanded enormously while filling with matter and energy. Briefly, Guth’s hypothesis says that the universe started out unimaginably small, far smaller than a proton, and immediately expanded. Very early, at a trillionth of a trillionth of a trillionth (!) of a second after the beginning, the universe experienced an even more rapid period of expansion at speeds greatly exceeding lightspeed, during which it stretched by a factor of 1025 during only 10–35 seconds. To see how mind-boggling this is, try writing out these two numbers. This breakneck expansion is called, appropriately, “inflation” (recall Figure 14).

Donna Coveney/Massachusetts Institute of Technology News Office Figure 22

In 1979, high-energy particle physicist Alan Guth made a monumental cosmological discovery: the idea of cosmic inflation. The hypothesis has significant experimental support in satellite observations of the cosmic background radiation and in other cosmological observations. Cosmic inflation is the best scientific explanation to date of the details of the first few moments of time.

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Einstein’s Universe and the New Cosmology Nowhere is the inherent unity of science better illustrated than in the interplay between cosmology, the study of the largest things in the universe, and particle physics, the study of the smallest things. Rocky Kolb, Physicist at Fermilab

Where the telescope ends, the microscope begins. Which of the two has the grander view? Victor Hugo

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This sounds pretty bizarre, but it’s been receiving some observational confirmation lately. One response to this hypothesis is “How can the universe expand at faster than lightspeed, since special relativity predicts that nothing goes faster than light?” We’ve already dealt with this in Section 3: Special relativity predicts that no object can move through space faster than light. But general relativity tells us that the expansion of the universe is an expansion of the fabric of space itself, and there is no speed limit on this. The expansion carries galaxies and other objects along with it while those objects remain at rest relative to the space around them. According to Guth’s hypothesis, our universe started out so small that quantum effects such as the uncertainty principle dominated. One implication of this principle is that in every region of space, the energy in the region fluctuates randomly (or unpredictably) up and down around its average value, a little like the surface of a small portion of a lake fluctuates up and down due to wind rippling its surface. Even in supposedly “empty” space, such energy fluctuations are still required by the uncertainty principle. At extreme submicroscopic sizes, it’s thought that space and time do not exist as we know them but are instead broken up or “quantized” into tiny separate fragments having durations of about 10–49 s (that’s short!) and diameters of about 10–35 m (that’s small!). According to the inflation hypothesis, an unusually large energy fluctuation occurred in just such a fragment. This fluctuation had an energy of only some 109 joules, about the energy of one automobile tank of gasoline. According to E = mc2, the mass of this much energy is 0.01 milligrams—about as massive as a grain of dust. This doesn’t sound like enough energy to start a universe, but amazing things can happen when it’s all crammed into such a tiny region. One of those amazing things was that so much energy in such a small region created an enormous temperature of some 1032 degrees (try writing it out). Our universe immediately began expanding simply because it was so hot (this is also the reason ordinary explosions expand), and the expansion cooled it from its initial 1032 degrees down to around 1028 degrees. A major theme of modern physics, already encountered in our discussion of gravitational and electromagnetic fields, is that the universe is made of just a few kinds of fields that extend throughout all space and time. The cosmic inflation hypothesis is based on a new type of field, not yet observed in nature, called the inflation field. When our then-tiny universe had expanded and cooled to 1028 degrees, the inflation field developed something called a “false vacuum” that amounts to a gravitational force that strongly repels instead of attracting like the gravity that we know. This repulsive force sent the universe into a brief period of rapidly accelerating expansion or “inflation” up to speeds far faster than lightspeed. The expansion was actually “exponential”—that is, it had a fixed doubling time. Exponential growth can be surprising. Although this inflationary period began at 10–36 s into the big bang and lasted only until 10–34 s into the big bang, the universe’s size doubled nearly 100 times, resulting in a universe that was about 1025 (10 trillion trillion) times larger than it was before inflation. Even after inflation our universe was only a millimeter across but nevertheless the expansion was enormous. Think of a balloon being filled by a fire hose. Physicists believe that there are just four types of fundamental force fields: the gravitational field, electromagnetic field, “weak force” field, and “strong force” field. The last two are apparent only at the level of the atomic nucleus, in connection with nuclear forces. But in the fires of the early universe, the four fundamental forces were all “melted together” and indistinguishable. There was only one force, not four.

Einstein’s Universe and the New Cosmology

Physicists say that the four forces had the same “symmetries” and so did not exist individually. As the universe cooled, the gravitational force suddenly “froze out” of the unified force; it lost the symmetry that had unified it with the other forces and took on its own distinctive gravitational properties. This “symmetry breaking” is analogous to the loss of symmetry when water freezes: All directions are equivalent inside water, but ice crystals line up in specific directions—a loss of symmetry. As the universe continued cooling, the strong force froze out and formed its own unique patterns such as the quark-gluon plasma simulated in Figure 23. Finally, the weak force and the electromagnetic force froze out also, leaving us with the four forces that have their four distinct sets of properties that we observe today. But where did all the mass and energy in the universe come from, if energy is conserved and if everything developed from an energy fluctuation having the mass of a dust grain? Here’s where: The gravitational energy of any isolated lump of matter such as a star, that is held together only by gravity, is negative (less than zero), because work must be done on (rather than can be gotten from) the star in order to pull it apart into separated pieces. In the same way, the gravitational energy of the entire universe, due to the attraction between all its parts, is enormously negative. Inflation didn’t alter the universe’s net energy, but instead created negative energy (gravitational) and positive energy (kinetic, radiant, and the energy needed to create matter) in equal amounts. It’s like a man who spends a lot of money by going into debt; he spends like a millionaire, but his net financial balance remains zero. Thus the universe’s net energy remains very close to zero, balanced between an enormous negative gravitational energy and a slightly more enormous (by one gasoline tank) positive energy. The positive energy of matter and motion that you see today was scavenged in the early universe from gravity. As Alan Guth puts it, cosmic inflation is “the ultimate free lunch”: That gasoline tank’s worth of energy was the seed for everything. It’s a powerful story of how things came to be. Figure 24 shows some of the details of the time sequence. The time line is plotted in powers of 10, rather than simply in seconds, because a lot happens fast in the early universe due to the high energies involved!

It is said that there’s no such thing as a free lunch. But the universe is the ultimate free lunch. Alan Guth, Originator of the “Inflation” Idea That Explains How the Big Bang Could Have Created Our Universe out of a Vacuum

Figure 23

Simulated “snapshot” of two lead nuclei colliding at very high energy. The simulation portrays the nuclei just 6 * 10 - 24 seconds after impact, showing protons and neutrons in white. The smaller particles portrayed in darker hues are “quarks,” the particles of which protons and neutrons are made. This is a simulation of a real experiment that reproduced the theoretically predicted “quark plasma” that is believed to have existed at 10 microseconds after the big bang.

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Einstein’s Universe and the New Cosmology time in seconds 10⫺42

10⫺40

R ⫽ 10⫺35 m This is the shortest time, and the smallest distance, that can exist. All forces unified, dominated by quantum gravity. An energy fluctuation of 109 J having a mass of 0.01 milligrams occurs.

10⫺22

10⫺38

10⫺36

Gravity “freezes out” as a separate force.

10⫺20

10⫺18

T ⫽ 1028 K R ⫽ 10⫺28 m The universe begins “inflating” at speeds far larger than c, doubling 100 times and becoming 1025 times larger. 10⫺16

10⫺34

10⫺32

10⫺30

10⫺28

10⫺26

10⫺24

10⫺8

10⫺6

10⫺4

T ⫽ 1026 K Strong force freezes out. R ⫽ 1 mm Inflation ends, universe resumes its “normal” expansion at speed c.

10⫺14

10⫺12

10⫺10

T ⫽ 1015 K R ⫽ 3 centimeters Weak forces freezes out from EM force, so that four separate forces are now apparent. EM force dominates universe. 10⫺2

100

102 T ⫽ 109 K R ⫽ 10 million km Universe is cool enough for protons and neutrons to form into nuclei.

104

106

T ⫽ 108 K R ⫽ 40 million km Nuclei in Table 1 formed during the past few minutes. Universe is now too cool and diffuse for further nuclei to form.

108

1010

1012

30,000 years Gravity amplifies the lumpiness that was formed by quantum fluctuations prior to the inflationary expansion.

1014

400,000 years T ⫽ 3600 K. First atoms. Cosmic background radiation released: first light in universe (Fig. 13).

T ⫽ 1012 K R ⫽ 3 km It is now cool enough for quarks to form into protons and neutrons as shown in Figure 23.

1016

1018

30 A few 9 14 million hundred billion billion years million years years First years Sun, T ⫽ 3 K. stars. First Earth, You galaxies. planets are formed. born.

Figure 24

A really brief history of the universe. All numbers are only approximate, and the first millionth of a second is hypothetical (not yet checked directly by observation)! Temperatures are in degrees above absolute zero, or Kelvins, abbreviated K. The radius of the observable universe is abbreviated as R. For all times after the end of inflation, the universe is 1025 (10 trillion trillion) times larger than the observable universe, because the universe expanded far faster than lightspeed during inflation so that nearly all of it is so far away that light cannot reach here from there during the entire history of the universe.

How do we know that cosmic inflation occurred? Cosmic inflation has already passed several observational tests. First, it provides a convincing explanation of the origin of the large-scale gathering or “clumping” of stars into galaxies, of galaxies into clusters of galaxies, and even of clusters into superclusters, seen in today’s universe. It’s not hard to understand how any initial lumpiness would be amplified by gravitational forces into today’s quite “lumpy” universe of stars and galaxies—just as gravity can create stars out of diffuse clouds of gas and dust. But prior to the inflationary hypothesis, the big bang model offered no clue as to what created the initial lumpiness. Cosmic inflation’s answer is that quantum uncertainties during the big bang caused microscopic lumps that were then stretched by the expansion of the universe. Without inflation, the amount of stretching would be far too small for quantum fluctuations to explain the vast lumps (clusters of

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Einstein’s Universe and the New Cosmology galaxies, etc.) seen today. Inflation resolves this problem: Inflationary expansion stretches the initial quantum lumps enormously, and gravity works on these stretched lumps to produce precisely the clumping observed today. Second, Guth’s hypothesis predicts and explains the observed flatness of our universe. The reason is simple: Inflationary expansion plus additional "normal" expansion since that time stretched the universe so hugely that any overall curvature is now stretched flat, the way that the surface of an expanding balloon gets flatter and flatter as perceived by an ant on the balloon’s surface. It’s surprising that our universe should be flat, because a flat universe represents a delicate balance right at the borderline between the finite closed geometry and the infinite open geometry of Figure 15. Without inflation, there is no convincing explanation for why the universe should be so delicately poised. Guth predicted a flat universe more than a decade before the first observation, in 1992, of the patterns in the cosmic microwave background suggested that the universe really is flat. In 2001, more accurate observations of these patterns provided further confirmation of Guth’s prediction.

It appears that, without initial energy fluctuations and inflation, our universe could not have developed the patterns seen today in the layout of the galaxies. The great clusters of galaxies stretching across the universe still retain the microscopic pattern of those initial quantum fluctuations occurring in an unimaginably tiny lump of energy that started all of this. It all sounds too amazing to be true, but the truly amazing thing is that it’s been checked in some detail by specific observations. Just as ice crystals freeze along a direction that is previously undetermined or random, so cosmic inflation predicts that the specific “direction” in which the inflation field “froze” during the big bang was also random. But when I speak of “different directions” of inflation-field freezing, I really mean different properties of the various fundamental forces as they froze out of the preexisting symmetric unified force. In this process, basic properties of our universe such as the masses and charges of the fundamental particles might have been determined randomly. It’s even possible that ours is just one of many universes created in similar processes, each born in a new toss of the quantum dice and each characterized by different physical properties. According to the inflationary view, it’s possible that in our universe the numbers turned out to have just those values that allowed intelligent animals to evolve. In any other universe, in which these numbers were very different, life and intelligence might have been physically impossible. Our own existence might turn out to be the best explanation we have for these numbers having the values that they do have. This idea, that our universe must be organized in the way that it is because any other organization would not allow intelligent beings to be here to ask the question in the first place, is called the anthropic principle. And this outrageous but plausible connection between the big bang and our lives on Earth is a good place to end our excursion into cosmology. CONCEPT CHECK 9 Can anything go faster than light? (a) Yes, space can expand at faster than lightspeed. (b) Yes, certain subatomic particles can move through space at faster than lightspeed. (c) No, special relativity forbids it. (d) No, general relativity forbids it.

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© Sidney Harris, used with permission.

Einstein’s Universe and the New Cosmology

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Einstein’s Universe and the New Cosmology Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions EINSTEIN’S GRAVITY: THE GENERAL THEORY OF RELATIVITY 1. List two experiments you could do in a spaceship accelerating at 1g through outer space that might make you think you are at rest on Earth. 2. According to the equivalence principle, to what is acceleration equivalent? 3. In your own words, state the equivalence principle. 4. Give one piece of evidence showing that gravity bends light. 5. As observed in an accelerating reference frame, does a light beam bend? What does this tell us about the effect of gravity on light beams? 6. According to Newton, gravity is a force exerted by material objects on other material objects. What is gravity according to Einstein?

THE BIG BANG 7. About how old is the universe? 8. Describe two different pieces of evidence supporting the big bang. 9. Of what element is the universe mostly made? 10. Following up on the preceding question, what is the second most prevalent element in the universe? 11. Name two elements that were not made in the big bang. Name two that were.

THE GEOMETRY OF THE UNIVERSE 12. Give an example of a flat two-dimensional space, a curved two-dimensional space, and a two-dimensional space of finite extent. 13. How might we tell from inside our actual three-dimensional space whether space is curved? 14. List the three possible large-scale geometries of the universe, and describe at least two of them. 15. In what fundamental way does the big bang differ from an ordinary explosion? 16. Due to the expansion of the universe, are the galaxies moving through space? Explain.

THE SHAPE OF THE UNIVERSE 17. What does the evidence tell us about the overall shape of the universe? 18. List one piece of evidence showing that we live in a flat universe. 19. What is the cosmic microwave background? 20. The big bang emitted lots of high-energy radiation. So why do we detect the big bang radiation primarily as low-energy microwaves?

DARK MATTER 21. Roughly what percentage of the universe’s total mass is made of ordinary matter? 22. Roughly what percentage of the universe’s total mass is made of dark matter? 23. What is “dark matter”? 24. Why is it called “dark” matter? 25. What led astronomers to hypothesize the existence of dark matter?

THE ACCELERATING UNIVERSE AND DARK ENERGY 26. Is the universe’s expansion slowing down, speeding up, or maintaining an unchanging speed? 27. Describe the observations that show that the universe is accelerating. 28. What is causing the universe’s expansion to speed up? 29. Roughly what percentage of the universe is made of dark energy?

COSMIC INFLATION AND A BRIEF HISTORY OF THE UNIVERSE 30. What does the cosmic inflation hypothesis try to explain? 31. According to the cosmic inflation hypothesis, what started the big bang? 32. Why do they call it “inflation”? 33. Since energy is conserved, and since the universe started from only a gasoline tank’s worth of energy, having a mass of only 0.01 milligrams, how can the universe have possibly attained the enormous amount of energy and mass that it has today? 34. Give two pieces of evidence supporting the hypothesis of cosmic inflation.

From Chapter 11 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Einstein’s Universe and the New Cosmology: Problem Set

Conceptual Exercises EINSTEIN’S GRAVITY: THE GENERAL THEORY OF RELATIVITY

22. What important event happened at about 400,000 years after the big bang? 23. About 400,000 years after the big bang, the cosmic background radiation was released. How did the universe after this event differ from the universe before this event? 24. Imagine a huge triangle stretching across a large portion of the observable universe. Will the three angles of this triangle add up to the usual 180°, or will they add up to more than, or less than, 180°? 25. If a living observer could have been there to observe the universe only 300,000 years after the big bang, would they have seen anything? Explain. 26. Why couldn’t light travel through the early universe? 27. What does it mean to say that the universe is “flat”?

1. If you were in a rocket ship in space (far from all planets and stars) accelerating at 2g, how heavy would you feel? 2. In the preceding question, what if your acceleration were instead 0.5g? What if you were not accelerating at all? 3. In what way is the general theory of relativity more “general” than the special theory of relativity? 4. Astronauts’ hearts and muscles weaken in space due to the prolonged weightlessness. How might artificial gravity be installed in a space station to deal with this problem? 5. If you were in a rocket ship in space (far from all planets and stars) accelerating at 2g and you dropped a ball, how would it move as observed by you? 6. In the preceding question, what if your acceleration were instead 0.5g? What if you were not accelerating at all? 7. In the equivalence principle, what is equivalent to what? 8. Why don’t we notice the gravitational bending of light on Earth? 9. Does a high-speed bullet’s path bend more than a light beam bends? Why? 10. A rifle barrel and a laser both point directly toward a target some distance away. General relativity says that the bullet and the light beam both experience the same downward acceleration during their horizontal travel, yet the bullet hits the target well below the laser beam. Explain.

DARK MATTER

THE BIG BANG

THE ACCELERATING UNIVERSE AND DARK ENERGY

11. Where did your body’s hydrogen nuclei originate? 12. Did your body’s oxygen nuclei originate in the big bang? 13. The big bang has been described as the place where cosmology meets submicroscopic physics. Why? 14. The big bang created just three chemical elements. Why didn’t it create more? 15. Suppose we could instantly reverse the expansion of the universe so that it becomes a contraction. If we then observed distant galaxies, how would they appear? 16. Is there a specific place in the present-day universe where the big bang happened? Explain.

34. Since the universe is accelerating as it expands, is there any doubt among cosmologists that the fate of the universe is to expand forever? Explain. 35. Cosmologists did not expect to find that the universe is accelerating. What did they expect? 36. Why are type 1a supernovas such good markers for determining the rate of expansion of the universe? 37. What is the universe mostly made of? 38. Why do we think there is dark energy? 39. Suppose that a certain galaxy, galaxy X, is so far from our galaxy that the expansion of the universe causes it to move away from our galaxy at half of lightspeed. Does this mean that galaxy X is moving through space at half of lightspeed? Explain.

THE GEOMETRY OF THE UNIVERSE 17. If we consider Earth’s surface to be a two-dimensional “space,” the equator is one “straightest possible line” in this space. Are there other such lines? 18. On Earth’s surface, are the north-south lines of longitude among the straightest possible lines? What about the eastwest lines of latitude? 19. If you draw a triangle on the surface of a sphere, the sum of its angles is greater than 180°. Is it possible to draw a triangle on the surface of a sphere for which each angle is 90 degrees so that the sum of the three angles is 270 degrees? Explain. 20. Is there a place in the present-day universe that is the center of the universe? Explain. 21. Are there places in the present-day universe that are at the edge of the universe? Explain.

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THE SHAPE OF THE UNIVERSE

28. What evidence is there that our Milky Way galaxy might contain “dark” matter? 29. According to current theories, is there dark matter in your room? 30. Why can’t you see the dark matter that is in your room? 31. Since dark matter is invisible, what leads us to think it might exist? 32. Why would the laboratory discovery of dark matter be momentous? 33. Does dark matter interact by means of the gravitational force? How do we know?

COSMIC INFLATION AND A BRIEF HISTORY OF THE UNIVERSE 40. In what ways was the emergence of the four different fundamental forces during the big bang similar to the change of the state of water from liquid to solid? 41. If the theory of cosmic inflation is correct, then what is undoubtedly nature’s single most important example of quantum uncertainties? 42. How could the large-scale structure we see in the universe today have originated from tiny quantum fluctuations? 43. Is the total gravitational energy of an isolated star positive, or negative, or zero? Defend your answer.

Einstein’s Universe and the New Cosmology: Problem Set 44. A huge amount of energy was needed to create all the matter and all the motion that we see in today’s universe. According to the cosmic inflation hypothesis, where did it come from? 45. Cosmic inflation might sound far-fetched, but there is evidence for it. Describe two pieces of evidence.

17. Yes. The lines (circles really) of longitude that run through 19.

Answers to Concept Checks 21. 1. 2. 3. 4. 5. 6. 7. 8. 9.

(b), (c) (b) (b) (c), (d), (e) (b), galaxies, stars, and other specific objects warp small portions of space within an overall flat universe. (c), (e) (a), (c) (b), (d) (a)

23. 25. 27. 29. 31.

Answers to Odd-Numbered Conceptual Exercises and Problems 33.

Conceptual Exercises 1. Twice as heavy as usual. 3. General relativity includes accelerating reference frames, while special relativity applies only to nonaccelerating reference frames. 5. It would fall toward the rear with an acceleration of 2g, or about 20 m>s2. 7. An acceleration is equivalent to the force of gravity. The effects of an accelerating reference frame cannot be distinguished from the effects of gravity. 9. Yes, because the bullet moves so much slower than light. 11. In the big bang. 13. The big bang began as a microscopic event. 15. Once the light from the reversed galaxies got to us, that light would be shifted toward shorter wavelengths instead of longer ones, because the galaxies would be approaching us instead of receding from us.

35. 37. 39. 41. 43. 45.

the North and South Poles are also “great circles” or straightest possible lines. There are also many other such circles. If you draw a triangle connecting the North Pole with a point A on the equator and with another point on the equator that is 1/4 of the distance around Earth from point A, every angle in the triangle will be a 90 degree angle. The sum of the three angles is then 270 degrees. No. There is no edge, just as there is no edge on the twodimensional surface of a three-dimensional sphere. Before this event, light couldn’t travel through the universe. Everything was extremely murky. This was before light was able to travel through the universe, so they wouldn’t have been able to see anything. It means that ordinary “Euclidian” geometry is obeyed: Lines that are started parallel remain parallel, the angles of a triangle add to 180 degrees, etc. Yes, dark matter probably exists everywhere in our galaxy. Other galaxies have been observed to have dark matter, because they are spinning so fast that they would fly apart without the gravitational pull of dark matter to hold them together. Also, the bending of light as it travels through space indicates that some of the bending is caused by dark matter. Yes. It pulls on stars as they rotate around their galaxy’s center, holding them into the center and keeping the galaxy from flying apart. This pull is due to gravity. They expected a deacceleration due to the gravitational pull of matter in the universe. Dark energy. No, galaxy X is sitting approximately at rest relative to the space around it. It is space itself that is expanding, and galaxy X is simply going along for the ride. The energy fluctuation that started the big bang. Negative, because work (i.e., positive energy) is required to separate an isolated star into its original parts. First, the large-scale structure of today’s universe of stars and galaxies is just what would be expected if the universe started from quantum fluctuations that were then expanded rapidly. Second, the universe is flat, as predicted by inflation (which predicts that the universe has been stretched so much that it is essentially flat today).

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Anyone who has not been shocked by quantum physics has not understood it. Niels Bohr

W

e now present science’s most accurate and complete description of the physical world: quantum physics—often called quantum mechanics because it replaces Newtonian mechanics. As you will see, however, quantum physics is anything but “mechanical.” Originating during 1900–1930 and still under active development, quantum physics is the set of ideas and experiments that scientists use to study the microscopic world. Its central notion is that, at the microscopic level, some physical quantities such as energy are discontinuous or “quantized,” rather than continuous. Using language from our computerized culture, the microscopic world is “digital” rather than “analog.” Quantization represents a radical break with Newtonian physics, leading to fundamental new developments in physics and its philosophical impacts. Section 1 sets the stage with a broad description of the general nature, aims, and cultural role of quantum physics. Section 2 takes a closer look at an old experiment, Young’s double-slit interference experiment, to introduce the quantization of the electromagnetic field and the quantum theory of radiation. Section 3 discusses aspects of the quantum theory of light, especially “uncertainty” and “nonlocality.” Section 4 presents another specific experiment, the double-slit experiment with electrons, which requires us to introduce a second kind of quantized field called a matter field, leading to a new way of looking at matter. Section 5 discusses the meaning of this theory. Section 6 looks more carefully at quantum uncertainty for both matter and radiation.

1 THE QUANTUM REVOLUTION The quantum idea slipped nearly unnoticed into physics in 1900. Although nobody realized it at the time, it was the dawn of the post-Newtonian era. It’s remarkable that a second revolutionary but entirely different post-Newtonian idea, Einstein’s relativity, was announced only five years later. The special theory of relativity was fairly complete when first announced in 1905, and its revolutionary nature was already clear.

From Chapter 12 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The discovery of quantum mechanics in the mid-1920s was the most profound revolution in physical theory since the birth of modern physics in the seventeenth century. Steven Weinberg, in Dreams of a Final Theory

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Quantum physics describes the nature and behavior of matter and radiation, particularly at the microscopic level. It developed slowly, but its impact ultimately went far beyond special relativity’s impact, and today it is far from being a closed book. Although the theory’s main principles had appeared by 1930, and despite the theory’s wide testing and application, it’s still not clear what the theory really means. Because it predicts such a wide variety of phenomena so accurately, quantum physics is probably history’s most successful scientific theory. Its practical impact extends to everything that depends on the details of the microscopic world: electronic devices such as transistors, silicon chips, and integrated circuits, and so all the information and communication technologies such as television and computers; most of modern chemistry and some of biology; lasers; our understanding of different types of matter ranging from superconductors to neutron stars; and nuclear physics, nuclear power, and nuclear weapons. Central to the entire high-tech world is an elusive and highly non-Newtonian particle: the electron. Perhaps more significant but certainly less appreciated is the philosophical impact of quantum physics. Quantum physics represents a more radical undoing of the Newtonian worldview than does relativity. I have emphasized throughout this text that a scientific worldview is by no means a trivial academic matter. Newtonian views are woven subtly into the entire fabric of Western civilization. The mechanical worldview has dominated Western culture for centuries and has been assimilated so deeply that it’s accepted without even realizing that it is a worldview. You’ll discover that contrary to the Newtonian worldview, quantum physics implies that randomness, or chance, is built into nature at the microscopic level. Nature doesn’t know what she will do next! No longer can the universe be a predictable machine in which the future is “hard-wired” into the present. Quantum physics also implies, contrary to the Newtonian worldview, that nature is deeply interconnected, that such parts of nature as electrons, protons, and light waves cannot be separated from their surroundings without fundamentally altering their character. No longer can the universe be viewed as a machine at all, even an unpredictable one, for the most basic feature of the machine metaphor has always been its separable parts. Quantum physics holds that changes in nature occur discontinuously, rather than continuously as Newtonian physics predicts. Here’s an example, at the macroscopic level: Suppose you are swinging in a child’s swing, and that you then stop pumping and let the swing die down to smaller and smaller oscillations. The process of dying down is continuous, gradual, and this continuous process is exactly what Newtonian physics predicts. It would be surprising if, without pumping, you maintained an amplitude (width of oscillation) of say 4 m for several oscillations and then instantaneously “jumped” to an amplitude of only 2 m, where you remained for several more oscillations without pumping, after which your swing suddenly stopped. Such a discontinuous process is not predicted by Newtonian physics, and it is not observed in the macroscopic world around us. But such discontinuous processes are the norm at the microscopic level. For example, nature requires an atom to vibrate at only certain precise energies, just as our imaginary swing could oscillate only at amplitudes of 4 m, 2 m, or 0 m. When an atom loses energy, it must do so in sudden jumps from one of its “allowed” energies to a lower one. In doing so, it must release an instantaneous burst or quantity or “quantum” of energy. This is a central new feature of the theory, and it is the origin of the term quantum physics. The energy of a microscopic system is “digital” rather than “analog.”

The Quantum Idea

2 RADIATION HAS WAVE AND PARTICLE PROPERTIES Let’s review what you learned about light. The double-slit experiment with light showed that light is a wave. In this experiment, light from a single source passes through two narrow slits and then impacts a viewing screen.1 Figure 1 shows the experimental setup, and Figure 2 shows the experimental result. Figure 2 is an interference pattern, caused by the wave-interference of light waves spreading out from the two slits. The brightly lit lines in Figure 2 are places where the waves from the two slits are exactly “in sync,” where wave crests from one slit meet crests from the other, and valleys meet valleys, to create big light waves (bright light). The dark lines in Figure 2 are places where crests from one slit meet valleys from the other, so that the waves cancel. This alternating reinforcement and cancellation of light shows that light is a wave phenomenon. This led to the question of what’s doing the waving. The answer was that an electromagnetic (EM) field is waving, an invisible force field that is created by charged objects and exerts forces on other charged objects. An EM field is the effect that every electrically charged object has on the space around it. The field fills the space around electrically charged objects, the way that smoke fills a room, and exists everywhere that a charged object would feel an EM force if a charged object were present. So much for our review. Now, I want to tell you something new about light: Light is “quantized,” meaning that it comes in tiny parcels or bundles. First, I’ll present the experimental evidence for this, and then I’ll discuss what it means.

A

Art Hobson

B

Very narrow slits, shown here greatly enlarged

1

Figure 1

Figure 2

The double-slit experiment with light: the experimental setup and result.

The double-slit experiment with light: experimental result.

The light must be single-frequency and synchronized.

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How do we know light is quantized? Imagine performing the double-slit experiment with extremely dim light. You might expect that the result would be just like Figure 2 only a lot dimmer. But that’s not what happens. Figure 3 shows what happens. In sufficiently dim light and with a short exposure time, light impacts only at a few tiny points on the screen [Figure 3(a)]! There is no trace of an interference pattern. If we extend the exposure time, we simply get more tiny impacts [Figure 3(b)] and still no trace of an interference pattern. With a longer exposure, we get more impacts [Figure 3(c)] and we begin to see an interference pattern in the pattern of individual impacts. Finally, with longer exposure times, we see that the interference pattern is a consequence of a huge number of individual tiny impacts [Figures 3(d) and 3(e)]. Figure 4 shows another example of the same phenomenon. Dim light and a short exposure time allow us to see individual particle-like impacts in an ordinary photograph. Figure 4 shows the photo emerging from these impacts.

Wolfgang Rueckner Figure 3

Close inspection using extremely dim light with time-lapse photography shows that the double-slit interference pattern of Figure 2 is formed by light striking at individual tiny points all over the screen. The five photos use exposures of about 0.2 s (when about 30 tiny impacts have occurred), 1 s (150 impacts), 5 s (800 impacts), 20 s (3000 impacts), and 2 minutes (20,000 impacts).

So the wave-interference pattern of Figure 2 builds up from tiny individual particle-like impacts of light on the screen. The process is analogous to the way painters of the pointillist school of impressionist painting made their pictures from tiny dots of color. It’s natural to hypothesize, from the tiny impacts, that light is after all made of tiny particles. But we’ve already seen that light is an extended wave in a spreadout EM field that comes through both slits, so this hypothesis must be discarded. After all, every impact must occur preferentially within the brightly lit lines of the interference pattern. Such impacts cannot be made by particles traveling from the light source to the viewing screen, because a single individual tiny particle coming through one or the other slit cannot “know” that both slits are open and that it is therefore supposed to hit preferentially within the brightly lit lines. So just what is coming through the double slits? How can we explain the particle-like impacts of light upon the screen? The answer has a long history, but rather than dwelling on the history I’ll present the answer as it’s understood today. The answer is that no particles come through the slits; instead, a spread-out EM field comes through both slits and interferes at the viewing screen. But EM fields are not quite what physicists had thought they were during the nineteenth century. The new feature is that all EM fields are quantized. Like the rest of modern physics, this new concept is simple, but odd. A quantized EM field is simply an EM field that, for reasons nobody understands, is not allowed to have just any old quantity of energy. Instead, the field is allowed to have just certain particular quantities of energy, and no others, just like the dyingdown swing of Section 1. To make this concrete, let’s imagine pure yellow light with a frequency of 5 * 1014 Hz. According to quantum physics, the EM field that carries this yellow light is allowed to have only the following amounts of energy: 3.2 6.4 9.6 12.8

You can probably see the pattern in these energies.2 They are all simple multiples of 3.2 * 10 - 19 J. If we call this energy E, then the allowed energies are simply 0, E, 2

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* * * *

0J 10 J, 10 - 19 J, 10 - 19 J, 10 - 19 J, and so on - 19

I’ve simplified the numbers a little to make it easier to follow. The lowest possible energy level should not be 0 joules, but should instead be 1.6 * 10 - 19 J, with the other levels all raised accordingly (by 1.6 * 10 - 19 J). Electromagnetic fields are not allowed to have zero energy, but this fact will not be needed.

The Quantum Idea

2E, 3E, 4E, etc. No other energy is allowed for an EM field carrying pure yellow light. For instance, 1.3E or 15.71E are not allowed. This example illustrates the general rule: The total energy of an EM field carrying radiation (it can be light, infrared, X-ray, etc.) must be a simple multiple of some single energy value. The German physicist Max Planck (Figure 5) made the first and most important contribution toward the eventual discovery of this general rule, and he found a formula for the allowed energy increment that we called E above. The following statement gives this formula and summarizes the general rule:

(a)

(b)

(c)

(d)

(e)

(f)

The Quantum Theory of Radiation All EM fields are quantized. More specifically, when carrying radiation of frequency f, an EM field is allowed to have only the following particular values of total energy: total energy = 0, hf , 2hf , 3hf, 4 hf, and so on

That is, the field’s energy must be a simple multiple of the energy increment E = hf, where f is the frequency (in hertz) of the radiation, and h is a universal constant called Planck’s constant: h = 6.6 * 10 - 34 joules per hertz.3

Dr. Albert Rose/Art Hobson

So EM fields are “digitized”: They can’t have just any old energy, but must instead have either 0, 1, 2, 3, and so on, units of the basic energy increment hf. Instead of “digitized,” physicists say that EM fields are “quantized” (restricted to particular quantities of energy). The smallest energy increment hf is referred to as one quantum (or quantity, or parcel) of energy. Here’s an analogy: If water were quantized in 1 liter increments, then your bathtub would only be able to hold 0, 1, 2, 3, etc. liters of water. Just as the quantized water fills the tub from side to side, the quantized EM field fills the entire region between source of light and the viewing screen, but it can only have a total energy of 0, hf, 2hf, 3hf, etc. Armed with the key concept of the quantized EM field, let’s return to the doubleslit experiment. When radiation strikes the screen, the EM field transfers some of its energy to the screen. But the field cannot transfer just any old amount of energy, because quantization implies that the field’s energy can only change by a whole number of quanta. The tiny impacts seen in Figures 3 and 4 are these individual quanta of EM field energy. Let me explain. Suppose the light is so extremely dim that the EM field can deposit, on average, only a single quantum of EM field energy on the screen during a span of, say, 5 seconds. The entire spread-out field comes through both slits and fills the region between source and screen, but during the full 5-second time span it can transfer at most one quantum of energy. This field must deposit its quantum of energy all at once, in a single instant, because the field cannot carry some fraction of one quantum—it must always contain either exactly one or exactly zero quanta. When the field deposits its quantum on the viewing screen, the entire spread-out field must instantaneously lose this much energy. In our bathtub analogy, the entire spread-out body of water would instantaneously reduce its volume by 1 liter. This energy must be deposited at only a single point in the screen, because the screen is made of atoms and these atoms are also quantized so that each one must either absorb or not absorb one whole quantum of energy. An atom can’t absorb half

3

Figure 4

A photo emerges from individual particle-like impacts. Each photo in the sequence has a longer exposure time. The approximate number of impacts in each photo is (a) 3 * 103, (b) 104, (c) 105, (d) 8 * 105, (e) 4 * 106, and (f) 3 * 107.

The unit “joules per hertz” (or, equivalently, joule-seconds) needs to be attached so that when multiplied by a frequency measured in hertz, the result will be an energy measured in joules.

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American Institute of Physics/ Emilio Segre Visual Archives Figure 5

Max Planck. His introduction of the formula E = hf at a meeting of the German Physical Society on December 14, 1900, is usually taken as the birthdate of quantum physics. In Planck’s theory, hf represented the smallest unit of exchange of thermal energy into radiant energy, that is, the smallest amount of energy that a microscopic particle could give up in order to produce light.

of an energy quantum. For example, each of the roughly 30 impacts seen in Figure 3a imparts one quantum of energy to an atom in the screen. So that’s the explanation of the particle-like behavior of light observed in Figures 3 and 4. Since the tiny impacts have energy, and occur at fairly precise points, they have a particle-like nature even though they aren’t really particles but are simply increments of the energy of the entire spread-out EM field. These energy quanta that act like particles are called photons and are often thought of as microscopic particles of light even though “particles” might be a misleading word. Insofar as it’s proper to think of them as particles, photons are parcels of EM field that travel at lightspeed and carry an energy (radiant energy, of course) hf, where f is the frequency of the oscillating EM field that carries the radiation. Since they travel at speed c, relativity tells us that photons must have a rest-mass of zero. Notice that the energy of a photon increases with its frequency—higher frequency implies higher energy, as expected from our general study of waves. It’s important to remember that photon’s aren’t really particles. A photon is simply an energy increment of a spread-out EM field, analgous to a spread-out liter of water in a bathtub. Speaking precisely, there is no photon in the double-slit experiment until the instant an impact (on the screen, or on an airborne dust particle, or anywhere else) occurs. Don’t imagine that individual particles move from the light source, through the slits, to the screen. If an impact occurs at some point, don’t imagine that a photon was approaching that point just a moment earlier. A photon is nothing like, say, a tiny fast-moving pea. What really happens is that the entire space-filling EM field instantaneously loses one quantum of energy, and at the same instant that quantum of energy shows up at a particular point on the screen. Figure 6 will help you visualize this. The figure shows the emission, transmission, and impact of one quantum of light, at five different instants during the double-slit experiment. At (a), a light source (a laser is used for this kind of experiment) has just emitted a small amount of light, or EM field, having hf joules of energy. At (b) this Slits, viewed from above

Viewing screen

A

Light source

(a)

Photon impact

B

(b)

(c)

(d)

(e)

Figure 6

The double-slit experiment for light, showing the EM field for a very low energy light beam (a laser is used for this kind of experiment) at five different instants. The diagram shows the experiment as viewed from above, with the openings at A and B representing the narrow dimensions of the long narrow slits. The light beam is emitted at (a), approaches the slits at (b), emerges from the slits at (c), approaches the viewing screen at (d), and impacts the screen at a specific point at (e). The impact is referred to as “a photon.” At the instant of impact, the entire spread-out field vanishes.

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field is approaching the double slits. At (c) a portion of the field has passed through the slits (we don’t show the remaining portion that reflects from the partition). At (d) the part that passed through the slits is approaching the viewing screen. At (e), a single impact—a photon—appears on the viewing screen. At the instant the photon appears, the entire spread-out field vanishes. Physicists often describe this as the “collapse” of the field. But as you’ll see, the energy doesn’t collapse to a true mathematical point having zero volume. Quantum physics demands that it be spread out over at least a certain minimal volume, a volume that is usually of atomic dimensions.

And these fifty years of conscious brooding have brought me no nearer to the question of “What are light quanta [photons]?” Nowadays every clod thinks he knows it, but he is mistaken. Einstein, Near the End of His Life

CONCEPT CHECK 1 During the double-slit experiment with light, the region between the slits and the screen contains (a) electrons; (b) an EM field; (c) photons; (d) energy; (e) none of the above. CONCEPT CHECK 2 Radiation made of yellow light, red light, and infrared radiation enters your camera and strikes the photographic film. Which of the three forms of radiation deposits the most energy per photon? (a) Yellow. (b) Red. (c) Infrared. (d) All three deposit the same energy per photon.

3 QUANTUM RADIATION Scientists don’t know why radiation is quantized, nor why Planck’s constant has the particular value it does have. The small number h plays a role in quantum physics that’s analogous to the role played by the large number c in relativity theory. The universe would be quite different if either h or c had a very different value. Although the patterns made by light waves are due to large numbers of photon impacts, keep in mind that each photon “knows” about the entire spread-out field because each photon represents an increment of energy of the entire field. As we see in Figures 3 and 4, photons strike the screen fairly randomly, the first hitting in one place, the second in quite another place, and so forth. But there’s a pattern in this randomness: Photons strike preferentially in the regions that will emerge as bright regions. The interference pattern is best described as a statistical pattern formed by large numbers of individual impacts. Judging from Figure 3, the precise impact point of any individual photon is unpredictable even though the emerging statistical pattern is predictable. This reminds us of dice throws, or insurance statistics, in which individual outcomes are unpredictable but the long-term statistics are predictable. As we’ll see, this unpredictability or uncertainty within an overall pattern is characteristic of quantum physics. Besides quantization and uncertainty, another key characteristic of quantum physics shows up in the double-slit experiment with light. One of this experiment’s oddities is that at the precise instant a photon impacts the screen, the entire spacefilling EM field suddenly shifts its energy downward by hf. How can, for example, the field in the vicinity of the two slits (Figure 1) suddenly lose energy precisely when the photon impact occurs on the screen? After all, it’s some distance between the screen and the slits. In principle, the distance could be interstellar, or intergalactic. How can the field at the slits “know” instantaneously that the photon impact occurred, when relativity says that lightspeed is the limiting velocity? This puzzling situation relates to another general quantum phenomenon known as nonlocality. One quantum is ridiculously small. For yellow light, it’s only 3.2 * 10 - 19 J, as you can see by multiplying h and f together, with f = 5 * 1014 Hz for yellow light. For example, a typical lightbulb emits around 10 J of light every second. Assuming that

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all of this is yellow light, this amounts to more than 1019 (10 million trillion) photons every second, as you can see by dividing 10 J by 3.2 * 10 - 19 J. So one quantum of energy—a single photon—is really tiny. There’s no way you could tell the difference between a bulb emitting 1019 photons every second and one emitting 1019 + 1. This smallness of the typical quantum of energy is the reason scientists didn’t notice quantization before 1900, and why you don’t notice it in your everybody life. CONCEPT CHECK 3 If Planck’s constant were ten times larger than it is, quantum effects would be (a) easier to detect; (b) more difficult to detect; (c) neither of the above. CONCEPT CHECK 4 Suppose the light source in Figure 1 is turned on so briefly that only a single quantum of energy passes through the double slits. When it arrives at the screen, this energy is deposited (a) all over the white bands in the drawing; (b) at one small point within the white bands; (c) at one small point, which could be anywhere on the screen; (d) at one small point on the screen, lying directly behind the slit through which the energy passed. M A K I N G EST I M AT ES On a clear day at noon, the sunlight striking each square meter of ground during each second carries 1000 J of energy. Estimate the number of photons striking 1 square meter during 1 second. Estimate the number of photons striking your hand during 1 second when you hold your hand open to bright sunlight.

4 MATTER HAS WAVE AND PARTICLE PROPERTIES

American Institute of Physics/ Emilio Segre Visual Archives

Sections 2 and 3 presented the quantum theory of radiation. Now let’s turn to matter. Recall that radiation has no rest mass while matter has rest mass. The conventional view until 1900 was that radiation is made of waves in an EM field while matter is made of particles. But we’ve just learned that the EM field is quantized and this means that, even though radiation is a wave, it behaves in some respects like particles. What about matter? Louis de Broglie (pronounced “de Broy”; Figure 7), a Ph.D. student at the University of Paris in 1923, felt that there should be a kind of symmetry, or balance, between radiation and matter. He thought it ugly that radiation should exhibit both wave and particle properties while matter behaved always as particles and suggested that matter should also have both wave and particle properties. This was weird. Despite the lack of experimental evidence at that time to support it, he found his weird idea so beautiful that he included it in his Ph.D. dissertation. De Broglie’s Ph.D. committee didn’t know what to make of it and sent the dissertation to Einstein for his opinion. Einstein was impressed and commented later that “it is a first feeble ray of light on this worst of our physics enigmas.” The committee approved de Broglie’s dissertation. Waves of matter? How could an individual particle of matter such as one electron or one atom also be spatially extended waves? Nevertheless, de Broglie pursued his

Figure 7

Louis de Broglie. Feeling that there should be symmetry between matter and radiation, he predicted that matter should display the same wave-particle nature as radiation.

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Sunlight is made mainly of visible radiation with a frequency around 1015 Hz. The energy of one photon of this radiation is (6.6 * 10 - 34) * 1015, or 6.6 * 10 - 19 joules, or about 10–18 joules. To get 1000 joules of energy, we would then need 1000>10 - 18 or 1021 photons. I measure my hand to be roughly 9 cm * 18 cm, or about 200 cm2. One square meter is 100 * 100 cm, or 10,000 cm2, in area. So a hand is about 200>10 ,000 m2, or 0.02 m2, and the number of photons falling on a hand in 1 second is about 0.02 * 1021 or 2 * 1019 - 20,000,000,000,000,000,000 photons every second. SO LU T I O N TO M A K I N G EST I M AT ES

The Quantum Idea

notion. Based on the symmetry that he envisioned between radiation and matter and working from Planck’s formula E = hf that connects the wave and particle aspects of radiation, he deduced a formula that predicted the wavelength of the wave associated with every material particle: Planck’s constant wavelength of material particle = (particle’s mass)(particle’s velocity) l = h>my This formula for these matter waves is analogous to the formula E = hf for quanta of radiation. Both connect a particle property to a wave property. Planck’s constant plays an important role in both formulas. The smallness of h implies that the wavelength l of a material particle is very small, just as it implies that the energy E of a photon is very small. The smallness of l means that the wave aspects of matter are difficult to detect, just as the smallness of E means that the particle aspects of radiation are difficult to detect. That’s why we normally assume that matter is made of particles while radiation is made of waves. If we apply de Broglie’s formula to a typical macroscopic object like a 1 kg baseball rolling across the floor at 1 m/s, we get a wavelength of l =

[The double-slit experiment is] a phenomenon which is impossible, absolutely impossible, to explain in any classical [Newtonian] way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by explaining how it works. Richard Feynman

6.6 * 10 - 34 J/hz = 6.6 * 10 - 34 m (1 kg) * (1 m>s)

The baseball’s wavelength is about a billionth of a trillionth of a trillionth of a meter! This is far smaller than an atom and far too small to detect. It’s no wonder that we have never noticed the wave aspects of baseballs. The wavelengths of microscopic particles are much larger. Since mass shows up in the denominator of de Broglie’s formula, the least massive material particles generally have the largest wavelengths. One of the least massive material particles is the electron. Electrons typically move at velocities of 107 or 108 m/s. At these velocities, de Broglie’s formula predicts an electron’s wavelength to be about 10–11 m. Although this is very small—about one-tenth the size of a typical atom—it’s large enough to be detected in careful experiments. Note that de Broglie’s idea says every material particle has wave properties, not just electrons but also protons, gold nuclei, molecules, and so on. At this point, you might wonder what’s going on here. How can a single material particle have a wavelength? An individual electron isn’t even spread out in space, while a wave requires an extended medium, so how can one electron be a wave? Let’s turn to experiment for guidance. We’re going to look at two experiments that answer these questions and that confirm de Broglie’s ideas, but in a completely unexpected way.

How do we know matter has wave properties? Figure 8 shows the experimental arrangement for a double-slit experiment that’s just like the double-slit experiment with light but that uses matter instead of light. I will assume that the experiment uses electrons, although any other material particles such as neutrons, protons, atoms, or molecules could be used and the results would be similar. The apparatus on the left side of the diagram represents an electron source plugged into a power supply. This source could be a metal wire, enclosed in a vacuum tube, heated electrically until electrons “boil off” of it; a similar electron source is central to TV picture tubes. We’ll call this setup the double-slit experiment with electrons. An “electron beam”—which you can think of for now as a fast-moving stream of billions of electrons per second—emerges from the electron source and spreads out as it

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The Quantum Idea travels toward the double slits.4 When it gets to the two slits, marked A and B in the diagram, a portion of the beam goes through each slit and the rest of the beam is stopped by the partition. So a narrow electron beam emerges from each slit and travels on toward the viewing screen at the right. What will we see on the screen? Figure 9 shows the experimental outcome. Although this outcome had been predicted since de Broglie’s work in 1923, it’s not easy to actually make the experimental setup because the slits must be extremely small, and so the experiment was not carried out until 1974, by physicist Claus Jonsson working in Germany. Just to reinforce what you’re looking at here, Figure 10 shows the experimental arrangement and the result.

The experimental outcome looks just like the outcome of the double-slit experiment with light, Figures 1 and 2! The pattern seen on the screen is a wave-interference pattern, showing that waves come through the two slits and interfere as they approach the viewing screen. This certainly confirms de Broglie’s idea that electrons and other material particles have wave properties, and in fact the quantitative results agree entirely with de Broglie’s formula for the wavelength of these waves. ⫹ ⫺ A

Figure 8

The double-slit experiment with electrons. The electron source is a thin tungsten metal wire that is heated electrically until electrons “boil” off it. A similar electron beam is central to TV picture tubes. In the experiment shown, what will we see on the screen?

B

?

Very narrow slits, shown here greatly enlarged

⫹ ⫺ A

Claus Jonsson/Art Hobson

B

Figure 10

Figure 9

A wave-interference pattern made by electrons. 4

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Outcome of the double-slit experiment with electrons. The electron beam creates the white bands shown on the screen. Compare this with the similar experiment using photons (in other words, light) instead of electrons, Figure 1.

The electrons must all have the same velocity, in other words the same wavelength.

The Quantum Idea

But it’s pretty puzzling. Probably as far back as grade school, you learned that matter is made of particles such as protons, neutrons, and electrons. Yet here is an experiment that fires electrons through a couple of slits, and it turns out that they must be waves! What’s going on? To answer this, we again ask nature. How do we know matter has particle properties? Now we’re going to look at the double-slit experiment with electrons again, but using a much lower-intensity electron beam—you could call it a much “dimmer” beam (although we’re talking here about electrons, not light). Physicists have predicted the outcome of this experiment since about 1930, but this difficult experiment wasn’t actually performed until A. Tonomura and his Japanese colleagues performed it in 1989. With a dimmer electron beam, you might expect the experimental result to look like Figure 9, only a lot dimmer. But that’s not what happens. Figure 11 shows what does happen. With a sufficiently low-intensity electron beam and a short exposure time, the electron beam impacts only at a few tiny points on the screen [Figure 11(a)]! There is no trace of an interference pattern. If we extend the exposure time a little, we simply see more impact points and still no trace of an interference pattern [Figure 11(b)]. But with longer exposure times we discover an interference pattern showing up in the pattern of individual impacts. The interference pattern is a consequence of a huge number of individual tiny impacts.

You might have already guessed the name given to these individual impacts. They are electrons! And you might have noticed that the two experimental outcomes in Figures 9 and 11 are just like the outcomes in Figures 2 and 3—except that now we’re using an electron beam instead of a light beam so the impacts are made by electrons, not photons. To ward off a possible misconception, the interference pattern is not the result of interactions between different electrons. This pattern shows up even for a beam so dim that at most one electron at a time comes through the slits. Even if only one electron came through per hour, the cumulative impacts over many hours would still form an interference pattern. The experiment shows that the wave-interference pattern of Figure 9 is built up from tiny individual electron impacts on the screen. Notice carefully that, like the double-slit interference experiment with light, each impact tends to occur only within the brightly lit constructive interference part of the figure.5 This means that each individual electron “knows” that it’s “supposed” to contribute to the doubleslit interference pattern—each electron “knows” that both slits are open. But we are accustomed to thinking of electrons as tiny particles, much smaller than either slit, particles that would necessarily come through either one slit or the other and certainly not both slits. How could a single tiny electron, coming through either one or the other slit, “know” that the other slit is open and that it is therefore supposed to contribute to the double-slit interference pattern? Quantum physics gives the same answer to this dilemma that it gave in Section 2 for the double-slit interference experiment with light: The explanation of the Figure 9 is that a spread-out field comes through the two slits and interferes in the region between the slits and the screen. But what kind of field? It cannot be an EM field as it was for light, because an electron beam is not an EM wave. In fact, the experiment has basically nothing to do with electromagnetism, despite the fact that the electron is an electrically charged particle. Even when this experiment is done with uncharged particles such as neutrons, the result is still a double-slit interference experiment pattern like Figure 9. The 5

You might have noticed that the pattern seen in Figure 11(e) is not as simple as the pattern shown in Figure 10. For instance, some impacts occur in the “dark” regions between the bright lines. This is because the predicted pattern in Figure 10 is simplified. The actual predicted pattern is graphed in Figure 13.

Akira Tonomura/Hitachi, Ltd., Advanced Research Laboratory Figure 11

The buildup of an interference pattern in the electron waveinterference experiment by individual impacts of electrons. The five photos use exposures of 0.01 s (when only 10 electrons have hit), 0.1 s (100 electrons), 3 s (3000 electrons), 20 s (20,000 electrons), and 70 s (70,000 electrons).

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The Quantum Idea

For me, the main purpose of doing experiments is to show people how strange quantum physics is. Most physicists are very naive; most still believe in real waves or particles. Anton Zeilinger, Physicist

field that comes through the two slits is something entirely new, something that nobody knew existed until de Broglie and others discovered it during the 1920s. We’ll call it a matter field.6 De Broglie’s matter waves are waves in a matter field, just as EM waves are waves in an EM field. And just like EM fields, matter fields are quantized. Since we’ve already discussed quantized EM fields, it’s not difficult to understand a quantized matter field: First of all, like EM fields and gravitational fields, a matter field fills up a region of space, such as the region between the slits and the screen in Figure 10. When we say that matter fields are quantized, we mean that, for reasons nobody understands, a matter field is not allowed to have just any old quantity of energy. Instead, the field is allowed to have only certain particular quantities of energy, and no others. For an electron beam, this energy can be mc2, 2mc2, 3mc2, 4mc2, and so on, where m means the mass of one electron. If m represents the mass (i.e., the total inertia) of a motionless or moving electron, then mc2 is its total energy (including kinetic energy). So when we say that the allowed energies of the matter field are mc2, 2mc2, and so on, we’re simply saying that the matter field must contain enough energy for one electron, or two electrons, or three electrons, and so on, and nothing in-between. Matter is quantized, just as radiation is quantized! Just as the quanta of the EM field are called photons, the quanta of the matter field are called electrons. In other words, electrons are not particles at all. They are not even remotely like a small pea, not like a small “thing” held rigidly together that maintains a fixed shape and follows a path from the electron source through the slits to the screen. An electron is simply an increment of matter field energy that acts in a unified way. When the matter field interacts with the viewing screen of Figure 11, one such increment instantly and entirely absorbs into the screen and the entire matter field in the space outside the screen reduces its energy by mc 2. Just as in the analogous EM field experiment, the interaction point on the screen is not predictable, and the process is non-local because the matter field loses energy everywhere at the instant of interaction. As mentioned earlier, the same idea applies to all other material particles: Protons, neutrons, atoms, and molecules are all matter field quanta, all parcels of a spread-out field energy, all capable of going through both slits in the double-slit experiment.7 There’s a beautiful symmetry here: Everything, all matter and all radiation, is made of spread-out fields, but these fields are quantized and this is why there are particle-like parcels of light (photons) and particle-like parcels of matter (electrons, protons, etc.) I’ll summarize this idea as follows: The Quantum Theory of Matter A new type of field called a matter field exists in nature. Like EM fields, matter fields are quantized. For example, the matter field for electrons is allowed to possess enough energy for either 0 electrons, or 1 electron, or 2 electrons, and so on. Electrons (and other material particles) exist because matter fields are quantized in just these energy increments.

6

7

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The matter field has a long history and goes by a variety of names: psi, wave function, electron field, electron-positron field, and matter wave. As the particles get more massive, it gets harder to demonstrate this experimentally. But in 2003, Austrian physicist Anton Zeilinger demonstrated wave interference for C60 molecules, showing that these large molecules (60 carbon atoms!) are quanta of a matter field.

The Quantum Idea

CONCEPT CHECK 5 According to quantum physics, what’s really happening when we say that an electron passes through the double-slit apparatus and hits the viewing screen? (a) A single tiny particle passes through one or the other slit (not both) and impacts the screen. (b) A single tiny particle passes through both slits and impacts the screen. (c) A spread-out matter field passes through one or the other slit (not both) and an increment of the field interacts with the screen. (d) A spread-out matter field passes through both slits and an increment of the field interacts with the screen. CONCEPT CHECK 6 Suppose the electron source in Figure 10 is turned on so briefly that only a single quantum of energy passes through the double slits. When it arrives at the screen, this energy (a) spreads out all over the white bands in the drawing; (b) strikes at one small point within the white bands; (c) strikes at one small point, which could be anywhere on the screen; (d) strikes at a small point on the screen, lying directly behind the slit through which the energy passed.

5 QUANTUM MATTER will help you visualize all this. The figure is analogous to Figure 6, but for matter instead of EM radiation. The figure shows the emission, transmission, and impact of a very low intensity matter wave, at five different instants. At (a), an electron source has just emitted a small amount of an electron beam, or matter field, having just mc2 joules of energy, where m is the total inertial mass of one electron. This field approaches the double slits, passes through the slits, and approaches the viewing screen. At (e), a single impact—an electron—appears on the viewing screen. At the instant the electron appears, the entire spread-out matter field vanishes.

Figure 12

Double slits

Viewing screen

⫹ ⫺ A

Single electron impact

(a)

B

(b)

(c)

(d)

(e)

Figure 12

The double-slit experiment with electrons, showing the matter field for a very low-intensity electron beam at five different instants. The diagram shows the experiment as viewed from above, with the openings at A and B representing the narrow dimensions of the long narrow slits. The electron beam is emitted, approaches the slits, emerges from the slits, approaches the viewing screen and, at (e), impacts the screen at a specific point. The impact is referred to as “an electron.” At the instant of impact, the entire spread-out field vanishes.

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The Quantum Idea In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields. Quantum field theory hence led to a more unified view of nature than the old dualistic interpretation in terms of both fields and particles. Steven Weinberg

To repeat some of the earlier remarks about light: Physicists view matter fields, rather than electrons and protons and so on, as the fundamental entity. That is, a matter field is physically real, just as an EM field is physically real. Just as photons are merely quanta of an EM field, electrons and so on are merely quanta of a matter field. The reason nature has a particle-like aspect is that it is made of quantized fields. Although it’s legitimate to think of electrons, protons, and so on as particles, it’s important to remember that they are not particles in the simple Newtonian sense. An electron is simply an energy increment of a spread-out matter field. When an impact occurs at some point, do not imagine that an electron was approaching that point just a moment earlier. Before that time, there was only a spread-out matter field. You may have seen the narrow paths or “tracks” of electrons or other microscopic particles made in high-energy physics experiments. Although these tracks are convincing evidence that electrons exist, they do not invalidate the view that only a matter field exists between impacts. The tracks are made by successive individual interactions between a matter field and gas or water molecules. The matter field collapses into a tiny electron impact each time it interacts with a molecule, while spreading out as a matter field between impacts. Keep in mind that, although an interference pattern such as Figure 9 is created by billions of electrons impacting the viewing screen during every second, each individual electron “knows” about the entire experimental arrangement because each electron is simply an energy increment—a quantum—of an entire spread-out matter field that comes through both slits. Note also the unpredictable nature of the individual electron impacts, just like the unpredictable nature of photon impacts in the double-slit experiment for light. We also see the characteristic nonlocality noted in the experiment with light: At the instant the electron impact occurs, the entire spread-out matter field instantaneously deposits an entire quantum of energy at the impact point. Matter waves are exploited every day in such devices as the electron microscope. Using electromagnetic fields instead of the glass lenses used by visible-light microscopes, electron microscopes bend and focus the waves associated with electrons to form electron images of microscopic phenomena. Since electron wavelengths can be smaller than an individual atom, electron microscopes can form images of atoms, something that visible-light microscopes cannot do because visible wavelengths are thousands of times larger than an atom. Recall the dilemma facing the Greek philosopher Democritus: Is matter continuous, or discrete? Democritus answered that it’s discrete, made of tiny indivisible particles that he called atoms. Today we define the word atom somewhat differently, but we still regard ordinary matter as being made of atoms. Quantum physics, however, gives a whole new significance to atoms and the particles of which they’re made. Such particles are made of spread-out matter fields, so in this sense matter is continuous. But matter fields are quantized into parcels, or bundles, of spread-out matter field energy, and these bundles can act separately, so in this sense matter is discrete. So, in a wholly unexpected way, modern physics says that matter is both continuous and discrete. More precisely, it’s made of discrete quanta of a continuous matter field. CONCEPT CHECK 7 How is an electron similar to a photon? (a) Both contain electric charge. (b) Both move at lightspeed. (c) Both impact at a tiny point on a viewing screen. (d) Both are quanta.

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The Quantum Idea

6 NATURE IS NONLOCAL AND UNCERTAIN In the double-slit experiments with light and matter, we noted that the entire EM field or matter field changed its character instantaneously when an impact appeared on the screen, a behavior called quantum nonlocality. In addition, the position of each individual impact on the screen was unpredictable, even though the overall pattern was predictable. Unpredictability and nonlocality are two significant and characteristic features of quantum physics. In order for a pattern like Figure 9 to emerge from billions of tiny electron impacts, different impacts must occur at different places. If you think in Newtonian ways, you might suppose that electrons impact at different places because they started out differently from the electron source. Could we then adjust the source so as to prepare every electron identically in order to make them all hit the same point on the screen? Experimentally, the answer is “no.” Even if we prepare the electron source identically prior to every impact, the impacts still occur at different points all over the interference pattern. We expect—and Newtonian physics teaches us—that identical physical conditions lead to identical outcomes. But this expectation, and Newtonian physics, are wrong. Contrary to Newtonian physics, there is an inherent uncertainty in nature. Identical causes can lead to different outcomes. The matter field is spread all over the interference pattern, and the impact point—the point where the field deposits a quantum of energy—can occur at any point within this pattern. There is no way of predicting the precise impact point, because even nature doesn’t know the precise point ahead of time. Newtonian physics had it wrong: The future is not encoded in the present. And this is not just a matter of microscopic physics; quantum uncertainties can be magnified into big, easily observed impacts in the macroscopic world, impacts such as radioactive decay. The universe even has quantum uncertainties imprinted on its largescale structure. A few physicists disagree with the notion that the future is undetermined, arguing instead that our current understanding (quantum physics) is simply not deep enough to penetrate the true principles governing the microscopic world and that these true principles would restore predictability to nature. Einstein argued forcefully during the 1930s that “God does not play dice,” citing detailed examples to try to show that an irreducible uncertainty would be absurd. But quantum physics continues to have a perfect record of experimental success, and the quantum predictions that Einstein believed to be absurd have now been tested and found to actually occur. Note that, despite the randomness of individual impacts, the overall double-slit interference pattern is predictable. We get the same interference pattern every time we do the experiment. Since the pattern represents the overall statistics of billions of impacts, the overall statistics are predictable, even though individual impacts are not. The precise pattern is not quite as simple as the one shown in Figure 10. Figure 13 shows the observed overall statistical pattern in more detail; the graph at the right shows the average number of impacts versus position on the screen. The points marked “o” on the screen are the positions of the dark lines in Figure 9, where no impacts occur.

A philosopher once said “It is necessary for the very existence of science that the same conditions always produce the same results.” Well, they don’t! Richard Feynman

I believe in the possibility of a theory which is able to give a complete description of reality, the laws of which establish relations between the things themselves and not merely between their probabilities. . . . Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice. Einstein. His Friend Niels Bohr Replied, “Albert, Stop Telling God What to Do.”

God not only plays dice. He also sometimes throws the dice where they cannot be seen. Stephen Hawking, Physicist

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The Quantum Idea

⫹

Position on the screen

⫺ A

(a)

B

(b)

(c)

(d)

Number of impacts

Figure 13

American Institute of Physics/ Emilio Segre Visual Archives Figure 14

Max Born. He was the first to conclude that the wave patterns observed in experiments involving microscopic material particles were probability patterns.

God rolls the dice every time a quantum interaction takes place. Heinz Pagels, Physicist

The right side of this diagram shows a graph of the distribution of impacts after millions of electrons have impacted the viewing screen. Figures 9 and 11 are photographs of this distribution of impacts. The points marked “o” are the positions of the dark lines in Figure 9.

In 1926, German physicist Max Born (Figure 14) was the first to conclude that data such as the graph in Figure 13 give the probabilities for a single electron to strike at various points on the screen, in the same way that “50% probability of heads and 50% probability of tails” gives the probabilities for the outcome of a single coin flip. More precisely, the intensity8 of the matter field at any particular point represents the probability that an electron impact will occur at that point if a viewing screen or some other detecting device happens to be at that point. For example, Figure 9 shows the intensity of the matter field at various points on the screen, and this intensity (or brightness) represents the probability that any individual electron will impact at that point. Probabilities were invented long before quantum physics and usually have nothing to do with quantum physics. Probabilities are useful whenever the outcome of a particular experiment is uncertain but the overall statistics of many repetitions are predictable. A simple example, having nothing to do with quantum physics, is the flip of a coin. What “50% probability of heads” means is that, in a long series of tosses, roughly 50% will be heads. This probability, 50% or 0.5, can be regarded as a statistic, a number representing the pattern that emerges in many repeated trials of the experiment. But there is a difference between the probabilities observed in macroscopic experiments such as coin flips and the probabilities referred to in quantum physics. Because coin flips obey Newtonian physics to an excellent approximation, the outcome is predictable in principle. That is, with enough information regarding the tension in the flipper’s thumb, the initial height of the coin above the table, the elastic properties of table and coin, and so forth, you can use Newtonian physics to predict the outcome. Our uncertainty about a coin flip arises only from ignorance of the precise details. But quantum events are not predictable even in principle. Quantum unpredictability arises from a fundamental uncertainty in nature, rather than simply from our own inability to predict nature. Nature herself doesn’t know what she will do next. 8

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Quantitatively, intensity means the square of the matter field’s amplitude.

The Quantum Idea

The predictability of the statistical patterns shows that matter waves are predictable, even though individual impacts are not. In 1926, Austrian physicist Erwin Schroedinger (Figure 15) invented a method of predicting the motion of matter waves. Schroedinger began with a well-known formula that had been used to describe waves in other situations not involving quantum physics. Into this wave formula, he inserted de Broglie’s relation l = h>my, along with some judicious guesswork. The result was a formula, now called Schroedinger’s equation, that correctly describes the motion of the matter wave for electrons or any other material particles in a wide variety of situations. Most important historically, Schroedinger showed that his equation could be applied to electrons within atoms and that the predicted results agree with atomic experiments. CONCEPT CHECK 8 During the double-slit experiment using a beam of neutrons, the region between the slits and the screen contains (a) a matter field; (b) individual neutrons; (c) an EM field; (d) a stream of photons; (e) none of the above. American Institute of Physics/ Emilio Segre Visual Archives Figure 15

© Sidney Harris, used with permission.

Erwin Schroedinger. He invented the equation that predicts the statistical pattern, or matter wave, in a wide variety of situations involving microscopic material particles.

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The Quantum Idea Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions

22. What do we mean when we say that matter fields are quantized?

THE QUANTUM REVOLUTION

QUANTUM UNCERTAINTY

1. What is quantum physics? 2. Describe at least one way in which the philosophical implications of quantum physics differ from those of Newtonian physics.

QUANTUM RADIATION 3. Describe the double-slit experiment with light and its outcome. 4. What is an electromagnetic field? 5. If we perform the double-slit experiment with dim light and a short exposure time, what will we see on the screen? 6. Following up on the preceding question, what will we see after a longer exposure time? 7. What do we mean by a quantized electromagnetic field? 8. How big is the smallest allowed energy increment in a quantized EM field? 9. What do we mean by a quantum (or energy quantum) of the EM field? 10. What is a photon? What is its speed? Its rest-mass? 11. Why don’t we normally notice that light is made of photons? 12. How does quantum uncertainty enter into the double-slit experiment with light? 13. How does quantum nonlocality enter into the double-slit experiment with light?

QUANTUM MATTER 14. Can a single electron have a wavelength? 15. How do we know that material particles are associated with waves? 16. What name do we give to the waves that are associated with material particles? 17. Which detects the smallest objects: a visible light microscope or an electron microscope? Why? 18. Describe the double-slit experiment with electrons and its outcome. 19. If we perform the double-slit experiment with electrons using a low intensity beam and a short exposure time, what will be see on the screen? 20. Following up on the preceding question, what name do we give to the individual impacts? 21. What evidence is there that a field called a “matter field” exists?

23. Describe an example in which identical causes do not result in identical outcomes. 24. How does quantum uncertainty differ from the ordinary uncertainty in the outcome of a coin flip?

Conceptual Exercises THE QUANTUM REVOLUTION 1. Name the two revolutionary physics theories of the first decade of the twentieth century. 2. What are some practical ways in which quantum physics has impacted modern life?

QUANTUM RADIATION 3. How do we know light is quantized? 4. In what sense are EM fields “digital” rather than “analog”? 5. A photon impact appears on the screen in the double-slit experiment with light. What happens to the EM field? 6. We don’t ordinarily notice photons. Suppose that Planck’s constant were much larger than it actually is. Would we then be more likely, or less likely, to notice photons? 7. Which has higher energy: a photon of red light or a photon of yellow light? 8. Which has lower energy: a photon of ultraviolet radiation, or a photon of infrared radiation? 9. In the double-slit experiment with light, are tiny photons actually coming through the slits? What is coming through the slits? 10. When we greatly dim the light used in a double-slit experiment, we don’t simply get a dimmer interference pattern. What do we get? 11. Suppose a red light beam has a variable intensity, or brightness. As you increase the intensity, do the energies of the individual photons increase, decrease, or remain the same? 12. In the preceding question, does the number of photons emitted each second increase, decrease, or remain the same? 13. As you increase the frequency of a light beam, does the color change? Do the energies of the individual photons increase, decrease, or remain the same?

From Chapter 12 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Quantum Idea: Problem Set 14. In the preceding question, do the speeds of the photons change? 15. What kind of waves are demonstrated by the experimental result shown in Figure 2? Waves in what (what is the medium called)?

27. Arrange these in order from shortest to longest wavelength, assuming that they all have the same speed: helium atom, automobile, DNA molecule, electron, neutron, baseball. 28. If a “proton microscope” could be devised, how would you expect its wavelength to compare with the wavelength of an electron microscope?

QUANTUM MATTER

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QUANTUM UNCERTAINTY 29. When you flip a coin, the outcome is uncertain. Does this arise from quantum uncertainty? Explain. 30. What is the percentage probability of getting two heads in a row in fair coin tosses? How could you experimentally test this prediction? 31. In the double-slit experiment with electrons, is the impact point predictable? 32. In the double-slit experiment with electrons, are there any points where we can predict that an electron will certainly not hit? 33. What is predictable in the double-slit experiment with electrons? 34. Would the answers to the preceding three questions be different if we were talking about photons instead of electrons? 35. List at least two differences between Newtonian physics and quantum physics.

Problems QUANTUM RADIATION 1. A light source emits two colors simultaneously: orange and violet. Which color has the higher energy per photon?

Claus Jonsson/Art Hobson

Art Hobson

16. What kind of waves are demonstrated by the experimental result shown in Figure 9? Waves in what? 17. Which has a shorter wavelength, an electron or a proton moving at the same speed? 18. Which has a shorter wavelength, a slow electron or a fast electron? 19. Suppose we use a very low intensity beam in the double-slit experiment with electrons, so low that only one electron appears per minute. Will we see an interference pattern on the screen? What will we see? 20. List some similarities between an electron beam and a light beam. 21. List some similarities between an electron and a photon. 22. List some differences between an electron and a photon. 23. The impact point of each electron is unpredictable in the double-slit experiment with electrons. What is predictable? 24. If an electron traveling through a double-slit apparatus strikes directly behind slit A, is it correct to say that the electron came through slit A? 25. If electrons behaved only like particles and not like waves, would you observe an interference pattern in the double-slit experiment? 26. You don’t notice the wave aspect of a pitched baseball. Is this because the baseball’s wavelength is very long or because it is very short?

Figure 2

Figure 9

The double-slit experiment with light: experimental result.

A wave-interference pattern made by electrons.

The Quantum Idea: Problem Set 2. In the preceding problem, the frequencies are 5 * 1014 Hz (orange) and 7 * 1014 Hz (violet). Find the energies of the photons. 3. Which has greater energy, a microwave photon or a visible photon? About how many times greater? 4. You charge an object by rubbing it, and then shake it at 1 Hz, creating EM radiation. How much energy does each photon carry? 5. How much energy does one photon of 1024 Hz gamma radiation carry? 6. MAKING ESTIMATES About how many visible photons would be needed to have enough energy to lift a 1 newton (about 1/4 pound) weight through 1 meter? 7. MAKING ESTIMATES About 10 visible photons are needed to cause a single photosynthesis reaction in living plants. About how much energy is carried by these 10 photons? 8. MAKING ESTIMATES The human eye can detect as few as 10,000 photons per second entering the pupil. About how much energy is this per second?

QUANTUM MATTER 9. If you double the speed of a proton, how does this affect its wavelength? 10. How would the wavelength of a proton compare with the wavelength of a deuteron (a proton and neutron held together by nuclear forces), assuming that both the proton and the deuteron have the same speed? 11. An electron and a proton are moving at the same speed. Which has the longer wavelength? How much longer? (Protons are about 1800 times more massive than electrons.) 12. Suppose we fire a high-velocity pellet gun that accelerates 1 gram (10–3 kg) pellets to speeds of 1000 m/s (three times the speed of sound). Find the wavelength of the pellet’s matter wave. 13. Find the wavelength of an electron that strikes the back of a TV screen at a speed of 0.1c. The mass of an electron is 9.1 * 10 - 31 kg. 14. Individual electrons have been slowed down to speeds as low as several centimeters per second. The mass of an electron is 9.1 * 10 - 31 kg. What is the wavelength of a single electron moving at 0.1 m/s (10 cm/s)? Express your answer in millimeters. 15. In a recent experiment, sodium atoms were cooled until they were moving at only a few meters per second. The mass of a sodium atom is 38 * 10 - 27 kg. What is the wavelength of a single sodium atom moving at 2 m/s? Express your answer in millimeters.

Answers to Concept Checks 1. 2. 3. 4.

(b) and (d) Yellow has the highest frequency, (a). (a) Each photon must strike somewhere within the interference pattern, even though that pattern has not yet been revealed because only a single photon has struck the screen, (b). 5. (d) 6. The reasoning is the same as in Concept Check 4, (b).

7. (c) and (d) 8. (a)

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Quantum physics, and the special theory of relativity. 3. When the light is dim enough, it makes tiny particle-like impacts on a viewing screen. 5. The EM field loses one quantum, or one increment, of energy. 7. Yellow, because its frequency is higher. 9. No. An EM field is coming through the slits. 11. The energies of individual photons remain the same because the frequency remains the same and the energy of each photon is hf. 13. Yes, the color is directly related to the frequency. The energies of individual photons increase because the energy of a photon is hf. 15. Electromagnetic waves. The medium is the electromagnetic field. 17. A proton has the shorter wavelength because wavelength equals h/mv and the proton has the larger mass, m. 19. After lots of minutes, the pattern of impacts will form an interference pattern. However, if the visible effect of the impacts lasts less than a minute, we’ll visually see only individual impacts (adding up, over many minutes, to the interference pattern). 21. Both are quanta of a field (EM field and matter field). Both impact a viewing screen or other surface as though they were tiny particles. 23. The overall interference pattern formed by many electron impacts is predictable. 25. No, “pure” particles that come through one or the other slit would not give an interference pattern. 27. Automobile, baseball, DNA molecule, helium atom, neutron, electron. 29. No, a coin flip obeys Newtonian physics (to a very good approximation), and so it is in principle predictable. 31. No, it has built-in quantum uncertainties. 33. The shape of an overall interference pattern obtained after a large number of impacts is predictable. 35. Newtonian: The future is predictable from the present, matter is made of tiny particles, Newton’s laws of motion are valid, the energy of a system varies smoothly over a continuous range. Quantum: The future is not predictable, matter is made of fields, Newton’s laws are not valid (except for the law of inertia), energy is quantized (it can assume only certain specific values). Problems 1. Violet, because E = hf and f is higher. 3. Visible. Microwaves have frequencies of about 1011 Hz and visible photons have frequencies of about 5 * 1014 Hz. The ratio of these frequencies is 5 * 103, or 5000, so a visible photon has about 5000 times more energy than a microwave photon.

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The Quantum Idea: Problem Set 5. E = hf = (6.6 * 10 - 34 J>Hz) * (1024 Hz) =

6.6 * 10 - 10 J. 7. Visible light has a frequency of around 1015 Hz, so the energy of the 10 photons is about 10 hf = 10 * (6.6 * 10 - 34 J>Hz) * (1015 Hz) = 6.6 * 10 - 18 J. 9. This halves its wavelength. 11. The electron has the smaller mass, so it has longer wavelength. About 1800 times longer.

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13. Speed = 0.1c = 3 * 107 m>s

l = = = 15. l = = =

h>my (6.6 * 10 - 34 J>Hz)>(9.1 * 10 - 31 kg * 3 * 107 m>s) 2.4 * 10 - 11 m h>my (6.6 * 10 - 34 J>Hz)>(38 * 10 - 27 kg * 2 m>s) 8.7 * 10 - 9 m = 8.7 * 10 - 6 mm (a few millionths of a mm)

The Quantum Universe

From Chapter 13 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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In order to understand atomic structure, we must accept the idea that the future is uncertain. It is uncertain to the extent that the future is actually created in every part of the world by every atom and every living being. This point of view, which is the complete opposite of machinelike determinism, is something that I believe should be realized by everyone. Edward Teller, Physicist

T

his chapter delves more deeply into quantum physics. Section 1 takes a closer look at quantum uncertainties and presents the uncertainty principle. Section 2 discusses the surprising effect of macroscopic observation on the behavior of microscopic systems. Section 3 takes a closer look at quantum nonlocality, which could lay claim to being the oddest notion that has cropped up yet in physics. Sections 4 and 5 ponder the kind of reality that quantum physics describes and ask how quantum physics affects, or might in the future affect, the Newtonian worldview that still pervades modern culture. Finally, Sections 6 and 7 study perhaps the most significant practical application of quantum physics: the quantum atom.

1 THE UNCERTAINTY PRINCIPLE: THE FUTURE IS NOT DETERMINED BY THE PAST One of quantum theory’s most characteristic features is the microworld’s inherent quantum uncertainty. That is, identical physical conditions often give rise to varying and thus unpredictable observed outcomes. It’s a feature that’s radically at odds with the predictably of nature according to Newtonian physics. You also saw that, despite this uncertainty, the overall statistics of large numbers of outcomes follows predictable patterns. German physicist Werner Heisenberg (Figure 1) found, in 1927, that quantum uncertainty can be quantified. To get a feel for Heisenberg’s argument, consider a quantized matter field containing enough energy for just one electron, moving through empty space along a direction that we will call the x-axis. As you know, the matter field’s intensity at any particular point represents the probability that an electron will be found at that point. Matter fields are spread out in space and generally have a wavelike character,

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as shown in Figure 2. In quantum physics, this figure is the natural way to represent the matter field for an individual particle such as an electron. I will call a matter wave such as is shown in Figure 2 a wave packet. The range of possible positions is indicated in the figure by the symbol ¢x (“delta x”). Keep in mind that there is no tiny particle called “an electron” traveling with, or in, the wave packet. Rather, the electron is the wave packet. The spread-out wave packet is a single quantum, a single parcel of matter field energy. It contains the total energy, and therefore the total inertial mass, as well as the other features such as charge, of a moving electron. “Particles” such as “one electron” are not really particles at all; they are quanta of spread-out fields, such as the wave packet shown. It’s only when the wave packet interacts with another system (such as a viewing screen) that the packet collapses to impart a tiny, particle-like impact. ¢x is the range within which such an impact is likely to occur. Quantum theory (the Schroedinger equation) predicts that a wave packet cannot be at rest. Furthermore, a wave packet cannot just move at a single velocity; it must instead move with a range of different velocities.1 This means that not only is an electron’s position uncertain, its velocity is also uncertain. A particle’s range of possible velocities is abbreviated ¢v. So a single moving electron (or any other material particle) has two kinds of uncertainties, ¢x and ¢v. Let’s compare one wave packet A with another wave packet B that has been squeezed into half of A’s length (Figure 3). As you can see, B’s wavelengths are shorter. But de Broglie’s formula, l = h>mv, tells us that shorter wavelengths correspond to higher velocities. So wave packet B represents a higher-velocity electron than does packet A. And it turns out that larger velocities mean a larger uncertainty in velocity and that in fact the halving of ¢x implies a doubling of ¢v.2 This illustrates a general feature of quantum physics: Whenever a particle’s ¢x is squeezed by some amount, ¢v expands by the same amount, and vice versa: Squeezing ¢v expands ¢x. Quantitatively, Heisenberg showed that the product of ¢x and ¢v remains unchanged. Working through these ideas in detail, Heisenberg found that this rule holds for every material particle (not just electrons) in every physical situation (not just when moving freely). Here is his result:

American Institute of Physics/ Emilio Segre Visual Archives Figure 1

Werner Heisenberg. Using the Schroedinger equation, he derived the famous uncertainty principle according to which every material particle has inherent and irreducible uncertainties in position and velocity. Thus, in the microscopic world, the future is not entirely determined by the past.

The Uncertainty Principle The position and velocity of every material particle are uncertain. Although either uncertainty can take on any value, its product must approximately equal Planck’s constant divided by the particle’s mass. In symbols, (¢x) # (¢v) L h>m

where h is Planck’s constant and m is the particle’s mass.3

1

2

3

Here’s why: According to the branch of mathematics known as “Fourier analysis,” a wave packet is a superposition of many different infinitely long waves, each having a definite wavelength. But de Broglie’s formula l = h>mv tells us that different wavelengths correspond to different velocities. Thus, a wave packet has a range of possible velocities. Here’s why: Since B is squeezed to half of A’s length, B’s wavelengths are half as long as A’s. So B’s component velocities are twice as big as A’s, because l = h>mv says that wavelength and velocity are inversely proportional. So the range of velocities, ¢v, is twice as big for B as for A. More precisely, (¢x) # (¢v) Ú h>4pm. The product can be greater than h>4pm but not less.

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Figure 2

The matter wave representing a single particle whose uncertainty in position is ¢x, moving along the x-axis. A matter wave like this, which is spread out over only a limited distance, is called a wave packet.

x-axis Direction of motion of wave packet

⌬x

Figure 3

Two wave packets, having different values of ¢x . Packet B can be constructed by squeezing packet A to half its size. In this process, all of A’s wavelengths get squeezed to half their original length, which means that the velocities and also the uncertainty in velocity get doubled.

A ⌬x

B

I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed? Werner Heisenberg

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We refer to a particle’s ¢x and ¢v as its uncertainty range. You can visualize a particle’s uncertainty range in a velocity-versus-position diagram (Figure 4). A single point on such a diagram represents a precise position x and velocity v [Figure 4(a)]. Newtonian physics assumes that every object has a precise x and v. For example, the location and motion of the center of a baseball can be described, according to Newtonian physics, by a particular x and a particular v. Newton’s law of motion is basically a method for predicting an object’s future x and v from its present x and v. For example, given the position and velocity of the center of a falling baseball at one time, we can predict the center’s position and velocity at any later time during the fall. But microscopic particles do not have precise positions and velocities, for the simple reason that the so-called “particles” are really quanta of a matter field, spread out over a range of positions and velocities. Quantum theory demands that an object’s position and velocity have uncertainties ¢x and ¢v whose product is roughly h/m. In an x-versus-v diagram, this product is the area formed by the rectangle whose sides are ¢x and ¢v, as shown in Figure 4(b). If for any reason ¢x is reduced, then ¢v must expand to yield the same product ¢x # ¢v, as shown in Figure 4(c). And if ¢v is reduced, ¢x must expand, as in Figure 4(d). Either x or v can be as highly predictable as you like, but if one is highly predictable, the other must be highly uncertain. You can think of these diagrams as rough pictures of a particle’s matter field. Like other physical fields, a matter field is spread out over a range of positions in space, and different parts of the field move at different velocities. An uncertainty range such as Figure 4(b) simply shows those ranges of positions and velocities.

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Particle’s speed v

v

⌬v

x

x

Particle’s position x

⌬x (b) An uncertainty range for a single particle. According to quantum theory, the total area of the shaded region, (⌬x)⭈(⌬v), must be roughly equal to h/m.

(a) A single point on an x-versus-v diagram, such as the point shown here, represents a precise value of both x and v. Quantum theory does not allow such precise values. v

v

⌬v

⌬v

x ⌬x (c) If for any reason ⌬x is reduced, then ⌬v must expand to fill up an uncertainty range having the same area.

x ⌬x (d) And if ⌬v is reduced, ⌬x must expand.

Since the uncertainty principle says that (¢x) # (¢v) L h>m, more massive particles have smaller uncertainty ranges. A proton, with a mass 2000 times larger than an electron’s mass, has an uncertainty range 2000 times smaller (in area) than does an electron (Figure 5). Because x and v are both needed in order to predict an object’s future behavior, a proton is more predictable than an electron. And a baseball, one million trillion trillion times more massive than an electron, is so predictable that quantum uncertainties are negligible (Figure 5). That’s why the macroscopic world is Newtonian! Even a grain of sand is so massive (it contains some 1018 atoms) that quantum uncertainties are negligible. Macroscopic objects such as baseballs and dust grains are predictable, but the atoms, electrons, and protons of which they are made are not predictable. Suppose a particle’s ¢x has been squeezed into a very small range. This particle must then have a large ¢v. But you can’t have a large ¢v without at the same time having a large v; for instance, if ¢v were 1000 km/s, the lowest (slowest) uncertainty range for v alone would be 0 to 1000 km/s, so the average v must be at

Figure 4

Position and velocity uncertainty ranges.

This again emphasizes a subjective element in the description of atomic events, since the measuring device has been constructed by the observer. . . . We have to remember that what we observe is not nature in itself but nature exposed to our method of questioning. Werner Heisenberg

The belief in an external world independent of the perceiving subject is the basis of all natural science. Einstein

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Uncertainty range of the center of a baseball (greatly enlarged)

v

Proton’s uncertainty range

Electron’s uncertainty range

Figure 5

More massive objects have smaller uncertainties. That’s why quantum uncertainties are negligible for such macroscopic objects as baseballs.

x

least 500 km/s. So when ¢v is large, v must be large too. This means that a highly confined particle ( ¢x small) must move fast. The smaller the confinement, the larger the velocity. The uncertainty principle will not permit the microscopic world to sit still! For example, protons and neutrons in a nucleus must move at some 10% of lightspeed because nuclear forces confine them to such a tiny region within the atom. Quantum uncertainties are of considerable practical importance. As you’ll see in Section 3, they might someday be used to practical advantage in quantum computers. Quantum uncertainties lie at the heart of the nuclear phenomenon known as radioactive decay and cause this process to be fundamentally unpredictable. When a child is conceived, the DNA molecules of each parent are randomly combined in a process in which quantum phenomena play a role. Thus, quantum uncertainty played a role in your genetic inheritance. Microscopic quantum uncertainties during the big bang formed the “seeds” for the later gravitational gathering of matter into the great clusters of galaxies that you see today. The expansion of the universe stretched these initially tiny seeds to astronomical sizes, and matter gravitated toward these seeds. Today we see, forever imprinted on the overall layout of the universe, microscopic quantum uncertainties writ large. We are, in these and many other subtle ways, in the hands of the god who plays dice. CONCEPT CHECK 1 Which of these has the largest quantum uncertainties? (a) Proton. (b) Automobile. (c) Helium atom. (d) Water molecule. CONCEPT CHECK 2 Just after the matter wave passes through the slits, its uncertainty range (a) covers the entire range of positions from above slit A to below slit B in the figure; (b) is broken into two separate pieces, one of them behind slit A and the other behind slit B; (c) is located either behind slit A or behind slit B, but not both.

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CONCEPT CHECK 3 A particle having a very precise velocity has a wave packet that (a) occupies a wide region of the x-axis; (b) occupies only a narrow region of the x-axis; (c) moves with a wide variety of velocities; (d) moves with a narrow range of velocities.

2 THE EFFECT OF DETECTORS Einstein was among those who found quantum theory too counterintuitive to believe. He and two other physicists showed in 1935 that quantum theory predicts nonlocal phenomena that are, as he put it, so “spooky” that “no reasonable definition of reality could be expected to permit this.” Einstein and others took these predictions as evidence that the theory needed repair. However, Einstein did not suggest a way to put quantum theory’s spooky predictions to an experimental test. Because quantum theory proved so gloriously successful in practice, few physicists worried much about such untested objections. Among those who did worry were David Bohm and John Bell (Figure 6). Bohm began publishing his analysis during the 1950s. Working from Bohm’s ideas, Bell showed in 1964 that some of quantum theory’s spooky predictions are experimentally testable. John Clauser (Figure 6) carried out the first such test in 1972 and found that contrary to the expectations of Einstein and others, the spooky phenomena actually occur! In 1982, Alain Aspect (Figure 6) refined Clauser’s test so as to leave little doubt that the real world is stranger than Einstein and others had thought. The spooky predictions are related to sudden alterations in the quantized EM and matter fields. Consider, for example, a single freely moving electron approaching a viewing screen. As you’ve seen, up until the moment of impact the “electron” is really a wave packet—a ripple in a matter field—approaching the screen; the impact that we call “an electron” is really just the deposit of a quantum of energy from the matter field to the atoms of the screen. The packet can be quite spread out, stretching even over macroscopic distances. Now think about what happens when this 1 cm wide wave packet for a single electron hits the viewing screen: The interaction between the packet and one of the atoms of the screen causes a single “grain” (similar to a sand grain) of the screen to emit a burst of light. At this instant, the entire spread-out wave packet suddenly alters radically because the entire energy of the quantized packet must be delivered to a single atom. The electron’s uncertainty range is now confined to one atom within the grain that emitted the burst of light, about a billionth of a meter in size. The packet suddenly becomes 100 million times smaller. Such an instantaneous reduction in the size of a wave packet upon detection of a particle is called collapse of the wave packet. There has always been lots of controversy about this process and about other cases in which microscopic particles interact with macroscopic devices such as viewing screens. Such a process is called a measurement for obvious reasons, but this term need not refer only to cases in which a human observer is actually present to record the measurement. It refers, rather, to any situation in which a microscopic particle causes a macroscopic event such as a visible flash, whether or not a human is present to observe it.

The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole. Werner Heisenberg

Marvelous, what ideas the young people have these days. But I don’t believe a word of it. Einstein, After Heisenberg’s 1927 Lecture Enunciating the Uncertainty Principle

I cannot seriously believe in [the quantum theory] because it cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. Einstein

Attempts have been made to add laws to quantum mechanics to eliminate uncertainty. Such attempts have not only been unsuccessful, they have not even appeared to lead to any interesting results. Edward Teller

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Figure 6

Four explorers of quantum theory: Clockwise from upper left: David Bohm, John Bell, Alain Aspect talking with Bell (r.) and physicist Albert Messiah (l.), John Clauser.

Mark Edwards/Still Pictures/Whole Earth Photo Library; CERN/Photo Researchers, Inc.

The Quantum Universe

Collapse of the wave packet can occur over large regions. For example, the EM field for each wave packet from any very distant star is spread out over many kilometers by the time it reaches Earth. British physicist Robert Hanbury Brown confirmed this prediction in 1965 by measuring, for the light from an individual star, interference patterns that were over 100 meters in diameter. Despite each photon wave packet’s large size, the field for each photon instantaneously collapsed to atomic dimensions when the photon hit a detector. Collapse of the wave packet is controversial among physicists because of its instantaneous and “nonlocal” character: The entire wave packet vanishes, simultaneously, over an extended region. I’ll discuss nonlocality further in the next section. The double-slit experiment with electrons offers interesting examples of quantum measurement issues. Based on Newtonian ways of thinking, one might suppose that we could place a detector near one or both of the slits and thus detect individ-

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ual electrons coming through one or the other slit. What will such a detector observe, and what will be the pattern on the viewing screen? Before answering these questions, we need to see what happens when we completely close either one or the other slit. With one slit closed, the wave packet for each electron must obviously come through the other slit, either slit A or slit B. Figure 7 shows each of these single-slit patterns: Part (a) is the pattern when only slit A is open, and part (b) is the pattern when only slit B is open. Each pattern shows the intensity of an individual electron’s wave packet (the intensity of the matter field, or the probability that the impact will occur at various points on the screen) as the packet approaches the screen. There is no trace of interference. Schroedinger’s equation predicts these patterns, and they can be observed experimentally as the statistical result obtained after millions of electron impacts. Part (c) is simply the sum of the first two graphs. It shows what would happen if each electron wave packet in the double-slit experiment actually came through one or the other slit and not both. Finally, part (d) shows what actually happens when both slits are open, but there is no detector to see which slit the electron goes through. What actually happens is an interference pattern. Now you’ll see what happens in the double-slit experiment when a detector determines the slit through which the electron came. Figure 8 shows the detector (it’s supposed to look like an eye seen from the side) located at point D just behind slit B. Such detectors are usually electromagnetic devices designed to have as little effect as possible on the motion of the electron, allowing it to pass nearly unimpeded to the viewing screen. As long as such a detector is switched off so that it cannot detect electrons, the usual interference pattern appears on the screen [Figure 8(a)]. But when the detector is switched on, it immediately begins indicating that about half of the electrons are coming through slit B and half are not! This makes us think that

A

B

(a)

(b)

(c)

(d)

Figure 7

Results of different single-slit experiments with electrons. (a) The pattern of electron impacts on the viewing screen for the case that slit A only is open and slit B is closed. (b) The pattern for the case that slit B only is open and slit A is closed. (c) The patterns (a) and (b) added together to show what would happen in the double-slit experiment if each electron wave packet simply came through one or the other slit rather than through both slits. (d) The actual result of the double-slit experiment.

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Newtonian physics has it right after all: Electrons do come through one or the other slit but not both. However, precisely when the switch is turned on, the interference pattern vanishes and the “noninterference pattern” (b) appears on the screen. This is precisely the pattern that we saw, in Figure 7(c), should be the net effect of electrons coming through either slit A or slit B but not both! Apparently, detectors have strong and instantaneous effects on matter waves: When the “slit detector” is turned off, each electron comes through both slits; turning on the detector causes each electron to come through one or the other (but not both) slits. Can the effect of the detector be reduced? For example, researchers might place the detector further from the slits (Figure 9). Again, the entire pattern shifts from (a) to (b) as soon as the detector is switched on. Extremely fast switching devices have even been devised to turn on the detector only after an electron must have already come through the slits. And still, pattern (a) switches to pattern (b) Figure 8

Merely switching on a particle detector at a point such as D causes the matter field to jump from the interference pattern (a) to the noninterference pattern (b).

A

⫹ ⫺

B

D

(a)

(b)

Figure 9

Even if the detector is placed far behind the slits, near the screen, the pattern still jumps from pattern (a) to (b) whenever the detector is activated.

A

⫹ ⫺

B

D (a)

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(b)

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as soon as the detector is switched on! The detection device causes the packet to instantly shift from the interference pattern to the noninterference pattern after it has already passed through the slits. This strange influence of the detector is actually predicted by the standard rules of quantum physics, and observed in experiments. CONCEPT CHECK 4 Suppose that, in Figure 8, two detectors were used, one behind each slit. The pattern that the matter field makes on the screen would then be (a) an interference pattern that is broken into two separate parts, one behind each slit; (b) a noninterference pattern that is broken into two separate parts, one behind each slit; (c) an interference pattern like the one shown in the figure; (d) a noninterference pattern like the one shown in the figure.

3 QUANTUM ENTANGLEMENT: SPOOKY ACTION AT A DISTANCE So far, we’ve discussed quantum uncertainty and nonlocality only in situations involving separate particles that don’t interact with each other. Recall that quantum nonlocality refers to the instantaneous alteration of an entire spreadout EM field or matter field, even at some distance from the interaction (energy exchange) that caused the alteration. Now we’re going to look at the consequences of quantum uncertainty and nonlocality when applied to two or more particles. We’ll just consider two particles, but the same conclusions apply to any number of particles. If two particles physically interact with each other, quantum theory predicts that their matter fields (remember that a particle is its matter field) usually become intimately connected and remain connected even after the particles have separated. The two particles become a single quantum system with a single shared matter field. Such particles are said to be entangled. Figure 10 is a way to picture this. The figure shows wave packets for two particles. The two packets are entirely separate initially, then they move close enough together to interact, and then they separate. Quantum physics predicts that their matter waves get mixed up with each other during the interaction so that, even after separation, the two packets form a single two-particle wave packet. I’ve tried to indicate this in Figure 10 by coloring the two initial packets black and green. When they separate, part of each packet goes to the right and part of each packet goes upward. After the interaction, both packets contain both black and green and are really two “subpackets” of a single black-and-green packet, even though the two subpackets might be widely separated in space. Entangled particles are part of a single quantum object, namely a two-particle wave packet. They form a single thing, but in two different places. Now suppose that one of the two entangled packets in Figure 10 impacts a viewing screen. This wave packet instantly collapses everywhere. But this would have to affect the other wave packet because the two packets really form a single connected packet. This instantly alters the other, second particle, even if the two particles are light-years apart. This is the action at a distance that seemed so “spooky” to Einstein. Experiments since 1972 have amply confirmed the reality of entanglement at distances up to 144 kilometers.

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Particles 1 and 2 entangled

Interaction zone Particles 1 and 2 entangled

Particle 1 before interaction

Figure 10

When two particles interact and then separate, their matter fields usually become entangled. See the text for explanation.

Particle 2 before interaction

One is led to a new notion of unbroken wholeness which denies the classical idea of analyzability of the world into separately and independently existing parts. We have reversed the usual notion that the independent “elementary parts” of the world are the fundamental reality. Rather, we say that the interconnectedness of the whole universe is the fundamental reality, and that the “parts” are merely particular and contingent forms within this whole.

How do we know that nature is nonlocal?4 In 1990, British physicists John Rarity and Paul Tapster performed an entanglement experiment based on double-slit interference. This experiment begins with the creation of two entangled photons (the experiment would be harder to do with electrons, but quantum physics predicts that the result would be the same) whose wave packets then move directly away from each other, as shown in Figure 11. The two packets then pass through separate double-slit apparatuses and, with the help of the mirroring devices shown, impact on separate viewing screens. Rarity and Tapster observed the overall pattern formed by millions of such entangled pairs. As in the ordinary double-slit experiment, each particle’s wave packet goes through both slit A and slit B. If the two particles were not entangled, the left-hand screen and the right-hand screen would each show the usual double-slit interference pattern. Because the two photons move in opposite directions, if they had been ordinary Newtonian particles they would have impacted at identical distances x below the midpoint of the first screen, and y above the midpoint of the second screen (see the figure). That is, x would have been equal to y. But, because of quantum uncertainties, y does not necessarily equal x and the second impact point y can’t be predicted from knowledge of the first point x. In fact, quantum physics predicts that the difference y – x should form a typical interference pattern as shown in Figure 12.

David Bohm

4

358

This experiment was suggested in 1986 by Michael Horne and Anton Zeilinger; a similar experiment was performed by Z. Y. Ou and Leonard Mandel.

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Mirror Particle 1

x

Detection screen for particle 1

Particle 2

A

A

B

B Particle 1

y

Particle 2

Mirror

Mirror

Detection screen for particle 2

Source of two entangled particles

Figure 11

The position-entanglement experiment. Because of their entanglement, particles 1 and 2 coordinate their impact points x and y instantaneously, regardless of the distance between them. The wave packets shown are created at the “source” at the center of the figure. The mirrors only reflect these wave packets and are introduced only to bring each packet back together.

According to Figure 12, the two photons must mutually correlate their impact points x and y so as to make y – x form an interference pattern, despite that fact that neither a precise x nor a precise y even existed (because of the uncertainty principle) prior to impact. Suppose that the experiment were altered slightly to allow the first photon to impact its screen just before the second photon impacts its screen (this would not change the experiment’s outcome). Despite the fact that a precise x doesn’t exist prior to impact, as soon as the first photon impacts its screen at some point x, the second photon’s wave packet (which could be light-years away) must instantly alter itself to just “fit” the first particle’s impact point, as shown in Figure 12. To see the significance of this, suppose that the interference pattern of Figure 12 has high points that are 1 mm apart, so that constructive interference occurs when y – x equals 0 mm, 1 mm, 2 mm, 3 mm, and so forth. Then, after photon 1 impacts at some particular point x, photon 2 must impact preferentially at a point y that differs from x by 0 mm, 1 mm, 2 mm, etc., and must avoid the points that differ from x by 0.5 mm, 1.5 mm, 2.5 mm, etc. How can the second photon “know” which points to hit and which to avoid, when a specific x didn’t even exist prior to the first photon’s impact, and when the two photons are some distance (even light-years) apart? The second photon instantaneously obtains “knowledge” about the first photon’s impact point, and alters its wave packet accordingly, despite their separation. Spooky, indeed!

Maybe this cooperation between different particles across a distance is not spooky. Maybe it’s merely an example of the following common type of correlation between separated events: Suppose I inform Mort in Paris and Velma in Beijing that I’ve mailed one of them a gold coin and the other a silver coin. Without further information, neither one knows which coin they’ll receive. But as soon as Velma opens her envelope she knows immediately what kind of coin Mort received, because the two coins must be different. There’s nothing spooky about this correlation between separated events; it’s due entirely to the prior information that I gave

y–x

0

Number of 2-particle impacts

Figure 12

If, instead of studying x or y separately, we study the difference y – x between the two impact points on the two screens, we get an interference pattern. How does the second photon, impacting at some point y, “know” at which point x the first photon impacted? The second photon instantly coordinates its impact pattern with the first photon’s impact point, despite the fact that the uncertainty principle says that both impact points are uncertain in advance.

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to Mort and Velma. Furthermore, no real physical change occurred in Mort’s coin when Velma opened her envelope. Mort’s coin did not, for example, suddenly change from gold to silver. Quantum entanglement is not like the gold and silver coins because there’s no prior information. Precise positions x and y of the two photons didn’t even exist prior to the impacts. Furthermore, an actual physical change in the second photon—a sudden alteration of its wave packet—occurs when the first photon hits the screen. In 1964, John Bell analyzed this question in quantitative detail and proved that the correlations between entangled particles are not of the ordinary goldand-silver-coin variety. It’s as though Velma’s receipt of a gold coin in Beijing instantaneously caused Mort’s coin in Paris to turn into a silver coin, even though his coin was neither gold nor silver before Velma observed her coin. Here’s a summary of Bell’s conclusion: The Nonlocality Principle Non-locality means that we cannot discuss the different parts of space independently. John Bell

Entanglement is the essential characteristic of quantum physics. Erwin Schroedinger

For me it’s a dilemma. I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. John Bell, Referring to the Implications of Aspect’s Experiment Verifying Nonlocality

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Quantum theory predicts that entangled particles exhibit behavior that can be explained only by the existence of real nonlocal (that is, instantaneous and distant) correlations between the particles. That is, a physical change in one particle causes instantaneous physical changes in all other particles that are entangled with that particle, no matter how far away those other particles may be.

Bell also discovered ways in which the quantum predictions about entanglement could be experimentally tested. Clauser was the first to carry out such tests. Alain Aspect was the first to show that the connection occurs at faster than lightspeed and appears to be instantaneous, just as quantum theory predicts. The “two” particles literally form a single unified object, described by some physicists as a “two-particle.” Two entangled particles do not coordinate their actions by means of communication between them; rather, their actions must be coordinated because they are a single unified object, but in two different places. Such a conclusion might seem to contradict relativity theory’s prohibition on faster-than-light motion. But relativity says only that energy (matter or radiation) cannot travel faster than light. The connections referred to in Bell’s principle do not transfer energy, so Bell’s principle does not contradict relativity. Quantum entanglement is quickly destroyed if one of the entangled particles contacts the external world. In the Rarity-Tapster experiment, for example, the entanglement is destroyed when either particle hits a screen. Despite this fragility, Danish physicists in 1999 proposed a practical method for entangling any number of ions (electrically charged atoms) by trapping them in electromagnetic fields and using lasers to create entanglements between them. This method was used in 2001 to entangle two tiny separated gas clouds, each containing a trillion cesium atoms. The two clouds were only a few millimeters apart and were demonstrated to remain entangled for only 0.0005 seconds, but larger distances and times are expected in the future, perhaps using solid samples rather than gases. Entanglement and uncertainty could lead to powerful quantum computers. Conventional computers are built from many simple individual physical devices such as electronic switches that can have two values, namely “on” and “off.” Such physical devices are called bits and their two states are labeled “0” and “1.” Quantum computers would be built from many individual quantum systems, such

The Quantum Universe

as a single ion trapped in an electromagnetic field, that have two possible quantum states, such as a higher-energy state and a lower-energy state. Such a quantum system is called a qubit and, like ordinary bits, the two quantum states are labeled “0” and “1.” But qubits exploit the quantum nature of these states. To understand this, let’s return to the double-slit experiment where we saw that quantum uncertainties allow each individual electron to come through both slits. In this same sense, quantum uncertainties allow a qubit (such as an ion) to be in both its possible states, 0 and 1, at the same time. Physical operations carried out on such a qubit then operate on both states simultaneously. This doesn’t sound terribly impressive, until you begin to consider the implications of more than a single qubit. Consider two qubits. A conventional computer built from two bits would have four possible states: 00, 01, 10, and 11. The computer can be in only one of these states at any one time. But a quantum computer, with each qubit in both the states 0 and 1, is in all four of its possible states simultaneously, and thus it can perform calculations on all four simultaneously instead of one at a time. And three qubits can be in eight states simultaneously. The number of simultaneous states increases enormously as the number of qubits increases, providing far more computational power. Quantum computers would operate on the quantum states of their qubits by employing “control” qubits that would be connected with the computational qubits via quantum entanglement. If a quantum computer turns out to be feasible, it will be the quintessential quantum device, depending crucially on the two characteristic quantum phenomena: uncertainty and entanglement.

The lesson to be learned from ... the origin of quantum mechanics is that ... somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road. Max Born

CONCEPT CHECK 5 How many simultaneous operations could a 10 qubit quantum computer perform? (a) 10. (b) 100. (c) 8. (d) 64. (e) 512. (f) 1024. CONCEPT CHECK 6 If two electrons are entangled then (a) if one of the particles suddenly alters its wave packet, the other must also; (b) they must exert forces on each other; (c) they will become less entangled as they move farther apart; (d) both are part of a single matter wave; (e) they will become more entangled as they move farther apart.

4 WHAT DOES IT MEAN? QUANTUM REALITY Quantum physics has a well-deserved reputation for being odd. Quantum uncertainty, nonlocality, and the surprising effect of detectors are about as far-removed as you can get from the world described by Newtonian physics. The odd results come from the non-Newtonian view that the world is made not of rigid, unchanging, pointlike particles but rather of continuous fields, and that these fields come in unified parcels or “quanta” of energy. The oddness of quantum physics has stimulated unfounded rumors that there is something paradoxical or even mystical about quantum physics. The simultaneous appearance of wave and particle properties, for example, leads some to believe that it’s impossible to consistently describe what’s really going on in the microworld. But you’ve seen that quantum physics is basically about fields, and that particlelike aspects such as the tiny flashes seen on the screen are really fields spread out over a ¢x of atomic dimensions. There’s no paradox here.

In a completely deterministic world, what we know as free will in humans is reduced to a mere illusion.... According to quantum mechanics, we cannot exclude the possibility that free will is a part of the process by which the future is created. Edward Teller

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As another example, one sometimes hears that quantum physics necessarily involves human observation, especially in connection with the surprising effects of detectors, as though some quantum phenomena couldn’t occur without humans present to witness them. But the detector effect depends only on the interaction between an inanimate macroscopic device called a detector and a microscopic system such as an electron. It occurs perfectly well with no humans present to read the detector. In fact, the detector could be any macroscopic object upon which a microscopic object leaves a permanent mark. For instance, when a cosmic ray hits a moon rock and leaves a permanent mark, a similar “detection” process occurs even though no human is involved. The quantum uncertainty of matter arises because each material quantum, an electron for example, is spread out in both position and velocity simply because it’s a field. When we say that an electron’s position is uncertain, we simply mean that its matter field is spread out over a range ¢x of positions. The electron really has no definite position. In the double-slit experiment with electrons, for example, each electron (each quantum) comes through both slits. Just after passing through the slits, the quantum has two separated parts, one near each slit, yet the entire quantum acts as a single unified object. When it arrives at the screen, its two parts form a spread-out interference pattern that’s seen in the overall pattern formed by many individual interactions. But the quantized nature of the matter field demands that each individual quantum’s energy transfer is “all or nothing,” so all its energy transfers to a single atom. At the instant of the transfer, the entire spread-out quantum (it might be 1 cm wide for example) instantaneously collapses to atomic dimensions. Electrons are still spread-out quanta even after being absorbed by an atom, but with a ¢x that’s now spread over a region of only atomic dimensions. A similar collapse occurs whenever any detector measures the position of an electron or any other particle. The electron wave packet interacts with an atom or molecule in the detector, and thus the packet collapses to a small ¢x around that location. The electron resided all over a much larger region just before the measurement occurred, and the measurement created a position (to within a ¢x of atomic dimensions) for the electron. Measurements partly create the properties they detect. A position measurement creates an (approximate) position, and a velocity measurement creates an (approximate) velocity (Figure 13). The surprising effect of detectors, noted in connection with Figures 8 and 9, happens for reasons similar to the collapse of the wave packet in the double-slit experiment. You’ll recall that each electron (each quantum) goes through both slits so long as the detector is in the “off ” mode, but as soon as the detector is switched on, half the electrons go through slit A and the other half go through slit B. This is because each electron (each quantum) must either entirely interact, or not interact, with the switched-on detector, and the interaction (or non-interaction) causes each quantum to collapse to the vicinity of one or the other slit. Non-locality is written all over these phenomena, even though this section so far has related only to non-interacting particles. But when two or more particles interact, non-locality can become quite explicit via quantum entanglement. Entanglement means that two or more particles share a single wave packet. The two must then behave as a single unified object. If something happens to one of them, the entire two-particle wave packet collapses and so some other corresponding thing must instantaneously happen to the other. This has been demonstrated with pairs of photons.

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Particle’s range after measurement of x: An approximate position x has been created.

Particle’s uncertainty range before measurement: Both ⌬x and ⌬v are large.

Particle’s range after measurement of v: An approximate velocity v has been created.

Figure 13

Position

Quantum physics predicts that any pair of particles that have ever, at anytime in the past, interacted with each other are entangled with each other, although the degree of entanglement might be tiny. In fact, if particles A and B are entangled, and if another particle C then interacts with B, not only will B become entangled with C but A will also become entangled with C. Thus the entire universe, which was created in a single microscopic event—just the sort of thing that creates entangled particles—might be entangled with itself. But such a statement is hypothetical to say the least, because it’s always dangerous to extrapolate the theories of physics to the entire universe. I think that what we will eventually make of all this is still anybody’s guess. We haven’t yet worked out a “post-Newtonian viewpoint” of how the world works, a viewpoint having the philosophical grandeur of the Newtonian clock-like universe, and maybe we don’t need such a viewpoint. There have been attempts to align these quantum phenomena with religious or psychological notions—efforts that have in my opinion been interesting but dubious. In the next section, I’ll discuss a few notions that are directly tied to what we already know about quantum physics.

The effect of a position measurement or of a velocity measurement is to create a position and velocity for the measured particle.

There are two sorts of truth: trivialities, where opposites are obviously absurd, and profound truths, recognized by the fact that the opposite is also a profound truth. Niels Bohr

When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images. Niels Bohr

5 TOWARD A MODERN WORLDVIEW Recall three key features of the Newtonian worldview: Atomism Atoms form the fundamental reality. Newton called them “solid, massy, hard, impenetrable particles” that “never wear or break in pieces.” Predictability The future is hard-wired into the present. Once it got started, the clockwork universe had to evolve precisely as it has evolved, right down to you scratching your nose just now. Analysis Science progresses by separating phenomena into their simplest components and studying those components. Thus we can understand the universe by understanding its simplest component particles.

We shall always be able to imagine other [false] theories—like the boring world of particles governed by Newtonian mechanics. Steven Weinberg, Physicist, in Dreams of a Final Theory

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I don’t think there’s one unique real universe.... Even the laws of physics themselves may be somewhat observer dependent. Stephen Hawking

Contemporary physics denies all three of these Newtonian principles: Atomism Atomism was first contradicted by the electromagnetic field, which is physically real but not made of atoms. The material world is made of matter fields, and matter fields are certainly not made of atoms. In fact, material particles are merely quanta, or energy increments, of matter fields. Far from being solid, hard, and impenetrable, atoms are entirely empty and made only of fields. Their restmass is a consequence of the energy of these fields. Far from never wearing or breaking, atoms can be entirely annihilated. Although energy is indestructible, matter can be destroyed and created. Atoms are not things in the same way that a pea, even a very small pea, is a thing. Predictability Identical causes no longer lead to identical effects. A single radioactive decay, the flash of a photon, and chemical reactions such as those that determine a person’s genetic inheritance, are unpredictable quantum events. The universe is not like a predictable clock. But statistical patterns are predictable, even though single events are not. Analysis The analytic process assumes that it’s possible to divide a phenomenon into parts without changing it. This works well for macroscopic systems, but quantum theory contradicts this notion. For instance, it’s useful to separate the solar system into the sun, planets, and so forth and to consider the ways that each part interacts with each other part. But quantum entanglement implies that we cannot always consider a microscopic system to be made of separable parts. Two entangled particles are so closely connected that it is not possible even to think of them as independent particles. There is a microscopic wholeness that is not obvious to our macroscopic eyes. In short, the quantum worldview asserts that the universe is made of nonmaterial fields, the particles of the microscopic world are merely quantized increments of these fields, the future is inherently unpredictable, and nature is deeply interconnected and indivisible. This is radically different from the Newtonian view of the world as a machine or a clock. Despite more than a century of modern physics, a post-Newtonian worldview is still not in sight, and the metaphor of the mechanical universe continues to deeply and inappropriately influence our culture’s view of physical reality. Will we construct a scientifically accurate and humane worldview that can sustain us in the modern age? Humankind has barely scratched the surface of this task.

6 HOW DO WE KNOW? OBSERVING ATOMIC SPECTRA So far, we have presented the fundamental principles of quantum physics and their significance. Now let’s study perhaps the most significant practical example of quantum physics: the quantum atom. I’ll begin by presenting what scientists know experimentally, and how they know it. The most accurate scientific measurements known are made with spectroscopes, devices that measure the frequencies or wavelengths present in radiation. Figure 14 shows how a spectroscope studies the visible radiation emitted by a light source such as a heated, glowing gas. Radiation from the source passes through a single thin slit and emerges as a narrow beam. This beam passes through a glass prism or other device that can separate the light beam’s different frequencies (colors). Light beams bend when they pass from one medium into another, such as from air into glass. You might have noticed this effect in a pool of water, where partly submerged objects appear to bend at the water’s surface. The reason a prism separates a light beam’s frequencies is that different

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Red

Narrow beam of radiation containing various frequencies Radiation source such as a heated glowing gas

Yellow

Prism

Violet Partition with a thin slit in it

Viewing screen or photographic film

Figure 14

One type of spectroscope.

frequencies bend by different amounts at each glass surface. This separation of frequencies is also seen in a rainbow, where each raindrop acts like a small prism for sunlight. By the time the light beam exits the far side of the prism, it has separated into many beams, one for each frequency present in the original beam. A screen or photographic film intercepts all these light beams and displays their various colors. Each beam’s frequency or wavelength can be determined by measuring the position at which it strikes the screen. The set of frequencies measured in such an experiment is called the spectrum of the source that emitted the radiation. Different kinds of spectroscopes operate in every part of the electromagnetic spectrum. For example, a radio receiver is a kind of spectroscope for separating and detecting the frequencies of radio radiation present in a room. Spectral measurements yield an enormous quantity and variety of information. For instance, by placing a spectroscope at the viewing end of a telescope, astronomers can infer information about the mass, temperature, motion, chemical composition, and other properties of stars and galaxies. Most of our data about the microscopic world come from spectral measurements. A glowing solid or liquid, such as a lightbulb’s metal filament heated to 3000°C, emits a continuous spectrum, one that contains an unbroken range of visible frequencies and spreads out in a continuous band of color. Rainbows show the continuous spectrum of the sun. But surprisingly, if a dilute (low pressure) gas is heated until it glows, it emits a spectrum that is not continuous. Instead, it is restricted to a limited number of precise frequencies, each frequency appearing on the screen as a narrow slit-shaped line (Figure 14). Such a collection of precise separated frequencies is called a line spectrum. Figure 15 shows a continuous spectrum and four line spectra from four different gases. As you can see, the line spectra for different gases are different. Because each gas has its own characteristic spectrum, it’s possible for spectroscopy to identify different gases. This is, for example, how we know the chemical compositions of stars.

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Figure 15

The continuous spectrum created by an incandescent bulb and the line spectra produced by several different kinds of gases: sodium (Na), mercury (Hg), hydrogen (H), and helium (He). Frequency increases from left to right.

Atoms are completely impossible from the classical [Newtonian] point of view. Richard Feynman

Heating is one way to excite a gas, in other words, to cause it to emit radiation. Most gases glow once they reach temperatures above about 2000°C. Flames are glowing gases of this sort, heated by combustion. The sun’s light comes from hot gases on its visible surface, which has a temperature of 5500°C. A second way to excite a gas is to send an electric current through it. This process, called electric discharge, creates the light seen in neon tubes, mercury or sodium vapor bulbs, sparks, and lightning strokes. Electric discharge tubes containing a dilute gas can be used to study the gas’s spectrum (Figure 16). How can we explain the observed spectra? As you know, when any substance is heated, the random kinetic energy of its atoms increases. The Greek model of the atom offers no reason why this should cause materials to glow, but the planetary model of the atom does: Heating energizes the subatomic parts of the atom, some of these parts are electrically charged, and these vibrating and orbiting charged particles should send out EM radiation. But why do gases emit line spectra rather than continuous spectra? Why are only some wavelengths emitted, rather than all wavelengths? What determines which wavelengths are emitted? The planetary atom offers no clue. There is an even more glaring problem with the planetary atom. As explained in Figure 17, an orbiting electron can be thought of as vibrating along two directions at once. But you know that vibrating charged particles emit radiation, so an orbiting electron should radiate electromagnetic energy all the time! But observation shows that atoms do not radiate all the time. Worse yet, if an electron did radiate all the time, it would have to continually lose energy, which would cause it to spiral into the nucleus and cease orbiting. So the planetary model predicts that atoms should collapse! Something’s wrong. One can imagine a universe in which Newtonian physics would be correct even down to the smallest sizes, but it would be a pretty boring place. Atoms could not exist, so there would be no chemistry, so life would be impossible. The universe would be a predictable, lifeless, machine. CONCEPT CHECK 7 You might have noticed that as you heat a metal hot plate, it first glows dark red and then becomes brighter and whiter. Just before it begins to glow, we might expect such a hot plate to emit (a) ultraviolet radiation; (b) infrared radiation; (c) no radiation at all.

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x

⫹

⫺

Figure 16

Figure 17

An electric discharge tube containing a dilute gas. With a large enough charge on the two electrodes at the ends of the tube, the electrodes discharge by forcing electrons off the negative electrode. These electrons excite atoms of the gas by colliding with them as the electrons move through the tube toward the positive electrode. The gas atoms then lose their energy of excitation by emitting photons having the characteristic frequencies of these atoms.

An orbiting electron (black circle) can be thought of as making two vibrational motions: When viewed from below, it appears to be vibrating along the x-axis (green circle), and when viewed from the side, it appears to be vibrating along the y-axis (white circle).

CONCEPT CHECK 8 As the hot plate in the preceding Concept Check goes from dark red to white, its spectrum would (a) change from a spectrum containing only red lines to one containing only white lines; (b) change from a spectrum containing only red lines to one containing many different colors; (c) change from a dim continuous red spectrum to an intense continuous white spectrum; (d) change from a dim continuous red spectrum to an intense continuous spectrum that included all the colors.

7 THE QUANTUM ATOM To see how quantum physics describes atoms, we’ll examine only the simplest atom, hydrogen, made of one proton and one electron. Because the electron is 2000 times less massive than the proton, it does nearly all the moving, orbiting in the electromagnetic field of a nearly stationary proton. To a good approximation, you can ignore the proton’s motion, treating it as a tiny material particle at rest. The quantum model of the atom describes the electron’s matter field. Imagine a hydrogen atom that’s been at rest and isolated for some period of time. Since there is no reason for anything to be changing in such an atom, you would expect the electron’s matter field to have a stationary, unchanging shape. A detailed mathematical study of the Schroedinger equation for a hydrogen atom yields precise predictions as to the allowed shapes, or patterns, for the electron’s matter field. There turn out to be many such allowed patterns. Figure 18 is one way of picturing a few of these quantum states of the hydrogen atom. Each of the 10 patterns

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(a) z z

(c)

(d)

(b) z

z

z

(g)

(e) (f) z

z z

(j)

(h)

(i)

Figure 18

Patterns of the microworld. Ten different allowed matter waves, or quantum states, for the electron in a hydrogen atom. If the electron’s position were measured, it would have a greater probability of being found in the darker regions where the matter field is more intense.

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shown is an allowed pattern for the electron’s matter field. Darker regions are regions of higher intensity, and unshaded regions are regions of low or zero intensity. To visualize the full three-dimensional patterns, imagine rotating the twodimensional diagram around the vertical z-axis shown in each diagram. Recall what the intensity of a matter field means. If you measure an electron’s position sufficiently precisely, you’ll find it to be at some fairly precise point x within the hydrogen atom. The intensity of an electron’s matter field at any particular point x is the probability that, when a sufficiently precise measurement is made, the electron will be found to be at that point x. Briefly, the electron is more likely to be found in the darker regions of Figure 18 and less likely to be found in the lighter regions. However, don’t let the language of the preceding sentence mislead you into thinking that “the electron” was actually at point x before the measurement was made; as you know, “the electron” is a field quantum and the position measurement creates a position x for it. Before the measurement, the quantum had one of the shapes shown in Figure 18. Let’s discuss some of these shapes. State (a) occupies a smaller volume than does any other state. In this state, the electron is highly likely to be found close to the nucleus and is equally likely to be found in any direction out from the nucleus (upward, downward, to the left, etc.). State (b) is larger, so the electron is likely to be found farther from the nucleus than is an electron in state (a). State (b) has an interesting gap partway out from the nucleus, representing a distance from the nucleus at which the electron will never be found. It is interesting that an electron in state (b) can be found inside or outside this distance but never at this distance. How can an electron be sometimes inside and sometimes outside this distance without sometimes being at this distance? The answer is that a tiny particle-like electron is not present except when a position measurement is made; between measurements, only the matter field shown in the figure exists. State (e) is larger still. The electron is likely to be found still farther from the nucleus and there are now two gaps where the electron will not be found. Unlike states (a), (b), and (e), the remaining seven states shown are not the same in every direction. State (d) is shaped like a fat doughnut circling the z-axis and is reminiscent of the planetary model of the atom. State (c) is shaped like a dumbbell (two spheres) along the z-axis. It is separated into two parts, between which the electron is not found. The figure shows 10 of the most common quantum states of hydrogen, nature’s simplest atom. There are many more states, not shown in the figure. Each pattern represents one state (or condition) in which a hydrogen atom can exist.5 Atoms with more than one electron have more complex quantum states, but they all are found by solving the Schroedinger equation in the form appropriate to that particular atom. In addition to predicting these states, the Schroedinger equation predicts that each of them has just one specific energy. That is, the energy of each state shown in Figure 18 has no quantum uncertainty. From the figure, we can even make educated guesses about the energy level (the amount of energy) of each state. Because the force by the proton on the electron is attractive, one would have to do work to pull an electron outward, away from the nucleus. So the electromagnetic energy of

5

A hydrogen atom can also exist in a combination of two or more of these allowed quantum states.

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Schroedinger, during a Conversation with Niels Bohr

Figure 19

The lowest five energy levels for the electron in a hydrogen atom. When measured in joules, these atomic energy levels are quite small: The energy difference, E2 - E1, between the lowest two levels is only 1.6 * 10 - 18 joules.

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You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to nonsense.... If we are still going to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory.

the atom increases as the electron gets farther from the nucleus. This is just like gravitational energy: Because Earth exerts an attractive force on a rock, the rock’s gravitational energy increases when the rock is lifted upward. So the smallest matter field, the one bunched most tightly around the nucleus, should have the lowest energy. Judging from the figure, this is state (a). Because of the gravitational analogy, this is called the ground state. It is the state in which the electron is as close to the nucleus as it can be. Recall that if the universe obeyed Newtonian physics, atoms would collapse because orbiting electrons would radiate their energy away and fall into the nuclei. In contrast to this, there is a smallest possible quantum state of hydrogen, namely state (a). The atom cannot radiate energy when it is in this state, simply because there are no states of lower energy. An atom in its ground state is like a ball that’s rolled all the way downhill and can’t roll any lower. Quantum physics prevents atoms from collapsing! Other states are called excited states because they are more energetic than the ground state. The precise energy of each quantum state can be calculated using Schroedinger’s equation. Figure 19 shows the lowest five of these precise energies (but without showing any actual numerical values). As expected, state (a) has the lowest energy, labeled E1. States (b) (c) and (d) all happen to have the same energy, labeled E2. The remaining six states pictured in Figure 18 all happen to have the same energy, labeled E3. Two further energy levels, labeled E4 and E5, corresponding to additional quantum states, are shown. Notice that the energy levels get closer together as the energy increases. An energy-level diagram like this Figure is a prime example of the quantum or “digital” nature of the microscopic world: If the energy of a hydrogen atom’s electron is measured, it will be found to have one of these energies and no other. For instance, it cannot have an energy between E1 and E2. Each of these quantum states represents an isolated hydrogen atom that isn’t changing. What happens when something does change? What happens, for example, when an atom emits radiation? As we know, radiation is quantized and so can be observed only in energy bundles called photons. An atom must emit at least one quantum of energy—one photon—whenever it radiates. This means that it must be in an excited state to begin with, and it must transition to a lower-energy state. The transition must be instantaneous, because the atom is not allowed to have any energy other than the ones shown in Figure 19. Such an instantaneous transition of an atom from one quantum state to another is called a quantum jump.

E5 E4 E3

States (e) through (j)

E2

States (b), (c), (d)

E1

State (a)

The Quantum Universe Figure 20 shows a common way of representing quantum jumps. The transition is shown as an arrow on an energy-level diagram stretching from the initial to the final energy. The diagram represents an atom making a transition from the E4 to the E2 energy level and also indicates that a single photon is emitted, carrying away the energy. You can picture this by imagining that, in Figure 18, a state (not shown in Figure 18) having energy E4 suddenly vanishes and is replaced by state (b), (c), or (d). The hydrogen atom truly jumps from one pattern to another. Now you can understand atomic spectra and the emission of radiation by an atom. Atoms emit radiation when they quantum-jump to a lower energy level, creating and emitting a photon in the process. Recall that a photon’s energy is hf, where h is Planck’s constant and f is the photon’s frequency. Conservation of energy tells us that the energy hf of the emitted photon must equal the energy difference in the quantum jump; that is,

hf = (energy of high-energy state) - (energy of low-energy state) So if you know the energies E4 and E2, you can find the frequency of the photon emitted in a quantum jump between these two levels. Physicists can calculate the precise energy levels from the Schroedinger equation and then find the frequency of the photon emitted in each possible quantum jump between pairs of energy levels.

Energy

How do we know Schroedinger’s equation is reliable? Figure 21 shows, on an energy-level diagram, the 10 downward quantum jumps that are possible between the lowest five energy levels for hydrogen. Since the photon’s energy is equal to the atom’s energy change, the length of the arrow representing each quantum jump is proportional to the frequency of the radiation emitted in that quantum jump. So a hydrogen atom can emit 10 different frequencies by quantum-jumping from the E2, E3, E4, or E5 levels downward into one of the lower levels. Figure 22 shows these 10 frequencies quantitatively. Since Schroedinger’s equation predicts the energy levels, it also predicts these frequencies. When one uses a spectroscope to measure the spectrum of atomic hydrogen gas, the frequencies turn out to be precisely those indicated in Figure 22 and predicted by quantum theory. Schroedinger’s equation first gained fame because Schroedinger was able to show that it correctly predicted these frequencies. For just one example, the Schroedinger equation predicts the wavelength (which can be calculated from the frequency) of the photon emitted when a hydrogen atom quantum jumps from energy E2 to E1 to be 1.21568 * 10 - 7 meters. Actual measurement shows it to be 1.21566 * 10 - 7 meters

E5 E4 E3

States (e) through (j)

E2

Photon States (b), (c), (d)

There is no part of chemistry that does not depend, in its fundamental theory, upon quantum principles. Linus Pauling, Chemist

Figure 20

E1

State (a)

A symbolic representation of a quantum jump from one quantum state to another. A photon, carrying energy E4 - E2, is emitted at the instant the quantum jump occurs.

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E5 E4 E3

E2

Figure 21

The possible downward quantum jumps between the lowest five energy levels of the hydrogen atom.

E1

Into E4

Into E3

Into the E2 level

Four quantum jumps into the E1 energy level

Figure 22

The frequencies of the photons that are given off during the quantum jumps shown in Figure 21.

0

500

1000

1500

Frequency in trillions

2000 (1012)

2500

3000

of Hz

plus or minus a small error. Many other hydrogen frequencies and wavelengths have been predicted and measured with similarly accurate agreement. Physicists know that there must be something right about any equation that can predict six-figure numbers.

CONCEPT CHECK 9 In three dimensions, the quantum state in Figure 18(h) is best described as having the shape of (a) a dumbbell; (b) a doughnut; (c) two dumbbells oriented in different directions; (d) two doughnuts oriented in different directions; (e) a dumbbell and a doughnut. CONCEPT CHECK 10 Among the 10 quantum jumps between the five energy levels of hydrogen shown in Figure 21, the one that will create the photon with the highest frequency is (a) E5 to E4; (b) E5 to E1; (c) E5 to E2; (d) E2 to E1. CONCEPT CHECK 11 How many different frequencies can be created by quantum jumps among only the lowest six energy levels of hydrogen? (a) 6. (b) 5. (c) 10. (d) 14. (e) 15.

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The Quantum Universe Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions

7. Give an example in which the switching on of a detector causes a particle’s matter field to quantum-jump. 8. What is meant by a nonlocal effect?

THE UNCERTAINTY PRINCIPLE 1. Does the particle represented by the matter field of Figure 2 have a precise position? A precise velocity? 2. Which wave packet of Figure 3 has the more precise position? The more precise velocity? 3. Does the uncertainty principle say that a particle must have a ¢x that is larger than some prescribed value? What does it say? 4. Does a baseball have large quantum uncertainties or small ones? Why?

THE EFFECT OF DETECTORS 5. What happens to a particle’s wave packet when a position measurement is performed? 6. Is it possible for a single microscopic particle’s matter field to be spread out over macroscopic dimensions, such as several meters or larger? Give an example.

QUANTUM ENTANGLEMENT 9. 10. 11. 12.

What is entanglement? What does Bell’s principle tell us about entangled particles? What does the Rarity-Tapster experiment demonstrate? Can the nonlocal connections described by Bell’s principle transfer energy instantaneously?

QUANTUM REALITY AND A MODERN WORLDVIEW 13. According to the standard interpretation of quantum theory, which of the following are actually inherent in nature: predictability, precise positions for microscopic particles such as electrons? 14. Describe at least two key ideas of the Newtonian worldview that are contradicted by quantum physics.

⌬x

Figure 2

x-axis Direction of motion of wave packet

⌬x

A ⌬x

The matter wave representing a single particle whose uncertainty in position is ¢x, moving along the x-axis. A matter wave like this, which is spread out over only a limited distance, is called a wave packet.

Figure 3

Two wave packets, having different values of ¢x . Packet B can be constructed by squeezing packet A to half its size. In this process, all of A’s wavelengths get squeezed to half their original length, which means that the velocities and also the uncertainty in velocity get doubled.

B

From Chapter 13 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

375

The Quantum Universe: Problem Set

OBSERVING ATOMIC SPECTRA 15. 16. 17. 18. 19. 20.

What is the purpose of the prism in a spectroscope? What is the purpose of the thin slit in a spectroscope? Exactly what is measured by a spectroscope? Describe two ways to excite a gas. When we excite a gas, what happens to its atoms? Describe one way in which the planetary model disagrees with observations of atomic spectra. 21. There’s a really huge problem with the planetary model of the atom. What is it?

THE QUANTUM ATOM 22. Describe the three-dimensional shapes of some of the states in Figure 18. 23. Exactly what does one of the states in Figure 18 represent? 24. Which state(s) in Figure 18 has the lowest energy? 25. Which state(s) in Figure 18 is a ground state? Which are excited states? 26. Consider any one of the states in Figure 18. In this state, does the electron have a predictable energy? A predictable position? A predictable velocity? 27. Describe the process by which atoms create radiation. 28. What is meant by a quantum jump in an atom? 29. How many different frequencies are emitted in the quantum jumps shown in Figure 21?

Conceptual Exercises THE UNCERTAINTY PRINCIPLE 1. Arrange the following objects in order, beginning with the object having the largest uncertainty range and ending with the one having the smallest: proton, glucose molecule C6H 12O6, helium atom, baseball, electron, grain of dust, water molecule, automobile. 2. If Planck’s constant were smaller than it is, how would the uncertainty principle be affected? What if Planck’s constant were zero? 3. How would it affect you if Planck’s constant were 1 J/Hz instead of 6.6 * 10 - 34 J>Hz? 4. If Planck’s constant were smaller than it is, would this affect the sizes of atoms? If so, how?

THE EFFECT OF DETECTORS 5. Think of a few common situations, unrelated to quantum theory, in which observation changes reality. Would public opinion polls be an example? Would looking at the moon be an example? 6. One everyday example in which a measurement disturbs the measured object is the measurement of the temperature of a pan of water using a thermometer. How does this disturb the temperature? Is this a quantum effect? 7. What would happen to the wave packet of Figure 2 (see prevous page) if an accurate velocity measurement were performed? How would the measurement affect ¢x and ¢v? 8. Your friend flips a coin but covers it up so that neither of you can tell whether it is heads or tails. What odds (probability) would be fair to put on heads? Suppose he uncovers it and

376

you see that it is tails. What odds should you now assign to heads? Does this sudden shift in the probabilities have anything to do with quantum theory? 9. Figure 8(a) shows the pattern formed by the matter wave on the screen in the double-slit experiment. Is this a graph of a single electron’s matter field just before or just after the electron hits the screen? What happens to the matter field when the electron hits the screen?

QUANTUM ENTANGLEMENT 10. How would the graph of Figure 12 look if the photons in the Rarity-Tapster experiment behaved like ordinary Newtonian particles? 11. Suppose that the Rarity-Tapster experiment could be performed using electrons instead of photons. Would the outcome still be an interference pattern like Figure 12?

QUANTUM REALITY AND A MODERN WORLDVIEW 12. Electrons do not normally have precise positions. How can you cause an electron to have a (fairly) precise position? 13. Electrons do not normally have precise velocities. How can you cause an electron to have a (fairly) precise velocity? 14. List several general ways in which nature is non-Newtonian. 15. List several specific experiments that show that nature is non-Newtonian. 16. List several specific experiments that show that nature is Newtonian.

OBSERVING ATOMIC SPECTRA 17. In what ways is your radio a type of spectroscope? 18. In what ways does a radio (preceding exercise) differ from the spectroscope described in the text? 19. Why do spectroscopes use a thin slit (Figure 14) rather than, say, a round hole? 20. Why, when different materials burn, do they often create flames of different colors? 21. How might the chemical composition of a burning substance be determined? 22. If you compared the spectra from two sodium vapor lightbulbs, would they be the same? What if you compared a sodium vapor bulb with a mercury vapor bulb?

THE QUANTUM ATOM 23. Explain, in terms of inertia, why the electron does nearly all the moving in a hydrogen atom. 24. Describe the three-dimensional shape of the quantum state shown in Figure 18(f). 25. Describe the three-dimensional shape of the quantum state shown in Figure 18(g). 26. Describe the three-dimensional shape of the quantum state shown in Figure 18(i). 27. Describe the three-dimensional shape of the quantum state shown in Figure 18(j). 28. If a very accurate measurement of an atom’s mass could be made in an excited state and in its ground state, would any difference be found? (Hint: Remember E = mc2.) 29. What happens to an atom’s mass when it emits a photon? (Hint: Remember E = mc2.)

The Quantum Universe: Problem Set z

(a) z z

(c)

(d)

(b) z

z

z

(g)

(e) (f) z

z z

(j)

(h)

(i)

Figure 18

Patterns of the microworld. Ten different allowed matter waves, or quantum states, for the electron in a hydrogen atom. If the electron’s position were measured, it would have a greater probability of being found in the darker regions where the matter field is more intense.

377

The Quantum Universe: Problem Set y–x

Figure 12

E5 E4 E3

0

E2

Number of 2-particle impacts

E1

Figure 21

The possible downward quantum jumps between the lowest five energy levels of the hydrogen atom.

A

⫹ ⫺

B

D

(a)

(b)

Figure 8

Merely switching on a particle detector at a point such as D causes the matter field to jump from the interference pattern (a) to the noninterference pattern (b).

378

If, instead of studying x or y separately, we study the difference y – x between the two impact points on the two screens, we get an interference pattern. How does the second photon, impacting at some point y, “know” at which point x the first photon impacted? The second photon instantly coordinates its impact pattern with the first photon’s impact point, despite the fact that the uncertainty principle says that both impact points are uncertain in advance.

The Quantum Universe: Problem Set

Red

Narrow beam of radiation containing various frequencies Radiation source such as a heated glowing gas

Yellow

Prism

Violet Partition with a thin slit in it

Viewing screen or photographic film

Figure 14

One type of spectroscope. 30. Among the 10 quantum jumps between the five energy levels of hydrogen shown in Figure 21, which one creates the lowest-frequency photon? 31. In Figure 21, which quantum jump creates the higherfrequency photon, E4 to E3 or E4 to E2? Which of the two photons has the longer wavelength? 32. In Figure 21, which quantum jump creates the highest frequency, E5 to E4, E4 to E3, E3 to E2, or E2 to E1? Which creates the longest wavelength? 33. The four spectral lines of hydrogen photographed in Figure 15 have wavelengths and frequencies that agree precisely with the four lowest-energy transitions into

hydrogen’s second energy level, E2. Which three of these four lines are graphed in Figure 22?

Problems THE UNCERTAINTY PRINCIPLE 1. An electron (mass = 9.1 * 10 - 31 kg) has a velocity uncertainty ¢y = 1 m>s. How large must its position uncertainty be? Express your answer in millimeters.

Figure 15

The continuous spectrum created by an incandescent bulb and the line spectra produced by several different kinds of gases: sodium (Na), mercury (Hg), hydrogen (H), and helium (He). Frequency increases from left to right. Into E4

Into E3

Into the E2 level

Four quantum jumps into the E1 energy level

Figure 22 0

500

1000

1500

2000

Frequency in trillions (1012) of Hz

2500

3000

The frequencies of the photons that are given off during the quantum jumps shown in Figure 21.

379

The Quantum Universe: Problem Set 2. A proton (mass = 1.7 * 10 - 27 kg) has a velocity uncertainty ¢y = 1 m>s. How large must its position uncertainty be? Express your answer in millimeters. If you worked the preceding problem, then compare the two answers. 3. MAKING ESTIMATES The electron in a ground-state hydrogen atom remains within a sphere measuring roughly 10–10 meters across. An electron’s mass is about 10–30 kilograms. Use this data along with Heisenberg’s uncertainty principle to estimate the velocity of this electron. (Hint: In the ground state, the electron’s velocity should be roughly equal to the uncertainty in its velocity, in other words ¢y = y. What fraction of lightspeed is this?

THE QUANTUM ATOM

Energy

4. For the hydrogen atom, the energy difference E2 - E1 between the lowest two levels (Figure 19) is 16 * 10 - 19 J. Find the frequency of the photon emitted when a hydrogen atom quantum-jumps from state 2 to state 1. In which region of the spectrum is this (Figure 27)?

E5 E4 E3

States (e) through (j)

E2

States (b), (c), (d)

E1

State (a)

Figure 19

The lowest five energy levels for the electron in a hydrogen atom. When measured in joules, these atomic energy levels are quite small: The energy difference, E2 - E1, between the lowest two levels is only 1.6 * 10 - 18 joules. 5. For the hydrogen atom, the energy difference E3 - E2 between the second and third levels (Figure 19) is 3 * 10 - 19 J. Find the frequency of the photon emitted when a hydrogen atom quantum-jumps from state 3 to state 2. In which region of the spectrum is this (Figure 27)? 6. From the information given in the preceding two problems, find the energy difference E3 - E1 between the third and first energy levels of the hydrogen atom. Find the frequency of the photon emitted when a hydrogen atom quantum-jumps from state 3 to state 1. In which region of the spectrum is this?

Answers to Concept Checks 1. (a) 2. (b)

380

3. (a) and (d) 4. It takes only a single detector to determine through which slit

5. 6. 7. 8. 9. 10. 11.

the electron came, so the additional detector is superfluous and the matter field is identical with the matter field for one detector, (d). Two multiplied by itself 10 times (in other words, 210) is 1024, (f ). (a) and (d) The type of radiation that comes from heated but nonglowing objects is infrared, (b). Solids emit continuous spectra, so the spectrum would look similar to a rainbow, (d). When rotated about the z axis, the figure becomes a dumbbell along the z-axis plus a doughnut around the z-axis, (e). (b) In addition to the 10 quantum-jumps shown in Figure 21, there are 5 more quantum-jumps from level E6 into the other five levels. So the total is 15, (e).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Electron, proton, helium atom, water molecule, glucose molecule, grain of dust, baseball, automobile. 3. Quantum indeterminacies would be very large and observable on the macroscopic level. Newtonian physics, including predictability, would not be even approximately correct. 5. Public opinion polls that alter public opinion are one example. Here are a few of the many other examples: A thermometer slightly alters the temperature of the object it is measuring, your own observation of your psychological responses can alter those responses, observation of another person might cause that person to become tense and thus alter that person’s performance, the presence of a crowd at a sporting event can affect the outcome of the event. Observation of the moon is not an example. 7. It would change into a much more spread-out wave, with a larger ¢x and a smaller ¢y. 9. Before. When the electron hits the screen, the spread-out psi-wave collapses to a small point. 11. Yes. 13. Measure its velocity. Just after the measurement, its velocity will be fairly precise. 15. The double-slit experiment with light, double-slit experiment with electrons or other forms of matter, Rarity Tapster experiment, other experiments referred to in the “How do we know” sections. 17. Your radio detects radiation of specific frequencies (namely, the frequency of your radio dial). So you can use a radio to detect the radio-range frequencies that are present. 19. With a round hole, the spectrum would appear as a series of circles instead of a series of lines. A slit works better because two neighboring lines on the screen are more distinctly separated than are two neighboring circles. 21. You could determine the composition by determining the spectrum of the light from the flame and matching it with the spectrum of some known chemical compound.

The Quantum Universe: Problem Set Typical Sources That Send out Waves at This Frequency:

Typical Object Whose Size Is the Same as This Wavelength:

Frequency, Hz

1022 Processes by protons and neutrons in atomic nuclei

Electrons in atoms, high-energy processes Electrons in atoms, low-energy processes

Gamma ray

X-ray

1018

Ultraviolet

1016 1014

Microwave oven

1012

Radar antenna

violet green yellow red

Cell phone

Infrared

108

TV, FM radio

AM radio antenna

106

AM radio

Atom

10⫺8

DNA molecule Amoeba

10⫺6

Fine dust particle

10⫺4 Millimeter

Radar

FM radio, TV antenna

10⫺10

Visible

Microwave 1010

10⫺2

Centimeter

1

Meter

102

Soccer field Kilometer

Radio

60 Hz power-line radiation

Nucleus

10⫺12

1020

Thermal vibrations of molecules

10⫺14

104

104

102

106

1

108

Earth

Wavelength, m

Figure 27

The electromagnetic spectrum. There are no definite ends to the spectrum and no sharp boundaries between the regions.

23. The electron is much lighter, so it has less inertia, so it can 25. 27. 29. 31. 33.

be set into motion much easier. A small “doughnut” around the origin, surrounded (at a larger distance from the origin) by a larger doughnut around the origin. A single large “doughnut” around the z-axis. When an atom emits a photon, the atom loses energy, so it loses mass. Energy level 4 to 2. Longest wavelength energy level 4 to 3. According to Figure 21, the three lines graphed come from the following three quantum jumps: Energy levels 3 to 2, 4 to 2, and 5 to 2; they are the three longest wavelengths in Figure 15 (the first three, counting from the left). The other line (red) must then come from the E6 to E2 quantum jump.

Problems 1. From ¢x¢y = h>m, we get ¢x = h>m ¢y = (6.6 * 10 - 34 J>Hz)>(9.1 * 10 - 31 kg * 1 m>s) = 0.72 * 10 - 3 m = 0.72 mm 3. (¢x) # (¢y) L h>m, where ¢x L 10 - 10 meters and m L 10 - 30 kg. So ¢y L (6.6 * 10 - 34)>(10 - 30)(10 - 10) = 6.6 * 106 m>s. As explained in the hint, this is also the approximate speed of the electron. The ratio of this speed to lightspeed is 6.6 * 106>3 * 108 L 0.02. So the electron moves at about 2% of lightspeed. 5. E = hf, where the photon’s energy is E = E3 - E2, so f = (E3 - E2)>h = 3 * 10 - 19 J>6.6 * 10 - 34 J>Hz = 4.5 * 1014 Hz. This is in the visible region.

381

382

The Nucleus and Radioactivity: A New Force

From Chapter 14 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

383

The Nucleus and Radioactivity: A New Force— The unleashed power of the atom has changed everything save our modes of thinking, and we thus drift toward unparalleled disaster. Einstein, Commenting On the Threat of Nuclear War

O

ne way that science has expanded human awareness is by expanding the range of distances humans can comprehend. Prescientific cultures were aware of what they could see, down to the smallest dust particles (10 - 5 m) and up to the distance a person might see on Earth (100 km, or 105 m). Today, telescopes have extended our awareness to the edge of the observed universe at some 1026 m, while microscopes and giant accelerators have probed down to atoms (10 - 10 m in size), the nucleus (10 - 14 m), and subnuclear particles (10 - 19 m and counting). The nucleus is the star of this chapter. Although the nucleus might seem remote from human concerns, technology has exploited it as a source of great power. Power always has both dangers and opportunities; it’s up to all of us to see that when used, it’s used wisely. So we study nuclear1 physics not only for its intellectual significance but also because you and I must figure out how to use this powerful knowledge beneficially and nondestructively. This chapter explores the structure of the nucleus and the nuclear reaction known as radioactive decay. Section 1 discusses the forces acting within the nucleus, and Section 2 explores the energetics of the nucleus, a topic crucial to our further discussions of nuclear physics. Then I’ll present the physics of radioactive decay (Section 3), including the concept of half-life (Section 4). The next two sections explore two radioactivity-related cultural and social topics: radioactive dating and its implications for Earth’s history (Section 5), and human exposure to radioactivity (Section 6). Section 7 expands on Section 6 by studying technological risks more generally.

1

384

Many people advertise their scientific ignorance by mispronouncing this word. Please say “nuc-le-ar,” not “nuc-u-lar.”

The Nucleus and Radioactivity: A New Force

1 NUCLEAR FORCES: THE THIRD GLUE Like detectives, scientists form hypotheses and deductions from observed clues. Let’s do some nuclear detective work. The nucleus occupies only a tiny region about 10 - 14 m across and is made of protons and neutrons.2 Figure 1 pictures a typical nucleus. Such a picture is highly simplified. Most importantly, it neglects quantum uncertainty. The matter fields of all the nuclear particles overlap, with each particle’s matter field filling the entire nucleus. Furthermore, protons and neutrons do not resemble the small spheres shown. Each proton and neutron is made of three tiny pointlike “quarks.” Nevertheless, pictures like Figure 1 are useful guides. Since protons repel each other electrically and neutrons are electrically neutral, there must be an attractive force between these nuclear particles to prevent the nucleus from being blown apart by electrical repulsion. This attractive force must be strong enough to overcome the enormous electrical repulsion between two protons only 10 - 15 m apart (between their centers). Gravity is always attractive. Could it hold the nucleus together? As you might guess, gravity can’t do the job because the proton’s and neutron’s small masses make gravitational forces between nuclear particles insignificant compared with electric forces. Now recall that the forces experienced in your daily life can be explained in terms of only two fundamental forces: gravity and electricity. Since gravity is too small, and electricity is only repulsive inside the nucleus, we deduce that there must be a third fundamental force that holds the nucleus together. This third force must strongly attract protons to one another when they are separated by about 10 - 15 m. It must also attract neutrons to one another and to protons, since otherwise neutrons would fall out of the nucleus. But despite its strength at short separations, this force cannot extend very far. It certainly cannot extend from one nucleus to the next in solid matter (about 10 - 10 m), because if it did, all the nuclei would clump together. In fact, we could hypothesize (remember, this is a detective story) that this force extends only far enough to hold the largest nuclei together, because if it extended much farther, still larger nuclei would be possible and would be observed in nature. As it turns out, experiments show that this “strong nuclear force,” or simply strong force, extends only 10 - 15 m, about the distance between adjacent nuclear particles (Figure 1). So there are three kinds of “glue” that bind things together. At the nuclear level, the strong force holds the nucleus together. At the atomic level, the electric force binds orbital electrons to their nuclei, binds atoms into molecules, and holds solids and liquids together. And at the astronomical level, the gravitational force holds planets, stars, solar systems, and galaxies together and reaches across clustered galaxies to determine the shape of the universe. So far as scientists know, every force in nature can be reduced to the action of these three forces plus just one other: the “weak nuclear force,” or simply weak force, that plays a role in radioactive beta decay (Section 3). Together, these four

2

Nuclear diameters range from about 3 * 10 - 15 (hydrogen) to 20 * 10 - 15 m (uranium).

10⫺14 m

10⫺15 m

Figure 1

A schematic representation of a nucleus. The colored spheres represent protons, and the white spheres represent neutrons. Diagrams like this, showing subatomic particles as if they were ordinary Newtonian objects, are useful aids to thought, but they are greatly simplified. Nature at this level is highly quantized.

385

The Nucleus and Radioactivity: A New Force

fundamental forces determine the structure of our universe. Nobody knows why they have the properties that they do, properties that make the universe such an interesting and varied place. What if the properties of any one of them were different? For example, what if the strong force had a longer range, or were weaker? What if the electric or gravitational force were stronger or weaker than they actually are? What if there were three kinds of electric charge, or only one? What if gravity were repulsive instead of attractive? If any one of the four fundamental forces were altered by much, the universe would be vastly different and life probably could not exist. CONCEPT CHECK 1 Suppose that the strong force had a somewhat longer range than it actually has. How would this affect the list of elements (the periodic table)? (a) The periodic table would be shorter than it is. (b) The periodic table would be longer than it is. (c) The periodic table would be left unchanged.

2 NUCLEAR ENERGY AND NUCLEAR STRUCTURE Since the strong force is by far the strongest of the four fundamental forces, the energy changes accompanying individual nuclear processes are large compared with chemical processes (which are dominated by the electric force). That’s why nuclear weapons explosions and nuclear reactors yield huge energies per kilogram of material and why electromagnetic radiation from the nucleus lies in the highly energetic gamma-ray region of the spectrum. There’s a fundamental quantum reason why nuclear energies must be large. Because the strong force has a short range, any nuclear particle is trapped in a small region of space. The uncertainty principle tells us that any such well-localized particle must have a highly uncertain speed and its average speed must therefore be large, so its kinetic energy is large. Quantitatively, any nuclear particle trapped in a region as small as 10 - 14 m must have an average speed of at least 3 * 107 m>s, or about 10% of lightspeed. This is about the speed at which relativistic phenomena begin to be important. This is indicated in Figure 2. The x at the edge of the region that is forbidden by the quantum uncertainty principle indicates a typical nuclear size and speed. A similar argument applies to entire atoms: Since the matter field for an electron in an atom is about 10 - 10 m across, the uncertainty principle implies that atomic electrons must move at about 0.5% of lightspeed. This is indicated in Figure 2 by the point y. Since nuclei are made of parts, you might suspect that it’s possible to alter their structure. Any process that does so is called a nuclear reaction. The medieval chemist-magicians known as “alchemists” went to fantastic lengths trying to transform one chemical element into another, especially lead into gold (at a profit). Neither their chemistry nor their magic produced any gold, but the dream has turned out to be achievable. Although magic doesn’t help, chemical reactions are on the right track. The problem is that ordinary chemical energies are far too low to do the job. Today, nuclear chemists routinely turn one element into another. It’s even possible to convert lead to gold, but you can’t make a profit because the needed energy is worth much more than the gold. Nuclear reactions are a little like chemical reactions. An atom’s chemical properties are determined by its number of orbital electrons, that is, by the element to which the atom belongs, specified by its atomic number. The elements and their

386

The Nucleus and Radioactivity: A New Force Speed Forbidden by relativity c

Typical size of a nucleus and speed of a nuclear particle

Quantum ⫹ special relativity

Special relativity General relativity

0.1c

x

Typical size of an atom and speed of an atomic electron

Quantum Newtonian y

Forbidden by quantum theory

10⫺14

10⫺5

1022

Size or distance in meters

Figure 2

The domains of Newtonian, relativistic, and quantum physics. The numbers and boundaries are only representative; there are no definite borders between the domains of the theories. As shown on the diagram, atomic physics falls into the quantum domain, while nuclear physics falls at the borderline between the quantum and the quantum relativistic domain.

atomic numbers are listed in the periodic table (inside back cover). The atomic number is important to nuclear reactions, too, because it’s the number of protons in the nucleus. But neutrons are also significant in determining nuclear behavior. Two nuclei with identical numbers of both protons and neutrons are said to belong to the same isotope. Just as atoms of a particular element have identical chemical properties, nuclei of a particular isotope have identical nuclear properties. The numbering system for isotopes is only slightly more complicated than that for elements. An isotope is numbered by its atomic number, its number of protons, and also by its mass number, its total number of protons and neutrons—the total number of particles in the nucleus. Because protons and neutrons have about the same mass, the mass of the entire nucleus is nearly proportional to the mass number, hence the term “mass number.” For example, a nucleus with mass number 8 is about twice as massive as a nucleus with mass number 4. As an example, the element carbon has atomic number 6, so every carbon nucleus has six protons. Because some carbon nuclei contain six neutrons, others contain seven, and still others contain eight, there are three different isotopes of carbon. These three isotopes have identical chemical properties but different nuclear properties. Their mass numbers are 12, 13, and 14. I’ll indicate specific isotopes by their chemical symbol preceded by their atomic number as a subscript and their mass number as a superscript. So the three isotopes of carbon are 126C, 136C, 146C. But I’ll often drop the atomic number, because the chemical symbol actually specifies it, and simply write 12C, 13C, 14C, pronounced “carbon-12, carbon-13, carbon-14.” CONCEPT CHECK 2 Which fundamental forces come into play during chemical reactions? (a) Gravitational. (b) Electromagnetic. (c) Frictional. (d) Nuclear.

387

The Nucleus and Radioactivity: A New Force

The nuclei 3H and 3He have (a) identical atomic numbers but different mass numbers; (b) different atomic numbers and different mass numbers; (c) different atomic numbers and identical mass numbers; (d) identical atomic numbers and identical mass numbers. CONCEPT CHECK 3

3 RADIOACTIVE DECAY: SPONTANEOUS NUCLEAR DISINTEGRATION

Marie Curie is, of all celebrated beings, the only one whom fame has not corrupted. Albert Einstein’s Eulogy Upon the Death of Marie Curie in 1934

In 1896, French physicist Henri Becquerel finished his research for the week and stored a certain uranium compound away in a drawer for the weekend. By chance, an unexposed photographic plate was stored in the same drawer. When he returned the following week, Becquerel found to his surprise that the film had been exposed, despite having been kept in a dark drawer. A lesser scientist might have shrugged his shoulders and tossed out the ruined film, but Becquerel suspected a connection between the uranium and the exposure. He discovered that he could reproduce the effect whenever he placed the uranium near photographic film. Apparently, the uranium radiated something that could expose a photographic plate. The phenomenon was called “radioactivity.” When Becquerel subjected the uranium to various chemical treatments, they produced no change in the effect. So radioactivity had little to do with chemistry. Science had had its first brush with the nucleus, even though the nucleus had not yet been discovered. Two years later, the Polish physicist Marie Curie (Figure 3) and her husband Pierre detected radioactivity in pitchblende, a tarry black substance. They were not surprised at the radioactivity because pitchblende is a known ore of uranium, but they were surprised to find that the radiation was more intense than the radiation from pure uranium, even though the pitchblende contained only low concentrations of uranium. Apparently some other substance, much more radioactive than uranium, was present in pitchblende. The Curies took on the heroic task of chemically separating this sub-

Marie Curie shared, with Pierre Curie and Henri Becquerel, the 1903 Nobel Prize for Physics. Pierre fell beneath the wheels of a carriage and was killed in 1906. Marie Curie continued her research, confident of success despite the widespread prejudice against women in physical science. She did succeed: She was the first woman to teach at the Sorbonne in Paris, the first person to receive two Nobel prizes, and element 96 is named in her honor. Her daughter Iréne became a nuclear scientist, winning the 1935 Nobel Prize in Chemistry. One of Marie Curie’s contributions was opening the doors of science to other young women. In 1934 she developed cataracts and lesions on her fingers and died of radiation-induced leukemia. Iréne Curie also died of leukemia.

388

American Institute of Physics/Emilio Segre Visual Archives

Figure 3

The Nucleus and Radioactivity: A New Force

stance from 8 tonnes of pitchblende. This involved some monumental detective work, because the new substance and its chemical properties were unknown. They managed to get only a bare powdery pinch, 0.01 grams, of the stuff. Like uranium, it radiated spontaneously, but it gave off rays at a much higher rate than did an equal mass of uranium. Because of its powerful radiation, they named the new element “radium.” Since the discovery of uranium and radium, scientists have found lots of radioactive substances. Every isotope whose atomic number is greater than 83 (bismuth) is radioactive, and there are many radioactive isotopes of the lighter elements as well. For example, among the three isotopes of carbon, 14C is radioactive, but 12C and 13C are not. Experiments (Figure 4) show that radioactive materials emit three distinct types of rays, known as alpha, beta, and gamma rays. The way these rays respond to electric or magnetic fields shows that alpha rays are positively charged, beta rays are negatively charged, and gamma rays are not charged. These rays come from the nuclei of various isotopes. Closer examination reveals that most nuclei are stable, meaning they will remain forever unchanged unless outside influences disturb them. But some nuclei are unstable or radioactive; they will eventually change their structure even if they experience no outside disturbance. Such a spontaneous change in structure is called radioactive decay. There are two main kinds of radioactive decay.3 In alpha decay, a radioactive nucleus spits out a particle called an alpha particle that is identical with the nucleus of helium, 42He—two protons and two neutrons bonded together by the strong nuclear force (Figure 5). If the alpha particle gets into the air, collisions

Alpha rays Gamma rays Beta rays

Metal plate carrying positive electrical charge

Metal plate carrying negative electrical charge ⫺

⫹

Figure 4

An experiment showing that radioactive materials can emit three different types of rays. The two metal plates create an electric field in the space between the plates. Because they are attracted to the negative plate and repelled by the positive plate, alpha rays must carry a positive electric charge. Similarly, beta rays are negatively charged, and gamma rays are not charged.

Lead block

Radioactive material

Battery ⫹

3

⫺

In addition to the two types discussed here, there are other less common types of radioactive decay processes, such as positron decay in which the nucleus creates and emits a positive electron or “positron.”

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The Nucleus and Radioactivity: A New Force

Daughter nucleus after radioactive decay

Alpha particle breaks away from the nucleus

Figure 5

Alpha decay.

An electron (also called a beta particle) is created in the nucleus and immediately ejected.

Daughter nucleus after radioactive decay

Figure 6

Beta decay.

with air molecules will soon slow it down, after which it will pick up two electrons from nearby atoms to become a normal atom of helium. In beta decay, a radioactive nucleus spits out an electron (Figure 6). This is surprising because there are no electrons in the nucleus! I’ll straighten out this mystery later in this section. Once it gets into the air, the electron collides with air molecules, slows down, and is captured by some nearby atom to become an ordinary orbital electron. But when it’s emitted by a radioactive nucleus, it’s called a beta particle to indicate the process that created it. Most radioactive isotopes decay by only one of these two processes. For example, uranium and radium are alpha emitters, and 14C is a beta emitter. Because alpha and beta decay violently disturb the nucleus, both cause the nucleus to emit electromagnetic radiation, so most decays are accompanied by a gamma-ray photon. In terms of quantum physics, the nucleus quantum-jumps into a more stable, lowerenergy state, emitting a gamma-ray photon in the process, just as an atom emits a visible photon when it quantum-jumps to a lower-energy state. Although alpha and beta rays are often called “radiation” because they radiate outward from the nucleus, they are not electromagnetic radiations. They are, instead, streams of material alpha or beta particles. Gamma rays, however, are a form of electromagnetic radiation. Radioactivity occurs because some nuclei don’t stick together so well. One source of such instability is simply large size: A very large nucleus has a hard time sticking together because each proton tends to be pushed out of the nucleus by the long-range electrical repulsion of the many other protons while being held in by the short-range nuclear attraction of only the nearest neighboring protons and neutrons. This is why all nuclei having atomic numbers larger than 83 (bismuth) are radioactive. In alpha decay, a small part of the nucleus is pushed out (Figure 7). Because the alpha particle 42He, is one of nature’s most stable structures, it is this combination of protons and neutrons that breaks away. Once separated from the nucleus, an alpha particle is pushed strongly away by the long-range electric force from the protons in the remaining nucleus, called the daughter nucleus. Whereas alpha decay is the sort of falling apart one might expect in an unstable nucleus, beta decay is more surprising. It’s caused by the weak force, which actually causes a neutron to transform spontaneously into a proton while simultaneously creating a high-energy electron (Figure 8). When this process occurs within a nucleus, the nucleus loses a neutron and gains a proton. Because electrons have such a small mass, the uncertainty principle tells us that the uncertainty in position of the created electron is quite large—much larger than the entire nucleus. In other words, the electron is not confined within the nucleus and is ejected at high energy.4 The nucleus transforms into a different isotope during radioactive decay. It’s the alchemist’s dream, and it’s been occurring spontaneously all the time! For example, when 146C beta decays, it loses a neutron and gains a proton, so its atomic number increases by 1 while its mass number remains unchanged. The daughter nucleus, with atomic number 7 and mass number 14, is 147N. I’ll represent nuclear reactions the way I have represented other processes: with an arrow from the initial to the final situation. For example, the beta decay of 14C is 14 6C

4

390

: 147N + beta

A tiny uncharged particle called a “neutrino” also flies out of the nucleus during beta decay.

The Nucleus and Radioactivity: A New Force

As another example, 238 92U is an alpha emitter. Alpha decay reduces the atomic number by 2, from 92 to 90 (thorium), and reduces the mass number by 4, so this nuclear reaction is 238 92U

: 234 90Th + alpha

It’s always enlightening to view processes in energy terms. What energy transformation occurs in radioactive decay? (Pause, for thinking.) . . . Alpha and beta particles carry microscopic kinetic energy (thermal energy) into the environment around the nucleus, and gamma photons carry radiant energy. These energies came from the nuclear structure of the radioactive material. So the universe loses nuclear energy and gains thermal and radiant energies: nuclear energy ¡ thermal energy + radiant energy Radioactive decay is like a landslide, but caused by nuclear forces instead of gravitational forces. In a landslide, gravity pulls part of a hill downward into a more stable, compact configuration. The slide transforms the gravitational energy of the elevated land into kinetic energy during the slide and finally into thermal energy. In radioactive decay, the forces in the nucleus cause a similar spontaneous “sliding” of the protons and neutrons in an unstable nucleus into a more stable configuration, causing the nucleus to fall apart instead of downhill. In the process, nuclear energy (instead of gravitational energy) is converted to thermal and other forms. Radioactive isotopes exist—or can be manufactured artificially in nuclear reactors or particle accelerators—for nearly every chemical element. Because they have chemical properties identical to the chemical properties of the stable isotopes of the same element, radioactive isotopes have many medical and other uses, as well as many health dangers (Section 6). Another significant application of radioactive isotopes is radioactive dating (Section 5). But first I must discuss “half-life.”

⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹ ⫹

Alpha particle about to break away

Figure 7

During alpha decay, an alpha particle becomes separated from the rest of the nucleus and is pushed rapidly away by the repulsion from the protons in the daughter nucleus.

Before

⫹ After

Figure 8

CONCEPT CHECK 4

Which fundamental forces come into play during nuclear reactions? (a) Gravitational. (b) Electromagnetic. (c) Frictional. (d) Strong or weak nuclear. CONCEPT CHECK 5

nucleus is (a)

127 51Sb;

(b)

When radioactive iodine (131 53I) beta-decays, the daughter 131 131 (c) 132 ; (d) ; (e) Xe Cs 54 54 54Xe.

The details of beta decay: A neutron transforms into a proton and a fast-moving electron, and the electron moves rapidly away. Compare this with Figure 6.

132 53I;

4 HALF-LIFE: WHEN DOES A NUCLEUS DECAY? A central feature of quantum physics is that individual microscopic events are unpredictable, but the statistics of these events are predictable. It’s like flipping coins: You can’t predict the outcome of one coin flip, but you can predict that you’ll get about 50% heads during many flips. The difference between a macroscopic process like a coin flip and a microscopic process is that “nature knows” how the coin will fall. You could use Newtonian physics to predict the coin flip, but microscopic processes are inherently unpredictable. Given the submicroscopic nature of the nucleus, it’s not surprising to learn that radioactive decay is inherently unpredictable. It’s one of nature’s most prominent examples of quantum uncertainties.

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The Nucleus and Radioactivity: A New Force

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⫹

⫹ ⫹ ⫹ ⫹ ⫹ ⫹

⫹

⫹ ⫹

⫹

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⫹ ⫹

Figure 9

Think of the surface of a big nucleus as a collection of alpha particles drifting near the surface. When, by chance, one of these finds itself so far from the nucleus that it no longer feels the inward pull of the short-range strong force by its neighbors, it’s immediately pushed away by the long-range electric forces of the other protons.

To be specific, consider the alpha decay of one uranium nucleus. Because of nature’s preference for the highly stable alpha particle, you can think of the surface of a big nucleus like uranium as a collection of alpha particles that drift near the surface, attracted to the nucleus by the strong force but repelled by the nucleus’s protons (Figure 9). Each alpha particle is really a quantum matter field of the same sort that is responsible for the quantum properties of electrons. So there is always some probability that any particular alpha particle will find itself far enough outside the nucleus that the strong force (which, remember, has a short range) can no longer be felt. Such an alpha particle is immediately pushed out of the nucleus by the long-range electric forces of all the protons. Because of quantum uncertainties, nature “knows” only the chances that an alpha particle will be ejected, not when it will be ejected. A particular uranium nucleus might alpha-decay in 1 second, in 1 year, or in 20 billion years. However, given a large number of uranium nuclei, it’s possible to predict roughly what fraction of them will decay in any particular period of time. It’s just like coin tosses: You can predict the statistics, but not the individual outcomes. For any particular radioactive isotope, the most important statistic is the half-life, the time during which 50% of a large collection of nuclei decays. Because some radioactive nuclei are highly unstable and others are much more stable, different isotopes have widely different half-lives. A highly unstable nucleus is like a landslide waiting to happen: Just as the waiting landslide will probably slide soon, the nucleus will probably decay soon. A more stable nucleus will probably take longer to decay. Table 1 gives the half-lives of several radioactive isotopes. For example, suppose you are given one gram of 14C, a radioactive isotope with a 6000-year half-life that beta-decays to 14N, the stable form of nitrogen. During the next 6000 years, 50% of the 14C nuclei will decay by transforming into nitrogen, and just 0.5 gram of 14C will remain. How much 14C is left after another 6000 years? (Pause....) The answer is half of the half-gram, or 0.25 gram, because the half-life statistic still applies. Six thousand years is the time during which 50% of any macroscopic amount of 14C decays. So 0.50 grams of 14C remains after 6000 years, 0.25 grams after 12,000 years, 0.125 grams after 18,000 years, and so forth. Figure 10 graphs these values and connects them with a smooth curve showing the amount remaining at any time. This is the decay curve for 14C. The decay curve for any radioactive isotope is identical to that for 14C, only with a different half-life. Thus Figure 10, with the time measured in half-lives instead of in years (bottom line along the horizontal axis), may be used for any radioactive isotope. Table 1 Half-life and decay process of several radioactive isotopes

392

Isotope

Name of element

Decay process

Half-life (approx.)

14 6C

carbon

beta

6000 yr

90 38Sr

strontium

beta

30 yr

131 53I

iodine

beta

8 days

214 84Po

polonium

alpha

0.000 16 s

222 86Rn

radon

alpha

4 days

235 92U

uranium

alpha

0.7 * 109 yr

238 92U

uranium

alpha

4.5 * 109 yr

239 94Pu

plutonium

alpha

24,000 yr

The Nucleus and Radioactivity: A New Force 1.00

Figure 10

0.90

Radioactive decay curve for 14C and for any other radioactive isotope.

Fraction remaining

0.80 0.70 0.60 1/2

0.50 0.40 0.30

1/4

0.20 1/8 0.10

1/16 0

6000

12,000 18,000 Years (for 14C)

24,000

1 2 3 4 Number of half-lives (for any radioactive isotope)

1/32 30,000 5

MAKI NG ESTI MATES Starting with 100 pennies, suppose you toss all of them and remove the ones that come up tails. You toss the remaining coins and again remove the tails. If you continue the process, about how many tosses must you make before you get down to a single remaining penny? Try it! What is the half-life of pennies in this game?

CONCEPT CHECK 6 Suppose that a radioactive substance has decayed until only 1/64th of it remains. For how many half-lives has it been decaying? (a) 2. (b) 3. (c) 4. (d) 5. (e) 6. (f) 7.

5 RADIOACTIVE DATING: WHEN DID WE COME FROM? Radioactive decay is a kind of clock. If you know how much of a substance has decayed, you can read the elapsed time from the decay curve (Figure 10). Carbon dating is one example of radioactive dating. Essentially all of Earth’s carbon is one of the two stable carbon isotopes, 12C and 13C. But in Earth’s atmosphere, about one carbon atom in a trillion is the radioactive form, 14C. Since the half-life of 14C is only 6000 years and Earth is far older than 6000 years, you might wonder how any 14 C could still be in the atmosphere. The answer is that cosmic rays, high-energy particles that travel through outer space, continually replenish it. They occasionally enter the atmosphere and collide with atmospheric nitrogen, transforming the nitrogen into 14C. Because the carbon in all biological organisms comes ultimately from the atmosphere, 14C is distributed throughout the biological world at one 14C atom per trillion

In all of us there is a hunger, marrow deep, to know our heritage, to know who we are, where we have come from. Without this enriching knowledge, there is a hollow yearning. No matter what our attainments in life, there is a vacuum, an emptiness, and a most disquieting loneliness. Alex Haley, in Roots

SO LUTION TO MAKI NG ESTI MATES After one toss, you will on the average be down to 50 pennies. After two tosses, 25 pennies. After three, 12.5 or about 12 pennies. After four, about 6 pennies. After five, about 3 pennies. After six, 1 or 2 pennies. After seven, 0 or 1 pennies. So the number of tosses is about six or seven. The half-life of pennies is one toss.

393

The Nucleus and Radioactivity: A New Force Table 2 Isotopes used for radioactive dating Isotope

Comparison nucleus

238

U

206

238

U

234

235

U

207

234

U

230

187

Re

187

147

Sm

143

Pb U

Pb

Th Os

Nd

87

Rb

87

40

K

40

14

C

total C

10

Be

total Be

Sr

Ar

The world has been converted in an instant of time from a wild natural one to one in which humans . . . are consuming, wasting, or diverting an estimated 45% of the total net biological productivity on land and using more than half of the renewable fresh water. Peter Raven, American Association for the Advancement of Science Presidential Address, 2002

carbon atoms, the same as the atmospheric ratio. This ratio is maintained until a living organism dies. Then the 14C gradually decays without being replenished. The time elapsed since death can be determined by measuring the amount of 14C remaining compared with the amount of stable carbon. For instance, if an old ax handle has only a quarter of the normal amount of 14C, the tree from which the ax handle was made must have died two half-lives, or 12,000 years, ago. Such a measurement can determine the time elapsed since death if one knows how much 14C was present when the organism died. The usual assumption is that the fraction of 14C in the atmosphere in the past was nearly the same as it is today, so the fraction in a long-dead tree when it died would have been one 14C atom in every trillion carbon atoms, the same as today. But is this assumption correct? I’ll discuss this in a How Do We Know subsection following. Depending on the type of object to be dated (wooden tools, rocks, fossils, etc.), on the radioactive materials available at any particular site, and on the age of the dated object, scientists use a variety of different radioactive decay processes. Carbon dating, for example, works only on materials of biological origin, and only for ages up to about 10 half-lives of 14C because after that time there is so little 14C left that it cannot be accurately measured. Each method compares a radioactive isotope with a second nucleus to determine what fraction of the radioactive isotope has decayed and how long it has been decaying. Table 2 lists a few of these radioactive nuclei and their comparison nuclei. There are also many nonradioactive ways of dating old objects, some providing only relative ages and some providing highly accurate ages in years (Table 3). Some of these rely on changes that occur at a steady rate over long periods of time in the crystal structure of rocks or in the structure of biological molecules. Others rely on simply counting the annual rings in trees and annual ice deposits in long cylinders of ice removed by deep-drilling techniques from Greenland and Antarctica. Such records extend surprisingly far backward in time: Tree ring dates extend as far back as 11,000 years (with the help of fossilized trees), and ice cores extend back 800,000 years. Such a wide variety of independent dating methods provides strong cross-checks on the resulting dates. Table 3 Nonradioactive dating methods Method

Property that is measured

Tree rings

number of annual rings

Ice cores

number of annual layers of ice deposited

Rock strata

position and composition of sedimentary layers

Astronomical

age of solar system from meteorites age of stars from star type and location age of universe from cosmic background radiation

394

Electron spin resonance

radiation-induced changes in rocks

Thermoluminescence

radiation-induced changes in rocks

Optical spin luminescence

radiation-induced changes in rocks

Mitochondrial DNA

number of mutations of DNA molecules

Amino acid analysis

amount of change in amino acids

Y-chromosome

number of mutations of Y-chromosome

The Nucleus and Radioactivity: A New Force Table 4 shows some of the geological ages obtained for the biological and cultural evolution of life on Earth. To put these dates in perspective, the table’s third column compresses Earth’s history into a single 24-hour day. This perspective can be an eye-opener (Figure 11). Throughout most of Earth’s history, the dominant lifeforms have been simple organisms such as algae. On the 24-hour clock, complex animals do not appear until nighttime; the earliest humans evolve at 2 minutes before midnight; and our species evolves at 2 seconds before midnight. All of human culture spans a fraction of a second. Great movements such as the spread of agriculture, the human population explosion, the Industrial Revolution, and the information revolution, dash across the world stage in the blink of an eye. As Norman Mailer put it, the itch has been to accelerate. In the past, many scientists and nonscientists believed that Earth was only a few thousand years old. For example, Kepler suggested that “God waited six thousand years” for an observer such as Tycho Brahe. Such estimates were based on counting backward through the generations of the Old Testament and so calculating a date for Adam and Eve. Today, the hypothesis that Earth is only a few thousand years old conflicts with data and principles from astronomy, physics, chemistry, geology, biology, paleontology, archaeology, and history. Of course, this implies no criticism of the Old Testament, which in the opinion of most scholars should be treated as a spiritual work rather than a scientific text.

The concept of the unity of life should be introduced in grade school . . . [and] be linked firmly to an understanding of the way in which the genome has gradually changed over the more than 3 billion years that life has been unfolding. The fascinating descriptive biology of diverse organisms . . . can come later, once there is a framework to hang it on. That way, future generations will be able to appreciate the beauty of the Tree of Life without its form being obscured by the tangle of twigs and leaves. Jennifer A. Marshall Graves, Research School of Biological Sciences, Australian National University, in an Editorial for the Journal Science

Table 4 When we came from: some approximate dates relevant to our species Event

Years before present

On a 24-hour clock

Origin of solar system

4667 million

Origin of Earth

4557 million

00:00 (midnight)

Chemical evidence of life

3800 million

04:00

First fossils (single cell)

Life 3300 million

07:00

First vertebrates

500 million

21:30

First reptiles

300 million

22:30

First mammals

200 million

23:00

First primates

60 million

Humans First hominidsa Genus Homo Use of stone tools

23:40 seconds before 24:00

6 million

120 s

2.4 million

48 s

2 million

40 s

Homo erectus

1.9 million

38 s

Homo sapiens

100 thousand

2s

Culture Invention of agriculture First cities, earliest writing

a

10 thousand

0.2 s

5 thousand

0.1 s

Scientific age (Copernicus)

500

0.01 s

Industrial age

250

0.004 s

Twentieth century

100

0.002 s

Apemen that (unlike modern apes) walked upright and were direct human forebears.

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The Nucleus and Radioactivity: A New Force Figure 11

The “cosmic clock” compresses Earth’s history into 24 hours. Homo sapiens does not appear until 2 seconds before midnight. A lot happens during these last 2 seconds: Agriculture is invented at 0.2 s before midnight, followed by cities, the scientific revolution, and the Industrial Revolution.

100 s before midnight first hominids 23:40 first primates 23:00 first mammals

2 s before midnight first Homo sapiens 24:00

21:30 first animals with backbones

04:00 first life

18:00

06:00

12:00

How do we know that radioactive dating is reliable? Scientists continually crosscheck results such as Table 4 in a variety of independent ways. If several independent methods, perhaps based on both radioactive and nonradioactive processes, all agree, our confidence in all of them is increased. It would be amazing if they were all wrong in exactly the same way; scientists tend not to believe in such amazing coincidences. Because of this habit of cross-checking, science has been called a “web of consistency.” Carbon dating furnishes us with a nice example of cross-checking, because there is reason to expect errors in carbon-inferred dates: If the number of cosmic ray impacts on the atmosphere was different in the past, the 14C content in the biological world would have been different then than now. For this reason, scientists have extensively crosschecked the carbon-based dates. One method of cross-checking is by studying 14C in the annual growth rings of trees. It’s easy to date living trees (up to 5000 years old) by simply counting these growth rings, and scientists can date dead wood of unknown age by matching the growth patterns in the rings of the dead wood (variations in ring thicknesses, caused by varying climate) with the growth patterns in dated specimens. Tree specimens up to 10,000 years old can be dated in this way. There is little reason to doubt these dates, for they are obtained by simple counting. The results show that the older rings are as much as 15% older than is indicated by their carbon dates. Another method of cross-checking studies the 14C content in coral reefs. These reefs can be dated by the carbon method and also by a uranium method that is thought to be reliable to within 1%. Figure 12 shows the results of this cross-check (dots on the graph) and also the tree-ring cross-check (crosses). The dots and crosses show the uranium or tree-ring age (along the vertical axis) at which a given carbon-inferred age (horizontal axis) occurs. If both dating methods were accurate, the dots and crosses would lie on the straight line shown, along which the uranium or tree-ring age equals the carbon age. Since tree-rings and uranium are regarded as highly accurate dating methods, Figure 12 is used to correct or “calibrate” the dates obtained by 14C dating. For example, the data point circled shows that any object having a carbon age of 16,000 years is actually 19,000 years old.

396

The Nucleus and Radioactivity: A New Force Figure 12 Age as determined by uranium dating (dots) or tree-ring dating (crosses), in thousands of years before the present

30

20 The two methods disagree to the extent that the points do not fall on this line.

Checking carbon dating by using the tree-ring method (crosses) and a uranium method (dots). Apparently carbon dating gives ages that are a few thousand years too young for objects that are around 10,000 to 20,000 years old.

10

0

0

10 20 30 Age as determined by carbon dating, in thousands of years before the present

In a living person, the ratio of 14C to total carbon is 1 to one trillion. The C>C ratio 6000 years (one half-life of 14C) after a person has died is (a) 2 to one trillion; (b) 1 to one trillion; (c) 1 to two trillion; (d) 1 to four trillion. CONCEPT CHECK 7 14

CONCEPT CHECK 8 An archaeologist digs up a bone and measures an average of one 14C decay per minute in 1 gram of the bone’s carbon. This is about 10% of the decay rate in living organisms. This animal has been dead about (a) 6000 years; (b) 13,000 years; (c) 19,000 years; (d) 60,000 years; (e) 600 years.

6 HUMAN EXPOSURE TO IONIZING RADIATION The walls of your room, the air you breathe, and even your body are radioactive (Concept Check 7). What are the effects? Are the effects different today than they were before the nuclear age? What are the risks? Can or should anything be done to prevent harmful effects? The alpha, beta, and gamma particles emitted by radioactive materials damage biological cells. The damage is done when these high-energy particles pass, like little bullets,5 through a cell, ionizing (knocking electrons out of) some of the cell’s molecules. Because they can do this, alpha, beta, and gamma rays are called ionizing radiations. Since X-rays also have enough energy to ionize biological material, they too are classified as ionizing radiation, even though they don’t come from the nucleus. Ionization changes the cell’s chemistry. Any of the cell’s functions can be altered, depending on which molecules are ionized. The most important effects result from damage to a cell’s DNA molecules, because DNA carries the biological information inherited by other cells. The biological damage done in humans by ionizing radiation is measured in a unit called the sievert. If a person receives ionizing radiation, the number of sieverts 5

Even though they are really only field quanta, alphas and betas and gammas carry energy and momentum and so they act like particles when their fields interact with a human cell.

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The Nucleus and Radioactivity: A New Force

Masao Tsuzuki and Gon’ichi Kimura/AP World Wide Photos Figure 13

A victim of radiation sickness, 23 days after the Hiroshima bombing. The spots on his face are hemorrhages beneath the skin, caused by a weakness of the blood vessels and blood-clotting defects. He died a few days later. These acute, short-term effects are quite different from the long-term effects, primarily cancer, caused by low levels of ionizing radiation.

398

received is a direct measure of the number of damaged cells. A quantitative feel for the sievert is best obtained by looking at examples.6 For instance, the amount of radiation that an average person in the United States receives every year from all sources is about 0.003 sieverts, or 3 millisieverts (mSv). At the other extreme, a sudden dose of 6 sieverts causes death within 30 days. There are three main types of biological damage to humans. The most immediately obvious is radiation sickness, caused by damage to the red blood–forming cells of the bone marrow and to the cells that line the intestinal wall. A sudden dose of 0.25 to 1 sievert to the whole body causes short-term changes in the blood that the victim might not notice; 1 to 3 sieverts produces symptoms of radiation sickness: fever, vomiting, damaged red blood cells, reduced white blood cells and platelets, loss of hair, spontaneous bleeding, and small hemorrhages beneath the skin; 3 to 5 sieverts produces 50% fatalities; 6 to 10 sieverts causes death within 30 days; and 100 sieverts causes death within hours. Fortunately, humans have seldom experienced doses large enough to produce acute effects. The most severe examples have resulted from the nuclear bombs dropped in 1945 by the United States on the Japanese cities of Hiroshima and Nagasaki (Figure 13), the 1986 Chernobyl nuclear reactor accident in Ukraine in the former Soviet Union, and nuclear weapons tests during the 1950s in Kazakhstan in the former Soviet Union. Most of our knowledge of radiation damage to humans comes from these events and from medical uses of radiation. The second form of radiation damage is mutation, an inheritable alteration of the genetic material (DNA) in a sperm or egg cell. Mutations can produce successive generations of altered offspring. They are almost always harmful, but occasionally a mutation is advantageous, and this effect is in fact essential to biological evolution. The only observed cases of radiation-induced mutations in humans occurred downwind of Soviet nuclear weapons tests in Kazakhstan. Individuals exposed to “fallout” (see the following discussion) from the tests experienced an 80% increase in their mutation rate, and their children (born after the fallout occurred) experienced a 50% increase. These mutations occurred in portions of the sperm or egg DNA that did not, so far as researchers could determine, directly affect the physical characteristics of the children. The third form of damage is cancer in ordinary body cells. The rate of some cancers observed in nuclear bomb survivors has been far above normal. Among Hiroshima survivors, the leukemia rate between 1950 and 1985 was four times the normal rate. Many other forms of cancer occurred at double the normal rate. Based on available statistics, the National Academy of Sciences estimates that a sudden radiation dose of 0.5 sieverts produces about a 4% probability of eventual death by radiation-caused cancer. This means that out of every 100 people exposed to 0.5 sieverts, an average of 4 will ultimately die of radiation-caused cancer. Although ionizing radiation can cause cancer, it can also treat it. Cancer cells, because they grow rapidly, are especially susceptible to destruction by radiation. A narrow beam of gamma rays or X-rays is directed at the tumor. The radiation may come from a radioactive isotope such as 60Co, or from an X-ray machine. In some cases, a tiny radioactive source is inserted directly into the tumor. To treat thyroid cancer, radioactive 131I is injected into the blood. Because the thyroid gland absorbs

6

Here is the precise definition of the sievert: For gamma rays and X-rays, the sievert is the amount of radiation that would produce 1 joule of absorbed ionizing energy in 1 kilogram of biological material. The definition is a little more complicated for alpha and beta rays.

The Nucleus and Radioactivity: A New Force

any iodine present in the bloodstream, the 131I becomes concentrated in the thyroid, particularly in cells that are growing abnormally, killing the defective cells. Radioactive isotopes are also put to beneficial use as tracers in medicine, agriculture, and industry. A given compound is chemically synthesized using a radioactive isotope such as 14C or 3H. Radiation detectors then follow these “tagged” molecules as the compound moves through the human body, through a living plant, or through an industrial process. For example, the details of how a medical drug distributes itself in the body can be traced in this way. Until recently, there was lots of disagreement about the effects of low radiation doses, comparable to the amounts people receive every day. Because the effects are hard to observe, predictions are hard to check. Some scientists argued that even tiny doses cause harm; while others argued that small doses are harmless or even beneficial. In 2005, the U.S. National Academy of Sciences concluded, based on extensive data developed since 1990, that even tiny doses cause harm; even a single microscopic decay process has a small probability of causing a cancer or mutation, with the probability of harm being proportional to the amount of radiation received. As an example, one cancer-causing isotope produced by nuclear weapons and 90 nuclear reactors is radioactive strontium, 90 Sr and 38Sr. After a nuclear explosion, other radioactive isotopes attach themselves to atmospheric dust particles that eventually fall to Earth as radioactive fallout. As you can see from the periodic table, strontium is chemically similar to calcium. If you breathe or eat 90Sr, it will do what calcium does, namely, migrate to your bone marrow. Since the bone marrow is where red blood cells are created, the connection between radioactivity and leukemia (a blood condition) is not surprising. Radioactive isotopes such as 90Sr that are chemically active in the human body are especially dangerous, because once inside the body they combine with other chemicals and stay there. Because of isotopes like 90Sr, radioactivity is much more dangerous inside the body than outside it. Table 5 shows what kinds of natural and artificial radiation most Americans receive. As you can see, people generally receive about 3 mSv during each year of life. Most of it is natural, from sources that have been present in nature for thousands of years. Two widely discussed artificial sources, nuclear power and nuclear weapons tests, contribute only a tiny fraction. By far the largest artificial source is medical. Nearly half of the average dose comes from a single natural source, radon, which is a daughter nucleus from the decay of radium in the ground. Because radon is a gas, it escapes into the atmosphere shortly after being created underground. It’s not really radon itself that is dangerous, because it’s chemically inert and is breathed in and right back out before it can decay (its half-life is 4 days). But radon’s daughter nuclei are both radioactive and chemically active, and they attach themselves to microscopic airborne particles, are breathed in, become lodged in the lungs, and can lead to lung cancer. Because radon collects inside closed houses, it is five times more concentrated in the average home than in outdoor air. Most of the radon in homes enters through the substructure. Radon levels vary widely among different houses, with some not much above outdoor levels and others a hundred or a thousand times greater. You can check your home’s radon level by buying a small device called a track detector at a hardware store. Alpha particles emitted by radon leave a track as they pass through the detector. After the detector has been in your house for a few months, you can mail it to a laboratory where the tracks are counted and used to calculate your home’s radon level. If your home has a high level, you might want to seek professional assistance in reducing it. Sealing cracks doesn’t help much, because air pressure differences suck air from the ground through the substructure

399

The Nucleus and Radioactivity: A New Force Table 5 Ionizing radiation received by the U.S. population Estimated annual effective dose received in one year from various sources, averaged (per person) across the U.S. population. Source

Annual dose per person (mSv)

Natural Radon from the ground

1.25

Cosmic rays

0.39

Rocks and soil

0.48

Internal consumption

0.28

Subtotal

2.40

Artificial Medical and dental X-rays

0.31

Nuclear medicine

0.11

Consumer products

0.08

All other

a

0.03

Subtotal

0.53

Grand total

2.93

a

Occupational, nuclear weapons, nuclear power and its fuel cycle, and miscellaneous. SOURCE: National Research Council’s seventh committee on the biological effects of ionizing radiation, 2005.

and up into the house, even in well-sealed houses. Simple ventilation can help, though. The most effective solution is a blower inserted between the house’s concrete base and the gravel on which the concrete is laid to change the pressure system beneath the house so that the house will no longer suck air from the ground. You might have noticed that food irradiation is not in Table 5. In this process, gamma rays from a radioactive isotope are passed through raw meat and other foods in order to eliminate bacteria. These rays are of course not radioactive themselves, and they create no radioactivity in the meat. So, although one can debate other side effects of this process, food irradiation causes no radiation exposure to the consumer. CONCEPT CHECK 9 Which of these are electromagnetic ionizing radiations? (a) X-rays. (b) Infrared rays. (c) Alpha rays. (d) Beta rays. (e) Gamma rays. CONCEPT CHECK 10 Which of these causes radiation damage in some of your cells? (a) Medical X-rays. (b) Food irradiation. (c) Gamma rays passed through your body during cancer treatment. (d) Ingesting a radioactive isotope during cancer treatment.

MAKI NG ESTI MATES How radioactive are you? The human body is 18% carbon by weight. Biological material contains some 50 billion 14C atoms per gram of carbon, of which some 10 atoms decay every minute. Estimate the number of radioactive carbon atoms in your body and the number inside you that decay during 1 minute. SO LUTION TO MAKI NG ESTI MATES If your body’s mass is 60 kg (130 pounds), it contains about 12 kg, or 12,000 g, of C. The number of 14C atoms in your body is about (50 * 109) * (12,000) = 600 * 1012, or 600 trillion. The number of atoms that decay in 1 minute is 10 * 12,000 = 120.000. Your total radioactivity is actually twice this large, owing to other radioactive isotopes in your body.

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The Nucleus and Radioactivity: A New Force

7 DEALING WITH TECHNOLOGICAL RISK To live is to risk: There is risk in leaving your house (you could get hit by a car), and there is risk in staying home (you could breath radon). The nuclear incident at Chernobyl provides a good starting point for thinking about risk. An explosion and fire in 1986 at the former Soviet Union’s (now Ukraine’s) Chernobyl nuclear power plant threw massive amounts of radioactive isotopes into the air. This contaminated vast areas of Ukraine, Russia, and Belarus and spewed a radioactive cloud over Europe carrying 100 times the amount of radiation released in the atomic bombing of Hiroshima and Nagasaki (Figure 14). It was history’s worst nuclear power accident. The immediate toll was 237 cases of radiation sickness, with 50 fatalities, among emergency workers. A haphazardly built concrete and steel sarcophagus covers the ruined reactor, but it is leaking gas, contaminated water, and high radiation levels. The structure is believed to contain 66 tons of melted nuclear fuel, plus 37 tons of radioactive dust. Ukraine hopes to build a new, airtight covering, but that will not entirely solve the problem. It will take several more decades to develop and carry out an engineering decision on what to do with the nuclear fuel. The reactor operators were careless, to say the least. The reactor was of a type that can suffer a runaway nuclear chain reaction that releases thermal energy rapidly enough to create a low-grade nuclear explosion, and this in fact happened at Chernobyl. The reactor lacked a containment dome such as covers all U.S. nuclear power reactors. The incident occurred during a safety test that was conducted in a careless manner and that included some risky procedures such as disconnecting the emergency cooling water that is held in reserve to keep the reactor from overheating in an accident. It is difficult to determine the number of long-term cancer deaths caused by Chernobyl during the succeeding several decades. Radioactive fallout spread over much of Europe, producing the irregular pattern seen in Figure 14. Many Europeans received total individual doses of more than 10 mSv during only the first four days (compare Table 5). Fallout doses were much larger closer to Chernobyl. Over 100,000 people were evacuated from a 30-kilometer zone around the accident. Significant effects persist today in Ukraine and Belarus. Pripyat City, a former Soviet model city of 40,000 adjacent to the reactor, remains a ghost town now used only as a laboratory for investigating the effects of a possible radioactive or “dirty bomb” attack by terrorists. The region within 37 km around the accident has been abandoned and won’t be safe for human habitation for centuries. A study organized by the International Atomic Energy Agency reported in 2005 that approximately 4000 excess cancer deaths have or will occur during the next 70 years in Russia, Belarus, Ukraine, and the rest of Europe as a result of the accident. In the same population, one might normally expect about 125 million cancer deaths. So, although the number of excess deaths is large, they represent an increase in the cancer death rate of only 4000>(125 * 106), or about 0.003%. This tiny percentage increase is undetectable in the overall cancer statistics. One way to make sense of such numbers is by making numerical comparisons with other risks, a procedure known as quantitative risk assessment. For example, the 4000 worldwide deaths during 70 years from Chernobyl are one-tenth the number killed by automobiles in only one year in the United States alone (over 40,000— a number that I like to remember for comparison with other statistics in the news) and one-fifth the number of murders per year in the United States (20,000).

The health of the people is the wealth of the country. Inscription On an Enormous Sign Posted on a Now-Empty Medical Clinic in the Town of Pripyat, Near the Chernobyl Power Plant. Pripyat was Evacauted During the Accident and Remains a Ghost Town Today

401

The Nucleus and Radioactivity: A New Force Figure 14

The spread of radiation following the Chernobyl nuclear power plant accident. The three shaded regions represent three different levels of exposure to 131I. During the first four days following the accident, people in the three gray areas received the iodine radiation exposures indicated.

10 mSv or more

1 to 10 mSv

0.1 to 1 mSv

Comparisons such as these can put abstract numbers into perspective. For another example, radon exposure causes between 5000 and 20,000 (the number is highly uncertain) U.S. lung cancer deaths per year, which is comparable to the murder rate. Another way to make sense of such risks is to look at probabilities of death for one person. For example, fallout from Chernobyl might kill 4000 out of a total European and former Soviet Union population of about 750 million, representing a fraction of 4000>(750 * 106), or about 5 * 10 - 6, or 5>106. One way to look at this is that each of these people has on the average about 5 chances in a million of dying from Chernobyl-caused cancer. That is, in a randomly chosen group of 1 million, about 5 will die of this cause. Scientists have used such methods to assess the risks to Earth from impacts of comets or asteroids, such as the impact that destroyed 2000 square kilometers of Siberian forest in 1908 or the much larger impact that made the dinosaurs extinct 65 million years ago. One conclusion: Taking all impact sizes into account, each person has about 1 chance in 20,000 of being killed by such an impact. This is far less than the car crash risk, but roughly the same as the risk of an average American dying in an aircraft accident. Since America takes deadly aircraft accidents very seriously indeed, it follows that the risk of such an impact should also be taken very seriously—especially if something can be done to reduce this risk. In fact, much can be done, by detecting and deflecting threatening comets in space. As a result of this analysis, many nations now cooperate to address this problem.

402

The Nucleus and Radioactivity: A New Force Table 6 is an unnerving example of quantitative risk assessment. The table lists several activities that carry the same quantitative risk of death, 1 in 1 million. All these risks are equivalent in the sense that if everybody in a population of 1 million were to perform any one of the indicated activities, one of them (on the average) would eventually die from it. Every time you perform one of these activities, there is one chance in a million that it will kill you. It’s enough to keep you from getting out of bed in the morning. To say that everything has its risks is really another way of saying that we all must die. In the long run, the total risk of death is 100%. It’s sad but true, and one might as well try to deal with it sensibly. Many risks, such as radon exposure, are impossible to reduce to negligible proportions, and few risks can be reduced to zero. In fact, attempts to reduce risk can be counterproductive. For example, if you Table 6 The risks of daily life: Activities carrying an average risk of death of one part in a million Activity

Cause(s) of death

Ionizing radiation One chest X-ray at a good hospital

Cancer from ionizing radiation

Cross-country round trip by jet

Cancer from cosmic ionizing radiation

Living 1 week in a building

Cancer from indoor radon

Living 5 weeks outdoors

Cancer from outdoor radon

Living 2 months in Denver

Cancer from cosmic ionizing radiation

Living 5 years next to a nuclear power plant

Cancer from ionizing radiation

Living 50 years within 8 km of a nuclear power plant

Accident

Internal consumption Smoking 1.4 cigarettes

Cancer and heart disease

Living 2 months with a cigarette smoker

Cancer and heart disease

Drinking 0.5 liters of wine

Cirrhosis of the liver

Normal consumption of tap water for 1 year

Cancer from chloroform

Drinking 30 12-ounce cans of diet soda

Cancer from saccharin

Eating 40 tablespoons of peanut butter

Liver cancer from aflatoxin B

Eating 100 charcoal broiled steaks

Cancer from benzopyrene

Travel 5 km by motorcycle

Accident

16 km by bicycle

Accident

50 km by car

Accident

1300 km by train

Accident

1600 km by commercial airplane

Accident

10,000 km (cross-country round trip) by jet

Cancer from cosmic ionizing radiation

Work Spending 1 hour in a coal mine

Black lung disease

Spending 3 hours in a coal mine

Accident

Other Living 2 days in New York or Boston

Air pollution

Adapted from Richard Wilson, “Comparing Risks,” Physics and Society, October 1990, pp. 3–5.

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The Nucleus and Radioactivity: A New Force

try to avoid radiation exposure by skipping a recommended chest X-ray, you might die from tuberculosis. You could significantly reduce your radon risk by living outdoors, but that would expose you to other risks. You could decide to do nothing that is nonessential if it carried any risk, but then you would die of boredom. Radiation safety specialists have thought a lot about radiation risk, and they offer two general pieces of wisdom: First, every radiation dose may carry some risk, so no exposure is permissible unless it carries a compensating benefit. Second, the dose to any person should be kept as low as is reasonably possible, taking into consideration all other factors (social, economic, and so forth). In other words, balance the risks against the benefits, and be aware. Similar principles apply to all of life’s risks. CONCEPT CHECK 11

137

Cs has a half-life of 30 years. The time after the Chernobyl incident at which the radiation from this isotope decreases to 1% of its original level is roughly (a) 60 years; (b) 100 years; (c) 200 years; (d) 500 years; (e) 900 years.

© Sidney Harris, used with permission.

CONCEPT CHECK 12 About how far would you have to travel by car in order to have the same risk of death as traveling across the United States by train (4000 km)? (a) 12,000 km. (b) 100,000 km. (c) 1000 km. (d) 250 km. (e) 150 km.

404

The Nucleus and Radioactivity Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions NUCLEAR FORCES 1. In what ways is the nucleus non-Newtonian? 2. Name the four fundamental forces, and describe the main function of each of the three that act as “glues” to hold things together. 3. Which of the four forces holds the nucleus together, and which tends to push it apart? 4. What property of the strong force causes nuclei to be so small? Why can’t much larger nuclei exist?

NUCLEAR ENERGY AND NUCLEAR STRUCTURE 5. Explain why nuclear particles must move rapidly and so must have high energy. 6. How are nuclear reactions similar to alchemy? 7. What is an isotope, and what quantities need to be known in order to specify a particular isotope? 8. What are the differences among 126C, 146C, and 147N? Compare their numbers of protons, numbers of neutrons, chemistry, nuclear chemistry (behavior in nuclear reactions), numbers of orbital electrons in the neutral atom, and mass.

RADIOACTIVE DECAY 9. What kinds of rays, or particles, are emitted by radioactive nuclei? Describe each kind. 10. What happens to the atomic number and mass number during alpha decay? 11. What happens to the atomic number and mass number during beta decay? 12. What energy transformation occurs during radioactive decay?

HALF-LIFE 13. In radioactive decay, what quantity cannot be predicted? Of what basic principle is this an example? 14. 131I has an 8-day half-life. If you start with 100 grams, how much will remain after 24 days? 15. If you started with 100 grams of 14C (6000-year half-life) and only 3 grams remain, about how much time has elapsed?

RADIOACTIVE DATING 16. Explain how carbon dating works. On what kinds of objects does it work? From where does radioactive carbon come?

17. An ax handle has a 14C>C ratio that is only 1/32 of the ratio found in living organisms. About how old is this ax handle? 18. According to science, about how old is Earth: a few thousand years, a few million years, a few hundred million years, a few billion years, or a few trillion years? How about the human race (hominids)? 19. Describe at least one way to cross-check a particular dating method such as carbon dating.

HUMAN EXPOSURE TO IONIZING RADIATION 20. Which of the following are ionizing radiations: radio waves, ultraviolet radiation, gamma rays, alpha rays, X-rays? 21. What is a sievert? 22. Name and describe the three main types of biological damage caused by ionizing radiation. 23. List two natural sources of ionizing radiation and one artificial source. 24. List some useful applications of radioactive isotopes.

DEALING WITH TECHNOLOGICAL RISK 25. What will be the long-term health effects of the Chernobyl accident? 26. What is fallout, and where can it come from? 27. What is the meaning of a risk (of cancer, for example) of 3/1,000,000 per person? 28. Where might you find radon in your normal living environment? How does it get there?

Conceptual Exercises NUCLEAR FORCES AND STRUCTURE 1. Which force is stronger between two protons separated by 10 - 15 m (the size of a small nucleus), the electric or the strong force? What evidence do you have for your answer? 2. Which force is stronger between two protons separated by 10 - 10 m (the size of an atom), the electric or the strong force? What evidence do you have for your answer? 3. How many protons and neutrons are there in these nuclei: 13 56 6C, 26Fe? 4. How many protons and neutrons are there in 90Sr? In 3H? 5. How many protons and neutrons are in a nucleus of 235 92U, and of 238 92U?

From Chapter 14 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

405

The Nucleus and Radioactivity: Problem Set 6. How do the masses of 1H, 2H, and 3H compare? How do their charges compare? 7. How do the masses of 3H and 3He compare? How do their charges compare? 8. Suppose that the electric force were somewhat stronger than it actually is. Would this lengthen, or shorten, or leave unchanged, the periodic table? 9. Referring to Figure 1, how would the periodic table be affected if the range of the strong nuclear force were only 10 - 16 m instead of 10 - 15 m?

RADIOACTIVE DECAY 10. Why are radioactive materials often warm? 11. What do you suppose heated the water in a naturally heated hot spring? 12. Radioactive materials often glow in the dark. But the gamma radiation emitted by a nucleus during decay is not visually detectable, so where does the light come from? 13. Which ray is most similar to X-rays: alpha, beta, or gamma rays? 14. Can a hydrogen nucleus emit an alpha particle? 15. Can an element decay “forward” in the periodic table to a higher atomic number? 16. Use the periodic table to find the residual nucleus in each of the following: beta decay of 3H, alpha decay of 222Rn. 17. Use the periodic table to find the residual nucleus in the beta decay of 90Sr.

HALF-LIFE 18. If a radioactive isotope has a 1-year half-life, what fraction will remain after 5 years? 19. If a radioactive isotope has a 6-month half-life, what fraction will remain after 5 years? 20. Isotopes having atomic numbers larger than 92 (uranium) don’t exist in nature because they have half-lives much shorter than Earth’s age and hence have decayed away. How then can an isotope such as 226 88Ra, with a half-life of only 1600 years, exist in nature? 21. Earth is about 4.5 billion years old. Roughly how much 238U was there on the newly formed Earth as compared with today? (See Table 1.)

22. Earth is about 4.5 billion years old. Roughly how much 235U was there on the newly formed Earth as compared with today? (See Table 1.) 23. Starting with 2 grams of radon, how much will remain after 12 days? (See Table 1.) 24. If you start with a gram of pure 14C, about how much will remain after 12,000 years? 25. Starting with 100 atoms of radon, how many will remain after 12 days? (See Table 1.) Is this a precise prediction? 26. Starting with 10 atoms of radon (half-life 4 days), about how long would it take before all 10 had decayed? What fundamental physical principle prevents you from making a precise prediction of this time? 27. Which of the isotopes in Table 1 is the most stable? Which is the least stable? 28. If you had 1 gram of 235U and 1 gram of 238U. which would be more highly radioactive, that is, which would emit more alpha particles per minute? (See Table 1.) 29. You have only 100 atoms of a certain radioactive substance. Approximately how many atoms will remain after four halflives? Will you have precisely this many? Explain. 30. You have only five atoms of 222Rn (half-life 4 days). What can you say about the number remaining after 4 days? After 8 days? After 8 days, might all five atoms still remain undecayed?

RADIOACTIVE DATING 31. Can scientists carbon-date ordinary rocks? Why? 32. Would carbon dating be useful in dating the age of the earliest hominids? The earliest cities? (See Table 4.) 33. Suppose that the number of cosmic rays impacting the atmosphere had been greater in the past than it is now. Would this affect our estimate, based on carbon dating, of an old ax handle’s age? Would it cause us to estimate an age that was too old, or would our estimate be too young? 34. Carbon dating was used to find the age of the Dead Sea Scrolls. Would this method have worked if the scrolls had been carved in stone? 35. Prior to the 1963 treaty banning nuclear weapons tests in the atmosphere, weapons testing created large amounts of radioactive isotopes in the atmosphere. One of these isotopes was 14 C, whose atmospheric concentration doubled as a result of testing. How will this affect radioactive dating in the future?

Table 1 Half-life and decay process of several radioactive isotopes

406

Isotope

Name of element

Decay process

Half-life (approx.)

14 6C

carbon

beta

6000 yr

90 38Sr

strontium

beta

30 yr

131 53I

iodine

beta

8 days

214 84Po

polonium

alpha

0.000 16 s

222 86Rn

radon

alpha

4 days

235 92U

uranium

alpha

0.7 * 109 yr

238 92U

uranium

alpha

4.5 * 109 yr

239 94Pu

plutonium

alpha

24,000 yr

The Nucleus and Radioactivity: Problem Set Table 4 When we came from: some approximate dates relevant to our species Event

Years before present

On a 24-hour clock

Origin of solar system

4667 million

Origin of Earth

4557 million

00:00 (midnight)

Chemical evidence of life

3800 million

04:00

First fossils (single cell)

Life 3300 million

07:00

First vertebrates

500 million

21:30

First reptiles

300 million

22:30

First mammals

200 million

23:00

First primates

60 million

Humans First hominidsa Genus Homo Use of stone tools

23:40 seconds before 24:00

6 million

120 s

2.4 million

48 s

2 million

40 s

Homo erectus

1.9 million

38 s

Homo sapiens

100 thousand

2s

Culture Invention of agriculture First cities, earliest writing

a

10 thousand

0.2 s

5 thousand

0.1 s

Scientific age (Copernicus)

500

0.01 s

Industrial age

250

0.004 s

Twentieth century

100

0.002 s

Apemen that (unlike modern apes) walked upright and were direct human forebears.

Will this affect the apparent age of an ax handle that was made in 1940? What about an ax handle made in 1990? 36. Prior to the 1963 treaty banning nuclear weapons tests in the atmosphere, weapons testing created large amounts of radioactive isotopes in the atmosphere. One of these isotopes was 14 C whose atmospheric concentration doubled as a result of testing. Will this cause an ax handle made in 1990 to appear younger, or will it appear older?

DEALING WITH TECHNOLOGICAL RISK 37. Given that 131I has a half-life of 8 days, how much time must pass after the Chernobyl accident before the radiation from this isotope will have decreased to 1% of its original level? 38. At a party, Edgar drinks half a liter of wine and smokes four cigarettes. Which activity was riskier? How much riskier? (Assume that Edgar doesn’t drink and drive.) 39. You travel 200 km by car. Would the trip have been safer by train? How much safer? 40. How much safer is a car than a motorcycle? 41. How much safer is a car than a bicycle? Since cars are safer, why are so many more people killed in them every year than are killed riding bicycles?

42. You travel 3200 km by car. Use Table 6 to find your risk of death by accident, assuming you are an average driver. 43. Referring to the preceding exercise, if you had flown by jet, what would have been your risk of death by accident or by cancer from the cosmic radiation at high altitudes? 44. The number of people killed worldwide by volcanoes increased from 315 per year in CE 1800 to 845 per year in the mid–twentieth century. But population also increased during that time, from 750 million to 3 billion. So did the yearly risk, per person, from volcanoes increase, or decrease?

Problems HALF-LIFE 1. You have one gram each of 131I and 234Th. Use Table 1 to predict how much of each you will have after 24 days. 2. You start with 5 grams of 131I. How long will it take the radiation to get down to 5% of its original value? (Use Figure 10.)

407

The Nucleus and Radioactivity: Problem Set Table 6 The risks of daily life: Activities carrying an average risk of death of one part in a million Activity

Cause(s) of death

Ionizing radiation One chest X-ray at a good hospital

Cancer from ionizing radiation

Cross-country round trip by jet

Cancer from cosmic ionizing radiation

Living 1 week in a building

Cancer from indoor radon

Living 5 weeks outdoors

Cancer from outdoor radon

Living 2 months in Denver

Cancer from cosmic ionizing radiation

Living 5 years next to a nuclear power plant

Cancer from ionizing radiation

Living 50 years within 8 km of a nuclear power plant

Accident

Internal consumption Smoking 1.4 cigarettes

Cancer and heart disease

Living 2 months with a cigarette smoker

Cancer and heart disease

Drinking 0.5 liters of wine

Cirrhosis of the liver

Normal consumption of tap water for 1 year

Cancer from chloroform

Drinking 30 12-ounce cans of diet soda

Cancer from saccharin

Eating 40 tablespoons of peanut butter

Liver cancer from aflatoxin B

Eating 100 charcoal broiled steaks

Cancer from benzopyrene

Travel 5 km by motorcycle

Accident

16 km by bicycle

Accident

50 km by car

Accident

1300 km by train

Accident

1600 km by commercial airplane

Accident

10,000 km (cross-country round trip) by jet

Cancer from cosmic ionizing radiation

Work Spending 1 hour in a coal mine

Black lung disease

Spending 3 hours in a coal mine

Accident

Other Living 2 days in New York or Boston

Air pollution

Adapted from Richard Wilson, “Comparing Risks,” Physics and Society, October 1990, pp. 3–5.

RADIOACTIVE DATING 3. You measure the carbon-radioactivity of an old wooden ax handle to be only 20% of its original value. Estimate the age of the ax handle. 4. The 14C>C ratio in an old piece of cloth (made from natural fibers) is found to be 70% of the ratio in living organisms. How old is this piece of cloth? 5. About what fraction of Earth’s original 238U, which was here when Earth was created, is still here? 6. About what fraction of Earth’s original 235U, which was here when Earth was created, is still here?

408

7. You suspect that a certain wooden spear dates from 50,000 years ago. If you use carbon dating, how much radioactivity do you expect to find, as compared with that present in living organisms? Why might it be difficult to actually carry out this dating procedure? 8. The oldest rocks on Earth are meteorites that fell from space relatively recently but are presumed to have solidified when our solar system formed. Examination of the uranium in these meteorites, and of the various daughter nuclei that come from uranium, shows that these rocks contain a little less than 1% of the 235U that they contained when they first crystallized. Based on this data, about how old is our solar system?

The Nucleus and Radioactivity: Problem Set 1.00

Figure 10

0.90

Radioactive decay curve for 14C and for any other radioactive isotope.

Fraction remaining

0.80 0.70 0.60 1/2

0.50 0.40 0.30

1/4

0.20 1/8 0.10

1/16 0

6000

12,000 18,000 Years (for 14C)

1/32

24,000

30,000

1 2 3 4 Number of half-lives (for any radioactive isotope)

RADIATION RISKS AND RISK ASSESSMENT 9.

The average risk of daily life. Everybody dies precisely once. Average this one death over a typical life of 70 years, and show that the average risk of death per day from all causes is 1 chance in 25,000, or 0.000 04, or 40 chances in a million. (This average is not a good approximation to the actual day-to-day risk, because the daily risk varies greatly from year to year. For instance, the risk of dying before the age of 1 and over the age of 65 are considerably higher than during the intervening years.) 10. MAKING ESTIMATES The meaning of 1 in a million. Table 6 says that there is a death risk of 10 - 6 in smoking 1.4 cigarettes. Suppose you smoke an average of 1.4 cigarettes daily for 40 years. How large is your overall total risk from smoking? What if it’s a pack (20 cigarettes) per day instead? 11. MAKING ESTIMATES The human body is about 18% carbon, by weight. Most of this carbon is in the form of the stable isotopes 12C and 13C, but about one carbon atom in a trillion is radioactive 14C. About how many grams of 14C does a typical 70 kg living human contain? MAKING ESTIMATES

Answers to Concept Checks 1. Larger nuclei could hold together, so the list would be 2. 3. 4. 5. 6.

longer, (b). (b) (c) (b) and (d) (e) (e)

5

7. (c) 8. There must be only 10% as many 9. 10. 11. 12.

14 C atoms as there were when the animal died. The number of 14C atoms is down to 10% after about 19,000 years. (a) and (e) (a), (c), (d) Six to seven half-lives, or 180 to 210 years, (c). According to Table 6, the distance by car is only 50/1300, or 1/26, as large as the distance by train. So traveling 4000 km by train carries the same risk as traveling 4000>26 = 150 km by car, (e).

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. The strong force. If the electric force were stronger, the nucleus would fly apart. 3. 136C: 6 protons, 7 neutrons 56 26Fe: 26 protons, 30 neutrons 5. 235 92U : 92 protons, 143 neutrons 238 92U : 92 protons, 146 neutrons 7. Masses are about the same. Charge is in the ratio of 1 to 2. 9. Protons and neutrons would lie 10 times closer to each other in the nucleus, and nuclei would be 10 times smaller in diameter. This would increase the effect of the repulsive electromagnetic force between protons, because the electromagnetic force is stronger at smaller distances. This would tend to destabilize the nucleus, so the periodic table would be shorter.

409

The Nucleus and Radioactivity: Problem Set 11. Hot rock inside Earth; this rock is heated, at least indirectly,

41. As in Problem 39, the car is 50>16 L 3 times safer. More

by radioactivity inside Earth. Gamma rays, because they are a form of electromagnetic radiation. Yes, in beta decay the daughter nucleus has a higher atomic number. 90 39Y . Five years is 10 half-lives, so 1/1024 (about 0.001, or 0.1%) of it will remain. The half-life of 238U happens to also be 4.5 billion years. Thus there was twice as much here on the newly formed Earth as there is today. Radon’s half-life is 4 days. So 12 days is 3 half-lives. The amount remaining is 2 g * 1>8 = 2>8 = 1>4 g. Radon’s half-life is 4 days. So 12 days is 3 half-lives. The amount remaining is 100 atoms * 1>8 = 12.5 in other words, about 12 or 13 atoms. This is not a precise prediction because of statistical uncertainties when dealing with such a small number of atoms. Most stable: 238U (longest half-life). Least stable: 214Po (shortest half-life). (1>16) * 100 = 6.25, so there will be approximately 6 or 7 left. This answer is approximate because of the uncertainties involved in radioactive decay. We cannot carbon-date rocks, because they contain no formerly living material. Yes, it would affect our estimate. It would cause us to estimate too young an age, because it would have caused a larger amount of 14C to be deposited in the past. This will cause future estimated ages to be younger than they really are. This will not affect the apparent age of an ax handle made in 1940 (before nuclear testing), but it will affect the apparent age of an ax handle made in 1990. After 6 to 7 half-lives, the decay curve is down to about 1%. For 131I, 6 to 7 half-lives is 48 to 56 days. Yes. Since (from Table 6) 1300 km by train and 50 km by car are equally risky, the train is 1300>50 = 26 times safer (per km traveled) than the car.

people are killed in cars because so many more people ride in cars than on bicyles, and because bicycle riders ride only a few hundred miles per year while car riders ride many thousands of miles per year. 43. The accident risk is 2 * 10 - 6. For the cancer risk, note that 3200>8000 = 0.4, so the risk is 0.4 * 10 - 6. Thus the total risk is 2.4 * 10 - 6.

13. 15. 17. 19. 21. 23. 25.

27. 29. 31. 33. 35.

37. 39.

410

Problems 1. 131I: 1/8 gram. 234 Th: 1/2 gram. 3. According to Figure 10, the radioactivity drops to 20% of its original value after about 2.25 half-lives. Table 1 says that the half-life of 14C is about 6000 years, so the age of the ax handle is about 6000 * 2.25 = 13,500 years. 5. The half-life of 238U is about the same as Earth’s age (Tables 1 and 2), so about half of the original 238U still remains. 7. 14C half-life = 6000 years, so 50,000 years is a little more than 8 half-lives, so the fraction remaining is only 1/256, or 0.4%. This dating procedure would be difficult to carry out, because the amount of 14C radioactivity would be so small that it would be hard to measure. In fact, 50,000 years is near the upper limit of ages that are measurable by 14C radioactivity. 9. The number of days in 70 years is 70 * 365 = 25,550, or approximately 25,000 days. So the daily average risk is about 1 in 25,000. Expressed as a fraction, the daily probability of death is 1>25,000 = 4 * 10 - 5 = 0.00004, or 40 chances in a million. 11. 0.18 * 70 kg = 12.6 kg of C in a typical body. One trillionth of this is 10 - 12 * 12.6 kg = 12.6 * 10 - 12 kg = 12.6 * 10 - 9 grams, or about 13-billionths of a gram. Note: In this approximate calculation, we neglected the fact that the three isotopes of carbon have different masses.

The Energy Challenge Without energy there is no economy, without climate, there is no environment, and without economy and environment, there’s no well-being, so we had better figure out how to get this right. John Holdren, President Obama’s Science Advisor, Former President of the American Association for the Advancement of Science, 30 April 2009

T

o physically change anything, you must exert a force through a distance—you must do work. It isn’t surprising then that energy—the capacity to do work—is basic to society, especially today when Earth’s human population is expanding rapidly, technology is expanding rapidly, and so much is in flux. In fact, it’s difficult to convey the extent to which modern society depends on an array of natural energy resources outside of human muscular energy. As an exercise, list as many energyconsuming items as you can think of that you used during the past week. Time out, for listing. Here are a few that I used: car, air conditioner, lightbulbs, refrigerator, TV, computer, toaster, candle, fan, newspapers (paper, printing, delivery), foods (growing, processing, packaging, transporting), clothes (manufacturing, transporting), hot water, cold water (supply, wastewater treatment), and so forth. Our entire way of life depends on the availability of energy resources at a reasonable price. If people everywhere are to achieve greater prosperity, they will need adequate energy supplies at an affordable price and at an affordable cost to the environment. As John Holdren points out in the opening quote, climate issues are at the center of the environmental problem and environment is at the center of human well-being, “so we had better figure out how to get this right.” Although today’s energy is based largely on fossil fuels, this will and must change. As world population grows, as more nations develop powerful industries, as world fossil-fuel resources decline, and as global warming heightens, humankind approaches the end of the fossil fuel age—whether we like it or not. The question is not whether the fossil fuel age will soon end; the real question is how it will end. Will we, through switching to sustainable energy resources, purposely restraining fossil fuel use, and encouraging family planning to limit overpopulation, make a rational transition to a world in which the United States and other industrialized nations reduce their fossil fuel consumption to 10% or 20% of current consumption? Or will we continue our joyride until fossil resources run dry, global warming becomes global catastrophe, and the global economy declines? It’s up to you, dear reader, and up to each one of us, to answer that question. I’ve designed this chapter to help in that task by looking at the history and present status of energy production and use, and studying how humankind might convert to more sustainable sources of energy while using less of it.

From Chapter 16 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Energy Challenge

Section 1 takes a long-term view and then a short-term view of the history of energy use. Section 2 looks at today’s energy use and outlines tomorrow’s options. The next three sections look at the nonrenewable resources, especially nuclear and coal. To what extent can and should we continue using them? Section 3 describes how nuclear power works, Section 4 considers some of the issues involved in the continued use of coal power, and Section 5 looks at the issues involved in using nuclear power. Section 6 explores several renewable sources of energy. Section 7 looks at the physics, and a little of the economics, of energy efficiency. A personal note: Most students of energy issues have formed opinions about this topic, and I’m no exception. However, I have made every effort to restrain my own opinions and to present fairly all of the reasonable options. Do not, for example, assume that the emphasis given to nuclear power means that I am either especially friendly, or especially hostile, to nuclear power. Rather, I’ve tried to emphasize those topics that are important for our energy future and that have a strong physics component.1

1 A BRIEF HISTORY OF ENERGY Before deciding where you want to go, it’s smart to know where you’ve been. Figure 1 graphs, highly schematically, 6 million years of human energy use, plotting the approximate daily energy consumption per person (in megajoules) versus time. The differences between Stone Age culture and modern culture have everything to do with different ways of organizing energy to do work. The earliest humans used only their own muscular energy, obtained by respiration of food and oxygen. A typical person puts some 2000 Calories, or 8 million joules (8 MJ), of bodily energy to work every day, roughly equivalent to a continuously burning 100-watt bulb. Although it’s not indicated in Figure 1, humans began using fire around 1 million years ago. Some 10,000 years ago, humans began using the chemical energy of farm animals to do work, helping to usher in the earliest agriculture. Farm animals and fire might have increased the energy put to work by one person fivefold, to 40 MJ per day, equivalent to five 100-watt bulbs. Heat engines fueled by coal, the first fossil fuel, initiated the industrial age around 1750. Fossil fuels, including coal, oil, and natural gas, enabled people in industrialized countries to increase their personal energy use by another factor of 5 to perhaps 200 MJ every day, equivalent to twenty-five 100-watt bulbs. With the industrial age came many kinds of pollution including the beginnings of global warming, although the resulting temperature increase wasn’t noticeable until recent decades. During the past six decades, the intense use of fossil-fueled heat engines (mostly for transportation and electricity) has pushed industrialized nations’ energy use upward by yet another factor of 5, to 1000 MJ per person per day, equivalent to 125 continuously burning 100-watt bulbs. To put it another way, if this 1000 MJ were all put into lifting, they would lift a typical 600 newton (135 pound) person by 1700 kilometers! We Americans currently use an enormous amount of energy in our daily lives, partly because we buy it phenomenally cheaply. Eight cents buys 1 kilowatt-hour of electricity, enough energy to lift our typical person from sea level to 6000 meters—nearly 20,000 feet!

1

412

One source of current energy information is the U.S. Department of Energy’s Information Agency, whose Web site is http://www.eia.doe.gov.

The Energy Challenge Petroleum age: oil, gas, electricity, internal combustion engine

Daily energy consumption per person (megajoules)

1000

800

600 Industrial age: coal, steam engine

400

Agricultural age: farm animals and fire 40 MJ

200 Human energy from food, 8 MJ (2000 Calories) 6 million years ago

8000 BCE 6,000,000 years

1750 CE 1950 now 10,000 years

250 years

Figure 1

A brief and approximate history of the use of energy resources: individual daily energy consumption versus the approximate date. Note that the time axis is not drawn to scale: The preagricultural period is 600 times longer than the agricultural period, which is in turn 40 times longer than the industrial period. Although it’s not shown on this simplified graph, humans first began using fire around 1 million years ago.

Figure 2 graphs the shorter term picture in greater detail, for the United States only. The graph shows annual U.S. energy consumption, in “exajoules” (1 exajoule is 1018 joules), during 1840–2008. Each of the seven portions marked Biomass, Hydro, New renewables, Coal, Oil, Gas, and Nuclear represents the energy provided by one particular resource, and the upper boundary represents the total energy provided by all seven resources. Note the growth of the fossil fuels since 1880, the rapid growth of oil and gas since World War II (1945), and the huge rise in energy consumption, a rise that continues despite the threat of global warming. During the 168 years graphed, the nation’s population rose tenfold while per capita energy consumption rose fivefold, for an overall fiftyfold increase in energy use. Since the leading four energy resources graphed in Figure 2 are nonrenewable (finite), and since the world must radically reduce its use of the three fossil fuels because of global warming, it’s not surprising that most energy analysts expect the trends shown in the figure to change before long.

CONCEPT CHECK 1 The combined energy from oil and natural gas began to exceed that from coal in about the year (a) 1880; (b) 1910; (c) 1930; (d) 1950; (e) 1970. CONCEPT CHECK 2 During 1900 to 2000, U.S. energy consumption increased by a factor of about (a) 4; (b) 8; (c) 15; (d) 50; (e) 100. CONCEPT CHECK 3 About how much natural gas did the United States use in 1960? (a) 15 * 1018 J. (b) 35 * 1018 J. (c) 50 * 1018 J. (d) 20 * 1018 J.

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The Energy Challenge 110 100

Nuclear

Annual U.S. energy consumption, in units of 1018 joules

90 Natural gas

80 70 60

Oil

50 40 30

Coal

20 10 0 1840

1860

1880

1900

1920 1940 Year

New renewables* Hydro Biomass 1960 1980 2000 2020 * Wind, Geothermal, Solar

Figure 2

History of U.S. energy use, 1840–2008: total annual U.S. energy consumption of various resources. Source: U.S. Energy Information Agency, 2009.

MAKI NG ESTI MATES

Use Figure 2 to check roughly the estimate shown in Figure 1 for the year 2000, when the U.S. population was 275 million.

2 THE MAJOR RESOURCES, INCLUDING EFFICIENCY and 4 show how the United States uses energy today. Figure 3 shows how the energy consumed today by the United States is divided among the seven primary resources whose history is graphed in Figure 2. Fossil fuels provide nearly all of it, with smaller contributions from nuclear, biomass, hydroelectric, and new renewables. Figure 4 is an energy flow diagram showing how the energy consumed by the United States

Figures 3

In 2000, total U.S. annual energy consumption was about 100 * 1018 J, so annual consumption per person was

SO LUTION TO MAKI NG ESTI MATES

100 * 1018 J = 360 * 109 J 275 * 106 and daily consumption per person was about

360 * 109 J L 109 J = 1000 MJ 365

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The Energy Challenge

flows through the economy, from the seven primary resources to the three broad economic sectors (industry, residential/commercial, and transportation). More than onethird of the energy goes into the generation of electricity that then goes to the three sectors, while the other two-thirds goes directly to the three sectors. Coal, nuclear, hydroelectric, and new renewable resources go mainly to electric energy production, while oil, natural gas, and biomass go mainly to nonelectric uses. Figure 4 reflects the two great principles of energy. You can see the law of conservation of energy in the fact that the energy flows (the “pipe” widths and the numbers) match: Energy in always equals energy out. You can see the second law of thermodynamics in the transformation of energy from 106 exajoules of high-quality energy into 70 exajoules of waste thermal energy and only 36 exajoules of useful energy. The second law’s rigorous restrictions on heat engine efficiencies also shows up in the lower efficiency of electric power generation and transportation, both powered mainly by heat engines. The world is at a watershed in energy history. The patterns of Figures 3 and 4 will soon change. Fossil fuel use, comprising about 85% of U.S. energy consumption, will decline considerably over the next few decades due to resource depletion and environmental problems, particularly global warming. What will take its place? To begin to answer this crucial question, you need to know what’s available. Table 1 lists the major energy resources—natural resources containing useful energy. We’ll survey these resources and their availability in this section, and take a closer look at the most important options in the remainder of this chapter.

1

New renewables

3

Hydro 24

9

24 Supply: 106 exajoules of energy resources

Nuclear

20

Electric power generation, 39

8

1 40

Oil

Nuclear, 8.5% Coal, 23%

Gas, 24% Oil, 37%

Fossil fuels, 86%

Figure 3

The U.S. energy mix today. Source: U.S. Energy Information Agency, 2009.

24

14 Residential and commercial, 29

22

15 Industrial, 22

39 14

14

5 Gas

Useful work and heating, 36

24 20 31

4

Waste, 70

8

Nonelectric, 67 25

Hydro, 2.5% New renewable, 1%

Lost in generation and transmission, 24

7

Coal 4

Biomass, 4%

Transportation, 31

7

Biomass

Figure 4

Approximate energy flows in the U.S. economy in exajoules (1018 J) , in 2008. Source: U.S. Energy Information Agency, 2009.

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The Energy Challenge

Energy from nuclear fusion is probably now 50 years away, but we won’t need it until then. We’ll need it then, though, for several reasons: its abundance and concentration, its freedom from carbon emissions, its low radioactivity, its freedom from explosions, and its low risk of nuclear proliferation. Robert Goldston, Princeton Plasma Physics Laboratory Director

Fossil fuels, including coal, oil, and natural gas, store the chemical energy created by hundreds of millions of years of accumulated layers of energy-rich plant and animal remains. Time and pressure transformed these remains into great beds of coal, pools of oil, and pockets of gas. It’s a telling commentary on humankind’s environmental impact that, in only 250 years of fossil-fuel burning—one millionth of the time it took to store the energy in the ground—we have sent much of the carbon in these fuels into the atmosphere as CO2. Nuclear power, which obtains large-scale energy from the nucleus, supplies electricity today from uranium. The nuclear industry has been stagnant in the United States for 40 years, but has slowly grown worldwide. It could grow rapidly in the future, both in the United States and worldwide, driven by fossil-fuel shortages, rising energy demand, and global warming. In the future, it could come from plutonium using breeder reactors or from hydrogen using fusion reactors (Section 3). Fossil and nuclear resources are finite or nonrenewable. How long will they last? It’s not a simple question. In the real world, a nonrenewable resource never runs out completely. Instead, as the resource is depleted it becomes harder to recover, making it more expensive, until it’s effectively phased out. So the important issue is when will a nonrenewable resource’s production begin to decline? After this date, the resource’s price escalates rapidly because of continued demand and declining supply, and its use declines. A nonrenewable resource reaches its production peak and begins to decline when about half of the total resource that Table 1 Natural energy resources Fossil fuels Coal Oil Natural gas Nuclear fuels Uranium for nuclear reactors Plutonium for breeder reactors Hydrogen for fusion reactors Renewable resources Hydroelectric Biomass burning: wood and trash Methanol from wood (also from coal and natural gas) Ethanol from grains, grasses, sugar, trash Wind Photovoltaic (solar) cells Solar-thermal electricity Geothermal Active solar heating Passive solar heating Conservation (not a natural resource, but acts like one) Energy efficiency with no change in energy services Lifestyle changes to reduce energy use

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The Energy Challenge

was originally in the ground has been removed. Table 2 records the estimated times remaining until the production peaks of the major nonrenewable resources are reached. There is a wide range of estimates, because of uncertainties about how much of each resource remains in the ground and about the future growth of consumer demand. As you can see, the production peaks of oil and gas could occur in the near future, or even now in the case of oil. Many analysts predict major economic dislocations when oil, the fossil fuel in shortest supply but greatest demand worldwide, reaches its production peak and begins to decline. How do we know when oil production will peak? Unlike previous “how do we know” queries, the short answer to this one is that we don’t know. Oil pessimists—mostly former oil company geologists who are now speaking their minds—expect oil production to peak soon, or now. They base their conclusions on rising worldwide demand led by China and India, the inability of producers to meet that demand as evidenced by rising oil prices, declining production in the oil-producing nations outside of the Persian Gulf, and signs that even the Persian Gulf may be nearing its production peak. If these oil pessimist’s claims are true, then production will soon be unable to keep up with demand and prices will rise swiftly, causing fundamental changes in our economy, including great changes in our transporation systems and our car-dependent living arrangements. On the other hand, oil optimists—mostly economists who specialize in natural resource issues—argue that oil production depends more on economics and politics than on how much oil is actually in the ground. They believe that technological innovations, such as new drilling techniques, drilling far off-shore, oil from tar sands, and oil from shale, will intervene; that production will continue to rise; and that prices will remain relatively steady. Even the optimists give oil only 30 or so years. The bottom line is that, regardless of whether you believe the pessimists or the optimists, and regardless of what is done about global warming and other environmental challenges, the planet is at or near the end of the oil age.

Table 2 Number of years until global production rates of nonrenewable energy resources begin to decline, assuming a modest 1% to 2% annual increase in consumption. More precisely, this is the number of years until the “production peak” occurs, after which demand will exceed supply and prices can be expected to rise rapidly. Resource

Years

Coal

100

Oil

0–30

Natural gas Uranium a

a

10–50 50–100

Without breeder reactors.

Renewable resources (Section 6) are those that are replaced immediately or at least within a human lifetime. Although they contribute only a small but significant 7.5% of U.S. energy today, their use is rising and will continue rising because of concerns about global warming, pollution, escalating fossil-fuel prices, and international security problems associated with oil and natural gas. They include two resources that have been widely used for decades: hydroelectric energy from water raised up behind a dam, and biomass energy from burning wood and trash. Other, more recent biomass fuels include methanol or wood alcohol made from wood, and ethanol or grain alcohol made from corn, grasses, sugar, and trash. Electricity can be generated from several “new renewables”: wind turbines (windmills), photovoltaic (solar) cells, solar-thermal energy (the sun’s thermal energy), and geothermal energy (underground thermal energy). Geothermal energy isn’t really renewable, but there’s so much hot rock at drillable depths that it’s classified as renewable. Solar energy can also provide direct space heating or hot water heating, either “actively” with the help of pumps and fans, or “passively” by just letting the sun shine in. A transition from fossil to renewable energy will take decades. Some experts predict this will require massive economic investment, but others predict that new technology, energy efficiency, and the profit motive will reduce costs greatly and might even make the net cost “negative” (that is, switching to renewable energy might cost less than continuing to use fossil fuels). Energy conservation—reduced energy consumption—is a key to solving the energy-enviroment-economy puzzle. Many analysts think the United States could cut its energy consumption by 50% without harming its economy. Such industrialized

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The Energy Challenge

nations as Germany, Britain, and Japan operate on about half as much energy—whether measured per person or per dollar of gross national product—as America does. Although not really an energy resource, conservation acts like an energy resource. Conservation includes energy efficiency measures (Section 7) such as home insulation, energy-efficient lighting, and energy-efficient automobiles that reduce energy consumption without reducing energy services. Conservation also includes less energy-intensive lifestyles— for example, using mass transit instead of cars, living in smaller homes, and building more compact communities. Many studies show that energy consumption can be reduced dramatically by efficiency alone, without controversial lifestyle changes. Beginning in 1973, Americans began using energy far more efficiently. Figure 5 documents this important point. The curve marked “Total annual energy” traces total U.S. energy consumption. The curve marked “U.S. annual inflation-adjusted GDP” traces the nation’s annual gross domestic product, its annual output of goods and services. The dollar GDP amounts are not shown. Instead, the scale of the GDP graph is chosen to make the GDP and energy graphs coincide in 1950 so that the two graphs can be compared. Since GDP measures the nation’s total economic output, which in turn depends on the energy it consumes, it’s not surprising that U.S. energy consumption rose almost exactly in step with GDP between 1950 and 1973. But then came a surprise: The first international oil crisis, in 1973, broke this close connection between energy consumption and industrial growth. Energy prices increased rapidly in response to decreased foreign oil supplies, and Americans looked for ways to save money by using energy 200 180

Annual energy use, in exajoules, 1018 joules

160

Efficiency, 94

140 U.S. annual inflation-adjusted GDP, appropriately scaled

120

Total annual energy

100 80 60

Energy 106 40 20 0 1950

1955

1960

1965

1970

1975

1980 Year

1985

1990

1995

2000

2005

2010

Figure 5

History of total U.S. energy consumption and GDP, 1950–2008. GDP is one measure of the goods and services provided by the economy. In order to compare the two graphs, GDP is scaled to match total energy in 1950. The two graphs are parallel until the 1973 energy crisis, after which higher energy prices encouraged Americans to conserve. The wide gap that then opens up between the two graphs is a measure of the energy saved by efficiency measures since 1973. Source: U.S. Energy Information Agency.

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The Energy Challenge

more efficiently. The effect of this crisis, and of the second oil crisis in 1979, is evident in the graph. Although GDP fell briefly following each crisis, it soon resumed its upward trend. But total energy use declined after each crisis and did not resume its rapid upward trend. Apparently the efficiency measures, promoted by increased prices, became permanent. Rapid increases in energy efficiency supported a rapidly increasing GDP while energy consumption increased much more slowly. Without efficiency gains, energy consumption would have stayed in step with GDP. So the difference between the two graphs is appropriately labeled “Efficiency.” By 2008, efficiency contributed 94 exajoules to the nation’s energy mix, nearly outstripping the 106 exajoules of real energy use. In other words, nearly 50% of America’s energy services now comes from efficiency improvements since 1973. Because efficiency is environmentally harmless and comes “at negative cost” (at a savings), this is very nice. It also illustrates a crucial point: The right efficiency measures make dramatic energy savings possible. CONCEPT CHECK 4 According to Figure 4, the overall energy efficiency of electric power generation is about (a) 20%; (b) 30%; (c) 40%; (d) 50%; (e) 60%. CONCEPT CHECK 5 According to Figure 5, the amount of energy saved by energy efficiency measures in 1985 was about (a) 100 exajoules; (b) 80 exajoules; (c) 60 exajoules; (d) 40 exajoules; (e) 20 exajoules. MAKI NG ESTI MATES

According to Figure 1, the daily average energy consumption per person in industrialized nations is about 1000 MJ. Use this figure to estimate the average person’s power consumption, in watts. Express this in kilowatts. If all this energy were in the form of electricity, how many 100 watt bulbs could it light up?

3 NUCLEAR POWER: HOW IT WORKS Nuclear power currently comes from uranium that provides thermal energy for steamgenerated electricity. Most U.S. nuclear power reactors operate as shown schematically in Figure 6. Nuclear plants operate pretty much like every other steam-electric generating plant. Thermal energy from the primary energy source (nuclear fission, in this case) heats water to make high-temperature steam that turns a turbine that turns an electric generator that makes electricity. Three essentials in all power reactors are fuel to convert nuclear energy to thermal energy, coolant to transfer thermal energy away from the fuel, and neutron-absorbing control rods that can be moved in or out to stop, slow down, or speed up the chain reaction. Most U.S. reactors are water cooled. As shown in Figure 6, high-pressure water circulates through the center of the reactor to transfer thermal energy away from the chain-reacting fuel rods. This thermal energy then creates steam. The fuel in water-cooled reactors is uranium, slightly enriched from its natural 0.7% 235 U content to 3%. The energy comes only from the 3% fraction of nuclei that are 235U, and not from the 97% that are nonfissionable 238U. A nonexplosive chain reaction is

SO LUTION TO MAKI NG ESTI MATES Power is energy consumed per second. Accordingly, divide the 1000 MJ of daily energy consumption by the number of seconds in a day: 1000 * 106 J>(60 * 60 * 24 s) L 12,000 watts, or 12 kilowatts—the equivalent of one hundred twenty 100-watt bulbs!

419

The Energy Challenge Electricity

Containment dome

Hot steam

Generator

Control rods

Hot water at high pressure

Turbine

Steam generator

Cooler steam Cold water

Core Condenser Hot water Fuel rods Water Reactor vessel

Pump Pump

Water

Lake or cooling tower

Figure 6

Schematic diagram of a steam-electric generating plant powered by a nuclear reactor.

maintained in the uranium. Natural uranium won’t work in water-cooled reactors because both 238U and 11H (in the water molecules) can absorb neutrons and this spoils the reaction. Since power reactors use uranium that is only slightly enriched rather than highly enriched (90%) bomb-grade uranium, a power reactor cannot explode the same way that a fullfledged nuclear weapon would, and it is impossible to use the uranium in a bomb. The uranium fuel is shaped into small cylindrical pellets and stacked in long, thin metal tubes. Some 40,000 of these fuel rods, 100 tonnes of fuel, form the power-producing core of the reactor. Interspersed with the fuel rods is a far smaller number of control rods, made of a neutron-absorbing material such as cadmium or boron, which can be inserted

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The Energy Challenge

or withdrawn as needed. The core is enclosed in a heavy steel reactor vessel designed to withstand high pressures and shield against radiation. To separate the highly radioactive water that circulates through the core from the rest of the plant’s operations, water circulates in two physically separated loops (Figure 6). The first loop circulates through the core, removing heat from the fuel rods. Although this water is heated to above 300°C, the high pressure maintained inside the reactor vessel prevents bubbles from forming, keeping it from boiling. This water circulates around to a “steam generator” where it heats the water in the second loop, turning this “secondary water” into steam. Thermal energy is transferred without allowing the water in the two loops to mix. Because the chain reaction causes the core, the reactor vessel, and the first water loop to become highly radioactive, these elements are encased in thick concrete. For further shielding and protection against accidents, a large airtight containment dome—made of steelreinforced concrete about a meter thick and built to absorb an impact as great as that of a jetliner crash—surrounds the radioactive elements (Figure 7). Since the secondary loop is not kept at high pressure, its water immediately turns to steam in the steam generator. The rest of the operation (turbine, generator, condenser, lake or cooling tower) is identical to every other steam–electric power plant. Ever since the Three Mile Island nuclear power plant accident in Pennsylvania in 1979 (see Section 5), new nuclear power plant construction has halted in America. But this might now be changing. Because of global warming and growing electricity demands, support for new nuclear plants is increasing in the United States and around the world. The U.S. Nuclear Regulatory Commission expects up to 30 applications for new reactors at 20 sites during the next few years, and new plants are opening in China, India, Europe, and elsewhere. To guard against power plant accidents, most new plants have enhanced safety features such as multiple independent systems to keep reactor cores from overheating in an emergency, multiple backup power systems, and “passive” systems (requiring no human or mechanical control mechanism) to open and close valves automatically by gravity or water flow and thus avoid human error. Some of the new reactors will be enhanced versions of existing ones, while others will be next-generation designs such as the “pebble bed reactor” in which some half million hollow tennis-ball-sized metal spheres are filled with low-enriched uranium fuel and placed in the reactor’s core. This reactor is cooled with chemically inert helium

Figure 7

EFDA-JET

Nuclear power plant under construction. This view shows a cooling tower and a reactor containment dome under construction.

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The Energy Challenge

gas instead of with water. It’s considered safer than existing reactors because it exploits the tendency of the non-fissioning 238U, comprising 97% of the reactor’s uranium, to absorb additional neutrons as it heats up. Thus, if the reactor’s temperature rises dangerously in an accident, the 238U will absorb more neutrons and passively shut down the chain reaction. The pebble bed reactor also has the great advantage of not needing to be shut down for re-fueling. Instead, a few “pebbles” (spheres) are removed from the bottom of the reactor every day, checked to see that they still contain sufficient fissionable 235 U, and put back onto the top of the pile. Most of the spheres work their way through the reactor from top to bottom several times before being permanently removed. But there’s a problem. As you can see from Table 2, there’s only a finite supply of uranium. If a large expansion of nuclear power occurs, as is recommended or predicted by many observers, uranium supplies could begin running out within a few decades. Enter the breeder reactor, a possible solution to this problem. Recall that while 235U nuclei fission inside a reactor, the much more numerous 238U nuclei absorb neutrons and transform into plutonium. As you know, plutonium is a second chain-reacting nucleus that can be used in a nuclear reactor. Breeder reactors are designed to create more than one new Pu nucleus for every 235U nucleus fissioned. So breeder reactors actually create more fuel (in the form of Pu) than they use (in the form of 235U) and can convert much of the 238U in any country’s uranium resources to fissionable plutonium, extending these resources enormously. The United States and several other nations built experimental breeder reactors during 1970–1990, but they were extremely costly, plagued by technical problems, and raised concerns about contributing to the worldwide proliferation of nuclear weapons (see the next section). Today, due to global warming and expanding electricity demands, a new generation of experimental breeder reactors is coming online in China, India, and Russia, a retired breeder reactor in Japan is restarting, and other nations are considering breeder reactors. A more futuristic new direction in nuclear power is the fusion reactor, based on the nuclear reaction that fuels a fusion bomb: 2 1H

+ 31H :

4 2He

+ neutron

In a fusion reactor this reaction would take place nonexplosively, yielding a continuous source of thermal energy that could boil water to make power-plant steam. The 21H would be extracted by isotope separation from ordinary water—about 1 hydrogen atom in 6000 is 21H and the remainder are 11H. 31H is a radioactive isotope that is not found naturally. It would be “bred” during the fusion reaction itself, by surrounding the fusion chamber with lithium and reacting the lithium with the neutrons created in the fusion reaction: n + 63Li :

4 2He

+ 31H

It’s not easy to make a fusion reactor. One must heat the 2H and 3H to millions of degrees in order to start a self-sustaining thermonuclear reaction. This would be done by passing an electric current through the gaseous hydrogen fuel. To get a “net energy gain” (more useful energy produced by the reaction than is put into the reaction in order to maintain it), three conditions must be met: The fuel must be sufficiently compressed, the temperature must be sufficiently high, and these two conditions must be sustained for a sufficiently long time (more than a tenth of a second). This is difficult. For instance, if the fuel touches the walls of its container, the walls immediately cool the fuel far below the fusion temperature, so the fuel must be held away from the walls by electromagnetic forces. Figure 8 shows the interior of the Joint European Torus (JET) that has achieved 50% of the “breakeven” (or net energy gain) energy production. Inside the “torus” (doughnut)

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The Energy Challenge Figure 8

Rollin Geppert

Inside the JET experimental fusion reactor. Within this “torus” configuration, hydrogen gases are heated to over 100 million degrees by a combination of electrically neutral particles, radio waves, and electric currents. If held at sufficiently high temperatures and pressures for a long enough time, the hydrogen will fuse to form helium and release nuclear energy to both run the reactor and provide energy to the outside world.

configuration shown, hydrogen gases are heated to over 100 million degrees with beams of particles, radio waves, and electric currents. The United States and five other nations agreed in 2005 to build an experimental fusion reactor, the International Thermonuclear Experimental Reactor (ITER), in Cadarache, France. Twice the size of JET, it’s designed to finally decide whether taming the sun’s energy to generate electricity is even viable, and to exceed breakeven sufficiently to achieve a tenfold energy gain. ITER, which will not be used for commercial purposes, will be under construction until 2016. If it’s successful, construction of a prototype fusion power plant might begin in 2022 and be completed by 2032. And if that plant is successful, the first commercial fusion power plant might be built and go online by 2050. But those are big “ifs,” and some knowledgeable physicists are skeptical that fusion will ever be a power source on Earth. At any rate, there’s broad agreement that commercial nuclear fusion won’t be ready before 2050, and that our current energy/environment dilemma must be resolved well before that time, and hence that fusion can’t be the key to that solution. CONCEPT CHECK 6 Which are possible fission-reactor fuels? (a) Uranium. (b) Thorium. (c) Hydrogen. (d) Plutonium. (e) Hot dogs.

4 TRADE-OFFS: ISSUES FOR COAL POWER The world faces big decisions regarding energy and the environment. The biggest question is what to do about the fossil fuels that supply 84% of our energy but that cause global warming and are increasingly in short supply. Energy efficiency is one answer that nearly everybody supports; less-polluting renewable sources of energy are another widely supported answer. I’ll discuss these in Sections 7 and 6, respectively. Nuclear power is another potentially large energy source that’s widely mentioned as part of the solution because it doesn’t cause global warming and it has a strong resource base if breeder reactors are used. Nuclear power, supplying 23% of

We nuclear people have made a Faustian bargain with society. On the one hand, we offer an inexhaustible source of energy. But the price that we demand of society for this magical energy source is both a vigilance and a longevity of our social institutions that we are quite unaccustomed to. Alvin Weinberg, Former Director of Oak Ridge National Laboratory, 1972

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America’s electricity, is useful only for generating electricity. The leading electricity source, coal, supplies 51%. Together, these sources provide 74% of America’s electricity and 31% of its total energy. Both provide a sizeable chunk of America’s electricity, but both have significant drawbacks. Expert and popular opinion can be found both for and against both coal and nuclear power as big components of the energy future. Coal and nuclear power stand at the heart of the energy/environment dilemma. Both deserve serious debate, and they’ve been receiving it. I’ll provide food for this debate by discussing the pros and cons of both in this and the next sections. Europe must reduce its annual per-capita greenhouse gas emissions by 80 percent, or from 11 to 2.2 tons per person, India’s current level, by 2050. The United States, which emits 27 tons per person each year, must also decrease its emissions to these levels if the world is to prevent a significant rise in temperatures. David King, Britain’s Former Chief Scientific Adviser, in 2008

CONCEPT CHECK 7 The drawbacks of nuclear power include (a) land degradation from mining; (b) pollution from acid rain; (c) health problems among workers; (d) global warming; (e) waste disposal; (f) proliferation (or spread) of weapons of mass destruction. CONCEPT CHECK 8

The big “pro” for both coal and nuclear power is that ample resources exist for most of this century, although a major expansion of nuclear power would probably require the widespread use of breeder reactors. Now let’s consider the “cons.” For starters, please write down (at least in your mind) all the “cons” of coal power and of nuclear power you can think of. ———— (a pause, for writing down) Table 3 gives my lists. Because both resources generate electricity, the two lists have a lot in common. In fact, there are parallel, but not identical, entries for all but two problems: global warming and nuclear weapons proliferation. But the similarity of problems does not necessarily mean that the evaluations will be similar. For example, both cause land degradation, but coal degrades far more land than nuclear because coal’s volume of fuel per unit of energy is so much greater. For another example, nuclear power creates much more of a terrorism threat than does coal power, because terrorists could release radiation, steal radioactive material, or even (if it’s a breeder reactor) steal bomb material from a nuclear plant. As you can see from the list, coal has all sorts of problems. Coal has made considerable progress in reducing them, for example, by installing devices known as “scrubbers” that remove 98% of the acid-rain-causing sulfur from the stack emissions. However, the cons list remains long and severe, and “clean coal” is a misnomer just as “clean nuclear power” would be a misnomer as compared with efficiency and renewable energy sources. Coal’s biggest drawback is undoubtedly global warming. Carbon dioxide emissions, mostly from fossil fuels, cause 55% of global warming. Coal is the worst fossil fuel in this regard, releasing 24 kg of C per billion joules of energy as compared with oil at 19 kg and natural gas at 14 kg of C per billion joules. Table 4 indicates the molecular basis of these facts: Most carbon-bearing compounds also contain hydrogen, and both the C and the H atoms combust with oxygen to make CO2, H 2O, and thermal energy. Only the CO2, and not the H 2O, contributes significantly to global warming.2 So fuels with a higher ratio of H to C create less global warming per unit of energy. 2

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Which of the above are drawbacks of coal power?

Although water vapor is the most important greenhouse gas, human activities have very little effect on its concentration in the atmosphere because the atmosphere can hold just so much H 2O before the H 2O gas condenses into water drops and “rains out.”

The Energy Challenge Table 3 Pros and cons for coal and nuclear power Coal power

Nuclear power

Pros:

Abundant electricity

Abundant electricity

Abundant resources

Abundant resources (assuming breeder reactors)

Cons:

Land degradation from mining

Land degradation from mining

Air pollution: acid rain, SO2, NO2, ash

Nuclear waste: Radiation in environment

Workers’ health: black lung disease, etc.

Workers’ health: radiation in mines and plants

Mining accidents

Power plant accidents

Heating of lakes and rivers

Heating of lakes and rivers

Solid waste: ash, sludge

Used fuel rods, low-level radioactive waste

Costs: plant, fuel, operations, waste disposal Costs: plant, fuel, operations, waste disposal Major source of global warming Proliferation of nuclear weapons Terrorism: electricity shutdown

Terrorism: release of radiation, theft of bomb material

To reduce CO2 emissions, the coal industry and U.S. government are developing carbon capture and storage (CCS) technology. It’s a tall order: A typical coal plant consumes 10,000 tonnes of coal every day, enough to fill a long “unit train” that transports coal. When burned, this produces over 30,000 tonnes (every C atom combines with two O atoms) of CO2 every day. And that’s just one plant. Most experts agree that CCS is the key to getting through the transition from our reliance on fossil fuels for 84% of our energy today to less than 20% by 2050 without in the meantime allowing atmospheric CO2 to reach dangerous levels. Here’s how it works. The general idea is to capture CO2 at generating plants, compress it, and pipe it to a facility where it can be safely stored for hundreds to thousands of years. All the steps required to accomplish this have already been taken, but not at the large scales required to help solve global warming, and they haven’t yet been integrated in a single facility. In conventional coal plants, after the coal is burned the low-pressure post-combustion gases pass through devices that remove particulates and gases of sulfur and nitrogen before being exhausted via smokestacks into the air. CCS could be installed in such plants, either as a retrofit to an existing plant or as part of a new conventional coal plant, by extracting CO2 from the post-combustion gases after conventional pollutants are removed but before reaching the smokestack. This means that CO2 would have to be Table 4 Carbon released by several fuels kg of C per 109 J

Ratio of H to C combusted

Coal

24

1 H to 18 C

Oil

19

2 H to 1 C

Natural gas

14

4 H to 1 C

Hydrogen

0

H only

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removed from enormous volumes of low-pressure exhaust gas, a process that would raise the plant’s coal consumption by 30%, with a corresponding increase in price. The removed CO2 would then be compressed (causing more expense) and piped to a storage facility. A more effective approach is to design the plant from the start with CCS in mind. The most likely design is the “integrated gasification combined cycle” (IGCC) plant. Upon entering the plant, coal is mixed with water and oxygen to create a high-energy gas called “synthesis gas” (this is the “gasification” stage). Conventional pollutants (particulates and gases of sulfur and nitrogen) are then removed, and the synthesis gas is chemically reacted with steam to create separate gas streams of hydrogen (H 2) and CO2. The hydrogen then burns to turn both a gas turbine generator and then a steam turbine generator in what is called a “combined cycle.” The IGCC process consumes less coal, and is cheaper, than the conventional coal CCS process because the extraction of CO2 from the high-pressure low-volume synthesis gas is much easier than extraction from a conventional plant’s post-combustion gases. Three favorable places to store CO2 are depleted oil or gas reservoirs, unminable coal beds, and underground natural saltwater aquifers. There’s some experience with this: Oil companies have for decades injected high-pressure CO2 into old oil wells in order to force out the last remaining oil; Norway has, since 1996, injected a million tons of CO2 every year into the ground beneath the North Sea; a similar amount has been injected into an Algerian gas field; and several storage projects are starting up in Texas. The Intergovernmental Panel on Climate Change (IPCC) states that a toxic sudden release from a well-engineered facility is highly unlikely, and estimates that there’s storage space worldwide for all of the twenty-first century’s CO2. The IPCC estimates that appropriate reservoirs are likely to retain over 99% of their CO2 for more than 1000 years. This is important because even a small non-toxic leakage rate of, say, 1% per year could, within a few decades, defeat the purpose of CCS by allowing large amounts of CO2 to reach the atmosphere. In order to limit CO2 emissions, the United States is soon likely to put a price on emissions; this might have already happened by the time you read this. This will probably happen by putting a “cap” on allowed emissions, but a simple carbon tax is also possible, making renewable energy sources more competitive and providing economic incentives for CCS and IGCC plants. Many observers fear that humankind is fast approaching a climate tipping point beyond which natural feedback mechanisms could start the irreversible melting of large portions of Greenland or the West Antarctic Ice Sheet, eventually raising ocean levels by a catastrophic several meters and altering the face of the planet. Human activity has already raised CO2 concentrations from their roughly 280 ppm maximum of at least the past half million years to 388 ppm today, nearly a 40% increase. The IPCC states that a doubling of the pre-industrial concentration, to 560 ppm, will cause a warming of about 3°C. The IPCC also states that temperatures were raised by 3°C during the last interglacial (between the ice ages) period, about 125,000 years ago, and reductions in polar ice at that time raised ocean levels by 4 to 6 meters. For this and other reasons, many observers conclude that we’d better keep warming to less than 2°C, and that to achieve this we’d better keep CO2 concentrations below 450 ppm. If the surge of over 1000 new conventional coal-fired power plants currently on the world’s drawing boards is built without CCS, CO2 concentrations will almost certainly climb to over 450 ppm. So CCS is a critical issue, with several possible outcomes: (1) entirely stop building new coal plants; (2) halt new plant construction for about 10 years until CCS can be installed; (3) continue building new plants but install CCS as soon as possible; and (4) install new plants without bothering about CCS.

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CCS development is still at an early stage. It’s likely that it will eventually be successful, but it will be a few years before we know and perhaps 2018–2020 before it’s ready for commercial use. The historical trend from coal to oil to natural gas to CCS (in which only hydrogen is burned) represents a decarbonization of the energy supply. Global warming has caused decarbonization to be a policy aim of most nations today. Natural gas is often preferred over coal or oil for electricity generation, solar energy is growing rapidly, and there is talk of a revival of nuclear power. In fact, Table 4 suggests that this trend could lead to carbon-free energy based on hydrogen alone. Although most of the visible universe is made of hydrogen, hydrogen gas—H 2—doesn’t occur naturally on Earth today because it’s so light and fast-moving that it all escaped Earth billions of years ago. However, hydrogen can be produced by passing an electric current through water. If the electricity is generated from solar or nuclear energy, the process becomes carbon-free. The hydrogen gas can be piped to distant locations much like natural gas and used for transportation, for home heating, and to generate electricity locally using fuel cells. Thus hydrogen will become more important in the world’s energy future.

Global climate change. . . poses dangers which may be very large. The problem can be ameliorated by reducing fossil fuel consumption through conservation and expanded use of nuclear and solar power. . . . The most obvious role for nuclear power is to replace coal in electricity generation. It could also replace all the oil and much of the natural gas. . . . A program of this sort could be implemented over three or four decades, as existing fossil fuel plants are retired. David Bodansky, Physicist and Energy Specialist

5 TRADE-OFFS: ISSUES FOR NUCLEAR POWER Let’s turn now to nuclear power. The first commercial nuclear power plant opened in 1957. By 1975, with 54 plants providing 10% of the nation’s electricity, the nuclear age seemed firmly established. But then the boom faded. The last new U.S. plant order was placed in 1974, and it eventually became clear—especially following the Three Mile Island accident in 1979 (see the following discussion)—that the first nuclear power era peaked during the 1970s and ended soon thereafter (Figure 9). The big issue for nuclear power today is, should there be a second nuclear power era? Nuclear power has always attracted strong proponents and opponents. Proponents argue that global warming, fossil-fuel shortages, and the prospect of a safer generation of nuclear reactors call for a revival of nuclear power, a nonfossil resource that produces large amounts of electricity and could expand to produce much more. Opponents contend that safety concerns, waste disposal problems, high cost, and nuclear proliferation make nuclear power unacceptable. Nearly all observers agree that, because of global warming, it’s high time to begin decarbonizing our energy economy. Of the nuclear power issues listed in Table 3, the most significant are nuclear waste, power plant accidents, and nuclear weapons proliferation. I’ll discuss these here. Although lower-level nuclear waste poses some problems, the more serious problem is the intensely radioactive high-level nuclear waste in used fuel rods.3 Used fuel rods are currently stored in large pools of water inside the containment domes of the country’s 104 nuclear power plants, where they are subject to theft and sabotage. These pools were never intended for long-term storage and would eventually leak radiation into the environment at all 104 sites if they were maintained for centuries (Figure 10). Because these wastes must be stored safely for thousands of years, a long-term solution is essential. Used fuel rods contain fission fragments and other radioactive isotopes created during the chain reaction. Shorter-lived isotopes

3

The attention was all on the front end of the fuel cycle and mostly on the reactor itself. Here’s where the jobs and the career opportunities were. Here’s where the commercial interest lay. Engineers were not interested in dealing with waste. It was not glamorous; there were no careers; it was messy; nobody got brownie points for caring about nuclear waste. The Atomic Energy Commission neglected the problem. . . . It is a little surprising that no group [pointed out] that if some critical part of the system were missing perhaps the whole system would come to a grinding halt. Carroll Wilson, General Manager of the U.S. Atomic Energy Commission from 1947 to 1951

To give you a feel for how radioactive the rods are, an unprotected person standing within a meter of a typical used fuel assembly—a bundle of about 250 rods—that had been in storage for 10 years would receive a lethal dose of radiation within about 15 minutes. A “younger” fuel assembly, that had had less time to radioactively decay, would be more radioactive.

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The Energy Challenge 180

180

Thousands of megawatts of generated electric power

Total 160

160

140

140

120

120

Under active construction

100

100

80

80

60

60

40

40 Operating

20 0 1960

20 1965

1970

1975

1980 Year

1985

1990

1995

0 2000

Figure 9

The U.S. commitment to nuclear power, 1960–2000: total megawatts installed and under construction.

dominate the radioactivity for the first few centuries, so that the waste’s radiation level decreases by a factor of 300 during the first 10 years and by a factor of 100,000 during the first 1000 years. Nevertheless, some isotopes remain potentially toxic for tens of thousands to millions of years. In 1987, Congress designated Yucca Mountain in Nevada (Figure 11) as the sole site to be considered for waste burial. After two decades of controversy and $10 billion spent examining this location, the U.S. Environmental Protection Agency in 2008 announced that the Yucca Mountain facility would be required to guarantee that an average exposed individual living and gathering food near the site should receive a maximum annual United States Department of Energy exposure of only 0.15 mSv at any time during the next 10,000 years, and a maximum annual exposure of only 1.0 mSv at any time during the period from 10,000 years to Figure 10 1 million years. 0.15 mSv/year is only 6% of the natural background rate, and 1.0 Sites in the United States at which mSv/year is 40% of the natural background rate. It’s also worth noting that 10,000 years spent nuclear fuel, surplus plutonium, is longer than recorded history, and 1 million years is some 10 times longer than the age and other high-level radioactive waste of our species, Homo sapiens. Also in 2008, the U.S. Department of Energy submitted an are stored at the surface; these include application to construct and operate the Yucca Mountain site. The application was the nation’s 104 nuclear power plants, accompanied by an analysis indicating that the site would easily meet the EPA’s 10,000whose used nuclear fuel rods are stored on-site. year and million-year standards. Nevertheless, in 2009 the U.S. government, prompted by public sentiment (especially in Nevada), decided to nix the Yucca Mountain location. But the government is still committed to finding a long-term nuclear waste site, and is committed to nuclear power in general. As John Holdren, President Obama’s science advisor, put it in 2009, “I think we are going to see more nuclear power plants in this country. They’ll be of a new generation that will be characterized by better safety characteristics. . . . We still have a problem in this country that there’s no agreed upon approach for managing the radioactive waste in the long run, and [we’re] going to be paying some attention to figuring out how we’re going to deal with that.”

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United States Department of Energy

The Energy Challenge

Figure 11

Yucca Mountain, Nevada.

The accident in 1979 at Three Mile Island illustrates how things can go wrong in complex technologies. It began with a routine event: A pump failed in the outer water loop that carries steam to the turbine (Figure 6). Control rods immediately and automatically dropped into the reactor and fission ceased. But stopping fission in a reactor doesn’t stop all the heating, because some 5% of a reactor’s power comes not from fission, but from radioactivity. So water must be kept moving through the reactor to prevent overheating. So a backup pump took over. But a valve in this backup pump had been left closed by mistake, and a warning light that should have alerted operators to the closed valve was obscured by a tag, so this water didn’t get into the reactor for another 8 minutes. During this time, the temperature and pressure rose, forcing a pressure-relief valve on the steam generator (Figure 6) to open. The open valve allowed steam to escape, flooding the containment building floor with radioactive water. Some of this water was automatically pumped to an adjoining building, releasing a relatively small amount of radioactivity to the environment. Water in the overheated core evaporated and escaped. Because of the threat of overheating, every reactor contains a tank of emergency cooling water. But the operators interpreted their control room dials to mean that there was too much water in the core, rather than too little. So they shut off the emergency cooling water. The water level dropped below the top of the fuel rods, and the fuel heated until much of the core had melted, an event known as a meltdown. This permanently destroyed the

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reactor. Only the dwindling water still in the bottom of the core prevented the entire reactor vessel from melting and spilling molten fuel into the containment building. Unusual chemical reactions in the hot reactor created hydrogen gas that remained in the reactor for several days, causing concern that a hydrogen explosion might rip open the reactor, releasing a large amount of radioactivity to the environment. There were no immediate deaths, and few, if any, long-term cancer deaths are expected. The accident cost the utility company $1 billion to clean up, plus the loss of the reactor. This accident and the much worse accident at Chernobyl led to new safety procedures and technologies, and it’s thought that new reactors will be more accidentproof than previous reactors. Nevertheless, with nearly 500 nuclear power plants either operating or under construction worldwide, there will always be some probability of a serious accident. But any serious consideration of nuclear power plant accidents should compare the estimated 4000 deaths caused by the 1986 Chernobyl meltdown with other accident tolls such as the 24,000 probable deaths caused every year in the United States alone from coal power plant pollution. Most energy experts agree that nuclear weapons proliferation is by far the most serious issue for nuclear power, because a nuclear war would be much more catastrophic than any conceivable nuclear power plant accident or nuclear waste leakage. So-called “peaceful” nuclear power programs have developed in tandem with nuclear weapons programs, and provided cover for those weapons programs, in India, Israel, South Africa, Pakistan, Iraq, North Korea, and perhaps Iran. Nuclear power can provide knowledge and experience for nuclear weapons development. Most nuclear power plants use low-enriched uranium fuel (a few percent 235U and over 95% 238U), although a few use natural uranium (less than 1% 235U). Thus, most nations having nuclear power plants can claim a need for uranium enrichment plants. But enrichment plants are inherently dangerous facilities because any plant that can enrich uranium up to a few percent can continue the process up to the high-enrichment (over 90% 235U) needed for uranium fission bombs. Furthermore, every nuclear power plant, including even those using nonenriched fuel, is an inherently dangerous facility because they all produce 239Pu as a “waste” product, and 239Pu can be used to fuel a plutonium fission bomb. In order to make a plutonium bomb, the reactor fuel rods must first be reprocessed to extract 239Pu, a challenging technical operation that’s feasible for a nation and not feasible for a small terrorist organization. The United Kingdom, France, Japan, Russia, and India reprocess used fuel rods to extract and “recycle” plutonium and uranium as nuclear power fuel. The United States halted reprocessing in 1977 due to proliferation concerns, especially India’s entry into the nuclear club in 1974. India followed the reprocessing route to a fission bomb using supposedly peaceful U.S.-supplied reprocessing technology to obtain plutonium. Pakistan’s weapons program also benefited from nuclear power technology when a Pakistani physicist-spy, working in a commercial uranium enrichment plant in the Netherlands, copied the plant’s design to build a Pakistani enrichment plant that then produced weapons-grade uranium for nuclear weapons. Thus, the Pakistan–India nuclear arms race is intertwined with nuclear power issues. To make matters much worse, Pakistan also proliferated its nuclear knowledge to North Korea, Iran, and Libya. Helped by Pakistan's "assistance," North Korea entered the nuclear weapons club by detonating nuclear devices in 2006 and 2009 using plutonium from reprocessed fuel rods from its uranium-fueled nuclear reactor. As noted in the preceding section, a large expansion of nuclear power will probably run into uranium supply problems and thus require breeder reactors. Even

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today, several new experimental breeder reactors are coming online around the world. But there’s a problem with breeder reactors: They make the nuclear weapons proliferation problem much worse. Breeder reactors exacerbate proliferation because plutonium reactor fuel can also fuel a nuclear weapon, whereas uranium reactor fuel cannot because it’s not highly enriched. Widespread breeder reactors will create large amounts of pure plutonium to be stored, shipped to other reactors, and used as reactor fuel. An expanded nuclear power industry could put more than a million kilograms of plutonium into global commerce every year. Because only 10 kilograms are needed for a fission bomb, it might be difficult to keep significant amounts from going into weapons. Despite these concerns, Japan, China, India, and South Korea are developing breeder reactors as part of a rapid expansion of nuclear power in Asia during the next few decades. Breaking the link between nuclear power and nuclear proliferation will require an effective system of international controls on the two crucial proliferation-prone technologies, namely uranium enrichment and fuel rod reprocessing. The United Nations-sponsored International Atomic Energy Agency performs this function as best it can today, but it often lacks the information and the power to prevent enrichment and reprocessing for nuclear weapons purposes. Many observers suggest concentrating all enrichment and reprocessing technology within just a few centralized facilities under tight international controls. In light of their problems, there’s a good case for shrinking or eliminating both coal and nuclear power. The problem is that everybody wants more energy. Rampant world population growth and increased standards of living have increased this demand, and it’s not at all clear that renewables and efficiency alone can satisfy it. Most observers agree that global warming requires a radical reduction in all fossil fuels by at least 2050. So serious debaters tend to fall into two camps: those who think nuclear power must be expanded as part of a program to reduce fossil fuels, and those who think humankind can reduce both nuclear power and fossil fuels and rely on efficiency and renewables alone. CONCEPT CHECK 9 Which of the following has the largest mass? (Hint: Coal is made mostly of carbon, with other elements present only as minor contaminants.) (a) The waste fuel rods generated by a typical nuclear power plant during one year. (b) The carbon dioxide gas generated by a typical coal-fired power plant during one year. (c) The sulfur dioxide gas generated by a typical coal-fired power plant during one year.

6 RENEWABLES Although only hydroelectricity and biomass contribute much renewable energy today, other renewables are expanding rapidly and could provide much more energy in the future. Every energy resource has its drawbacks, but renewables have fewer than fossil or nuclear resources. Either renewable or nuclear energy or both could provide a decarbonized energy economy by generating hydrogen and electricity for homes, industries, and transportation. Hydroelectricity and biomass for burning contribute together nearly 7% of the U.S. energy budget. Hydroelectric energy, the gravitational energy of water that the sun’s warmth has raised by evaporation, goes entirely to centralized electricity. Although more energy could be squeezed out, it’s close to its practical limit because most of the dammable rivers in the United States are already dammed.

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No single technology will stop global warming, but there is a silver bullet: a cap on carbon that will launch all these technology solutions into the mainstream. Fred Krupp, President of the Environmental Defense Fund, and Miriam Horn, in Earth: the Sequel

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Biomass energy, the chemical energy of wood, sugar, grains, and trash, is available from many sources and can be transformed into many forms. In the past most of it has come from burning wood and trash for heat or power-plant steam. But since 2000 this has changed as biomass is increasingly processed to make transportation fuels, called biofuels. The explosion of biofuels since 2000 is driven by oil supply problems and global warming. Most biomass energy comes from agricultural products that consume atmospheric CO2 while growing and emit this CO2 back into the atmosphere when consumed, so they contribute zero net CO2 emissions except for their indirect effects. But these indirect effects are significant because mechanized agriculture uses lots of fossil fuel for planting, harvesting, transportation, and fertilizer production, and because CO2-storing forests are often cleared to make room for cropland. The use of food crops—especially corn-based ethanol—for fuel also decreases global food supplies, driving up the cost of food and exacerbating poverty. There are plans to enormously expand biomass consumption by replacing 30% of U.S. oil consumption with biofuels by 2030. Today and for the next few years, most of this would be ethanol, also known as grain alcohol, produced from corn. In 2008, Americans consumed 9 billion gallons of ethanol, largely for transportation, replacing about 3% of U.S. oil consumption. But there are questions about how much further expansion is desirable, because experts disagree on whether cornbased ethanol really saves oil and really reduces CO2 emissions. Some studies show that, when the indirect effects of agriculture are included, gasoline is better than ethanol on both counts. Furthermore, studies show that corn-based ethanol drives up food prices. Thus there’s a debate about whether any further expansion of foodbased biofuels is a good idea. There are suggestions, for example, to allow only those biofuels known to actually reduce oil use and CO2 emissions to be marketed. This situation will improve when scientists figure out how to cost-effectively produce biofuels from nonedible cellulosic biomass such as grasses, paper products, wood, agricultural waste, and municipal solid waste. These energy sources contain cellulose, the most common organic compound on Earth, constituting about 1/3 of all plant matter. Cattle and other ruminant animals can digest cellulose with the help of micro-organisms that live in their guts, but humans can’t. Biofuels made from waste products could help solve waste disposal problems. Grasses could be grown in large untended fields, without mechanized agriculture and without fertilizer. So it’s not surprising that studies show cellulosic biofuels to save both oil and global warming emissions as compared with gasoline. Scientists can make cellulosic biofuels, but they’re too expensive and not expected to be ready for the marketplace for several more years. Geothermal energy, wind, photovoltaic cells, and solar-thermal energy generate electricity. Together they contribute only about 1% of the world’s energy, but each has much larger future potential. The remaining renewables in Table 1, active and passive solar, can heat water, dry clothes, and heat buildings. The amount of energy they provide isn’t usually tabulated, but it far exceeds the combined global contributions of geothermal, wind, photovoltaic, and solar-thermal electricity, and it could be increased enormously. Geothermal energy, the thermal energy that radioactivity and pressure create underground, provides 7000 megawatts of electricity worldwide—the equivalent of seven large 1000 MW electric power plants. The easiest way to tap it is by drilling to directly remove hot water or steam. But this “direct geothermal” is a very limited resource. A nearly unlimited geothermal resource, amounting to many times more energy than is contained in coal deposits, lies several kilometers underground in the

The Energy Challenge

form of hot dry rock. Industry is just beginning to use the highly demanding drilling and underground fracturing technology needed to recover this energy. Figure 12 shows how it works. Because drilling this deep is expensive, this resource will be much used only if the price of electricity generation is high. Wind energy is the kinetic energy of air set into motion when the sun warms the daylight side of Earth. Since antiquity, it has driven sailing ships and turned windmills for grinding and pumping. Today, it also generates electricity by using wind turbines— electrical generators coupled to wind-driven rotating machinery (Figure 13). This is a proven decades-old technology. Wind has excellent near-term prospects for providing a major fraction of the world’s electricity: Many large windy sites are available, wind is already as cheap as coal for large-scale power, and new designs should reduce costs further even as environmental costs push coal prices upward. However, wind is less reliable than coal because of the wind’s unpredictability, and U.S. transmission lines do not currently reach into the many remote locations where wind energy is most available. This resource accounts for over 2% of the world’s electricity today and has been growing by nearly 30% per year for more than a decade. Germany is the world leader, followed by the United States, Spain, India, and China. Germany gets 7% of its electricity from wind, the United States gets 2%, and Spain gets 10%. In 2007, the United States added 5 gigawatts of wind-generated electric power, equivalent to 5 large electric power plants, and got 17 GW from wind. That same year, wind supplied 94 GW, equivalent to 94 large electric power plants, worldwide. As an indication of future trends, wind generation jumped 1500% during the past decade, while nuclear increased by 5% and coal increased by 33%. Photovoltaic (PV) cells exploit a fundamental quantum physics phenomenon to create electric current (flowing electrons) directly from solar radiation shining on a metal surface. Here’s how. Light and other electromagnetic radiation is quantized. This means that it must deposit its energy in tiny energy lumps called photons. Each of these concentrated lumps can be energetic enough to dislodge

Power plant

Water reinjected

Hot water

Fractured rock Granite A few kilometers

Figure 12

Thermal energy might someday be extracted from dry hot rocks by circulating water through large cracks created by hydraulic fracturing. Figure 13

Construction of a wind turbine at Carleton College in Minnesota. Rated at 1.65 MW, it’s the first commercial-scale wind turbine at a U.S. college. It began operation in 2004 and supplies 40% of Carleton’s electricity.

Tom Roster/Carleton College

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The Energy Challenge

an electron from its “parent” atom, allowing the electron to move freely along the metal surface or perhaps be ejected from the metal. If the radiation didn’t deposit its energy in lumps, calculations show that there would generally be too little energy at any one atom to dislodge an electron. Thus, this photoelectric effect— the ability of light to dislodge electrons from their parent atoms in metals—is direct evidence for the quantization of light and in fact provided some of the earliest evidence for quantum physics. PV cells are made of semiconducting materials such as silicon, having electrical properties midway between conductors that allow electrons to flow easily and insulators that do not. Semiconductors normally behave like insulators, but if their electrons are given a small amount of energy, the electrons can flow easily. These properties make semiconductors the basis for modern electronic technology. In PV cells, light provides the energy that puts electrons into the conducting state. A typical cell is made of two thin layers of silicon constructed differently so as to have different electrical properties, called “n-type” (negative) and “p-type” (positive) (Figure 14). The difference is that nonsilicon “impurity” atoms of different types are introduced into the two different layers. The n-type semiconductors contain impurity atoms that have more semiconducting electrons (per atom) than does silicon, while p-type semiconductors contain impurities that have fewer semiconducting electrons than does silicon. Suppose the two layers are simply placed in contact in the dark, without any external electrical contacts. Because of the impurities, microscopic electrical forces acting within each layer cause electrons to quickly flow from the n-type (where there were more electrons to begin with) to the p-type (where there were fewer). This creates an electric field at the p-n boundary (the junction between the two layers) that stops the flow of electrons. If light now shines on the two layers—still with no external electrical contacts— the photoelectric effect will energize some of the electrons, causing some of them to cross back across the p-n boundary from the p side to the n side. At this point, the n side is like the negative terminal of a battery that is not connected to anything, and the p side is like the positive terminal. Now suppose you electrically connect this tiny “battery” to an external device, as shown in Figure 14. Then the energized electrons that were pushed to the n side will flow through the wires and back around to the p side. As electrons arrive at the p side, light continues to energize electrons to move across the junction from the p side to the n side, creating a complete loop of flowing electrons. The p-n junction acts like a battery energized by light. PV energy is a good example of the contribution that sophisticated technology can make to the world’s energy problems. Arrays of photovoltaic cells can provide electricity for centralized electric power or they can power individual buildings or appliances, especially in remote locations that are difficult to reach with centralized power (Figure 15). PV is not yet a large resource but it’s being intensely developed and is growing rapidly. Its total global capacity is now around 15 GW, equivalent to 15 large electric power plants, a third of one percent of the world’s 4000 GW of electric generation capacity. Global production of PV cells has grown by a factor of 2000 over the past 20 years; this growth is expected to continue, with PV becoming a major contributor to power generation within 20 years. Larger production and continuing research have driven down the cost of this resource to the point that, assisted by a 30% federal tax credit for renewables, it now costs about the same as natural gas. As PV costs decline and natural gas prices increase, PV’s competitiveness as a utility option will increase.

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The Energy Challenge Figure 14

Solar radiation Electrical connections

Light bulb, hand calculator, etc.

n-type semiconductor

Electrons flow from n-type.

Electrons flow into p-type.

Electrons are energized by light to move across the p-n junction.

p-type semiconductor

This diagram shows how a PV cell works. When light shines on it, the junction (the interface between the “p-type” and “n-type” semiconductors) acts like a battery. Because of the differing microscopic properties of the two semiconductors, electrons that are energized by light cross the p-n junction from the p to the n side. These electrons can then flow through an external circuit. The junction acts like a battery. A typical cell is only 1 mm thick.

Figure 15

A series of photovoltaic cells, attached together, can provide a large electric current. The photo shows an experimental project.

National Renewable Energy Laboratory

Solar-thermal electricity is generated from thermal energy created by the sun. This resource generates the equivalent of one large power plant in the United States today, using two types of technologies. In the first, reflective solar collectors track the sun and focus it on a liquid that is then piped to a central location where it produces steam to drive an electric generator (Figure 16). The second uses sun-tracking mirrors to reflect solar energy to a central boiler that produces steam (Figure 17). Finally, solar energy can be used directly for solar heating. Figure 18 shows a rooftop “flat-plate” collector where a pumped liquid is heated and then circulated back indoors to be used for space or water heating. Collectors using pumps are active forms of solar heating; collectors based on natural flow are passive. The methods are older than humankind (animals and plants seek the sun), as simple as the backyard clothesline, and as high tech as the latest triple-pane argon-filled multilayer-coated windows. Figure 19 illustrates several passive concepts. Even in cold climates, these methods can reduce heating needs by 60% to 80%, simply by letting the sun shine in.

Least risk leads to the same conclusion as least cost. Energy companies can afford only options that are small, fast, cheap, and modular. Efficiency, renewables, and some natural-gas technologies meet these tests. Coal and nuclear generally don’t. Amory Lovins

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The Energy Challenge Figure 16

Solar collectors for a solar-thermal power plant. The mirrored faces focus sunlight on a liquid in the pipe running the length of the collectors. The pipes transfer thermal energy to a steam turbine coupled with an electric generator.

Black metal absorber plate with liquid tubes built in

National Renewable Energy Laboratory

Flirt Collection/Photolibrary Rear cover and insulation t

ted

id iqu

ou

l

a He

Figure 17

A 10 MW solar-thermal test facility in Barstow, California. The mirrors reflect sunlight onto a boiler on top of the tower, and the boiler makes steam for electricity generation.

Double-glass cover Cool liquid in

Figure 18

A flat-plate solar collector that uses forced circulation of a liquid to collect and transfer solarthermal energy.

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Economics has everything to do with the viability of these renewable resources. A primary advantage of many renewable resources is their low environmental impact. In order to fully exploit this advantage and still maintain free markets, environmental “costs” should be incorporated into the prices of energy resources. For example, in addition to its direct government subsidies, coal is effectively subsidized today by the environment because its price does not reflect its full pollution and global warming costs. This hidden subsidy distorts the market, leading to an irrational overuse of coal.

The Energy Challenge Summer sunlight

Insulation of all outside surfaces

Overhanging eave to block summer sunlight, permit winter sunlight

Winter sunlight Massive concrete, rock, or water tanks to store thermal energy in the winter

Few windows on north side

Deciduous trees to block summer sun, permit winter sun South

Double- or triple-paned south-facing glass

Massive concrete foundation in contact with the ground for warmth in winter, coolness in summer

Figure 19

Several passive solar-energy principles for keeping houses warm in cold weather and cool in hot weather.

Two methods have been suggested for incorporating one important environmental cost, global warming, into the market. The first is a simple carbon tax on the carbon content of all fuels. The second, more complicated, method is a carbon cap and trade system in which a national maximum or “cap” would be placed on total carbon emissions, and “tradable permits” to emit a certain tonnage of carbon (adding up to the allowed cap) would be issued to carbon-emitting companies. Companies could buy and sell permits among themselves, allowing less efficient companies who need additional permits to purchase them from more efficient companies who have permits to spare. A carbon market would develop and provide incentives to obtain the maximum emission reductions for the minimum cost. A quite successful sulfur emissions cap and trade system was imposed during the 1990s on the U.S. coal industry; it solved the serious problem of acid rain pollution in lakes and rivers. The essential difference between the carbon tax and the cap and trade methods is that a tax controls the emission rate by controlling carbon prices, whereas cap and trade directly sets the emission rate and allows that rate to determine carbon prices.

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The Energy Challenge

CONCEPT CHECK 10 Which of the following are “heat engines”? (a) Hydroelectric power plant. (b) Geothermal power plant. (c) Wind turbines. (d) Solar-thermal electricity generation. (e) Photovoltaic cells.

7 USING LESS Deficient building standards mean that more energy passes through the windows of buildings in the U.S. than flows through the Alaska pipeline. William D. Ruckelshaus, First Administrator of the Environmental Protection Agency

Making major gains in energy efficiency is one of the most economical and effective ways our nation can wean itself off its dependence on foreign oil and reduce its emissions of greenhouse gases. . . . Energy efficiency is one of America’s great hidden energy reserves. We should begin tapping it now. From the Summary of the American Physical Society’s Energy Efficiency Report, 2008

Table 5 Total energy consumption per capita, for several nations and groups of nations, for year 2005. Units: gigajoules. United States

331

France

185

Germany

176

Japan

174

United Kingdom

164

Europe

159

Switzerland

151

World

75

China

55

India

21

Low Income Countries

13

Source: World Resources Institute.

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Efficiency contributes a giant 94 exajoules per year to the nation’s energy services (Figure 5) but without the pollution, resource depletion, and expense that accompanies actual energy use. If the United States were still operating at the energy efficiency that existed up to the 1973 oil embargo, it would be using nearly twice as much energy as it is using. The saved energy reduces U.S. energy costs by nearly a trillion dollars annually! Despite U.S. improvements in efficiency since the 1973 oil embargo, comparison with other nations (Table 5) shows that Americans should be able to reduce their energy consumption to 50% or less of present levels without reducing standards of living or energy services. The average American consumes twice as much energy as do citizens of such prosperous (as measured by their gross domestic product per person) nations as France, Germany, Japan, the United Kingdom, and Switzerland. One reason is that other nations waste less power plant thermal energy than we do. Take a good look at the next cooling tower or other power plant cooling apparatus you see. Enormous quantities of thermal energy flow out of such a tower, representing something like 50% of the energy of the fuel that was burned (or fissioned) to run the plant. Think of the energy that would be saved if this thermal energy were put to use to heat homes or for industrial purposes. This is the thought behind combined heat and power, also called co-generation. These terms refer to any use of thermal energy to both generate electricity and provide useful heating, in either order. That is, exhaust power plant thermal energy might also heat homes, or exhaust thermal energy from high-temperature processes such as iron production might also run an electric generator. About 8% of the world’s electricity is co-generated. In contrast to the typical 40% efficiency of a coal or nuclear generating plant, combined heat and power systems run at efficiencies of 75% to 90%. Co-generation often provides heating to a compact group of residential or commercial buildings situated close to the electric generating plant so that the thermal energy (usually in the form of steam) needn’t be piped far. For such “district heating” applications, the power plant cannot be large or isolated as are most U.S. plants today. Thus co-generation is well suited to small generating plants such as renewable energy plants running on wood waste or biomass gas. For this warming planet, it can save a lot of CO2 emissions. As just one among many examples of the energy savings that are possible when efficiency is taken seriously, let’s look at recent advances in efficient lighting. Traditional incandescent bulbs create light by heating a thin wire until it glows. As you might expect, this produces a lot more heat than light. Fluorescent bulbs operate by a different principle, not involving heating. The bulb’s glass tube is filled with dilute mercury vapor or some other gas. An electric current passes through the tube, ionizing some of the mercury atoms by collision with the moving electrons and putting many atoms into excited quantum states. The excited mercury atoms radiate invisible ultraviolet photons that are absorbed by a powdery material called the phosphor that coats the inside of the glass tube, causing the phosphor to radiate visible light. These bulbs are far more efficient than incandescent bulbs, providing the same amount of lighting for one quarter as much energy.

The Energy Challenge

The invention of compact fluorescent bulbs has further improved fluorescent bulb efficiencies and has permitted them to be used in a wider variety of settings than was possible with the older long, skinny bulbs. Here’s how. In household electric circuits, electrons don’t keep flowing in one direction but instead vibrate back and forth 60 times per second. Older fluorescent bulbs operate at this 60 Hz frequency. But both bulb quality and efficiencies would be higher if the frequency within the bulb were much higher than 60 Hz. The reason is that at 60 Hz, electrons and ions have a full 1/60th of a second for each back-and-forth motion—a long time in the world of electrons and ions. This is time enough for large numbers of electrons and ions to crash into the ends of the tube, creating heat and reducing bulb life. Older bulbs were long and thin in order to reduce these “end effects.” New electronically controlled bulbs cause the current to oscillate at up to 50,000 Hz. This reduces energy losses by restricting electrons and ions to much smaller vibrations and allows bulbs to be compact enough to screw into ordinary light sockets. What are the consequences of this single efficiency improvement? For the consumer, a typical $10 compact fluorescent bulb lasts 10 times as long as an incandescent and uses one-fourth the energy, for a net saving of $45 over the life of the bulb. For society, the 3.5 billion compact fluorescent bulbs in use worldwide in 2003 were saving the electricity equivalent of 38 large 1000 MW power plants. Usage nearly doubled during 2001 to 2003, so by today the number has surely doubled again to exceed 7 billion, but there is no data past 2003 to verify this. Sales growth of compact fluorescents has been enormous; for example, U.S. sales grew 343% between 2000 and 2004. Avoided electricity generation translates into pollution reduction. For example, the 375 million compact fluorescents in use in North America in 2005 saved about 9 million tons of carbon emissions and 175,000 tons of sulfur dioxide emssions during the year. Energy efficiency is entwined with economics. Energy efficiency usually saves money, and when it does it’s possible for governments or companies to stimulate energy-saving programs that reward consumers financially. For example, some electric companies and some governments make large-volume, low-cost purchases of compact fluorescent bulbs and sell them to consumers at below cost, with the difference recovered in increased electricity rates to those consumers. The consumers save money because of reduced electricity consumption, which more than compensates for the increased rates. Everybody wins: the company, the consumer, and the environment. Because energy efficiency has been overlooked for so long, small investments can produce dramatic savings. For example, a $7.5 million compact fluorescent bulb factory saves as much electricity as a $1 billion power plant generates, while also avoiding the power plant’s fuel cost and pollution. A $10 million “superglass” factory making windows that block heat but permit light can produce the comfort that would be provided by the air conditioners run by $2 billion worth of generating stations. Energy prices strongly affect the amount and types of energy consumed. The lock-step link between GDP and energy growth was broken only when the 1973 Mideast oil embargo raised energy prices. Beginning in 1973, as energy efficiency took hold, GDP grew but energy use did not (Figure 5). The higher energy prices resulting from the oil embargo produced enormous energy and financial savings. Many studies suggest energy taxes as an incentive for efficiency. Energy taxes could be made “revenue neutral” by lowering other taxes in compensation, to discourage energy use while not increasing overall taxes. Incentives would encourage energy-conscious shopping. Many observers suggest gas-guzzler taxes on inefficient automobiles and gas-sipper rebates on efficient ones. An underlying view is that

Socialism collapsed because it did not allow the market to tell the economic truth. Capitalism may collapse because it does not allow the market to tell the ecological truth. Ecologist Lester Brown, from His 2003 Book Plan B: Rescuing a Planet Under Stress

You are not going to get energy innovation at scale when a barrel of oil is cheaper than a barrel of water. Thomas Friedman, Pulitzer PrizeWinning Editorial Writer for the New York Times, from His 2008 Book Hot, Flat, and Crowded

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The Energy Challenge Growth [in energy consumption] has declined primarily because conservation turned out to be far less expensive than new supply— 3 to 5 times cheaper than new power plants.

CONCEPT CHECK 11 If the entire world used energy at the same annual per capita rate as the United States, the world’s annual energy consumption would be about (a) twice as large as it is; (b) three times as large as it is; (c) four times as large as it is; or (d) six times as large as it is.

© Sidney Harris, used with permission.

Arthur H. Rosenfeld, Physicist Who Provided the Energy Services of 28 Large Generating Plants by Developing High-Frequency Fluorescent Bulbs

global warming, resource depletion, and other environmental concerns must be incorporated into the costs of doing business and consuming goods if a market economy is to address such concerns. And if humankind doesn’t address such concerns, our economy, as well as our socity, will surely founder on the shoals of a ruined evironment.

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The Energy Challenge Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions ENERGY HISTORY AND FUTURE 1. Is it correct to say that this chapter studies the predicted energy future? Suggest another, more accurate, phrase. 2. List the six main U.S. energy resources today. Which three provide the most energy? 3. Which of the six main U.S. energy resources are renewable? 4. Which of the six main U.S. energy resources are primarily used to generate electricity?

1

New renewables

3

Hydro

5. In Figure 4, why is the residential sector of the economy so much more energy-efficient than the transportation sector? 6. List the four broad categories of energy resources or energy options that will play a role in future U.S. energy policies. 7. Which yields more usable energy in the United States today: fossil fuels, nuclear power, or renewable energy resources? 8. List the fossil fuels. Why are they called fossil fuels? 9. Explain why the gap between the GDP graph and the total energy graph in Figure 5 is labeled “efficiency.” 10. Explain why, in Figure 5, GDP and total energy coincide for many years, and why they eventually separate.

24 9

24 Supply: 106 exajoules of energy resources

Nuclear

20

Electric power generation, 39

40

Residential and commercial, 29

8

1

Oil

24

14

7

Coal 4

Lost in generation and transmission, 24

8

22

15 Industrial, 22

39 14

14

Nonelectric, 67 5 25

Gas

Useful work and heating, 36

24 20 31

4

Waste, 70

Transportation, 31

7

Biomass

Figure 4

Approximate energy flows in the U.S. economy in exajoules (1018 J) , in 2008. Source: U.S. Energy Information Agency, 2009.

From Chapter 16 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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The Energy Challenge: Problem Set 200 180

Annual energy use, in exajoules, 1018 joules

160

Efficiency, 94

140 U.S. annual inflation-adjusted GDP, appropriately scaled

120

Total annual energy

100 80 60

Energy 106 40 20 0 1950

1955

1960

1965

1970

1975

1980 Year

1985

1990

1995

2000

2005

2010

Figure 5

History of total U.S. energy consumption and GDP, 1950–2008. GDP is one measure of the goods and services provided by the economy. In order to compare the two graphs, GDP is scaled to match total energy in 1950. The two graphs are parallel until the 1973 energy crisis, after which higher energy prices encouraged Americans to conserve. The wide gap that then opens up between the two graphs is a measure of the energy saved by efficiency measures since 1973. Source: U.S. Energy Information Agency.

NUCLEAR POWER 11. What is a nuclear reactor? 12. Which of the following is needed in a coal-fired power plant but not in a nuclear power plant: condenser, cooling tower or lake, turbine, stack, containment dome? 13. Which of the following is needed in a nuclear power plant but not in a coal-fired power plant: condenser, cooling tower or lake, turbine, stack, containment dome? 14. List three essential components of a nuclear power reactor, and explain the function of each. 15. Is the enrichment of U.S. reactor fuel closest to 1%, 3%, 10%, 50%, or 90%? 16. Is the enrichment of bomb-grade uranium fuel closest to 1%, 3%, 10%, 50%, or 90%? 17. Where might a fusion reactor get its fuel?

ASSESSING NUCLEAR AND COAL POWER 18. List five problems with nuclear power and five problems with coal power. 19. Of the four most-used nonrenewable energy resources, which one does the United States possess in greatest abundance (most years remaining at current rate of use)? In least abundance?

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20. Do most energy experts feel that coal use will continue rising over the long term? Why? 21. What are high-level nuclear wastes, and where are they stored today? What is the most likely long-term solution to this problem? 22. Describe in general terms what happened at Three Mile Island. 23. Describe in general terms what happened at Chernobyl. 24. What is a breeder reactor? How could it affect the uranium resource problem? 25. How could breeder reactors affect the nuclear proliferation problem?

RENEWABLES AND EFFICIENCY 26. Which two renewable energy resources are in widest use today? 27. List three renewable resources that could produce significant amounts of electricity in the future, and describe briefly how each works. 28. What are semiconductors, and what role do they play in photovoltaic cells? 29. What is the difference between active and passive solar heating? Describe some of the techniques used in each. 30. How does the per capita energy consumption of other nations compare with that of the United States? What does this sug-

The Energy Challenge: Problem Set gest about the potential of further energy efficiencies in the United States? 31. How does a fluorescent bulb work? 32. Why are fluorescent bulbs more energy-efficient than incandescent bulbs? 33. Describe a recent improvement in fluorescent bulbs that has increased their usefulness.

Conceptual Exercises ENERGY HISTORY AND FUTURE 1. According to Figure 2, in approximately what year did the United States begin getting as much, or more, energy from fossil fuels as from wood? 2. By about what factor did the energy consumed in 1980 exceed that consumed 100 years earlier? 3. Which are renewables: wood, uranium, trash (as fuel), coal, wind, natural gas, hydroelectric? 4. Which options listed in Table 1 contribute to global warming? 5. Which resources listed in Table 1 do not come ultimately from the sun?

6. Use Figure 2 to estimate the amount of energy the United States got from coal in each of the following years: 1900, 1920, 1940, 1960, 1980, 2000. 7. Use Figure 2 to estimate the amount of energy the United States got from oil in each of the following years: 1900, 1920, 1940, 1960, 1980, 2000. 8. Of the three major sectors, namely industrial, residentialcommercial, and transportation, which one is least efficient? Why? (See Figure 4.) 9. Use Figure 4 to find the energy efficiency of the U.S. transportation sector. 10. Use Figure 4 to find the energy efficiency of the U.S. residential-commercial sector. 11. Judging from the 70% efficiency of the U.S. residentialcommercial sector (preceding exercise), what can you plausibly conclude regarding the use of heat engines by this sector? 12. Which energy resource was dominant in the United States in 1860? 1880? 1900? 1920? 13. Which energy resource was dominant in the United States in 1940? 1960? 1980? 2000? 14. Use Figure 2 to estimate the percentage of U.S. energy resource consumption that came from coal in 1940 and in 1980. 15. Use Figure 2 to estimate the percentage of U.S. energy resource consumption that came from oil in 1940 and in 1980.

110 100

Nuclear

Annual U.S. energy consumption, in units of 1018 joules

90 Natural gas

80 70 60

Oil

50 40 30

Coal

20 10 0 1840

1860

1880

1900

1920 1940 Year

New renewables* Hydro Biomass 1960 1980 2000 2020 * Wind, Geothermal, Solar

Figure 2

History of U.S. energy use, 1840–2008: total annual U.S. energy consumption of various resources. Source: U.S. Energy Information Agency, 2009.

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The Energy Challenge: Problem Set 16. From Figure 4, find the approximate energy efficiency of the overall U.S. economy. 17. According to Figure 4, what fraction of U.S. energy resources goes into the generation of electricity? 18. According to Figure 4, what fraction of coal energy goes into the generation of electricity? What fraction of oil? Of natural gas? 19. From Figure 5, estimate the equivalent amount of energy services (in exajoules) provided by post-1973 energy efficiency measures in 1980 and also in 1990. Now estimate the percentage of the nation’s total energy services provided by efficiency in each of these years. 20. Use Figure 5 to estimate the percentage increase in annual U.S. energy use (actual energy—not energy services) during 1950–1970. Repeat for 1970–1990.

NUCLEAR POWER 21. Every heat engine has a thermal energy input, a work output, and a thermal energy output. At what places in Figure 6 does each of these occur? 22. Figure 7 shows a tall tower. Is it analogous to a coal-fired plant’s stack? What is the function of this tower? Might coal plants have a tower like this? 23. Does a nuclear power plant have a “smoke” stack? Why or why not?

24. Figure 6 shows that a nuclear power plant has a condenser. What is the function of this device? Do coal plants also have condensers? 25. Why is it important that a nuclear power plant have two separate water or steam loops to get hot steam to the turbine? What could happen if there were only one loop? 26. “Thermal pollution” is thermal energy put into a cooling lake or stream. If a coal plant and a nuclear plant operate at 40% efficiency, the one causing the most thermal pollution per joule of electric energy is: the coal plant, the nuclear plant, both the same. 27. Suppose the main water pipe breaks in a nuclear power plant, shutting off the water flow. If the control rods fall immediately into place, stopping the chain reaction, is there still a problem? Why or why not? What safety feature should be used in this case?

ASSESSING NUCLEAR AND COAL POWER 28. List two advantages that coal has over nuclear power. 29. List two advantages that nuclear power has over coal. 30. Since power plants fueled by natural gas create carbon dioxide, why would it reduce global warming to switch from coal to natural gas power plants? 31. Are radioactive wastes hot? Why or why not?

Table 1 Natural energy resources Fossil fuels Coal Oil Natural gas Nuclear fuels Uranium for nuclear reactors Plutonium for breeder reactors Hydrogen for fusion reactors Renewable resources Hydroelectric Biomass burning: wood and trash Methanol from wood (also from coal and natural gas) Ethanol from grains, grasses, sugar, trash Wind Photovoltaic (solar) cells Solar-thermal electricity Geothermal Active solar heating Passive solar heating Conservation (not a natural resource, but acts like one) Energy efficiency with no change in energy services Lifestyle changes to reduce energy use

444

The Energy Challenge: Problem Set Figure 7

EFDA-JET

Nuclear power plant under construction. This view shows a cooling tower and a reactor containment dome under construction.

Figure 6

Schematic diagram of a steam-electric generating plant powered by a nuclear reactor. Electricity

Containment dome

Hot steam

Generator

Control rods

Hot water at high pressure

Turbine

Steam generator

Cooler steam Cold water

Core Condenser Hot water Fuel rods Water Reactor vessel

Pump Pump

Water

Lake or cooling tower

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The Energy Challenge: Problem Set 32. How can a breeder reactor create more fuel than it consumes? Why doesn’t this violate the law of conservation of energy? 33. How might a country’s nuclear power industry contribute to developing a uranium bomb? 34. How might a country’s nuclear power industry contribute to developing a plutonium bomb?

RENEWABLES 35. Describe how hydroelectric energy is renewed. 36. List one possible disadvantage of each of the renewable energy resources listed in Table 1. 37. What are some ways that solar energy is routinely used around the home? 38. Is renewable energy used today for any form of transportation? Explain. 39. What energy transformation occurs for each of these ways of making electricity: coal, uranium, hydroelectric, biomass? 40. What energy transformation occurs for each of these ways of making electricity: geothermal, wind, solar-thermal, photovoltaic? 41. What energy transformation occurs when you hang your wash outdoors to dry in the sun?

EFFICIENCY 42. In what way was the oil crisis, caused by the 1973 Mideast oil embargo, a good thing for the United States? 43. Are there any industrialized nations in which the energy use per person is half, or less than half, what it is in the United States? 44. If the entire world used energy at the same annual per capita rate as Great Britain, would the world’s annual energy consumption be larger or smaller than it is? How much larger or smaller? 45. If the entire world used energy at the same annual per capita rate as China, would the world’s annual energy consumption be larger or smaller than it is? How much larger or smaller?

Problems ENERGY HISTORY AND FUTURE 1. Energy consumption rose roughly exponentially in the United States during 1880 to 1920. Use Figure 2 to estimate its doubling time and its annual percentage increase. 2. Suppose that U.S. energy consumption had maintained a 3.5% increase after 1920. Would total consumption be larger or smaller than the actual total consumption by the year 2000? How much larger or smaller?

COAL AND NUCLEAR POWER 3. Thermal pollution is thermal energy put into a cooling lake or stream. Consider a power plant that is “cooled” by a lake (the waste heat goes into a lake), operating at 40% efficiency. How many joules of thermal pollution does the plant create, per joule of electrical energy? 4. A power plant heats steam to 450°C and exhausts hot water into a lake at 80°C. Find the theoretical, or maximum possible, energy efficiency of this plant, using the formula efficiency = (Tin - Tout)>Tin

446

with temperatures in degrees Kelvin ( 0°C = 273 K). Suppose that the actual energy efficiency is 40%. For every joule of electrical energy created by this plant, how many joules of energy must be used? 5. A geothermal power plant uses 150°C steam and exhausts to the atmosphere at 25°C. Using the information from the preceding problem, find the maximum possible energy efficiency of this power plant. Suppose that the actual energy efficiency is 20%. For every joule of electrical energy created by this plant, how many joules of energy must be used?

RENEWABLES AND EFFICIENCY 6.

If you covered a football field with photovoltaic cells, for about how many households could it provide electricity? Use the following information: Solar energy hits each square meter of Earth’s surface at a rate (averaged over day and night) of 200 watts, an average household consumes electricity at a rate of 1 kilowatt, and photovoltaic cells are 20% efficient. 7. MAKING ESTIMATES Use the information in the preceding problem to show that about 10,000 square kilometers of land area (3% of a sunny state such as Arizona), if covered with photovoltaic cells, could provide all of the electricity for the United States, which consumes electricity at an average rate of about 400 billion watts. What complications might arise if the nation tried to provide all its electricity this way? 8. A typical 18 watt compact fluorescent bulb costs $10, lasts 10,000 hours, and provides as much light as does a 75 watt incandescent bulb that costs $1 and lasts 750 hours. How much does it cost for each type of bulb to provide 10,000 hours of light? Do not forget to include energy costs, at about 8¢ per kilowatt-hour. 9. Using the information provided in the preceding problem, calculate the “payback time” for a typical 18 watt compact fluorescent bulb—in other words, the number of hours of lighting required before the cost of the bulb is recovered in saved energy costs. How many months is this, assuming that the bulb is lit 8 hours per day? MAKING ESTIMATES

Answers to Concept Checks 1. 2. 3. 4. 5. 6. 7. 8. 9.

10.

(d) (b) (a) Of the 39 exajoules going into electric generation, 8 + 7 = 15 useful exajoules are generated: 15>39 = 38%, (c). (b) (a) and (d) (a), (c), (e), (f ) (a), (b), (c), (d), (e) The amount of coal burned in a year is far more than the amount of uranium fissioned, so (a) is ruled out. Since coal contains far more carbon than sulfur, combustion must produce far more CO2 than SO2, (b). In both geothermal and solar thermal, thermal energy is used to generate electricity, (b) and (d).

The Energy Challenge: Problem Set 11. The world annual rate is about 75 billion joules per person, while

37. Drying clothes, rain watering the lawn, helping to warm the

the U.S. rate is about 331 billion joules per person. 331>75 = 4.4, (c).

house by day, keeping the house at a comfortable temperature by opening and closing windows at appropriate times, using sunlight for light to see by, sunbathing, growing plants inside and outside the house, burning wood in a fireplace. Coal, biomass: chemical to thermal to electric. Uranium: nuclear to thermal to electric. Hydroelectric: gravitational to electric. Radiant to thermal. Yes. According to Table 5, France, Germany, Japan, and the United Kingdom use half or less than half as much energy, per person, as does the United States. According to Table 5, China uses less energy, per person, than does the world as a whole, so consumption would be smaller. The ratio of per-capita energy use for China and for the world is 55>75 = 0.73 = 73%. So world energy consumption would drop to 73% of its present value.

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Around 1880. 3. Wood, trash, wind, hydroelectric. 5. Uranium, plutonium, and hydrogen for nuclear power. Geothermal energy. Also, conservation does not come from the sun—it comes from human ingenuity! 7. 0 in 1900, 1018 J in 1920, 4 * 1018 J in 1940, 18 * 1028 J in 1960, 36 * 1018 J in 1980, 4 * 1018 J in 2000. 9. 7>31 = 23%. 11. Heat engines are probably not very widespread in the residential-commercial sector, because their widespread use would lead to an overall efficiency less than 52%. 13. From Figure 2: Coal in 1940, oil in 1960, oil in 1980, oil in 2000. 15. 1940: about 4>25 = 16%; 1980: about 36>85 = 42%. 17. 39>106 = 37%. 19. In 1980: about 10 exaJ. In 1990: about 40 exaJ. In 1980: 10>90 = 11%. In 1990: 40>125 = 32%. 21. Thermal input: in the core of the reactor. Work output: at the turbine. Thermal output: at the condenser. 23. Nuclear power plants do not have a stack because they do not operate by combustion of fuel. 25. We do not want the radioactive water that goes through the reactor to move outside of the containment dome. If there were only one loop, either radioactive water would have to move outside the dome to reach the turbine, or the turbine and condenser would have to be moved inside the containment dome (which would pose great dangers for the workers who must service the turbine and condenser). 27. Yes. Because the rods are radioactive, and this generates thermal energy. A supply of cooling water is kept on hand to keep the reactor cool. 29. Does not contribute to global warming, much less transportation needed, less mining needed. 31. Yes. The alpha, beta, and gamma particles emitted by radioactive materials deposit their high energies in the surrounding material, heating it. 33. By building a uranium enrichment plant, and by training nuclear scientists and technologists. 35. The sun’s radiation warms water, evaporating some of the water. The evaporated water rains down on the land, and is collected behind dams, where it provides the gravitational energy needed to produce hydroelectric power.

39. 41. 43. 45.

Problems 1. Energy use roughly doubled during 1880–1900, and doubled again during 1900–1920, so the doubling time was 20 years. P = 70>T = 70>20 = 3.5, so the annual percentage increase was 3.5%. 3. Efficiency = useful output/total input, so total input = useful output/efficiency. So, for 1 J of electrical energy, total energy input = 1 J>0.4 = 2.5 J. Thus the exhausted thermal energy (or thermal pollution) is 2.5 J - 1 J = 1.5 J. 5. The temperature difference is Tin - Tout = 125 K. The input temperature, in Kelvins, is 150 + 273 = 423 K. So, ideal efficiency = 125 K>423 K = 0.30 = 30%. Efficiency = useful output/total input, so total input = useful output/efficiency. So, for 1 J of electrical energy, total energy input = 1 J>0.2 = 5 J. 7. To provide 400 * 109 W at 20% efficiency, 2000 * 109 W (2 * 1012 W) must be collected. This amount of solar power falls on an area 2 * 1012 W>(200 W>m2) = 1010 m2. But 1 km2 = 1000 m * 1000 m = 106 m2, so the land required is 104 km2, or 10,000 km2. Complications: The sun is an intermittent source, so an energy storage method would have to be found. Energy storage would make the process less efficient. It would be difficult to distribute the energy from Arizona to the rest of the country; solar power plants would need to be located in many less sunny regions in order to solve the distribution problem. There would be land-use problems and materials problems (supply, disposal, resource use, pollution). 9. In 1 hour, the money saved due to lower energy consumption is $0.08 per kW # h * (0.075 - 0.018) kW * 1 hr = $0.00456. So the number of hours needed to save $10 is $10> $0.00456 per hour = 2200 hours. (Note: This neglects the cost of the many incandescent bulbs that would be used.) At 8 hours a day, the number of days is 2200>8 hr per day = 275 days, which is about 9 months.

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Fusion and Fission

From Chapter 15 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

449

Fusion and Fission —and a New Energy

The Dark Ages may return on the gleaming wings of science. Winston Churchill, British Prime Minister During World War II

P

eople get useful energy from each of the three fundamental “glues” that hold things together: gravity, electromagnetism, and the strong nuclear force. For example, we can get electric power from the gravitational forces acting on a lake held up behind a hydroelectric dam and from the microscopic electric forces that cause molecules to combust chemically in a coal-burning electric power plant. As you will see, we can also get electric power from the strong nuclear force. In the familiar macroscopic world, gravity is the most obvious, and the strong nuclear force the least obvious, of the three. But this order is reversed in the microscopic world. Acting between such subatomic particles as neighboring protons within a nucleus, the strong nuclear force is by far the strongest of the three, the electric force is next in strength, and gravity is by far the weakest. For example, acting between two protons, gravity is a trillion trillion trillion times weaker than the electric force! Because of the different strengths of the three forces, equal amounts of energy output from each of the three require quite different amounts of fuel. A 1000 MW hydroelectric power plant uses the gravitational energy of some 60,000 tonnes of water every second, a 1000 MW coal-burning power plant requires 10,000 tonnes of coal (150 truckloads or 1 trainload) every day, and a 1000 MW nuclear power plant uses only some 100 tonnes of uranium (a few truckloads) every year. These three forces also differ in their destructive power. Towns of a few thousand people have been leveled by the gravitational energy of millions of tonnes of earth or water in a landslide or flood. A town of this size can also be leveled by 1000 tonnes of explosive in several hundred chemical bombs. But Hiroshima, a city of a quarter of a million people, was leveled by one nuclear bomb carrying only 42 kilograms of explosive uranium. The strongest of the three forces is the least understood. Humans have probably had some intuitive understanding of gravity for millions of years. Electromagnetism began to be understood in the eighteenth century. But scientists became aware of the strong nuclear force only during the twentieth century and still lack a fundamental understanding of it. Fusion and fission are nuclear reactions—processes that alter the structure of one or more nuclei. I’ll discuss these reactions primarily in terms of energy. Sections 1 and 2 continue the discussion of nuclear energy. Section 1 presents the energetics of hydrogen fusion and why the stars shine. Section 2 discusses the energy present in the

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various nuclei found in nature. Section 3 applies these ideas to tell the fascinating tale of how the stars forged the atoms that form Earth and your body. Section 4 presents the physics of fission, and Section 5 discusses the method, called a chain reaction, by which fission is used to get useful energy from the nucleus. Unfortunately, the first major application of nuclear knowledge was the nuclear bomb. Because the bomb continues to be a threat, and because of its many lessons for our scientific age, Sections 4, 5, and 6 discuss the fission bomb in the historical context of building the world’s first nuclear weapon. Section 7 presents another product of nuclear knowledge, the fusion bomb. Section 8 discusses the grim possibility of nuclear terrorism. Later, I’ll discuss a more positive application of nuclear knowledge, namely, nuclear power.

1 FUSION: FIRE OF THE SUN My dictionary says that to “fuse” means to unite and to “fission” means to split. Thus, nuclear fusion is the uniting of two nuclei to form a single larger nucleus, and nuclear fission is the splitting of a single nucleus roughly in half to form two smaller nuclei. Continuing the nuclear detective story, let’s see what we can deduce about the energetics of the simplest multiparticle nucleus, the hydrogen isotope 21H. Suppose you tried to separate this nucleus into an isolated proton and neutron. Because the proton and neutron are held together by the strong nuclear force, this would not be easy (Figure 1). Compared with the 21H nucleus before separation, a separated proton and neutron have (a) more energy; (b) less energy; (c) the same amount of energy. CONCEPT CHECK 1

CONCEPT CHECK 2 Compared with the force exerted by the proton and neutron on each other before the 21H nucleus is separated, the force between them after separation is (a) greater; (b) less; (c) the same.

The separated proton and neutron have more energy than the 21H nucleus. Since it is due to nuclear forces, this excess energy is a form of nuclear energy. The energy relationship here is like that of two objects, such as Earth and a rock, that are attracted by gravity: The gravitational energy is larger when the rock is farther from Earth’s surface (Figure 2). Now imagine putting a 21H nucleus together, instead of pulling it apart. This process could be represented as

Figure 1

You would have to do work to pull apart the two particles in the nucleus of 2H.

n + p : 21H where n and p stand for neutron and proton. As you have seen, the left side of this nuclear reaction has more nuclear energy than the right side. Since energy is always conserved, this energy must show up in some other form after this process. In other words, this reaction is one way to transform nuclear energy into other forms. It is, in fact, one form of nuclear fusion. It occurs whenever neutrons and protons come within range of each other’s strong force (recall that the strong force has a short range). The strong force then pulls the two tightly together—like a stretched rubber

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Fusion and Fission Figure 2

Nuclear energy is similar to gravitational energy: Greater separation means greater energy.

(a) In which case does the system have greater gravitational energy: when the rock is at a lower or a higher altitude?

(b) Which has greater nuclear energy: a proton and neutron that are closer together or farther apart?

band snapping together. When a large mass of neutrons and protons fuse in this manner, this snapping together causes heating and the emission of high-energy gamma radiation. So the energy transformation is NuclE : ThermE + RadE I’ll refer to any such transformation of nuclear energy to other forms as a release of nuclear energy. Essentially all the 21H in the universe was formed by neutron-proton fusion 13.7 billion years ago, during the first few minutes after the big bang. This reaction occurs today during supernovae explosions. A more significant fusion reaction today is the fusion of two hydrogen nuclei, either 11H (a proton) or 21H. Again, nuclear energy is released when the two nuclei come within range of each other’s nuclear force and snap together. In fact, the sun and other stars are made mostly of hydrogen1 and get much of their energy from the fusing of 11H with 21H. CONCEPT CHECK 3

(b)

3 2H;

(c)

2 2He;

(d)

3 1He;

The isotope created by the fusion of 11H with 21H is (a) 31H; (e) 32He.

There’s an interesting catch to 1H + 2H fusion. Unlike the n + p reaction, the electric force is involved in the 1H + 2H reaction because both nuclei are charged. The two nuclei repel each other electrically at relatively great distances, much greater than the nuclear distances at which their strong forces attract each other. So it’s not easy to get the two nuclei close enough to feel each other’s strong force. Stars solve this problem by first heating up to millions of degrees at their centers during the star-formation process. At such temperatures, the nuclei are moving so rapidly that they can push right through one another’s repulsive electric force fields and get close enough to fuse. So fusion will occur in a collection of hydrogen nuclei if you get them hot enough. Remembering that the fusion reaction creates radiant and thermal energy, we can summarize the energetics as ThermEin + NuclE ¡ ThermEout + RadE 1

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Astronomers once believed that stars were made of heavy elements. But astrophysicist Cecilia H. Payne, working on her doctoral dissertation at Harvard University in 1925, applied spectroscopic methods to the study of starlight to discover that stars are made mostly of hydrogen. Her dissertation, leading to the first doctoral degree ever granted by Harvard’s astronomy department, is described by some as “the most brilliant Ph.D. thesis ever written.”

Fusion and Fission

Quantitatively, the thermal energy output is far larger than the input needed to make the reaction occur. So the reaction, once started, is self-sustaining. This is just like a fire. It takes the thermal energy of a burning match to start paper burning, but once started, the combustion reaction creates more thermal energy than is needed to make the reaction occur, so it sustains itself. The difference between fusion and a fire is that fusion involves nuclear forces while a fire involves chemical forces (electromagnetic forces between atoms). Because of this central role of thermal energy, a self-sustaining fusion reaction is called a thermonuclear reaction. How do we know that E really does equal mc 2? Nuclear reactions are marvelous examples of mass–energy equivalence, because the energies involved are large enough to produce significant mass changes. Consider the 1H + 2H reaction. Since the 3He created by this reaction has less nuclear energy than the separated 1H and 2H nuclei (recall Figure 2), the principle of mass–energy equivalence predicts that the helium nucleus should also have less mass (Figure 3). The masses of all three nuclei are known from direct measurement: mass of 11H = 1.6727 * 10 - 27 kg mass of 21H = 3.3437 * 10 - 27 kg mass of 32He = 5.0066 * 10 - 27 kg The first two masses add up to 5.0164 * 10 - 27 kg, which is 0.0098 * 10 - 27 kg more than the mass of the helium nucleus. Just as Einstein predicted, the mass becomes less when the system loses energy. To check E = mc2 quantitatively, the energy loss during the reaction (the energy that is transformed into radiant and thermal energy) must be directly measured. This can be done by using the transformed energy to warm up water and measuring the resulting temperature change of the water. The measured energy released per individual fusion reaction turns out to be 8.815 * 10 - 13 joules. Let’s see if this does equal the known mass difference times the square of lightspeed:

Figure 3

The mass of the whole does not equal the sum of the masses of its parts: When 1H and 2H fuse to form 3He, the 3He has less total energy when it is at rest, so it must have less mass.

0.0098 * 10 - 27 * c2 = 0.0098 * 10 - 27 * 9 * 1016 = (0.0098 * 9) * (10 - 27 + 16) = 0.08815 * 10 - 11 = 8.815 * 10 - 13 joules It checks. M A K I N G EST I M AT ES The sun’s total power output of 400 trillion trillion watts

(400 * 1024 joules per second) comes from three types of fusion reactions whose net effect is to convert the sun’s hydrogen into 42He. About how much mass does the sun lose every second? Despite this enormous mass loss, the sun will end its life 5 billion years from now with only 0.06% less mass than it had 5 billion years ago when it turned osn!

SO LU T I O N TO M A K I N G EST I M AT ES

mass in 1 s = E>c2 = 400 * 1024>9 * 1016 L 400 * 1024>1017 = 400 * 107 = 4 billion kg

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Fusion and Fission

2 THE NUCLEAR ENERGY CURVE Many other nuclei, in addition to 1H and 2H, can fuse together to form larger nuclei. Here are two examples: When two 42He nuclei fuse, they form an isotope of the element (a) helium; (b) lithium; (c) beryllium; (d) boron. (Hint: Use the periodic table on the inside back cover.) CONCEPT CHECK 4

CONCEPT CHECK 5

(c)

12 4C;

(d)

12 6O;

(e)

12 8N.

The fusion of 42He with 84Be creates (a)

12 6C;

(b) 86C;

You can see from these examples that fusion builds heavier nuclei such as 84Be and 126C out of lighter nuclei such as 42He. As you’ll see in the next section, this is how many of the heavier nuclei were created in the universe. The energetics of these transformations is similar to the energetics of the fusion of hydrogen with hydrogen to make helium: The collection of nuclei must be hot in order to fuse, and the fusion process yields additional thermal energy plus radiation: ThermEin + NuclE ¡ ThermEout + RadE But there is an important difference in the energetics of these different fusion processes. As an example, let’s compare the fusion process 1H + 2H with 4 He + 4He. In the 4He + 4He process, the electric repulsion between the nuclei is stronger than it is in the 1H + 2H process, because each He nucleus contains two protons whereas each H nucleus contains only one proton. So a higher temperature (faster nuclei) is needed for the He + He process than for the H + H process, requiring a larger thermal energy input. As you can see from this example, fusing heavier nuclei requires higher temperatures and thus larger thermal energy inputs. It turns out that, as heavier and heavier nuclei fuse, they eventually come to a point where the thermal energy input required to sustain the reaction becomes larger than the thermal energy output, so the reaction can no longer be self-sustaining. This limit happens to be reached for mass numbers in the range 56–62 (iron through nickel). Nuclei lighter than this can be fused together in self-sustaining reactions, but the favorable energy balance becomes unfavorable for heavier nuclei. The nuclear energy curve, Figure 4, shows these points graphically. It graphs nuclear energy (more precisely, the nuclear energy per nuclear particle) versus the mass number (the number of nuclear particles) for all of the isotopes. The curve shows two important features: First, the entire curve lies below the straight line representing the energy of the separated nuclear particles. This must be so, because it takes work to separate any nucleus into its component protons and neutrons (Section 1). Second, the curve decreases until mass numbers 56–62, where it roughly levels off, after which it increases. The decreasing portion (mass numbers 1 to 56) tells us that for nuclei lighter than iron, fusion converts nuclear energy to other forms such as thermal energy and thus can be self-sustaining in energy. But the increasing portion (above 62) tells us that for heavier nuclei, fusion results in an increase in nuclear energy and thus a decrease in other forms such as thermal energy. Such a reaction can be maintained only if there is an outside source to provide the required thermal energy. The turnaround point occurs because of the large amount of thermal energy required to fuse together two nuclei when either of them is very large, as described above.

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Fusion and Fission Figure 4

The nuclear energy curve. The solid curve shows the energy per nuclear particle for nuclei of various mass numbers. Nuclei having mass numbers in the range 56–62 have the least energy per particle, so they are the most stable nuclei. Fusion can be self-sustaining for mass numbers below this range, and fission can be self-sustaining for mass numbers above this range.

Nuclear energy per nuclear particle

Nuclear energy of an isolated nuclear particle

56 – 62

1

50

100 150 Mass number

200

250

Although nuclear energy cannot be released by means of the fusion of heavy nuclei, the shape of the nuclear energy curve suggests another possibility: If, instead of fusing heavy nuclei, we began with a sufficiently heavy nucleus and fissioned (split) it, there would be less nuclear energy after the fission process than before. In other words, nuclear energy would be released. Such a process could be self-sustaining in energy. To emphasize this important point: Nuclear energy can be released not only by the fusion of very light nuclei but also by the fission of very heavy nuclei.

3 THE ORIGIN OF THE ELEMENTS: WE’RE MADE OF STAR STUFF The universe began in a big bang some 14 billion years ago, an event that created space and time themselves and that created the different forms of energy and matter. But the big bang created only three elements, mostly hydrogen and helium, plus a trace of lithium. Even today, hydrogen and helium created in the big bang form more than 99% of the ordinary matter in the universe, with all the other elements forming less than 1%. Despite their scarcity, these elements heavier than helium are crucial for life and modern technology. Where did they all come from? The answer is that these elements are made in stars, and are spread throughout the universe by the explosions of very massive stars. As you’ve seen, every star, including our sun, gets most of its energy by converting hydrogen to helium throughout most of its history. As they run out of hydrogen fuel at their centers, stars partially collapse. The energy of this collapse heats them further, and this ignites new higher-temperature, self-sustaining fusion processes such as 4 2He

+ 42He ¡ 84Be

4 2He

+ 84Be ¡

12 6C

These reactions can create all the nuclei from helium up to mass number 56, which happens to be iron, but they cannot go beyond that point because the nuclear energy

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Fusion and Fission

curve tells us that you can’t extract nuclear energy from iron.2 It’s like trying to extract money from your Uncle Scrooge. Any attempt to fuse other elements with iron could not be self-sustaining and would immediately fizzle out. Eventually, for most stars, all possible self-sustaining fusion material is used up, fusion ceases, gravity reasserts itself, and the star collapses all the way down to become a white dwarf. Any new elements, such as beryllium, carbon, and oxygen, created by such a star remain bound up in the white dwarf. So how did the elements heavier than helium get spread throughout the universe, and how were the elements heavier than iron created in the first place? Those stars that happen to be much more massive than our sun do not settle down to become slowly aging white dwarfs. Instead, they build up a large core of solid iron at their center and, when the growing core becomes too heavy to stand up against the pull of gravity, suddenly collapse, in just a single second, into a tiny neutron star or black hole. Such a supernova is one of the universe’s most violent events. Some 80% to 90% of the entire star is thrown out into space, while the remainder collapses. The ejected material includes not only all the elements up to iron but also elements heavier than iron that are created by the energy of the explosion. Scientists don’t yet understand the details of the process that creates these heavier-than-iron elements, but they appear to involve the “shock wave” (similar to the powerful audible “boom” created by a supersonic jet plane) from the collapse of the core. It’s thought that as this shock wave travels through the ejected material, it creates enormous numbers of neutrons in the ejected material. These neutrons combine with larger nuclei so that many of the ejected nuclei become larger and larger through the “capture” of more and more neutrons. These large nuclei then decay radioactively to convert themselves into normal nuclei of heavier-than-iron elements such as iodine, gold, and uranium (see Concept Check 6 below). The ejected material eventually finds its way into the wider universe where it can become part of newly forming stars and solar systems and, perhaps, part of you. Supernovae are fairly rare events. Only five have been visible to the naked eye during the past thousand years. One of these went off in a neighboring galaxy in 1987. Without these occasional supernovae, only the three elements that came directly from the big bang could be spread throughout the universe. All planets would be formed from that material and you and I wouldn’t be here to share this story. Because our sun formed several billion years after our galaxy first formed, our solar system incorporated heavier elements from supernovae that exploded before the sun was born. You and I can thank our stars for the rare, ancient, and distant supernovae that sent their stardust—namely elements heavier than helium—to places such as Earth. CONCEPT CHECK 6 During a supernova, if an iron nucleus captured three neutrons and then beta-decayed twice, it would be transformed into (a) chromium; (b) manganese; (c) cobalt; (d) nickel; (e) zinc. (Hint: Use the periodic table on the inside back cover.) This is the type of process that created the elements heavier than iron.

2

456

More precisely, 62Ni is slightly lower on the nuclear energy curve than 56Fe (iron), so we’d expect it to be formed by fusion in stars. However, another process, called “photodisintegration,” prevents the formation of 62Ni in stars, leaving 56Fe as the heaviest nucleus that’s created in large amounts.

Fusion and Fission

4 THE DISCOVERY OF FISSION: PASSAGE TO A NEW AGE3

It’s been said that those who cannot learn from history are condemned to repeat it. The saga of the discovery and first use of nuclear fission is a powerful lesson in science and society, the kind of story that you and I must assimilate if we want to use science and technology without destroying ourselves. It’s a heroic but tragic story of a job that needed to be done in the face of a world-threatening enemy. Once these events were set in motion in the early days of World War II, the story’s conclusion at Hiroshima and Nagasaki may have become, like all high tragedy, inevitable. Scientists discovered the first known nuclear reaction, radioactive decay, in 1896. During the next several decades, they studied the new phenomenon intensely. Using a simple technique now common in high-energy physics, scientists bombarded nuclei by throwing other tiny things at them and observing what happened. In 1933, Irène Joliot-Curie (Figure 5, daughter of Marie and Pierre) and her husband, Frédéric Joliot, bombarded a thin aluminum foil with alpha particles. This created a previously unknown isotope of phosphorus. Although natural phosphorus is stable, the new isotope was radioactive. It was the first creation of a radioactive isotope and, in the subsequent radioactive decay, the first artificial release of nuclear energy. Joliot foresaw the potential consequences: “We are entitled to think that scientists, building up or shattering elements at will, will be able to bring about transmutations of an explosive type.... If such transmutations do succeed in spreading in matter, the enormous liberation of useful energy can be imagined.” At about the same time, scientists bombarded beryllium nuclei with alpha particles and detected a previously unknown particle that was ejected from the beryllium during the collision. The new particle was electrically neutral. They had discovered the neutron. The subtle new particle played a key role in the application of nuclear energy. Being uncharged, neutrons can sneak into a nucleus without Figure 5

Acme/Corbis

Irène Joliot-Curie working with her mother, Marie Curie. Irène and her husband Frédéric Joliot, working at the Radium Institute in Paris around 1935, created previously unknown isotopes by bombarding the nuclei of the elements with alpha particles. The Radium Institute was founded by Marie Curie.

3

I am indebted to Richard Rhodes’s definitive and beautiful book The Making of the Atomic Bomb (New York: Simon & Schuster, 1986) for most of the historical details and quotations in Sections 4, 5, and 6.

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having to overcome the electrical repulsion that protons feel when they approach the positively charged nucleus. And unlike the electron, which does not feel the strong force, the neutron interacts strongly once it gets inside. Hungarian physicist Leo Szilard (Figure 6) was a visionary and a lifelong admirer of another visionary, the author H. G. Wells. Wells’s 1914 novel The World Set Free predicted nuclear energy, nuclear bombs, nuclear war, and world government. Szilard was extremely inventive and quick to grasp the possibilities presented by the neutron: Perhaps some energetically favorable nuclear reaction in some material would emit neutrons; perhaps these neutrons could then bombard other nuclei in the same material and create a whole series of similar reactions in a large mass of material. In this way, neutrons might be the key to releasing useful amounts of nuclear energy. But Szilard also realized that such a vision, if realized, would be a twoedged sword, both hopeful and fearful.4 In 1934, Enrico Fermi (Figure 7) tried bombarding nuclei using the newly discovered particle, the neutron, instead of using alpha particles as the Joliot-Curies had

Ernest Orlando Lawrence Berkeley National Laboratory/American Institute of Physics/Emilio Segre Visual Archives

Lotte Meitner-Graf/Leo Szilard Biography Figure 6

Leo Szilard. This extremely inventive physicist was the first to understand that the neutron could be the key to unlocking nuclear energy by means of a chain reaction. He was an activist both in promoting U.S. development of nuclear weapons during World War II and in promoting world peace and banning nuclear weapons after the war.

Figure 7

Enrico Fermi, in the middle, is talking physics with I. I. Rabi, as Ernest Lawrence, inventor of the “cyclotron” looks on. In 1938, he received the Nobel prize for discovering many new radioactive isotopes. He then immigrated from fascist Italy to the United States where, concerned that the Axis powers would beat the Allied powers to the development of nuclear weapons, he played a key role in the Manhattan Project. Element 100 is named in his honor. 4

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For a comprehensive biography of the life and times of this highly creative individual, read Genius in the Shadows: A Biography of Leo Szilard, the Man Behind the Bomb, by William Lanouette with Bela Silard (Chicago: University of Chicago Press, 1994).

5

For an excellent biography of her life and times, see Lise Meitner: A Life in Physics, by Ruth Lewin Sime (Berkeley, CA: University of California Press, 1996).

Figure 8

German chemist Ida Noddack was the first to predict the possibility of nuclear fission caused by neutrons striking heavy nuclei. Although her words were ignored in 1934, fission was discovered in 1938, suggesting the possibility of new military weapons.

Bettmann/CORBIS

been doing. He worked his way through the elements, creating 40 new radioactive isotopes in the process. One element that Fermi bombarded was uranium, element number 92 and the heaviest natural element. Fermi assumed that some uranium nuclei would absorb one neutron, resulting in unstable nuclei that would then decay radioactively and thus transmute into one or more other elements lying near uranium in the periodic table. But some of the nonuranium nuclei resulting from this experiment seemed not to fit this description, and Fermi was unable to understand why. German chemist Ida Noddack (Figure 8) published an interpretation: “One could assume ... that when neutrons are used to produce nuclear disintegrations, some distinctly new nuclear reactions take place which have not been observed previously.... [Perhaps] when heavy nuclei are bombarded by neutrons ... the nucleus breaks up into several large fragments.” In 1934, her prophetic words were universally ignored. In 1938, Irène Joliot-Curie reported that neutron bombardment of uranium had produced a mysterious element that she could chemically separate from the uranium target by using lanthanum (atomic number 57) as a “carrier” to pick up the new element and carry it away. But the mysterious element was chemically inseparable from lanthanum. Surely it could not actually be lanthanum. How could the bombardment of uranium, element 92, create an element that was 35 places away from uranium in the periodic table? Otto Hahn, who led a uranium research group in Berlin, was skeptical of such unusual results and accordingly directed his research toward what he believed were needed corrections in Joliot-Curie’s work. 1938 was a fateful year. Austria was annexed by Hitler’s Germany, the Munich Agreement allowed Hitler to occupy part of Czechoslovakia, and anti-Jewish mobs in Germany torched synagogues and beat Jewish families in the streets. Lise Meitner (Figure 9), a physicist and an Austrian Jew, had been a colleague of Hahn’s since 1907. She had been protected from German anti-Semitism by her Austrian passport, but the annexation of Austria made her a German citizen. In July, with Hahn’s help, daringly traveling on her now invalid Austrian passport, she fled from Germany to Stockholm, Sweden.5 As the clouds of war gathered across Europe, Hahn and his coworkers in a laboratory in a peaceful suburb of Berlin bombarded uranium with neutrons, trying to find the error in Irène Joliot-Curie’s work. The mystery only increased. Not only lanthanum but also a second element, barium (element 56), made a good carrier for some of the radioactive isotopes created by the bombardment. Once again, it proved impossible to separate chemically the mysterious isotope from its barium carrier. Hahn communicated the results to Meitner in Stockholm. Far from exposing any error in Joliot-Curie’s earlier work, Hahn’s results were similar to hers. Meitner enjoyed frequent 10-mile hikes “to keep me young and alert.” On Christmas Eve 1938, she and her nephew Otto Frisch took a long walk on crosscountry skis through the Swedish countryside. Frisch was a colleague, a physicist, and together they pondered Hahn’s data. Niels Bohr had suggested that a nucleus could be viewed as a liquid drop. With this picture in their minds, they debated whether a neutron added to a uranium nucleus might cause the nucleus to oscillate and elongate. Electric forces would then push the two ends away from each other, and two smaller nuclei would appear where the one had been before (Figure 10). It was like a drop of water that elongates and splits in two. One of the smaller nuclei

Ullsteinbild/The Granger Collection

Fusion and Fission

Figure 9

Lise Meitner (1878–1968). She did nuclear research on uranium in Berlin until 1938, when Germany’s anti-Semitism forced her to flee to Stockholm, Sweden. There, she did theoretical calculations showing that her previous group in Berlin had, in fact, discovered an entirely new nuclear process. She named it nuclear fission. Element 109 is named in her honor.

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Fusion and Fission Figure 10

Neutron

The fission of a U nucleus after being struck by a neutron.

Neutron

235U

Fission fragment

236U (unstable)

Neutrons Fission fragment

(a)

235U

Fission fragments, including the neutrons created during fission

Figure 11

The uranium nucleus is more massive than the pieces into which it splits (see the nuclear energy curve). According to Einstein, the mass difference multiplied by the square of lightspeed should equal the energy released during fission.

(b)

(c)

(d)

might be barium or lanthanum. Taking a cue from microbiology, they named the hypothetical new process nuclear fission. As the nuclear energy curve (Figure 4) shows, the final nuclear energy in this process is less than the initial nuclear energy, so the process releases nuclear energy. This nuclear energy transforms into the microscopic kinetic energy seen in Figure 10d plus the energy of the radiation created by this process. Using the liquid drop model, Meitner calculated that the nuclear energy consumed when electrical forces within the nucleus do work to push apart the two fission fragments should be about 3 * 10 - 11 joules. She then recalculated the energy in an entirely different way, by applying Einstein’s E = mc2 to the experimentally known mass difference between uranium and the fragments (Figure 11). That mass difference was known to be about one-fifth of a proton’s mass. Multiplying this mass by c2, she got about 3 * 10 - 11 joules. It checked. Meitner’s calculations were solid evidence of fission. The nuclear age had begun. When the Joliot-Curies bombarded 27 13Al with alpha particles, each aluminum nucleus absorbed an alpha particle and emitted one neutron. 30 30 29 29 The isotope created by this process was (a) 23 11Na; (b) 13Al; (c) 15P; (d) 15P; (e) 16S. CONCEPT CHECK 7

5 THE CHAIN REACTION: UNLOCKING NUCLEAR FORCES

Some recent work by Fermi and Szilard leads me to expect that the element uranium may be turned into a new and important source of energy Á . It may become possible to set up a nuclear chain reaction in a large mass of uranium Á . This new phenomenon would also lead to the construction of bombs, and it is conceivable, though much less certain, that extremely powerful bombs of a new type may thus be constructed. Einstein, in his Letter to President Roosevelt, August 1939

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By 1939, leading scientists such as Einstein, Fermi, and Szilard had fled to the United States from Hitler’s Europe. When Szilard heard that uranium could absorb a neutron and then break into two parts, he foresaw a way to realize H. G. Wells’s dream of nuclear energy. Because neutrons, being uncharged, are an especially good nuclear “glue,” heavier elements contain many more neutrons than protons. The lighter fragments formed when uranium splits should therefore have many more neutrons than is normal for their atomic number. Consequently, individual neutrons should split off during the reaction, which could then fission other uranium nuclei. As this chain reaction proceeded from one uranium nucleus to the next, a large mass of uranium might be fissioned (Figure 12). The number of neutrons would multiply quickly as the chain reaction spread, causing the nuclei in several kilograms of uranium to fission in a few millionths of a second. Szilard thought that if neutrons were in fact emitted during fission, this fact should be kept secret from the Germans. Within a week of the announcement of fission, Fermi and others had independently hit on the idea of a chain reaction using neutrons and were making estimates

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of the energy that might be released. Once, standing at his Columbia University office window overlooking the bustling streets of New York City, Fermi cupped his hands as if he were holding an orange. “A little bomb like that,” he mused, “and it would all disappear.” Szilard devised a simple experiment to detect directly the neutrons that he suspected were released when a neutron fissioned a uranium nucleus. From the results, he estimated the average number of neutrons released per fission. A number larger than 1 could be enough to allow a chain reaction to build up quickly and fission a large mass of uranium. The number turned out to be about 2. Szilard immediately telephoned a fellow Hungarian physicist now living in the United States, Edward Teller. Szilard said only one thing: “I have found the neutrons.” That night there was little doubt in Szilard’s mind that the world was headed for grief. Hitler ordered the invasion of Poland on September 1, 1939, starting World War II. German scientists were aware of the weapons potential of nuclear fission. Accordingly, the German government banned the sale of uranium and in 1939 started a secret nuclear weapons program. It was the beginning of the international nuclear arms race. Physicists such as Szilard and Teller understood the possibilities. Fission bombs could be winning weapons for Hitler if he were allowed to build them sooner than the United States. They discussed their fears with Einstein, who agreed to lend his prestige to an effort by scientists to alert the U.S. government to the problem. Together they drafted a letter from Einstein to President Franklin D. Roosevelt that they delivered in October 1939. Einstein suggested that the U.S. government stay informed of further developments and financially support fission research. The final paragraph noted, “Germany has actually stopped the sale of uranium from the Czechoslovakian mines which she has taken over,” and “in Berlin some of the American work on uranium is now being repeated.” Einstein’s letter had little effect. There was a meeting and a committee report. Nothing more. America did not enter the war until December 1941, and in 1939 only Szilard, Einstein, and other knowledgeable physicists took nuclear dangers seriously. In 1940, Germany invaded and occupied most of Europe and bombed Britain in preparation for an invasion. Both sides began bombing cities, and massive civilian casualties became a reality of modern warfare. Although the U.S. government declined an active role, U.S. uranium research proceeded between 1939 and 1941. It gradually became clear that there was an 238 important difference between the two uranium isotopes, 235 92U and 92U. When a neu235 238 tron strikes uranium, only U has much chance of fissioning; U just absorbs the neutron to become a new radioactive isotope, 239U. This means that a nuclear bomb requires nearly pure 235U to sustain the rapid chain reaction needed to fission a large mass of uranium. If much 238U is present, it will absorb most of the neutrons, and the bomb will fizzle. But natural uranium is less than 1% 235U. To make a bomb, this 1% must be separated from the 99% that is 238U (Figure 13). To many scientists, this appeared essentially impossible. The problem was that two isotopes of the same element behave identically in every chemical reaction, so chemistry cannot separate them. The difficulties of extracting enough 235U to build a bomb seemed so great that Niels Bohr insisted that “it can never be done unless you turn the United States into one huge factory.” Bohr believed that it would therefore not be done. His words proved prophetic, although not in the way he imagined.

Key: Uranium nucleus Neutron

Figure 12

A chain reaction. At the lower right, a single neutron strikes a uranium nucleus. When the uranium nucleus fissions, it emits two neutrons that then fission two other uranium nuclei, and so forth. In this way, the nuclei in several kilograms of uranium can be quickly fissioned.

235U

Figure 13

In natural uranium, only 1 atom in 140 is 235U. The others are 238U.

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Fusion and Fission The fateful question of the human species seems to me to be whether the cultural processes developed in it will succeed in mastering the derangements of communal life caused by Á aggression and selfdestruction. In this connection, perhaps, the phase through which we are at this moment passing deserves special interest. Men have brought their powers of subduing the forces of nature to such a pitch that by using them they could now very easily exterminate one another to the last man. They know this; hence arises a great part of their current unrest, their dejection, their mood of apprehension. Sigmund Freud, Written in 1930, Many Years before the Discovery of Fission

In 1940, scientists created the first nonnatural chemical element, that is, one not found naturally on Earth. They found evidence that when 238 92U is bombarded with neutrons, it absorbs a neutron to become 239 , which then quickly emits a beta parU 92 ticle to become element number 93. Its discoverers named the first element beyond uranium “neptunium” for Neptune, the planet lying just beyond Uranus, the planet for which uranium was named. Like all elements heavier than lead, neptunium is radioactive. Because it is a beta emitter, it decays to a higher atomic number, creating yet another nonnatural element, number 94. Early in 1941, scientists detected the new element, which turned out to have an important property: Like 235U, element 94 fissions readily when struck by a neutron. Furthermore, the new element can be chemically separated from the uranium in which it was created, thereby avoiding the difficulties of separating two isotopes of the same element. It was not until 1942 that its discoverers proposed a name for this new element that fissions like 235U but that can be chemically separated from uranium. They called it “plutonium” for the outermost planet (now no longer deemed to be a planet), which had in turn been named for Pluto, the Greek god of the underworld (Figure 14). In October 1941, scientists convinced President Roosevelt that fission weapons could work. Japan attacked the United States at Pearl Harbor on December 7, 1941. In 1942, a U.S. nuclear weapons program, known as the Manhattan Project, began in earnest. When a 235U nucleus is struck by a neutron, it splits into two large fragments and emits two to four neutrons. Although the fragments are different in different instances, one typical fragment is 142 56Ba . From the periodic table, you can deduce that the other fragment in this particular fission process is (a) argon; (b) krypton; (c) cesium; (d) rubidium; (e) strontium. CONCEPT CHECK 8

CONCEPT CHECK 9 The masses of one atom of each of the two uranium isotopes differ by about (a) 4%; (b) 3%; (c) 0.5%; (d) a little less than 1%; (e) a little more than 1%.

Beta Beta 92 protons 146 neutrons

92 protons 147 neutrons

93 protons 146 neutrons

94 protons 145 neutrons

Neutron 238U

(a)

239U (in an excited or high-energy state)

(b)

239Pu

239Np (in an excited state)

(c)

(d)

Figure 14

The creation of plutonium, element 94. After 238U absorbs a neutron, it beta-decays twice to become 239Pu.

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6 THE MANHATTAN PROJECT AND FISSION WEAPONS Fundamentally, and in the long run, the problem which is posed by the release of atomic energy is a problem of the ability of the human race to govern itself without war. From a Report of the U.S. Secretary of State, January 1953

Chicago Historical Society

Constructed on a monumental scale, the U.S. project to build a fission bomb or “A-bomb”6 arose from U.S. fears about a German fission bomb. In December 1942, a research group under Fermi at the University of Chicago created the first self-sustaining chain reaction (Figure 15). To achieve this, Fermi’s group constructed the world’s first nuclear reactor, a device to transform, in a controlled way, nuclear energy into other energy forms. The world’s first reactor illustrates several facts about a chain reaction of a different kind: proliferation of nuclear weapons to countries around the world. Just as Fermi’s reactor was a stepping-stone to a U.S. fission bomb, countries seeking to build their own nuclear weapons are likely to begin by building a reactor. Although the primary purpose of nuclear reactors today is to provide peaceful electric power, reactors can also provide research and materials relevant to nuclear weapons. An apparently peaceful nuclear power program can be used as cover for a secret weapons program, as has been demonstrated by India, Israel, South Africa, Iraq, Pakistan, North Korea, and, in the opinion of many, Iran. Another problem is that reactors can produce militarily useful plutonium by converting 238U to 239Pu, providing one possible path to a fission bomb. Since uranium

Figure 15

A painting of the opening ceremony, in 1942, of the world’s first nuclear reactor beneath the football field (now removed) at the University of Chicago. Photographs were not allowed because of wartime security. Note the “suicide squad” of three young physicists in the back; they were holding jugs of neutron-absorbing liquid to pour into the reactor in case something went wrong. 6

“Atomic bomb” or “A-bomb” is an inappropriate name, because the energy source is the nucleus rather than the entire atom. The term “nuclear weapon” is appropriate, but I’ll use “fission bomb” and “fusion bomb” to distinguish between these two.

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It was not very clear that the job of separating large amounts of uranium 235 was one that could be taken seriously. Enrico Fermi

This war, in contradistinction to all previous wars, is a war in which pure and applied science plays a conspicuous part. Sir William Ramsay in 1915, Commenting on World War I

is common in Earth’s crust, the 238U is easy to obtain. A reactor can create enough plutonium for a fission bomb during just a few weeks of operation. Near Hanford, Washington, the Manhattan Project engineers built three large natural-uranium reactors for making plutonium. 235 U is the key to the nuclear era. Among all the naturally occurring isotopes, it is essentially the only one that will chain-react.7 The other chain-reacting isotope used in nuclear weapons is 239Pu, and chain reactions in 235U are essential to produce it. There is no obvious reason why there should be exactly one naturally occurring chain-reacting nucleus rather than some other number, such as zero. In a sense, this dangerous yet useful isotope just barely exists on Earth: Uranium is the last natural element in the periodic table, and less than 1% of it is 235U. It’s ironic that nature provided us with this powerful isotope, as if it were some kind of test for the human race. Without it, we probably couldn’t build nuclear weapons. Both uranium and plutonium offer a path to fission bombs. The Manhattan Project pursued both paths. Along the uranium path, the key problem is to isolate the 1% that is 235U from the 99% that is 238U. Because these isotopes are identical chemically, any such isotope separation method must be based only on the tiny mass difference between the two. This is no simple matter. The isotope separation technique that is most important today is centrifuge separation. Any liquid or gas can be separated into heavier and lighter portions in a high-speed centrifuge—a cylindrical container that spins rapidly around a vertical axis through its center. Lighter material drifts toward the inside of the spinning container while heavier material drifts toward the outside, for the same reason that your body is “pulled” toward the outside of a curve when you ride in a rapidly moving vehicle rounding a turn. The easiest way to understand this is based on Einstein’s equivalence principle: The spinning container forms an accelerating reference frame, with the acceleration directed inward toward the center of the circle. But Einstein says that the effects of acceleration can’t be distinguished from those of gravity. So an “artificial gravitational force” pulls heavier things “downward” toward the outside of the container while lighter things float “upward,” toward the inside. In the separation process, natural uranium is put into a gaseous form that is spun in a centrifuge until the material on the inside of the container is slightly enriched in the lighter isotope, 235U. This enriched portion is extracted and fed into a second centrifuge, which spins until the material on the inside of the container is further enriched, then extracted, spun again in a third centrifuge, and so forth. After many such centrifuge stages, requiring tens of thousands of extremely high-quality, highspeed centrifuges, highly enriched uranium—bomb-grade uranium—is obtained. The material is suitable for nuclear weapons once 90% enrichment is achieved (90% 235U and 10% 238U). It’s not easy to enrich uranium. Acquiring the tens of kilograms of highly enriched uranium needed is the key obstacle to building a uranium bomb. In October 1942, the U.S. Army selected physicist J. Robert Oppenheimer (Figure 16) to direct the laboratory that would design and build the world’s first nuclear weapons. It proved to be an inspired choice. Oppenheimer chose a high, isolated desert mesa in New Mexico as the site of the new laboratory. They named the place after the boys’ school that had been on the mesa: Los Alamos. 7 233U

also chain-reacts but it occurs only in extremely small amounts in natural uranium and has never, so far as is publicly known, been used for bomb material.

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Ken Bainbridge/Bainbridge Collection/American Institute of Physics/Emilio Segre Visual Archives

Ernest Orlando Lawrence Berkeley National Laboratory

Figure 16

(a)

J. Robert Oppenheimer was one of the most brilliant U.S. physicists, politically left-wing and controversial, a wide-ranging intellectual and sensitive man given to literary pursuits, and scientific director of the laboratory that designed and built the world’s first nuclear weapons. (a) In the 1930s. (b) During the Manhattan Project.

(b)

A certain minimum amount of fissionable material is needed to sustain a chain reaction. The reason is that, for very small amounts, too many of the neutrons created during fission will simply pass right out through the surface without hitting anything, so a chain reaction cannot be sustained (Figure 17). One of the first things that the Los Alamos scientists did was calculate this critical mass needed to sustain a chain reaction. For 235U, the critical mass is a cantaloupe-sized 25 kilograms. For 239Pu, it is 8 kilograms—the size of a (large) orange, as Fermi had guessed. The design chosen for the world’s first uranium bomb was so straightforward that there was no need to test it before use [Figure 18(a)]. High explosive simply slammed one subcritical hunk of 235U into another subcritical hunk to equal or exceed a critical mass; simultaneously, neutrons showered this critical mass to start the chain reaction. There is a proliferation lesson here: A country need not test a uranium bomb in order to have one. If a group can make, buy, or steal enough highly enriched uranium, building a crude but dependable bomb isn’t terribly difficult. As I mentioned earlier, the Manhattan Project chose both the uranium and the plutonium paths to a bomb. For a plutonium bomb, the simple design of Figure 18(a) won’t work because plutonium is touchy: It begins to spontaneously chain-react very quickly once a critical mass is assembled, so quickly that spontaneous fission begins as soon as the two subcritical hunks approach each other, “spoiling” the explosion. Instead, a more technically difficult spherical design is needed in order to quickly assemble the critical mass before it has time to prematurely explode [Figure 18(b)]. At the sphere’s center is a small subcritical sphere of plutonium. Although subcritical, it contains enough plutonium to become critical if squeezed into a much smaller volume, because at the smaller volume the nuclei are so close together that neutrons created by a fissioning nucleus are highly likely to fission other nuclei rather than escape out the sides. The plutonium sphere is surrounded by heavy metal that briefly confines and thus enhances the nuclear explosion, and this metal is surrounded by chemical

(a)

(b)

Figure 17

The concept of critical mass. (a) If the lump of fissionable material is too small, most neutrons emitted during fission will escape through the surface without striking any nuclei, and a chain reaction cannot be sustained. (b) But if the lump of material is large enough, most neutrons will strike other nuclei before they escape through the surface, triggering a chain reaction.

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Fusion and Fission Shaped charge, high explosive

Heavy metal

Detonators

Explosive Subcritical propellant mass

Subcritical mass

(a) (b)

239Pu

Figure 18

Schematic sketches of fission bomb designs. (a) In the gun-type bomb, dropped on Hiroshima, a conventional explosive propellant rams one subcritical mass of 235U along a tube and into another subcritical mass, forming a critical mass that then chain-reacts. (b) In the implosion bomb, dropped on Nagasaki, conventional explosives press inward on a mass of 239Pu squeezing it enough to cause a subcritical mass to become critical.

I just could not understand why our surroundings had changed so greatly in one instant Á . I thought it might have been Á the collapse of the Earth which it was said would take place at the end of the world. Yoko Ota, Japanese Writer and Hiroshima Survivor

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explosive. The chemical explosive detonates from the outside, and a wave of exploding material moves inward, or “implodes,” squeezing the plutonium sphere into a small enough volume to become critical. At this instant, a neutron source releases neutrons at the center. Although this design is technologically demanding, plutonium is much easier to obtain than the highly enriched uranium needed for a uranium bomb. Plutonium is produced routinely in nuclear reactors, and reactors do not require highly enriched uranium. Highly enriched uranium began arriving at Los Alamos in late 1944, and by the following summer there was enough for one uranium bomb. By May 1945, enough plutonium had arrived to allow final critical-mass experiments for the plutonium bomb. In May 1945, Germany surrendered. The United States learned then that Germany had tried throughout the war to develop nuclear weapons, but that it never got close to its goal. Even though the feared German bomb had motivated the U.S. bomb, the United States did not halt the Manhattan Project when Germany surrendered. There are some lessons here: Once scientists find that something can be done, there is often a drive, a technological imperative, to do it. And once a project is started, it often develops a self-justifying technological momentum. On the other hand, there were good reasons to continue nuclear bomb development: Japan remained a dedicated enemy, and nuclear weapons might save lives while shortening the war. Oppenheimer helped choose the test site for the plutonium bomb, in a barren landscape south of Los Alamos. He code-named the site Trinity, referring to a line by poet John Donne: “Batter my heart, three person’d God.” Just before dawn on July 16, 1945, a burst of brilliant purple never seen before lit up the desert, and a small part of Earth was brought to temperatures that were unprecedented within the solar system, save at the center of the sun. The energy released was the same as would be released by 18,000 tons, or 18 “kilotons,” of a chemical explosive such as

Fusion and Fission

TNT. A kiloton is a unit of energy,8 the energy that would be released by 1000 tons of exploding TNT. For comparison, typical chemical bombs carry perhaps onequarter ton of explosives. The untested uranium bomb was loaded onto a B-29 bomber on August 5. Most Japanese cities had been firebombed to ashes by this time. But Hiroshima, an industrial city with an army depot, an ocean port, and 400,000 people, was still untouched. The B-29 arrived over Hiroshima by 9 A.M. on August 6. As the world’s first combat nuclear weapon fell toward its target, the airplane quickly turned and dove away to escape the blast. By the time its crew looked back, the city was hidden by an awful cloud. The bomb released 12 kilotons of nuclear energy; 140,000 lay dead with an equal number wounded; and the city, 5 kilometers (3 miles) across, lay in ruins (Figure 19). By 1950, the death toll had reached 200,000—50% of the city’s population. The war continued. A debate raged among Japanese leaders about whether to surrender. The Soviet Union, no longer fighting Germany, invaded Manchuria in northeastern China and was poised to go to war against Japan. On August 9, just three days after the bombing of Hiroshima, the United States dropped its plutonium bomb on Nagasaki, a city somewhat smaller than Hiroshima. The bomb released 22 kilotons of nuclear energy and killed 70,000 outright and 140,000 all together by 1950—again, a death rate of 50%. On August 14, 1945, Japan surrendered.

We regarded dropping the bomb as exceedingly important. We had just gone through a bitter experience at Okinawa Á . It was expected that resistance in Japan would be even more severe. We had had the 100,000 people killed in Tokyo in one night of [conventional] bombs, and it had had seemingly no effect whatsoever. So it seemed quite necessary, if we could, to shock them into action. We had to end the war; we had to save American lives. General George C. Marshall, Author of the “Marshall Plan” of U.S. Aid to Rebuild Postwar Europe

CONCEPT CHECK 10 How many World War II heavy bombers (5-ton bomb capacity) would be needed to carry enough high-explosive chemical bombs to equal the explosive power of the nuclear bomb dropped on Nagasaki? (a) Less than 1000. (b) Between 1000 and 2000. (c) Between 2000 and 4000. (d) Between 4000 and 6000. (e) More than 6000.

National Archives and Records Administration

Figure 19

8

Hiroshima, August 1945. The bomb released 12 kilotons of nuclear energy; 140,000 people lay dead, with an equal number wounded; and the entire city, 5 kilometers (3 miles) across, lay in ruins. By 1950, the death toll had reached 200,000, 50% of the population.

One kiloton = 4.2 trillion joules .

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7 FUSION WEAPONS: STAR FIRE ON EARTH In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose. J. Robert Oppenheimer, 1947

When you see something that is technically sweet, you go ahead and do it and you argue about what to do about it only after you have had your technical success. J. Robert Oppenheimer

How well we meant. Title of 1983 Speech by Physicist I. I. Rabi, at the Los Alamos Weapons Laboratory on the Fortieth Anniversary of its Founding

World War II led, almost immediately, to a “cold war” between the United States and the Soviet Union. Like the rest of the scientific world, Soviet physicists learned of fission in early 1939, and by 1940 they had concluded that a chain reaction could be established in uranium. More than 50 Soviet scientists worked on isotope separation and uranium and plutonium bomb designs during the war; the Hiroshima and Nagasaki bombing only spurred their efforts. The Soviet Union achieved a chain reaction in a reactor in 1946 and tested a fission bomb in 1949. In 1941, Edward Teller began calculations about a bomb based on the energy released when hydrogen fuses to form helium. His fusion group expanded after the war, and by 1949 it appeared that they might eventually succeed. But the United States had not yet decided to build a fusion weapon. The 1949 Soviet fission bomb test, coming as cold war tensions were building, alarmed U.S. President Harry Truman. A small circle of officials and scientists debated whether to proceed with an all-out U.S. effort to build a hydrogen bomb, or fusion bomb. Their fear was similar to earlier fears about Germany: The Soviet Union might build the winning weapon first. Believing that this would be intolerable, Truman decided in 1950 to develop a fusion bomb. In 1950, the U.S. fusion bomb project was, according to Oppenheimer, “a tortured thing that you could well argue did not make a great deal of technical sense.” But during 1951, mathematician Stanislaw Ulam came up with a clever new idea that solved many of the project’s problems. In a revealing comment on the allure of high technology, Oppenheimer stated, “By 1951 the program was technically so sweet that you could not argue about that.” In October 1952, the United States exploded the world’s first thermonuclear fusion device. As occurs at the center of the sun, hydrogen nuclei were fused to form helium. In this and all other fusion weapons, the hydrogen isotopes used were 2 H and the rare and radioactive isotope 3H because these isotopes fuse at a lower, more attainable, temperature than do the 1H and 2H that are fused in the sun. You might guess then that this reaction would create 5He but 5He is such an unstable isotope that the reaction results instead in 4He plus a free neutron: 2

H + 3H ¡ 4He + n

Figure 20 sketches how it works. To bring the hydrogen fuel to the multimilliondegree temperatures needed to ignite fusion, an implosion-type fission bomb is used Figure 20

Heavy metal

High explosive

The design of a fusion bomb.

239Pu and 235U Hydrogen fuel (fission trigger) for fusion Natural uranium Natural uranium to protect fusion jacket (more fission) reaction fuel from trigger’s blast (more fission)

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as a “trigger.” High-temperature X-rays from the fission bomb quickly heat the hydrogen to fusion temperatures. Ulam’s “technically sweet” idea was that this trigger should be physically separated from the hydrogen fuel so that X-rays, traveling at lightspeed, would reach the hydrogen and heat it to fusion temperatures during the fraction of a second before the trigger’s blast could reach the hydrogen and blow it apart. During the 10 years prior to Ulam’s contribution in 1951, the fission trigger and the fusion fuel had been wrapped together in one big sphere that was likely to be destroyed by the fission blast before fusion had a chance to get going. Inexpensive natural uranium is used at several places in the design. Under the conditions that exist while the hydrogen is fusing, even natural uranium can be made to fission, yielding a larger blast that is also higher in radioactive fallout. A fission bomb cannot be built with a larger-than-critical mass already assembled in one piece, because this mass would quickly explode spontaneously. This makes it difficult to design very large fission weapons. However, there is no natural upper limit to a fusion weapon because the hydrogen fuel will not explode spontaneously. The yield of the world’s first fusion test explosion was 10,000 kilotons, or 10 megatons, equivalent to 10 million tons of TNT. This is a thousand times the Hiroshima bomb’s energy, or about twice the total explosive energy released by all combatants during all of World War II! The success of the Soviet fission bomb test and reports that the U.S. government was considering a fusion program spurred the Soviets to move ahead rapidly with their own fusion program. In November 1955, the Soviet Union also tested a thermonuclear fusion weapon. You see here, once more, the action–reaction cycle. This dangerous and expensive process is hard to control as long as nations feel threatened. The U.S.–Soviet nuclear arms race was, by any measure, extreme. By the mid1980s, each side possessed about 25,000 nuclear weapons, enough to destroy the other side as a functioning society hundreds of times over. Each side held its weapons out of fear of what the other side might do if it had a significant advantage. Each side designed its arsenal to deter the other side from attacking. Any significant increase in either stockpile always produced an overcompensating increase in the other. On the other hand, the policy of nuclear deterrence was successful in helping ensure that neither conventional nor nuclear war broke out between the United States and the Soviet Union during the entire cold war period from about 1947 to 1989. And it’s notable that not a single nuclear weapon has been detonated as a weapon of war during the six decades since the destruction of Hiroshima and Nagasaki. In 2008 the United States and Russia each still possessed over 5000 large, or “strategic,” nuclear weapons, most of them large enough to destroy the center of a large city.

Concern for man himself and his fate must always form the chief interest of all technical endeavors Á in order that the creations of our mind shall be a blessing and not a curse to mankind. Never forget this in the midst of your diagrams and equations. Einstein

M A K I N G EST I M AT ES Estimate the number of large highway trucks (capacity 30 tons) needed to haul 1 megaton of TNT and the length of a single line of trucks carrying such a load on the highway. What about 10 megatons?

1,000,000>30 = 33,000 trucks. A large highway truck is about 15 m long, so the length of 33,000 trucks is 500,000 m, or 500 km, with no spacing. If trucks are separated by one truck length, the line is 1000 km long. For 10 megatons the line is 10,000 km long, or more than twice across the United States.

SO LU T I O N TO M A K I N G EST I M AT ES

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8 NUCLEAR TERRORISM9 To possess the weapons that could counter those of the infidels is a religious duty. Osama Bin Laden, When Asked about Reports that He Wanted Nuclear Weapons

Weapons of mass destruction include nuclear, chemical, and biological weapons. Terrorists could employ any of the three. I’ll discuss only nuclear terrorism here and leave chemical and biological terrorism to your chemistry or biology class. In order for science to be used for human benefit and not for harm, topics such as this should be included in all general science courses. If your other general science courses don’t include such socially relevant topics, I hope you’ll encourage the instructors to do so. Could terrorists acquire and use nuclear devices? There are, unfortunately, four routes by which this might happen. In decreasing order of destructiveness but increasing order of plausibility, they are the following: 1. 2. 3. 4.

Seizing and detonating an intact nuclear weapon; Seizing or purchasing weapons-grade uranium or plutonium leading to building and detonating a crude nuclear weapon; Sabotaging nuclear power plants and other nuclear facilities, releasing radioactivity; Acquiring radioactive material leading to building and detonating a dirty bomb—a bomb powered with conventional explosive but that does its damage largely by the dispersal of radioactive material.

Seizing a bomb. There is no confirmed case of the theft of a nuclear weapon, but with over 20,000 nuclear weapons currently spread around nine nations it’s possible that a terrorist organization could buy or steal one of them. For example, although Pakistan supports the U.S. war against terrorism, it’s impossible to know how many secret terrorists exist inside the country’s military intelligence agencies, and what access they might have to Pakistan’s roughly 50 nuclear weapons. Without such “insider” help, a terrorist organization would find it extremely difficult under normal circumstances to seize a nuclear weapon. But terrorists could take advantage of anarchy or revolutionary unrest in a failing nuclear state to gain control over a nuclear weapon. For example, Soviet president Gorbachev reportedly lost control of his country’s nuclear arsenal when his opponents cut off his communication links during a coup attempt against him in 1991. Once they obtained a bomb, terrorists would be faced with the further obstacles of overcoming the devices built into most nuclear weapons to prevent unauthorized use, transporting the weapon to its target, and figuring out how to trigger the device. As you know from the preceding two sections, the bomb could flatten the center of a large city. Seizing bomb fuel. There are 1700 tonnes of weapons-grade uranium and 500 tonnes of weapons-grade plutonium at hundreds of sites around the world, most of it in the United States or Russia. This is enough for 60,000 bombs of each type. Perhaps as much as half of this weapons fuel is already in nuclear weapons where it’s unlikely to be bought or stolen by terrorists (see above), but the nonweaponized remainder is far harder to secure. There have been a number of cases during the past decade involving illicit trafficking in small amounts of this material. None has approached the 25 kg of highly enriched uranium or 8 kg of plutonium needed for a bomb, but a terrorist organization could currently be in

9

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I am indebted to The Four Faces of Nuclear Terrorism, by Charles D. Ferguson and William C. Potter (Monterey Institute on International Studies, 2004), for much of the analysis of this section.

Fusion and Fission

possession of this much material. Three plausible settings where terrorists might obtain nuclear fuel are the following: • Dozens of sites that are under inadequate security in Russia • Pakistan, where terrorists could exploit political instability and uncertain loyalties • Some 130 reactors employed for nuclear research that are fueled by highly enriched uranium, located in Russia and 20 other nations and often supplied by the United States. The United States and other nations are trying to make these sites more secure, for example, by phasing out the enriched-uranium research reactors. The pathways by which a terrorist group might obtain weapons fuel are similar to the pathways for obtaining an intact weapon: purchase or theft with government or insider assistance and exploitation of unrest. Because it’s located in so many places, and is guarded less securely than nuclear weapons, nuclear fuel would be easier for terrorists to obtain than an intact nuclear weapon. As you’ve learned earlier, the main barrier to building the simplest type of uranium bomb [Figure 18(a)] is obtaining the roughly 50 kg of highly enriched uranium needed for this design. It’s far more difficult to construct a plutonium bomb. Once they have the uranium, technically competent terrorists would be able to construct a simple uranium bomb. As at Hiroshima, this bomb could release as much as 20 kilotons of energy and devastate the heart of a medium-sized U.S. city. Nuclear power plant sabotage. Nuclear power plants cannot explode like a

nuclear bomb, because a highly explosive chain reaction cannot occur in their lowenriched or nonenriched uranium fuel. The Chernobyl plant in the former Soviet Union, where a low-grade nuclear explosion occurred, was a singular exception. But nuclear power plants contain lots of highly radioactive materials within the reactor itself and in their spent-fuel storage pools, and this could be released by a terrorist attack. It’s not known whether the direct impact of a large fuel-laden airplane could breach these facilities. A waterborne attack could block vital water intakes to the plant and cause a meltdown or at least a shutdown. A commando attack could drive truck bombs into reactors and spent-fuel pools or fire multiple rockets from tens of kilometers away. Nuclear power plants might also be vulnerable to “cyberterrorism”—attacks on information and control systems by insider sabotage or external computer hacking. Terrorists could drain a spent-fuel storage pool, causing the highly radioactive fuel to heat up, ignite, and release radiation. Safety and security measures that are in place at all U.S. reactors would tend to thwart such plans, whereas collusion with sympathetic power plant insiders would make such attacks more likely to succeed. A successful attack by any of these methods would cause a radiation release rivaling the Chernobyl accident. Detonating a dirty bomb. As the most likely but least damaging form of nuclear terrorism, a group or even a single individual could insert a harmful amount of radioactive material into a conventional explosive device that would disperse this material over a wide area. In fact, alleged al Qaeda operative Jose Padilla was arrested in 2002 for planning a dirty bomb attack on the United States, although his bomb would have dispersed only natural uranium, which has a long half-life and therefore a very low level of radioactivity and would have caused little damage. The most important “fallout” would have been the psychological effect on

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Fusion and Fission

© Sidney Harris, used with permission.

the public. There are millions of radioactive sources all over the world and, unlike Padilla’s uranium, many of them are sufficiently radioactive to constitute some danger. Al Qaeda and Russia’s Chechen rebels have shown an interest in such highly radioactive material. Radioactive material for a dirty bomb may be found or stolen, but the easiest route is to simply purchase it legally as radioactive isotopes employed in thousands of medical, academic, agricultural, and industrial settings. The most harmful materials also have the broadest commercial applications and are widely available. The high radiation zone from a dirty bomb attack is unlikely to extend beyond the area destroyed by the blast. Thus casualties would be comparable to those from a conventional explosive device such as a car bomb, and few or no people would be killed by the radiation. But the economic damage could be enormous because economic activity would be suspended throughout a large area of less lethal low-level radiation, because decontamination would be costly and could take years, and because the attack could cause widespread panic even though the radiation danger would be low.

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Fusion and Fission Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions FUSION AND THE NUCLEAR ENERGY CURVE 1. Give the reaction formula for at least one fusion reaction. 2. What isotope is created when 12C fuses with 4He? (Hint: Use the periodic table.) 3. What energy transformation occurs in radioactive decay? In nuclear fusion of hydrogen? Nuclear fission of uranium? 4. Of the four fundamental forces, which are important inside the nucleus? 5. Which has more nuclear energy, a separated proton and neutron or an 2H nucleus? How do you know? Which has greater mass? How do you know? 6. If you separate a nucleus into its individual protons and neutrons, does its nuclear energy increase or decrease, or does the answer depend on which nucleus you started with? 7. Suppose you separate a nucleus into two equally massive parts. Does the system’s nuclear energy increase or decrease, or does the answer depend on which nucleus you started with? 8. Sketch the nuclear energy curve. What does this curve tell us about the possibilities of getting useful energy from fusion or fission?

20. What would happen if a fission chain reaction were attempted in a piece of 235U whose mass was below the critical mass? Explain why this would happen.

FISSION AND FUSION WEAPONS 21. Can natural uranium fuel a fission weapon? Why? 22. What is enrichment? Describe one enrichment process. 23. Name the two chain-reacting materials that can be used in fission weapons. 24. Explain how an implosion fission bomb works. 25. How is a fusion bomb heated to fusion temperatures? 26. What is meant by a “1-kiloton” nuclear weapon? 1 megaton?

NUCLEAR TERRORISM 27. What is meant by a weapon of mass destruction? 28. Describe the four ways by which nuclear terrorism could occur. Which of these would be most destructive? Which of these would be most likely to occur? 29. Could terrorists build a nuclear weapon? What special material might they need? 30. What is a dirty bomb? Describe the amount of damage it is likely to do.

ORIGIN OF THE ELEMENTS

Conceptual Exercises

9. 10. 11. 12.

FUSION AND THE NUCLEAR ENERGY CURVE

List two elements created in the big bang. Where do stars get their energy? What is a supernova? How were the elements up to iron in the periodic table created? What about the elements beyond (heavier than) nickel? 13. Referring to the preceding question: Why do iron and nickel happen to play this special role in element creation? 14. Where did the chemical elements that form your body come from?

FISSION AND THE CHAIN REACTION 15. Why do neutrons work better than protons in causing fission? Why do neutrons work better than alpha particles? Why do neutrons work better than electrons? 16. Describe what happens during a chain reaction. 17. When 238 92U absorbs a neutron, what isotope does it become? What new element is then created by a single beta decay of this isotope? 18. Where does plutonium come from? 19. What is meant by “uranium enrichment”?

1. Write out the reaction formula for the fusion of 11H and 21H. 2. Write out the reaction formula for the fusion of 42He and 84Be. 3. How does a nucleus’s mass compare with the sum of the masses of its protons and neutrons? Does the answer depend on which nucleus you are considering? 4. Can matter be destroyed? If so, give an example. Can energy be destroyed? If so, give an example. 5. An alpha particle is removed from 168O. Is this an example of fusion or fission? Write down the nuclear reaction formula for this reaction. Which side of this reaction formula, the left or the right, represents more nuclear energy? 6. An alpha particle is fused with 168O. Write down the nuclear reaction formula for this reaction. Which side of this reaction formula, the left or the right, represents more nuclear energy? 7. Would fusion, or fission, or neither, release nuclear energy from carbon? From gold? From iron? 8. In which of the following processes is there a change in restmass due to the mass–energy equivalence principle? In which

From Chapter 15 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Fusion and Fission: Problem Set is the change in rest-mass actually measurable? (a) Warming a cup of coffee. (b) Explosion of a fusion bomb. (c) Lifting a book. (d) Matter–antimatter annihilation ? 9. In which of the following processes is there a change in restmass due to the mass–energy equivalence principle? In which is the change in rest-mass actually measurable? (a) Operation of a nuclear reactor. (b) Explosion of TNT. (c) Explosion of a fission bomb. (d) Throwing a baseball. 10. Which of the four fundamental forces holds the nucleus together? Which one of the four forces tends to push the nucleus apart, that is, to separate it into pieces? 11. One of the forces operating inside the nucleus is the electromagnetic force. Does this force tend to assist nuclear fusion, or oppose it?

29. The hydrogen bomb’s fusion energy comes from the fusion of 2 H with 3H. One of the reaction products is an alpha particle. Write out the complete nuclear reaction formula.

NUCLEAR TERRORISM 30. What kind of nuclear bomb would terrorists be likely to build, and what kind of special material would they need to build it? 31. Could terrorists make a nuclear power plant blow up like a nuclear bomb? Explain. 32. What is the most likely kind of nuclear terrorism, and how much damage is it likely to do?

Problems

ORIGIN OF THE ELEMENTS 12. The fusion of helium nuclei into heavier nuclei occurs only during the later stages of a star’s history, when the star has reached a higher temperature due to partial collapse. Why does helium fusion occur only at higher temperatures than those needed for hydrogen fusion? 13. In what sense have humans always been sustained by the energy from nuclear fusion? 14. The supernova seen in 1987 occurred in a galaxy 180,000 light-years away. When did it actually occur? 15. Before it exploded, the 1987 supernova fused many elements. In one reaction, 12C fused with 4He. What nucleus did this create? Did this reaction release nuclear energy? 16. Another reaction occurring before the 1987 supernova exploded was the fusion of two 12C nuclei. What nucleus did this create? Did this reaction release nuclear energy? 17. Could the atoms in your body have been created in the sun? Explain. 18. Could the atoms in your body have been created by the North Star? Explain.

FISSION AND THE CHAIN REACTION 19. A neutron strikes a 235U nucleus and creates lanthanum. What other element is created? 20. A neutron strikes a 239Pu nucleus and creates strontium. What other element is created? 21. List at least one similarity between combustion and fission. List at least one difference. 22. List similarities and differences between a nuclear chain reaction and igniting and burning a sheet of paper. 23. When a 235U nucleus is struck by a neutron, it splits into a pair of large fragments and emits two to four neutrons. A typ91 ical pair of fragments is 142 56Ba and 36Kr. Write a reaction equation showing the isotopes and other particles that go into and come out of this reaction. 24. Why does the chain reaction work in 235U but not in 238U? 25. Would you expect that a chain reaction would be able to proceed in natural uranium ore? Why or why not?

FISSION AND FUSION WEAPONS 26. Is plutonium radioactive? Defend your answer. 27. Can natural uranium metal spontaneously explode? Why? 28. Is a chain reaction possible in a substance that emits no neutrons when it fissions?

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FISSION AND THE CHAIN REACTION 1. When 235U fissions, it loses about 1% of its rest-mass. Suppose that 10 kg of 235U fissions. How much rest-mass is lost? How much nuclear energy is released? 2. MAKING ESTIMATES A large nuclear power plant supplies energy at a rate of 1000 MW, or 109 joules/second. The energy comes from 235U. How much rest-mass vanishes in one day? 3. In the preceding question, suppose that the energy came from a coal plant rather than a nuclear power plant, still at a rate of 1000 MW. Would this change the answer? Explain.

FISSION AND FUSION WEAPONS 4. Since 1 kiloton = 4.2 * 1012 J, how much rest-mass vanishes when a 15-kiloton atomic bomb explodes? How much restmass vanishes when a 15-megaton hydrogen bomb explodes? 5. How high could the energy of a 15-kiloton atomic bomb (preceding problem) lift the U.S. population, assuming a population of 300 million with an average weight of 600 N (mass of 60 kg) per person. How high could a 15-megaton hydrogen bomb lift the U.S. population? 6. MAKING ESTIMATES Suppose that all the energy released in a 1-megaton (4.2 * 1015 J) fusion bomb were used to lift people to a height of 1600 meters (about 1 mile). About how many people could be lifted? What fraction of Earth’s population is this? (GravE = weight * height. You will need to estimate the weight, in newtons, of an average person).

Answers to Concept Checks 1. Work must be done on the proton and neutron in order to

separate them, so energy is added to the system, (a). (b) (e) The atomic number is 4, which is beryllium, (c). (a) (d) The atomic mass increased by 3, and the atomic number increased by 2, (c). 8. The atomic number is 92 - 56 = 36, which is krypton, (b). 9. They differ by 3 parts (238–235) in 238, or 3/238, which is a little more than 1%, (e). 10. 22,000 tons>5 tons = 4400, (d) 2. 3. 4. 5. 6. 7.

Fusion and Fission: Problem Set

Answers to Odd-Numbered Conceptual Exercises and Problems

23.

Conceptual Exercises 1. 11H + 21H : 32He. 3. The nucleus’s mass is smaller than the sum of the masses of its protons and neutrons. This is true for any nucleus, as you can see from the nuclear energy curve. 5. Fission (note that this is not radioactive decay, because 16O is not radioactive). 168O : 42He + 126C. According to the nuclear energy curve, the right side represents the most nuclear energy. 7. Use the nuclear energy curve. Carbon: fusion; gold: fission; iron: neither. 9. Change in rest mass: (a), (b), (c), (d) (all four). But only (a) and (c) are measurable. 11. It opposes nuclear fusion. 13. The sun’s energy comes from nuclear fusion. 15. 16O. According to the nuclear energy curve, this released nuclear energy. 17. No, because nearly all of the sun’s atoms are still in the sun. 19. Lanthanum’s atomic number is 57, and uranium’s is 92. 92 - 57 = 35, which is bromine. 21. The major similarity: Both convert microscopic forms of energy (chemical and nuclear) into thermal energy. The major difference: Burning is a chemical process involving the orbital electrons; fission is a nuclear process. Another difference: Fission releases far more energy (per individual reaction) than combustion.

25. 27. 29. 31.

235 142 91 92U + n : 56Ba + 36Kr + 3n , where “n” means “neutron.” Note that in this particular reaction, three neutrons must be present afterward in order to balance neutrons and protons before and after the reaction. No. Natural uranium contains only a small amount of the chain-reacting isotope 235U, as compared to the large amount of 238U. No. The fraction of 235U (as compared to 238U) is too small to sustain a fission chain reaction. 2 3 4 1H + 1H : 2He + neutron . No, because a nuclear power plant’s uranium is either nonenriched or only low-enriched, and not highly enriched as is needed for a bomb.

Problems 1. 1% of 10 kg is 0.1 kg, or 100 g. E = mc2 = (0.1 kg) * (3 * 108 m>s)2 = 9 * 1015 J. 3. The same amount of rest-mass would still have to vanish, because the same amount of electrical energy would still have to be created. 5. The weight of the U.S. population is 300 * 106 * 600 N = 1.8 * 1011 N. The energy available for lifting is 15 * 4.2 * 1012 J = 6.3 * 1013 J. Thus, from GravE = we get weight * height, height = GravE>weight = 6.3 * 1013 J>1.8 * 1011 N = 350 m, or 0.35 km. A 15 megaton bomb could do 1000 times as much lifting: 350 km!

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Quantum Fields Relativity Meets the Quantum The basic ingredients of nature are fields; particles are derivative phenomena. Steven Weinberg, Physicist, Winner of the Nobel Prize for His Theory of the Electroweak Force Field

S

pecial relativity and quantum physics extend Newtonian physics in different directions. One extends it up to lightspeed, and the other extends it down to at least the smallest dimensions yet measured, 10 - 19 meters, 10,000 times smaller than an atomic nucleus. But there’s a problem with these two theories. Special relativity doesn’t contain the quantum principles so it doesn’t work at small sizes, and quantum physics doesn’t contain the relativity principles so it doesn’t work at high speeds. Thus neither theory describes small-scale high-speed phenomena. What’s needed is a joining of relativity and quantum physics into a single theory covering all sizes and all speeds. Such a theory was developed during 1930–1950. It’s called quantum field theory. One part of this theory, quantum electrodynamics, is the most accurate scientific theory ever invented. Like most of modern physics, quantum field theory is basically simple but takes some getting used to. Its underlying idea, and an enduring theme of modern physics, is the field view of reality already discussed in connection with Einstein’s mass–energy relation—the view that the universe is made entirely of fields. In Section 1, we’ll further discuss what this means. Section 1 presents the general idea of quantum field theory, and the remaining sections apply this idea to each of the four fundamental forces: electromagnetic (Sections 2 and 3), weak (Section 4), strong (Section 5), and gravitational (Section 6). Along the way, I’ll present several of the most remarkable topics in all of physics: antimatter, creation and annihilation of matter, high-energy particle accelerators (including the Large Hadron Collider), the furious activity occurring in so-called “empty” space, neutrinos, quarks, gluons, the standard model of particle physics, the Higgs field and its quantum particle, quantum gravity, and the string hypothesis.

1 QUANTIZED FIELDS: THE REASON THERE ARE PARTICLES A field (examples include gravitational, electromagnetic, and matter fields) is spread out over a region of space. This region needn’t contain any matter or “things” at all. A field is a condition of space itself, a kind of stress in space, regardless of any matter that might be in it. For example, a magnetic field is the possibility of a magnetic force, regardless of whether anything feels that possible

From Chapter 17 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

477

Quantum Fields The unexpected and the incredible belong in this world. Only then is life whole. Carl Gustav Jung

The one part of today’s physics that seems to me likely to survive unchanged in a final theory is quantum mechanics. Steven Weinberg

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force. Recall also that fields, even when no matter is present, contain energy and this implies that they are physically real and not mere mental constructions. At the core of quantum field theory is the view that the universe is made only of fields. The table on which a book rests is simply a configuration of quivering force fields, similar to the invisible force field surrounding a magnet, and so is the book. The book doesn’t fall through the table, however, because the electric force fields in the table repel the electric force fields in the book. And your eye (which is also just fields) sees the book because the book’s force fields emit radiation. It’s an odd idea. There is no truly solid or enduring “thing.” In this sense, there is “nothing”: no thing. Only fields. But this doesn’t mean that everything is empty, or nonexistent, or imaginary. Far from it. In fact, the relatively solid table at which you are perhaps sitting right now is made of atoms that are in turn made of fields that exert quite real forces on the atoms (which are also made of fields) in your elbows which are perhaps leaning on the table. That’s why you don’t fall through the table. Quantum field theory assumes that each field, such as the electromagnetic (EM) field, obeys the principles of quantum physics and special relativity. You’ve already studied the basics, although we called it “quantum physics” instead of “quantum field theory.” Here’s a quick review of those basics: EM fields fill the universe and are quantized in specific energy increments. Each time such a quantized field interacts with, for example, a viewing screen or your eye, it must gain or lose a whole energy increment, or quantum. Even though each quantum is spread out over a region of space, these quanta of the EM field act somewhat like particles and are called photons. The theory also asserts that matter fields fill the universe and that these too are quantized. The quanta of these matter fields act somewhat like particles and are called electrons, protons, neutrons, atoms, and so forth. In this chapter, we’ll learn that there are other kinds of radiation quanta, similar to the photon, and other kinds of material quanta, similar to electrons and protons. This view stands Newtonian thinking on its head. Newtonian physics regards the universe as a vast collection of separate, unchanging particles whose motions and interactions determine everything that happens. Quantum physics regards the universe as made of just a few kinds of constantly changing spread-out fields whose motions and interactions are the source of everything that happens. Because these fields are quantized, their interactions must occur in specific energy increments, and these increments appear as photons, electrons, protons, etc. This view also explains why all electrons must be identical, why all photons of a particular frequency must be identical, etc. All electrons, for example, are just quantized bundles of field energy of a single type of matter field, so they must be identical, in the same way that 1 joule of energy in your gas tank is identical with any other joule of energy in your gas tank. So quantum field theory explains why nature exhibits itself as particles of just a few fundamental types. The list of nature’s fundamental ingredients no longer needs to include any particles at all—it needs to include only a few fields. This view puts matter and radiation on an equal footing: Both material particles such as electrons and radiation particles such as photons are quantized bundles of field energy. These particles are subject to the usual quantum uncertainties, with the field’s intensity at any point determining the probability that the corresponding particle will appear at that point. The fields (and the associated particles) are also subject to the rules of special relativity, namely, the principle of relativity and the constancy of lightspeed. To summarize:

Quantum Fields

The Quantum Theory of Fields The essential reality is a few fields, such as the EM field, that fill the universe and that obey the principles of quantum physics and special relativity. Everything that happens in nature is a result of changes in these fields. Quantization requires that, whenever an interaction occurs, these fields must exhibit themselves as bundles or quanta of field energy. All of nature’s particles of radiation and matter are quanta of this sort.

Why does quantum field theory obey the special theory of relativity rather than the more general and more correct (because it agrees with a wider range of observations) general theory of relativity? It’s because nobody has yet figured out how to make quantum physics jibe with general relativity. In other words, within the context of special relativity, quantum field theory incorporates three of the four fundamental forces: electromagnetic, weak, and strong. But nobody has been able to formulate any of these three forces within the context of general relativity; such a theory would have to encompass the fourth force, gravity. For some hypothetical stabs in this direction, see Section 6.

The notion that reality is a set of fields that give the probabilities for finding their associated quanta is the most important consequence of relativistic quantum field theory. It is the central concept for the picture of reality. Not only did the idea of matter disappear into the field concept, but the field specified the probability for finding quanta. Heinz Pagels, Physicist

2 QUANTUM ELECTRODYNAMICS: THE STRANGE THEORY OF ELECTRONS AND LIGHT

University of Tsukuba, Tomonaga Memorial Room/American Institute of Physics/Emilio Segre Visual Archives

Quantum field theory emerged during the 1930s as the world was marching toward war. Although nuclear physics flourished in the United States, quantum physics had to wait. Nevertheless, Shin’ichiro Tomonaga (Figure 1), working in

American Institute of Physics/ Emilio Segre Visual Archives

Segre Collection/American Institute of Physics/Emilio Segre Visual Archives

(a)

(b)

Figure 1

Three who independently invented the theory of quantum electrodynamics, a quantum theory of the EM force. (a) Shin’ichiro Tomonaga (gesturing from his desk) in 1948, five years after publishing his theory. (b) Richard Feynman. He was known to jerk his mind out of a rut by working at a back table in a nightclub, inspired by the blare of the sound system. (c) Julian Schwinger. A solitary worker, he says that he “became the night research staff ” at his wartime laboratory.

(c)

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Quantum Fields

1

Moving electron

Position

Photon 2 Stationary electron Time

Figure 2

A schematic diagram showing a single quantum interaction between two electrons. Diagrams like this are known as “Feynman diagrams.”

480

wartime isolation in Japan, published a fundamental paper presenting a quantum field theory of the EM force. His paper was not available in English until 1948. After the war, in 1947, two New Yorkers in their 20s, Richard Feynman and Julian Schwinger (Figure 1), completed quantum field theories of the EM force. The three theories, known as quantum electrodynamics, were invented independently and look strikingly different, but all three say the same thing. I’ll present Feynman’s more intuitive version. Quantum electrodynamics is about the interactions between two kinds of quantized fields: quantized EM fields, and quantized electron fields (matter fields for electrons). From the particle point of view, the theory is about photons, the quanta of the EM field, and electrons, the quanta of the electron field and the particles that experience the EM force in its purest form. It sounds simple. But the requirement that the EM field and electron field obey both relativity and quantum theory leads to astonishing results. In Feynman’s theory, the old idea of a continual electric force between two electrons is replaced with a quantized transfer of a “bundle” of force in the form of a photon. Figure 2 pictures this. The diagram graphs the positions of two electrons at various times and shows a single quantum interaction between the two electrons. Initially, electron 2 is at rest (its position, shown along the vertical axis, isn’t changing as time proceeds along the horizontal axis), and electron 1 is moving downward. Then electron 2 radiates a photon that travels through space and time to electron 1, and then electron 1 absorbs this photon. When electron 2 emits the photon, electron 2 veers downward, and when electron 1 absorbs the photon, electron 1 veers upward. The electrons repel each other by means of photon exchange, much as basketball players interact by passing a basketball back and forth. Surprisingly, however, quantum electrodynamics allows two oppositely charged particles, such as a proton and electron, to veer toward each other when a photon is exchanged. Every quantum event has quantum uncertainties. In Figure 2, the emission and absorption of the photon are uncertain. That is, it’s uncertain whether the emission and absorption will occur in the first place, and if they do, it’s uncertain where and when they will occur. Quantum field theory replaces the deterministic electric force law with a formula giving the probability of emission and absorption of a photon. In this theory, for a particle to be electrically charged means that it has the ability to emit and absorb photons. This theory replaces the smooth, deterministic, Newtonian paths with jerky, nondeterministic paths. If the force between the two electrons is small, then individual photons have low energy and quantum theory predicts a fairly smooth, nearly Newtonian, path [Figure 3(a)]. But when the forces are large, the quantum predictions are decidedly non-Newtonian [Figure 3(b)]. So far, this is the kind of thing you might have expected from quantizing the electric interaction: quantized force packages and randomness. But something radically new also emerges. In order for the theory to obey the special theory of relativity, a new type of material particle must exist in nature. The argument that leads to this prediction is an interesting one and is typical of modern physics. It’s based on symmetry, a concept that we’ve encountered several times before. It turns out that, in order to obey special relativity, quantum field theory must be “symmetric under time reversal.” In other words, if we imagine a universe precisely like ours, only with time running the other way, the laws of quantum

Quantum Fields 1

2

Position

Position

1

Time 2 Time (a)

(b)

Figure 3

(a) A Feynman diagram for a series of interactions between two weakly interacting (i.e. only low-energy photons are exchanged) electrons. The electrons’ paths approach smooth Newtonian paths. (b) At stronger interactions (high-energy photons), the paths deviate considerably from smooth paths, and Newtonian physics is no longer a good approximation.

field theory must be valid in that universe.1 Feynman found that an electron that is imagined to move backward in time would have precisely the same observable effects as would another particle just like the electron, only carrying a positive charge and moving forward in time. In order for the laws of physics to be properly symmetric under time reversal, this positive electron, or positron, had to exist. The prediction of the positron illustrates the enormous scope of quantum field theory: Earlier theories, whether Newtonian or relativistic or quantum, had described only how things change in time. Quantum field theory goes well beyond this extrapolation of the present into the future and the past by describing not only how things move but also what kinds of things can exist. How do we know that positrons and other strange new particles exist? A subatomic particle’s path can be revealed by a device known as a cloud chamber. A container or “chamber” is filled with air saturated with water vapor—gaseous H2O that is just at the point of converting to droplets of liquid water. When a charged subatomic particle such as an electron speeds through the chamber, it nudges some of the air molecules along its path strongly enough to ionize them. Each ion causes a water droplet to form, and the resulting trail of droplets reveals the particle’s path. Jet planes form similar vapor trails in the atmosphere, revealing the plane’s path. The cloud chamber was the workhorse of subatomic physics between 1930 and 1960. Its successor is the bubble chamber, based on the formation of tiny bubbles in a liquid. According to scientific lore, its inventor, Donald Glaser, came up with this innovation in a bar in Ann Arbor, Michigan, while watching the bubbles in a glass of beer. It won him a Nobel Prize. In 1932, Carl Anderson of the California Institute of Technology generated a strong magnetic field in a cloud chamber. Recall that magnetic fields exert sideways forces on moving charged particles. This sideways force makes electrons curve as they move through magnetic fields. A moving particle’s speed and mass can be assessed from this curvature because a particle’s path is straighter if it’s moving faster, and because if two particles move at the same speed, the more massive one will have the straighter path. 1

This raises the intriguing question of why, if our most basic physical theory is symmetric in time, the forward direction in time is different from the backward direction. For example, why aren’t as many people growing younger as are growing older? The answer is not understood, but it’s connected to the second law of thermodynamics and the big bang.

481

Quantum Fields

Ernest Orlando Lawrence Berkeley National Laboratory Figure 4

The photo that won a Nobel Prize. This photo alone established the existence of a positive electron.

In 1932, the only high-energy particles available for experiments came from space. Allowing these “cosmic rays” to pass through his cloud chamber, Anderson found a surprising number of fairly straight paths. Electrons and protons were the only charged particles known at that time. The paths appeared to be made by fast-moving electrons, but the direction of their curvature was the reverse of what was expected, indicating that the particles carried a positive charge. Anderson’s first hypothesis was that these paths were made by electrons that were somehow moving upward through the cloud chamber, despite the expectation that cosmic rays should move downward. He checked this hypothesis by inserting a thin lead plate across the middle of the chamber. Although the fast-moving particles passed easily through the lead, they slowed down in the process, and so the path’s curvature increased after passing through. In Figure 4—the photograph that won Anderson a Nobel Prize—the particle is clearly moving from top to bottom because it curves more in the bottom half of the photo, so its curvature shows that it carries a positive charge. Anderson had discovered the positron. In order to observe cosmic rays before they interact with much air, Anderson in 1936 built a new magnetic cloud chamber on Pike’s Peak in the Colorado Rockies. He found curious tracks that didn’t fit protons or electrons, even positive ones. The paths were too curved for protons, yet the particles passed easily through lead plates that should have stopped any particle whose mass was as small as the electron’s. This new particle was just like an electron but 200 times more massive. It was a real surprise. As Columbia University physicist I. I. Rabi put it, “Who ordered that?” Today, we still do not know. This particle is called a muon.

3 ANTIMATTER

Just as it is possible for a particle to be in a quantum state in which it is neither definitely here nor there. . . so also it is possible to have a particle in a state in which it is neither definitely an electron nor definitely a neutrino until we measure some property that would distinguish the two, like the electric charge. Steven Weinberg

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The positron was science’s first encounter with antiparticles. Relativity’s requirement that quantum theory be symmetric under time reversal implies that for every existing type of particle, there must be an antiparticle having the same mass but the opposite charge. For example, the electron’s antiparticle is the positively charged positron. Similarly, the proton’s antiparticle is the negatively charged antiproton, and the neutron’s antiparticle is the uncharged antineutron. Although it carries no overall charge, the antineutron does have magnetic properties that are the opposite of the neutron’s. One of the profound successes of quantum field theory and high-energy experimental physics is the prediction and observation of the creation and annihilation of matter. As you know, quantum field theory states that EM fields and electron fields interact with other systems, such as the viewing screen in a double-slit experiment, by exchanging quanta with the other system. The quanta of the EM field are called photons, and the quanta of the electron field are called electrons and positrons. Quantum field theory predicts what can happen when an EM field and an electron field interact with each other. As one possibility, the EM field could give up one or more quanta (photons) to the electron field, increasing the energy of the electron field. Normally, the observable consequences of this would simply be increased energy for any electrons that might be observed in, say, a cloud chamber. But if the EM field gives up sufficiently high-energy photons to the electron field, something new can happen: Additional electron field quanta can be created. That is, electrons and positrons can be created. However, experiments show that, in any microscopic interaction, the total electric charge is conserved, so it is always electron–positron pairs that are created. Quantum electrodynamics gives the probabilities for this to occur.

Quantum Fields

The discovery of particles and antiparticleshas changed our whole outlook on atomic physics. . . As soon as one knows that one can create pairs, then one has to consider an elementary particle as a compound system; because virtually it could be this particle plus a pair of particles plus two pairs and so on, and so all of a sudden the whole idea of elementary particles has changed. Up to that time I think every physicist had thought of the elementary particles along the lines of the philosophy of Democritus [Chapter 2], namely by considering them as unchangeable units which are just given in nature and are always the same thing, they never change, they never can be transmuted into anything else. They are not dynamical systems, they just exist in themselves. After this discovery everything looked different, because one could ask, why should a photon not sometimes be a photon plus an electron–positron pair and so on?. . . Thereby the problem of dividing matter had come into a different light.

tro

ns

c le

e

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Position

The other possibility is that the electron field could give up quanta to the EM field. One way this can happen is for an electron and a positron to vanish from the electron field while one or more high-energy photons appear in the EM field. Thus, electron–positron pairs can annihilate each other as well as pop into existence. So quantum electrodynamics predicts that a photon has a certain probability of being observed as an electron–positron pair, or as more than one pair, and that such a pair has a certain probability of being observed as one or more photons. Figure 5, a Feynman diagram for part of a photon’s life history, conveys this notion. This is a very non-Newtonian development. As Heisenberg commented:

s

on

r sit

on

tr

ec

El

2

po

n

ro

on

ot

Ph

sit Po

Time

Figure 5

A few moments in the life history of a high-energy photon (which is an electron–positron pair during part of this history and two pairs during another part).

Antiparticles imply the possibility of antimatter, similar to normal matter but made of antiprotons, antineutrons, and positrons. Indeed, antiprotons were first brought together with positrons in 1996 to form a few atoms of antihydrogen. Although they’re still a long way from powering the antimatter drive of Captain Kirk’s Enterprise, researchers today can create and study thousands of antihydrogen atoms at a time at very low temperatures. These cold atoms are moving so slowly that they interact with each other only weakly, enabling scientists to study antihydrogen’s spectrum and other properties and compare them with hydrogen’s properties. In one experiment, antihydrogen falling in Earth’s gravitational field is compared with the fall of hydrogen. Another experiment seeks the antimatter counterpart of the negative H ion (one proton orbited by two electrons), and the antimatter counterpart of the positive H 2 ion (two separate protons orbited by one electron that binds the protons into a single molecule). One goal is to trap large quantities of antimatter at very low temperatures in a single container for long periods of time. Large naturally occurring collections of antimatter, such as antigalaxies, are possible but are thought not to exist, because if they did we would observe high-energy radiation from annihilation processes when a galaxy collides with an antigalaxy. Because we observe many colliding galaxies but never observe such annihilation processes, the universe is believed to contain very little antimatter. But symmetry seems to suggest that the universe should be made of equal amounts of both. Why so much matter and so little antimatter? Russian physicist Andrei Sakharov suggested in 1967 that the big bang may have created equal amounts of matter and antimatter and that certain rare symmetry-violating processes during the first second gave rise to a slight excess—less than a part in a billion—of matter, and then the rest of the matter and antimatter annihilated so that the tiny excess formed all the matter that’s in the universe today. It’s a good thing for life in the universe, including us, that things worked out this way. If it weren’t for that slight excess of matter created during the universe’s the first second, the universe would be made nearly entirely of radiation, and we wouldn’t be here to think about antimatter!

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How do we know that antimatter exists? Matter and antimatter are routinely created and annihilated in high-energy physics labs when a high-energy particle enters a bubble chamber and collides with the particles of liquid (Figure 6). This creates a shower of new particles, including particle–antiparticle pairs. Carl Anderson got his high-energy incoming particles from naturally occurring cosmic rays. Today the incoming particles are first accelerated to high energies by EM forces in particle accelerators such as the Large Hadron Collidor (Figure 7).

Fermilab Visual Media Services

Ernest Orlando Lawrence Berkeley National Laboratory

Physicists have always “thrown” tiny things at other tiny things in order to see how they’re made. Rutherford’s 1911 experiment threw alpha particles at the atoms in a piece of metal foil and discovered the atomic nucleus. Today, particle accelerators use electromagnetic fields to speed up subatomic charged particles such as protons or electrons to high energies and smash them into other moving particles or into fixed targets. The Large Hadron Collider (LHC, Figure 7), lying in a circular tunnel 27 km around and buried more than 100 m deep near Geneva, Switzerland, will circulate two oppositely-moving beams of protons (a member of the class of particles known as “hadrons”) and allow some protons from each beam to collide with each other at various locations around the ring. Please take a few seconds to compare this “inner space observatory” with “outer space” observatories. Both figures are prime examples of the human thirst for knowledge. These structures are in some ways comparable to the cathedrals of old. When the LHC runs at maximum energy, each proton will carry seven trillion “electron volts” (eV) of kinetic energy. One eV is the amount of kinetic energy that

(a)

(b)

Figure 6

(a) A bubble-chamber photograph of electron–positron pair creations, caused by gamma-ray photons. In the event at the top, a photon has struck an atomic electron and knocked it out of its atom (long curving line), and it simultaneously created an electron–positron pair (tightly curling spirals). Why can’t you see the path of the photon? Toward the bottom, a different photon creates an electron–positron pair. How can you tell that each pair has two particles of opposite charge? Of the two pairs, which pair has the highest energy and speed? (b) A high-energy particle striking a particle in a bubble chamber creates a “spray” of particles of various sorts. The bright circle is part of the measuring device.

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Quantum Fields

(b)

(a)

(c)

(d)

CERN Figure 7

The LHC is the world’s most powerful particle accelerator. (a) The main two rings are shown drawn on an aerial photograph of the region. The two proton beams, each one thinner than a human hair, circle in opposite directions and cross at four points where they collide within four detectors named Atlas, Alice, CMS, and LHCb. (b) An engineer inside the main ring. He leans on one of the electromagnets, powered by superconducting electric currents, that bends the beam into a circle. (c) Inside the Atlas detector, during construction. For comparison, there’s a person standing in front. Atlas is half the size of the Notre Dame cathedral in Paris. It will seek out Higgs bosons, microscopic black holes, extra dimensions of space, and the dark matter particles that constitute most of the matter in the universe. (d) The LHCb detector, under construction. It will look for slight differences, or “asymmetries,” between matter and antimatter by studying the bottom (or “b”) quark. This will help solve the mystery of why our universe is composed almost entirely of matter with little antimatter.

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No point is more central than this, that empty space is not empty. It is the seat of the most violent physics. John Wheeler

an electron (or a proton, since it has the same amount of electric charge) gains when it’s allowed to “fall” freely through a voltage of one volt—for example, when an electron is allowed to move freely (through empty space) from the negative to the positive terminal of a one-volt battery. At the LHC’s maximum energy, each proton will be moving at 0.99999998 (7 nines followed by an eight) times lightspeed and have an inertial mass 7000 times larger than the proton’s normal rest mass (due to relativistic mass increase)! When two LHC protons collide, the total collision energy will be 14 * 1012 eV—equivalent to one proton “falling” through fourteen trillion volts. This is about three million times larger than the energy of Rutherford’s alpha particles. It’s a really large energy to put into two tiny protons, but the total energy isn’t as large as you might think. For example, the total chemical energy released (turned into thermal energy) when you strike a match is around 1022 eV, about a billion times larger than the LHC’s collision energy but spread among about a billion trillion atoms. In other words it’s easy to get energies this large; it’s just hard to get it all into a couple of protons. The fourteen trillion eV collision energy is seven times larger than the energy of the largest previous accelerator at Fermilab near Chicago. The energy of each proton–proton collision will be large enough to create the rest-mass energy mc2 of all sorts of other particles. Physicists think there’s a good chance that some of these other particles will be new, never directly observed before. You’ll be learning about some of these possible new particles in the remainder of this chapter. Although the LHC will create conditions resembling the first moments of the big bang, and it’s hoped that it will create microscopic black holes, there’s no chance of an unforeseen catastrophe such as another big bang. Cosmic rays from outer space, most of them protons, have been striking other protons in Earth’s atmosphere for billions of years at far higher energies and much larger numbers than the LHC can produce. And such high-energy proton–proton collisions have been occurring all over the universe throughout time. There have been no catastrophes from any of this. Quantum field theory paints an odd new view of “empty” space—space that is devoid of matter, commonly called vacuum. As you know, EM fields and other fields extend even into regions containing no matter. Quantum uncertainties require that the energies of all these fields at any point in space fluctuate, over short timespans, around its long-time average value. In Section 6, I’ll further discuss these energy fluctuations for the case of the gravitational field. The uncertainty principle implies that the smaller the region of space and the shorter the time interval, the larger these fluctuations must be. This means that at any point in so-called empty space there’s a certain likelihood that a photon or a particle–antiparticle pair, including any of the particles discussed in this chapter, will spontaneously pop into and out of existence during short times. So even in empty space there is always some probability of high energy events occurring in small regions. Empty space is not the quiet, uninteresting place we had imagined. Microscopically, it’s a seething soup of creation and annihilation. It seems that in nothingness, much is possible.2

2

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Quantum energy fluctuations mean that the law of conservation of energy must be revised. In sub-microscopic regions of space and for short times, energy is not strictly conserved. It is, however, conserved, on the average over larger regions of space or longer times.

Quantum Fields

How do we know that there is energy in “empty” space, and that it fluctuates? One consequence of energy fluctuations in vacuum is a tiny effect on the hydrogen atom’s energy levels. In Schroedinger’s nonrelativistic treatment of the hydrogen atom, the energies of the quantum states are identical. But when relativistic quantum field theory is applied to the hydrogen atom, it is found that vacuum energy fluctuations cause the orbiting electron to jiggle a little and that the energy of this jiggling is slightly different for state (b) than for states (c) and (d). This difference was first noticed experimentally in careful measurements of the hydrogen spectrum by Willis Lamb in 1947. After the experimental discovery of this Lamb shift, quantum field theorists calculated it. The theoretically predicted frequency of the radiation absorbed or emitted when a hydrogen atom shifts between these two closely spaced levels is 1057.860 ; 0.009 megahertz. The measured value is 1057.845 ; 0.009 megahertz. This uncanny one part in a million agreement is testimony to both the accuracy of quantum field theory and the precision of spectral measurements.

It is ironic how physics turned out in this [20th] century. The 19th and early 20th century was characterized by a materialistic outlook which maintained a sharp distinction between what actually was in the world and what wasn’t. Today that distinction still exists, but its meaning has altered. . . . Nothingness contains all of being. Heinz Pagels, Physicist

Quantum electrodynamics describes not only electrons and positrons but also the electron-like muons along with antimuons. Furthermore, a third type of electron, along with its antiparticle, was discovered in 1976. Called the tau, it’s much heavier than the muon, weighing in at 3500 electron masses, or nearly twice the mass of a proton. Again, nobody knows “who ordered that.” These three generations of electron-like particles appear today to be among the most fundamental constituents of matter. All three, along with their antiparticles, interact by exchanging photons, and all of their interactions are correctly described by quantum electrodynamics. The muon and tau are “unstable”; in other words, they decay spontaneously into lower-energy entities. Muons and taus play a role today only when fleeting pairs of them are created by vacuum fluctuations or in high-energy interactions. However, these two heavy electrons might have played a crucial role during the big bang. Sakharov’s process, mentioned earlier, for creating a slight excess of matter over antimatter requires all three generations. Although they seem esoteric, we might owe our existence to the activities of muons and taus during the first second of the universe. Are there more generations of still heavier electrons? As you will see, theory combined with astronomical observations predict that the answer is no. CONCEPT CHECK 1 If you visited an antigalaxy, (a) you would be pulled into its black hole and ripped apart; (b) any planets there would contain many of the same chemical elements as Earth but they would be made of antimatter; (c) you would find gravity to be repulsive rather than attractive; (d) you would be annihilated; (e) it would definitely be a one-way trip. CONCEPT CHECK 2 A certain gamma-ray source emits photons that have a 20% chance of being found as an electron–positron pair. The source emits 400 photons. How many individual material particles will be found? (a) Approximately 160. (b) Exactly 160. (c) Approximately 80. (d) Exactly 80. CONCEPT CHECK 3 Which of these feels the electric force? (a) Proton. (b) Electron. (c) Positron. (d) Antiproton.

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4 ELECTROWEAK UNIFICATION AND NEUTRINOS

At first glance, all of this sounds like medieval mystics discussing the music of the spheres, angels on the head of a pin, or some similar early approach to cosmology. Is it just a mathematical game we are playing, is it just semantics, or is it reality? Leon Lederman and David Schramm, in From Quarks to the Cosmos

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Wolfgang Pauli suggested in 1930 that during radioactive beta decay, the nucleus emitted, in addition to a beta particle, another particle of an entirely new type. The hypothesized new particle was dubbed the neutrino, or “little neutral one.” Although neutrinos would not be discovered experimentally for another 25 years, Enrico Fermi immediately took Pauli’s suggestion seriously and argued that neutrinios indicated a new fundamental force, the weak force, was at work. Fermi was aware of the work in progress on the quantum field theory of the electric force, and he quickly adapted these ideas to the weak force. Fermi’s theory succeeded in predicting the half-lives of radioactive nuclei and the range of energies with which beta particles emerged from the nucleus during beta decay. The weak force is the most obscure of nature’s four fundamental forces. Gravity and electromagnetism show up all the time in our macroscopic world because they can act over long distances. The strong force is short-ranged but it is, as its name says, strong. It holds the nucleus together, is the major actor in nuclear power and nuclear weapons, and is responsible for radioactive alpha decay. The most noticeable example we have of the weak force is beta decay. The weak force is elusive because it’s both weak and short-ranged. A neutrino barely exists at all. That is, it has almost no properties: no charge, only a tiny rest-mass (far less than an electron’s), and it feels neither the electric nor the strong force. Moving at almost lightspeed and feeling only the weak force (and gravity), it’s the most elusive known particle and one of the most fantastic. Because neutrinos have only weak interactions, they hardly “feel” matter as they travel through it. It would take 8 light-years of solid lead to stop just half the neutrinos emitted during beta decay! No wonder the physicists studying beta decay had so much trouble trapping this thing. There are millions of neutrinos from space passing in all directions through your body at any instant, yet it will probably be years before even one of them interacts within your body. The neutrinos now passing downward through you pass easily through our planet, exit Earth’s far side in less than a tenth of a second, and are beyond the orbit of the moon in less than 2 seconds. In 1967, Pakistani physicist Abdus Salam and U.S. physicist Steven Weinberg (Figure 8), working independently, uncovered a close connection between the weak force and the EM force. They proposed a new quantum field theory that incorporated both force fields into a single electroweak force field and that incorporated both the electron matter field and the neutrino matter field into a single electroweak matter field—a unification comparable to Maxwell’s unification, during the nineteenth century, of electricity and magnetism into a unified EM force. Recall that quantum electrodynamics describes the electric interactions of electrons and positrons and that this interaction occurs via photon exchanges between the charged particles. The Weinberg-Salam theory is a broader version of this picture. It says that the weak and EM forces both arise from a single force field and so are really different aspects of the same electroweak force. It describes the EM and weak interactions of electrons, positrons, neutrinos, and antineutrinos and states that this interaction occurs via the exchange of various other particles. These exchange particles include not only the photon but also three additional kinds of particles. The three new exchange particles differ a little from the photon, the main difference being that all three have mass—in fact, rather large masses for subatomic

Quantum Fields

Ettore Majorana Centre for Scientific Culture

Harvard University NewsOffice/American Institute of Physics/Emilio Segre Visual Archives

Figure 8

particles. Each of them is about 100 times more massive than a proton! They are labeled, W + , W - , and Z and can be thought of as photons that have, for reasons unknown, acquired a mass. Another difference from the photon is that the two Ws are charged, positively and negatively. The Z is, like the photon, not charged. The massive, charge-neutral Z particle was a striking new prediction of the electroweak theory, and its experimental detection six years later in 1973 was a key confirmation of the theory. Recall that, besides the electron, there are two other generations of heavier electron-like particles, the muon and tau. Since the electroweak force binds the electron and the neutrino together into a single family, we might guess that there is a second-generation neutrino to go along with the muon and a third-generation neutrino to go along with the tau. This would be a good guess. In fact, there is a second-generation matter field whose quanta are the muon and the “muonneutrino” and a third-generation matter field whose quanta are the tau and the “tau-neutrino.” But there are not three generetions of electroweak force particles. Instead, all three generations interact via the same electroweak force field and its four exchange particles: the photon, W +, W -, and Z. The electroweak theory correctly predicts all the observed interactions among all these fundamental particles. Table 1 summarizes the theory.

The co-inventors of the electroweak force. They combined the quantum theories of the electromagnetic field and the weak nuclear field into a single electroweak quantum field theory. (a) Abdus Salam, born in Pakistan, is one of the most prominent scientists of the Islamic faith. He donated his share of the Nobel Prize to the institute with which he is associated in Trieste, Italy, which encourages scientists from developing countries. (b) In addition to his Nobel Prize–winning work in quantum field theory, U.S. physicist Steven Weinberg has written several books for nonscientists. His Dreams of a Final Theory is about the fundamental forces and other topics, and The First Three Minutes describes and explains the early stages of the big bang.

How do we know that neutrinos exist? The neutrino’s existence was first suspected around 1930 when beta-decay experiments appeared to conflict with energy conservation. Application of energy conservation and other accepted principles led to the conclusion that, in addition to the observed beta particle, an unseen particle was created in beta decay. Furthermore, the data implied that this particle’s (rest) mass was either zero or very small—far smaller than an electron’s mass. Most physicists assumed it was zero. Neutrinos were finally observed in an experiment in 1956. Enormous numbers of neutrinos created by beta decay within a nuclear reactor entered a huge tank of water. Only about three of these neutrinos per hour interacted with protons in the water, creating high-energy gamma photons that scientists could observe, verifying that the interaction had indeed occurred.

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Table 1 The theory of the electroweak force. Two fundamental electroweak fields pervade the universe: an electroweak force field whose quanta are the four exchange particles listed below, and an electroweak matter field whose quanta are the electron and the electron-neutrino. In addition, there are “second-generation” and “third-generation” matter fields whose quanta are listed below. Generation

Particle type

Mass (proton = 1)

1

electron

1

electron-neutrino

2

muon (mu electron)

2

muon-neutrino

3

tau (tau electron)

3

tau-neutrino

Charge (proton = +1)

0.0005 a a

–1 0

0.11

–1

a

0

1.90 a

–1 0

Exchange particles: photon

0

0

W+

86

+1

W-

86

–1

Z

98

0

a

The three types of neutrinos have small but nonzero rest-masses, although the values are uncertain. The sum of the three masses of all three types of neutrinos is known to be less than 1 millionth of an electron’s mass.

But physicists were still unable to determine whether the elusive particle’s mass was zero, or nonzero but tiny. Today, it’s known that the sum of the masses of all three types of neutrinos is less than 1 millionth of an electron’s mass. Until recently, a mass of zero seemed most plausible; after all, why should this new particle have a mass far smaller than the mass of any other known material particle when a simple “zero” (like the photon) seemed to fit all the data? But nature chose a small number rather than zero. Nobody knows why. How do we know that neutrinos have mass? The tale of this turnaround from “probably zero” to “definitely nonzero” mass began during the 1960s with observations of neutrinos from the sun. Physicists used widely accepted theories of nuclear reactions occurring in the sun to calculate the number of high-energy neutrinos emitted by the sun. This was a prediction that could be checked using huge neutrino detectors, or “neutrino telescopes,” placed deep underground in order to prevent gamma photons and other high-energy particles from space from penetrating the detector. But the results disagreed wildly with predictions: The observed number of neutrinos was only one-third of the predicted number. Such disagreements between theory and observation are creative moments in science, when something really new can be learned. The experiment was repeated by different groups at different sites using different techniques, but the disagreement persisted. Scientists began to suspect that something was wrong with the theories—either the theory of nuclear reactions in the sun or of fundamental neutrino physics. Astrophysicists went over the theory of nuclear reactions in the sun with a fine-toothed comb but could find no holes in it. Suspicions turned toward neutrino physics. Several variations on the Weinberg-Salam electroweak theory were proposed. A new and surprising

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Quantum Fields theoretical prediction emerged: If two neutrinos have different masses, then they should be able to spontaneously transform their identity into each other. For example, if electronneutrinos and tau-neutrinos have different masses, then an electron-neutrino should be able to spontaneously change into a tau-neutrino, and vice versa, in much the same way that a high-energy photon can transform into a particle–antiparticle pair. Scientists realized that such neutrino transformations could solve the problem of the “missing” solar neutrinos. The neutrinos that were predicted to be emitted from the sun were all electron-neutrinos, and existing neutrino detectors were sensitive only to electronneutrinos. If some fraction of the neutrinos from the sun changed into one of the other two types of neutrinos during their journey from the sun, then a smaller number of electronneutrinos would be detected on Earth. New detectors, able to observe all types of neutrinos, were needed. The SuperKamiokande detector in Japan was built with this in mind. Astrophysicist Masatoshi Koshiba (Figure 9) used this detector to observe muon-neutrinos created when highenergy particles from space hit Earth’s atmosphere. He obtained a surprising result. The number of atmospheric muon-neutrinos coming through our planet and entering the underground detector from below was only about half the number entering from above. Apparently some of the upward-moving muon-neutrinos were lost during their 0.1-second trip through Earth. This was surprising, because it was known that only a negligible fraction of these particles could be lost due to interactions within Earth. It was suspected that this discrepancy was due to the spontaneous transformation of muon-neutrinos into some other type during that 0.1 second. In 2000, the SuperKamiokande scientists announced that transmutations from muon-neutrinos to tauneutrinos actually were occurring. Convincing icing was put on this result in 2001, when scientists at another new detector in Canada announced a definitive resolution of the solar neutrino problem. In the Canadian experiment, the total number of neutrinos of all types coming from the sun agreed precisely with the number of electron-neutrinos predicted to be emitted by the sun, but the number of electron-neutrinos from the sun was (as had been observed since the 1960s) only about one-third of the predicted amount. This showed that some two-thirds of the emitted electron-neutrinos from the sun transform into either muon- or tau-neutrinos during their journey to Earth. The conclusion is that at least some of the three types of neutrinos must have mass, because only neutrinos of different masses can transform into each other and so they cannot all have zero mass.

Are there more than the three generations of electroweak particles listed in Table 1? In a surprising turn of events, astronomical observations indicate that there are only three generations. The argument comes out of a close connection between the large-scale universe and the microscopic world: Outer space and inner space are connected through a microscopic event that quickly became macroscopic. This event was the big bang. After the first 4 minutes of the big bang, the universe was about 75% hydrogen and 25% helium. These numbers are predicted by theoretical nuclear physics, and they agree with observations of the oldest material in the universe. The theoretically predicted helium fraction depends on the number of generations of electroweak particles: The predicted helium fraction grows larger if the number of generations grows larger. If there are three generations, this leads to a predicted helium fraction of about 25%; if there are four generations, this leads to a predicted helium fraction that is much higher than the observed 25%. Conclusion: There are only three generations. Unification is a recurring theme of science (Figure 10). For example, Copernicus unified Earth with the other planets; Newton unified Earth-based physics with

Peter Menzel, Napa CA, Courtesy of AIP Emilio Segre Visual Archives/American Institute of Physics/Emilio Segre Visual Archives Figure 9

Astrophysicist Masatoshi Koshiba of the University of Tokyo. Using Japan’s Super-Kamiokande neutrino detector, he showed that many muon-neutrinos, created in Earth’s atmosphere by highenergy cosmic rays, change into tau-neutrinos during their passage through our planet.

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Quantum Fields Figure 10 Space

Some of the unifications in physics. The dashed lines represent unifications not yet established. Time runs from top to bottom. Electricity

Time

Heavenly motions

Earthly motions

Newton’s mechanics

Newton’s gravity

Magnetism Light

Electromagnetism

Electromagnetic field theory

Quantum theory

Special relativity General relativity

Quantum electrodynamics

Electroweak theory

Weak force

Strong force

Grand unification Theory of everything

physics throughout the heavens; and Maxwell found a field theory that unified electricity, magnetism, and light. By the end of the nineteenth century, scientists believed that there were only two fundamental forces, electromagnetism and gravity. Einstein, after fashioning the new theory that explained gravity as a consequence of the geometry of spacetime, spent much of his scientific career trying to unify electromagnetism with gravity in the hope that a single “unified field theory” would show electricity and gravity to be different aspects of spacetime geometry. He was not successful. Lately, scientists have sought unification at the microscopic level, based on quantum field theory. As you have seen, these efforts achieved significant success by unifying quantum theory, special relativity, and the EM and weak forces. Physicists today are trying to unify the electroweak with the strong force (Section 5) and to unify these with the gravitational force (Section 6) to actieve Einstein’s dream, a “theory of everything.” CONCEPT CHECK 4 Which of these particles can feel the electric force? (a) Muon. (b) Tau-neutrino. (c) Electron. (d) Photon. (e) W + . (f) Z.

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5 THE STRONG FORCE AND QUARKS As far as the measurements made to date can tell, all the electroweak particles (Table 1) are point particles. That is, their force fields appear to be centered on a single point that itself takes up no volume. The electric charge of the electron, for example, appears to be concentrated at a single point. But protons and neutrons are different. Experiments done in the 1950s showed that their electric and magnetic force centers are spread over a tiny volume about 10 - 15 meters across. Might they be composites that are made of still smaller particles? Early in the twentieth century, protons and electrons were thought to be the only subatomic particles. The discovery of the neutron and the positron in 1932 initiated an era of particle discovery that, by 1960, had produced hundreds of new kinds of supposedly fundamental particles. This bewildering list of particles was frequently referred to as the “particle zoo.” Surely the universe wasn’t made of so many different things. Murray Gell-Mann (Figure 11) hoped to bring order to the particle zoo by grouping the known particles into families that corresponded to physical regularities among them. Gell-Mann’s work was much like the work of the nineteenth-century chemists who found regularities in the chemical properties of the many known elements in the “atomic zoo” and grouped them accordingly into the pattern known today as the periodic table. It was only later that this periodic table found its natural explanation in a new model of the atom according to which the 100-plus elements are built of just electrons, protons, and neutrons. In a similar way, Gell-Mann’s classification scheme led him to speculate on the existence of a few simpler entities, which he called quarks, out of which protons, neutrons, and other particles could be built. That set experimentalists on a quark hunt. But despite strenuous searches among bubblechamber tracks, nobody could come up with direct evidence for quarks. How do we know that quarks exist? When Richard Taylor, Jerome Friedman, Henry Kendall (Figure 12), and 12 coworkers set out in 1967 to study the proton and the neutron, they weren’t looking for quarks. Using a high-energy electron accelerator at Stanford University, they were following up on earlier experiments showing protons and neutrons to be fuzzy balls 10 - 15 meters across. Hoping to get a clearer picture of these fuzzballs, they hurled highenergy electrons at protons and used huge detectors that they had built specifically to measure the angular deviation of the electrons after they were deflected by the protons (Figure 13). At lower electron energies, their “scattered” electrons merely gave them a higher-resolution picture of the same old fuzzballs. But at energies so high that the electrons blew the protons and neutrons to bits, they found a surprise. Some of the electrons were deflected through very large angles, as though they were bouncing off hard little granules buried deep within the fuzzball.

(a)

Henry W. Kendall/ Kendall Foundation

(b)

Donna Coveney/ Massachusetts Institute of Technology News Office

Segre Collection/American Institute of Physics/Emilio Segre Visual Archives Figure 11

Murray Gell-Mann devised a classification scheme for the thenknown subatomic particles. In about 1961 this scheme led to the prediction of new particles and suggested the existence of a small number of simpler entities, called quarks, out of which protons, neutrons, and other particles could be built. Quarks were discovered experimentally in 1967.

Figure 12

(a) Richard Taylor, (b) Jerome Friedman, and (c) Henry Kendall. In much the same way that Rutherford probed the interiors of atoms by bombarding them with alpha particles, they probed the interior of protons and neutrons by bombarding them with high-energy electrons hurled by an electron accelerator. And just as the scattering of Rutherford’s alpha particles revealed a small dense core within each atom—the nucleus—their experiment revealed that within each proton and each neuton lie three tiny force centers: quarks.

(c)

American Institute of Physics/Emilio Segre Visual Archives

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Quantum Fields Figure 13

The enormous electron detectors at the Stanford electron accelerator. The electron beam enters from the left and collides with protons in a target. The deflected electrons are then analyzed by three detectors: the cylindrical tank at the far left, the large detector in the foreground, and the other large detector in the background.

Stanford Linear Accelerator Center

The experiment and its outcome paralleled Rutherford’s discovery of a tiny hard nucleus deep within what had been supposed to be a fuzzball atom. Only this time there appeared to be not one but three tiny force centers within the proton and within the neutron. Taylor, Friedman, and Kendall had found Gell-Mann’s quarks.

Scientists had thought that the proton, neutron, and electron, the three building blocks of all atoms, were “fundamental”—not made of still smaller particles. This might be true of the electron, but quarks imply that the proton and neutron are composite objects, not fundamental particles. Maybe quarks are truly fundamental, or maybe not. The Large Hadron Collider will penetrate to new depths of smallness and could discover that quarks, too, are composite particles. Will we eventually come to the end of nature’s successive seeds within seeds (Figure 14)? Nobody knows. Physicists have found a version of quantum field theory that describes the interactions between quarks and that has so far agreed with all experiments designed to test it. In this theory, the strong force acts directly between quarks, and the force acting between protons and neutrons is a consequence only of the forces between their quarks. The force field (analogous to the EM field) that is quantized in this new theory is the strong force field, and the matter field (analogous to the electron field) that is quantized is the strong matter field. The quanta of the strong matter field are quarks of two types, called u-quarks and d-quarks (and their antiparticles). They are the material particles of this theory, playing a role similar to the electron’s role in quantum electrodynamics. The theory predicts that there are two stable configurations of u- and d-quarks, namely, the proton made of two u-quarks and one d-quark, and the neutron made of one u-quark and two d-quarks. This is why there are protons and neutrons! In addition to feeling and exerting the strong force, quarks must also experience the electric force, because protons experience this force and quarks are supposed to explain protons.

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CONCEPT CHECK 5 Surprisingly, quarks turn out to be fractionally charged, the u possessing a charge of +2/3 of a proton’s charge and the d possessing a charge of –1/3 of a proton’s charge. In this case, one u and two d’s would have a net charge of (a) 0; (b) 1; (c) 2.

The quanta of the strong force field are called gluons because they “glue” quarks together, and on a larger scale they bind the nucleus together. Think of them as the photons of the strong force. Like the photon, they have no mass and no charge. But there’s an important difference between the way gluons relate to the strong force and the way photons relate to the electric force. Gluons themselves exert and feel the strong force, unlike photons, which do not directly feel the electric force. In quantum electrodynamics, “electric charge” can be thought of as “the ability to emit and absorb photons.” In the same way, the property of feeling the strong force can be thought of as the ability to emit and absorb gluons. But gluons themselves feel the strong force, which means that gluons can emit gluons, unlike photons, which cannot emit photons. This ability of gluons to make more gluons explains one of the most curious features of quarks (Figure 15): The force between quarks grows stronger, not weaker, as they are separated, making it impossible to isolate single quarks. When a quark within a proton is pulled a short distance from its neighboring quarks, the gluons must fly farther in order to reach from that quark to its neighbors. This gives these gluons more time to proliferate in flight, which makes more gluons, which makes the force larger as the distance becomes larger. As the quark is pulled farther away, energy quickly builds up in the strong force field, and this energy creates quark–antiquark pairs. After a brief reshuffling, a new quark is created in the proton from which the first quark had been removed! Furthermore, the removed quark and the new antiquark team up to form an unstable pair. This provides a beautifully crazy explanation of why years of looking for isolated quarks in bubble chambers produced no results. Any attempt to pull a quark away from its neighbors just makes more nonisolated quarks.

Finally, all the gluon energy (strong field energy) creates a quark–antiquark pair, the new quark makes the proton whole again, and the new antiquark combines with the old quark to form an unstable quark–antiquark pair.

10⫺9 m

10⫺10 m

Molecule

Atom 10⫺14 m

Nucleus 10⫺15 m Proton Less than 10⫺18 m Quark ?

Figure 14

Nature’s successive seeds within seeds, from DNA to quarks. Note the approximate size of each level.

d u

As the quark is separated further, the gluons make more gluons, which makes the force between the quarks stronger.

DNA

Proton

Suppose you start with the three quarks in a proton—

and begin pulling away one of the quarks. Gluons travel between the quarks.

10⫺7 m

u

Gluons

d u

u

More gluons d u

u

New antiquark d u

u

u New quark

u

Figure 15

Here’s why you can’t separate quarks.

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Quantum Fields

Recall that there are three generations of electroweak particles (Table 1). In just the same way, observation reveals three generations of quarks. The second and third generations each consist of two quarks that are heavier and unstable (short-lived) variations on the u- and d-quarks. Table 2 shows the entire setup for the strong force. The last quark to be discovered experimentally, the t-quark, was confirmed in 1994. The t-quark was the most difficult to discover because its mass turned out to be so much larger than the masses of the other five quarks, which (because of E = mc2) meant that much more energy was needed to create it. Weighing in at an estimated 185 proton masses, the t-quark is about as massive as a gold atom! The resemblance between Tables 1 and 2 is striking and points to a close connection between the electroweak and strong forces. This suggests that there should be a grand unified theory that views the electroweak and strong forces as two facets of a single underlying force. So far, such a theory has eluded science’s grasp. Tables 1 and 2 summarize the current theory of matter at the microscopic level, a theory known as the standard model—a boring title for a theory with such fantastic predictions as antimatter, neutrinos, and quarks. To summarize: The Standard Model Neglecting gravitational phenomena, only two force fields pervade the universe: the electroweak force field, whose quanta are photons, Ws, and Zs, and the strong force field, whose quanta are gluons. And there are only six matter fields: three generations of electroweak matter fields and three generations of strong matter fields. Ordinary matter arises only from the two first-generation matter fields, whose quanta are electrons and electron-neutrinos interacting via the electroweak force, and u- and d-quarks interacting via the strong force. Second- and third-generation particles are unstable and existed only in the early moments of the big bang and today only briefly following highenergy microscopic events. The electroweak and strong particles, and their properties, are listed in Tables 1 and 2.

Table 2 The theory of the strong force. Throughout the universe there is a strong force field whose quanta are gluons and a strong matter field whose quanta are u-quarks and d-quarks. In addition, there are “second-generation” and “third-generation” matter fields whose quanta are listed below. Only the first-generation particles are stable and play a role in ordinary matter. Protons are made of u-u-d, and neutrons of u-d-d, bound together by the strong force acting between quarks. The unstable second- and third-generation particles decayed during the early moments of the big bang and exist today only during brief high-energy microscopic events. Generation

Particle type

Charge (proton = 1)

1

u-quark

0.003

+2/3

1

d-quark

0.008

–1/3

2

c-quark

1.4

+2/3

2

s-quark

0.1

–1/3

3

t-quark

3

b-quark Exchange particles: gluons

496

Mass (proton = 1)

185

+2/3

5.0 0

–1/3 0

Quantum Fields

The standard model represents an enormous unification of knowledge. Neglecting gravity, ordinary matter is a manifestation of only two matter fields and two force fields. Think of the material quanta (u-quarks, d-quarks, electrons, and neutrinos) as the bricks of the universe, and the force quanta (photons, Ws, Zs, gluons) as the cement. But the standard model cannot be the end of the story. For one thing, it does not incorporate gravity, leaving us with a nonquantum theory of gravity (general relativity) and a quantum theory of everything else. As you’ll see in the next section, this is unsatisfactory. For another thing, which I’ll now discuss, the standard model strongly suggests a new field whose quanta have not yet been observed but which might be observed soon. Because of E = mc2, 90% of the proton’s or neutron’s mass arises from the energy of the strong force fields between the quarks within these particles. So the standard model explains nearly all the mass of ordinary matter. But the standard model doesn’t explain why quarks and other particles in Tables 1 and 2 have mass in the first place. One widely supported hypothesis is that a new kind of fundamental field, called the Higgs field,3 exists throughout the universe. This field, created (like the other fundamental fields) during the big bang, permeates the entire universe in the sense that, except for photons and gluons, every particle interacts at all times with the Higgs field. Even completely isolated particles “feel” the Higgs field! This interaction acts on accelerated particles in such a way as to resist their acceleration, much as a vat of molasses resists the motion of any object that’s submerged in it. The interaction is stronger for quarks, W particles, and Z particles; weaker for electrons and neutrinos; and absent for photons and gluons. So the Higgs field confers a large mass (resistance to acceleration) on quarks, Ws, and Zs; a smaller mass on electrons and neutrinos; and no mass on photons and gluons. However, this molasses analogy is misleading on a couple of counts. First, molasses resists all motion, while the Higgs field resists only accelerated motion. Second, the Higgs field is not the only source of mass; for example, you’ve seen that the source of at least 90% of the proton’s mass arises from the interaction energy among its quarks via Einstein’s relation m = E>c2. Fortunately, this fantasy can be tested against reality. The Higgs field, like other fundamental fields, must obey relativity and quantum theory and so must interact in quantized bundles. High-energy particle accelerators might be able to create these Higgs particles within the next several years. The Higgs particle’s mass cannot be accurately predicted, but indirect evidence suggests it to be perhaps 200 proton masses—about the mass of a gold atom.4 Its large mass means, because of E = mc2, that enormous energy is needed to create it in high-energy physics experiments—energies that are beyond the reach of previous particle accelerators. However, the Large Hadron Collider (Figure 7) is coming online in 2009–2010, and physicists believe that it will spot the Higgs particle. If so, we will at last have an explanation of the ultimate origin of mass in the universe. It’s quite possible that, by the time you read these words, the Higgs particle will have been confirmed or, perhaps, disconfirmed! 3 4

The God Particle Title of a Book About the Higgs Particle, by Leon Lederman, Nobel Prize Winner and Former Director of Fermilab Near Chicago

After British physicist Peter Higgs, who invented this idea in 1964. You might wonder why such a particle, as heavy as a gold atom, cannot simply be discovered moving through space or within ordinary matter. The answer is that, like t-quarks and many other particles, Higgs particles are predicted to be extremely unstable, transmuting into other, less massive particles an instant after they are created. So they are around only briefly, following their creation in high-energy microscopic events such as the collision of two particles in a high-energy particle accelerator.

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CONCEPT CHECK 6 According to the standard model, which of the following are fundamental particles? (a) Proton. (b) Electron. (c) Positron. (d) Hydrogen atom. (e) Photon. (f) Water molecule. CONCEPT CHECK 7 Gluons move (a) slower than lightspeed; (b) at lightspeed; (c) faster than lightspeed.

6 QUANTUM GRAVITY: PHYSICS AT THE PLANCK SCALE Physicists are the Peter Pans of the human race. They never grow up, they keep their curiosity. I. I. Rabi, Physicist

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Physicists have had considerable success in unifying not only all known forces but also all known material particles. Except for gravity, all fundamental forces and all particles of ordinary matter have been shown to arise from just a handful of force fields and matter fields. The obvious parallels between the electroweak and strong forces (Tables 1 and 2) suggest that there should be a single grand unified theory that unites the electroweak and strong forces, although such a theory has not yet been found. But even an experimentally verified grand unified theory would leave gravity out of the picture. One reason it has been so hard to work gravity into these theories is that so little is known about it at the microscopic level because it is so weak at this level. For example, the gravitational attraction between two protons is a trillion trillion trillion times weaker than their electric repulsion. Only if there are large concentrations of matter, as in a planet or star, are gravitational effects strong enough to be easily observed. In large aggregations of matter, the electric effects of protons and electrons largely cancel each other, while gravity adds up because it’s always attractive, so gravity dominates. Einstein’s general theory of relativity has proven correct over an enormous range of phenomena. It is a nonquantum field theory whose field is the spacetime curvature that is caused by masses. The obvious path toward incorporating this theory with the theories of the other forces would be to subject the gravitational field to the principles of quantum theory. But this turns out to be no simple matter. General relativity describes gravity as a smooth curvature of space in response to the presence of mass. It works fine over astronomical distances and ordinary macroscopic distances. But over extremely small distances, the smooth curvature described by general relativity conflicts with the most basic quantum principle: the uncertainty principle. Here’s why. Recall that the uncertainty principle will not allow the microscopic world to sit still. A highly confined particle must have a highly uncertain speed and therefore a high average speed. In quantum field theory, this principle translates into fields whose motions at the smallest scale are highly agitated and uncertain. That is, if you enormously magnified a small volume of space, you would find the quantum fields in every tiny part of it are violently fluctuating like the surface of a rapidly boiling soup. The field we want to quantize is the gravitational field—the curvature of space. A quantum theory of the gravitational field would predict a violently fluctuating curvature of space at the smallest scale. As an illustration, Figure 16 shows a small region of space at five successive levels of magnification. Only at the fourth level of magnification do we begin to observe a little of the submicroscopic turbulence of the gravitational field—undulations of space itself. At the highest (fifth) level of magnification, space fluctuates violently, flying in the face of the smooth spatial curvatures described by general relativity. John Wheeler (Figure 17) describes this fluctuation of space as “quantum foam.”

Quantum Fields

National Renewable Energy Laboratory

Figure 16

Because these violent microscopic fluctions are too much for general relativity to handle, physicists run into absurd answers when they try to quantize the gravitational field. Typically, the probabilities of occurrence of certain microscopic events are predicted to be infinite, and other probabilities are predicted to be negative, even though these predictions are absurd because every probability must lie between 0 and 1. Physicists have made many ingenious attempts to overcome these difficulties. All have failed, except for one. That one is called “the string hypothesis.” I’ll describe it later. Taken together, general relativity and quantum theory predict a few fundamentals that are likely to prove valid in the long run regardless of which, if any, theory of quantum gravity is finally verified. One such fundamental is the graviton, the quantum of the gravitational field. Like photons (the quantum of the EM field), gravitons have zero mass and zero charge and move at lightspeed. From the quantum point of view, the gravitational forces between two bodies such as Earth and the moon occur via an exchange of gravitons between the two bodies. Gravitons have long been predicted but they have never been observed and perhaps never will be directly observed, because the gravitational force acting at the microscpic level is so weak. For example, if a single proton absorbs a graviton, the proton should recoil, but this recoil is predicted to be so tiny that one cannot hope to observe it. The basic numerical quantities or “constants” of general relativity and quantum theory would surely show up in any valid theory of quantum gravity. These are the speed of light, Planck’s constant, and the “gravitational constant” (6.7 * 10 - 11 in metric units) that fixes the strength of the gravitational force acting between two particular objects. These three constants of nature can be combined in such a way as to yield an estimate of the distance (between particles) at which we would expect quantum-gravitational effects to show up—in other words, the separation between two

A small region of space is taken through a series of five magnifications to reveal its submicroscopic properties. At the highest (fifth) level of magnification, we see the “quantum foam” predicted by quantum field theory. These violent fluctuations fly in the face of the smoother curvatures predicted by general relativity and create great difficulties for any attempt to quantize the general theory of relativity.

Roy L. Bishop, Acadia University/ American Institute of Physics/ Emilio SegreVisual Archives Figure 17

John Wheeler, a leading researcher in general relativity and the foundations of quantum theory, has just emerged from Black Hole, Nova Scotia. He appears somewhat dazed. His T-shirt proclaims, “I have experienced Black Hole, Nova Scotia.”

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Quantum Fields As an extreme possibility, it is possible that there is only one theory. . . that is consistent with the existence of intelligent beings capable of wondering about the final theory. If this could be shown, then we would be as close as anyone could hope to a satisfactory explanation of why the world is the way it is. Steven Weinberg

particles at which we expect their interaction to be significantly influenced by both gravitational and quantum effects. Because quantum effects happen mostly at microscopic distances, and because gravitational forces between two microscopic particles are so much weaker than other forces, it’s not surprising that this Planck length5 is tiny, in fact an ultramicroscopic 10 - 35 meters—10 trillionths of a trillionth of a trillionth of a meter! This is also the approximate spatial extent of the disturbances of Figure 16. In a similar way, a fundamental time duration can be worked out, the typical time during which significant changes (in, for instance, the mutual interaction of two particles) would occur when both quantum and gravitational effects are significant. Because the uncertainty principle implies that changes at these small distance scales must be rapid, this Planck time is extremely short: 10 - 43 seconds. Physicists can also work out the predicted energy of typical quantum-gravitational events. The uncertainty principle tells us that events within a region as small as the Planck length must be rapid and hence enormously energetic. This fundamental Planck energy turns out to be about a billion joules. This is not so large in our everyday world—it’s the amount of chemical energy in 8 gallons (about a gas tank) of gasoline. But this is an enormous amount of energy to pack into a submicroscopic distance. A billion joules has the mass (because of mass–energy equivalence) of some 1019 protons, which is surely colossal if packed into a volume measuring only 10 - 35 m across! This Planck mass is about 0.01 milligrams, the mass of a typical dust grain. The Planck length, time, and energy define the Planck scale, the approximate size, duration, and energy of typical quantum-gravitational phenomena. In the 1960s, John Wheeler pointed out a remarkable feature of nature at the Planck scale. He found that in a sphere whose radius is the Planck length and during time intervals whose duration is the Planck time, energy fluctuations as large as the Planck energy are likely to occur and that this much mass in such a tiny volume causes spacetime to bend back upon itself and form a black hole that is cut off from the rest of the universe. This phenomenon would break space and time into tiny bundles—quanta of spacetime itself—so that the Planck length and time are the smallest lengths and times that have any physical meaning at all! It’s difficult to observe such phenomena, because the energies of the microscopic events created at today’s high-energy accelerators are far smaller than the Planck energy. However, experiment and theory point to a significant trend: The differences among the fundamental forces diminish as the energy rises. The theory of the electroweak force suggests, for example, that at higher energies the weak force increases in strength until it is roughly as strong as the electric force. At still higher energies, the electroweak force becomes as strong as the strong force. And at even higher energies, namely the Planck energy, even the normally tiny gravitational force between microscopic particles becomes as strong as the other fundamental forces.

5

500

Around 1900, before there was a quantum theory of fields or even a completed quantum theory, Max Planck understood that this length, along with the time and energy discussed below, had universal significance.

Quantum Fields

Here’s why. Imagine pushing, say, two protons closer and closer. At “normal” microscopic separations, such as an atom’s size (10 - 10 m) or a proton’s size (10 - 15 m), the electric force is enormously larger than the gravitational force. But as the outside world does work to make the separation smaller, the forces get stronger and the energy in these force fields increases rapidly. But energy has mass, and mass always pulls gravitationally on other mass. So, as the separation decreases, the mass of the two protons increases, which causes the gravitational force to increase faster than the electric force. Eventually, the mass of the two protons becomes enormous, and in fact when the separation is the Planck length the mass becomes about the Planck mass. At this scale, the microscopic force of gravity about equals the strength of the electric force, and in fact all the forces become roughly equal. Among those who study quantum gravity, the predicted rough equality of all the fundamental forces at the Planck scale is a strong hint that these forces are aspects of a single underlying force, a unity that becomes obvious at the Planck scale. The string hypothesis6 is a beautiful and promising attempt to unify general relativity with quantum theory. Although it has had no direct experimental verification during its 25-year history, this hypothesis is good science because it does make specific verifiable predictions that should be tested soon, it does not conflict with any known results, and it could resolve fundamental issues. The string hypothesis’s key idea is that a fundamental particle such as an electron is not concentrated at one infinitely small point, but is instead a tiny loop— think of an infinitely slender rubber band—in a particular state of vibration. These loops are called strings. This spreading out of the point-particle model, so that it resides along a loop rather than at a single point, smoothes its effects on the space around it, smoothing the fluctuations in Figure 16 enough for them to be incorporated by general relativity. Strings are small, in fact comparable to—you guessed it—the Planck distance. Viewed from the nuclear or atomic scale, strings are so small that they appear indistinguishable from point particles—which is why we’ve always thought of them as point particles. Besides being able to move around in space, strings can vibrate. These vibrations are quantized, and quantum theory allows only particular “modes” (patterns, frequencies, energies) of vibration. According to the string hypothesis, each such mode of vibration is a different elementary particle: An electron is a string vibrating one way, a d-quark is a string vibrating another way, a photon is yet another string vibration, and so forth. Underneath all appearances, fundamental particles are really identical: They are all identical strings. Their different properties result merely from their different vibrational modes. The lowest-energy, and hence most stable, of these modes are the particles of ordinary matter—the first-generation particles and exchange particles of Tables 1 and 2.

6

It’s commonly called “string theory.” Because this text emphasizes the scientific process, I prefer the term hypothesis rather than theory, indicating the still-tentative, observationally unconfirmed, and incomplete nature of this wonderful idea. As I’ve emphasized before, the word theory is reserved for useful explanatory ideas that have been directly and repeatedly confirmed by observation. For more about the string hypothesis, check out www.superstringtheory.com. For nontechnical discussions, click “basics.”

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Quantum Fields

This sounds promising, but there is one small fly in the ointment. Strings remove the inconsistencies plaguing quantum theories of gravity only if the space around us is not 3-dimensional but instead 10-dimensional, plus one time dimension for an 11-dimensional spacetime. Fewer than 10 spatial dimensions produce logical inconsistencies, as do more than 10. But at exactly 10 spatial dimensions, everything is fine. Of course, this is absurd. Where could the other 7 dimensions be? Or is it absurd? Remember that the quantum-gravitational effects we want to describe happen only at tiny distances. What if the 7 extra dimensions were, somehow, very small (whatever that might mean), so small that we aren’t aware of them in our normal activities? In line with this suggestion, the string hypothesis assumes that the other 7 dimensions are tightly “curled up” at every point of our 3-dimensional space. To help you understand this, here’s an analogy.7 Think of a long straight garden hose. When you view it from afar, for instance from a balloon hovering a few thousand feet above your backyard, the hose appears to be a thin straight line, an “uncurved 1-dimensional space.” But as your balloon descends and you see the hose up close, you see that the hose’s surface is actually 2-dimensional, with the second dimension going around the hose in a circle. From the high-altitude balloon point of view, that second dimension is “curled up” and “small.” Once you accept general relativity’s notion that gravity curves space, the string hypothesis’s notion of 7 tightly curled spatial dimensions doesn’t seem so absurd. The curled-up dimensions exist at every point of our 3-dimensional space—just as the garden hose’s curled-up second dimension exists at every point along the hose—but people aren’t aware of them because the force of gravity (the only force that can directly detect curvatures in space) cannot probe such small distances in our normal world. In fact, even if an extra dimension were as large as 1 millimeter, it’s possible that it would not yet have been detected experimentally, because it’s difficult to detect variations in the gravitational force acting over such small distances. The string hypothesis specifies that strings, which do respond to the gravitational force at these small distances, stretch over the full 10 spatial dimensions. The many distinct manners in which these identical strings can wrap around and vibrate within the curled-up dimensions gives strings their distinct properties. Why on Earth would one entertain such an odd notion, especially when one lacks any real evidence? The reason is that at small distances, quantum field theory and general relativity contradict each other. Yet within their own domains, both theories are as theoretically compelling and as experimentally verified as any scientific theory ever invented. The domain of general relativity is the macroscopic and cosmological level, while the domain of quantum field theory is the microscopic level. There must be a logically consistent way to extend general relativity into the microscopic realm, because, after all, gravity doesn’t just vanish at microscopic distances. One observable verification of the need for a theory of gravity that extends into the microscopic realm is the collapse of the centers of galaxies and of some stars into black holes with all their matter concentrated within a microscopic volume that, according to general relativity, is actually a mathematical point. A correct theory of gravity should be able

7

502

This analogy, and Figure 16, come from Brian Greene’s fine nontechnical book for nonscientists and scientists, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (New York: Norton & Co., 1999).

Quantum Fields

to describe such microscopic phenomena without running into logical contradictions, but as you’ve seen, today’s “standard” quantum field theory is unable to do this. The only theory found so far that has some chance of resolving this is string theory.8 New theories should predict new things, or at least explain things not yet explained. For example, the existence of three generations of particles (Tables 1 and 2) might be explainable from general features of the geometry of the seven curledup dimensions. The string hypothesis also offers a framework for predicting the masses and other properties of every particle, such as why quarks are electrically charged the way they are. Unfortunately, the geometry of the seven curled-up dimensions is so complex that nobody has yet made such predictions. In the category of as-yet-unobserved phenomena, the graviton turns out to be one of the fundamental patterns of string vibrations. Since gravitons are the most widely expected feature of quantum gravity, this prediction indicates that gravity is woven into the fabric of the string hypothesis. Finally, the string hypothesis predicts that there is, in addition to the standardmodel particles, a new set of particles called “supersymmetric partners,” one for each particle of the standard model. They are called “supersymmetric” because, if the grand list of standard-model particles plus the proposed partners actually existed, there would be a certain beautiful symmetry between the material “building-block” particles (electrons, quarks, etc.) and the force-carrying exchange particles (photons, Ws, etc.). This idea, called “supersymmetry,” is found in many theories. It is expected to be confirmed (or perhaps disconfirmed), perhaps at the Large Hadron Collider. Supersymmetry emerges quite naturally from the string hypothesis, because patterns of string vibration turn out to come in pairs having just the right supersymmetric properties. The discovery of supersymmetry won’t confirm the string hypothesis, but it will put it on a more solid experimental foundation. This concludes our tour of quantum field theory, and it concludes this text (but do read the epilogue). When we consider general relativity, quantum physics, the string hypothesis, and other contemporary science, it’s clear that the natural universe holds possibilities that, to quote philosopher-scientist John Haldane, “are not only queerer than we suppose, but queerer than we can suppose.” Perhaps our universe is one among many universes, having their own spacetimes, having different spacetime dimensionalities, and having different physical laws. Perhaps, over many different “times,” an infinity of different universes passes into and out of existence, forming collectively a reality that occurs not in space and time at all but that is in some sense beyond space and time. In one such universe, in one galaxy called Milky Way, on one planet called Earth, you who read these words and I who write them are privileged beyond measure to be alive and to hold such ideas in our minds. Perhaps our best response to such an immense gift is simply “Thanks.”

8

Another hypothesis called “loop quantum gravity” has been proposed. It seems to be free of contradictions, and it doesn’t require extra dimensions. But it “pays” for this simplification by requiring spacetime itself to consist of movable loops.

503

© Sidney Harris, used with permission.

Quantum Fields

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Quantum Fields Problem Set Answers to Concept Checks and odd-numbered Conceptual Exercises and Problems can be found at the end of this section.

Review Questions

15. Name the exchange particle for the electric force. Name the four exchange particles for the electroweak force. 16. The electroweak particles are laid out in “generations.” Describe this pattern. How many generations are there?

QUANTIZED FIELDS 1. 2. 3. 4.

What two theories are combined to form quantum field theory? What is a field? What is a quantized field? Name the quanta of the EM field. Are electrons also “quanta”? Quanta of what?

QUANTUM ELECTRODYNAMICS AND ANTIMATTER 5. What role does the photon play in the electric force between two electrons? 6. Describe the events that are diagrammed in Figure 3(a) and (b). 7. What is a muon? A tau? 8. What is an antiparticle? Name two antiparticles. 9. What is antimatter? 10. Describe the creation of a particle–antiparticle pair. 11. Name and describe several devices used to observe the subatomic world. 12. Is empty space really empty? What happens there?

ELECTROWEAK UNIFICATION 13. Why is the neutrino so hard to detect? Which of the four fundamental forces does it experience? 14. Name the six particles that interact via the electroweak force.

THE STRONG FORCE 17. Name the fundamental (not composite) particles responsible for the strong force. 18. How were quarks discovered? 19. Are protons fundamental particles? If they are composite particles, of what are they composites? What about electrons? 20. What force or forces do quarks exert on one another? 21. One property of quarks is that they exert and feel the strong force. List at least two other properties. 22. How many kinds of quarks are there? How many of these are found in ordinary matter? 23. Name the exchange particles that carry the strong force. 24. Why do we never observe an isolated quark?

QUANTUM GRAVITY 25. Which of the four fundamental forces can be felt over macroscopic distances? 26. What is a graviton? Has it been discovered experimentally? If so, how? If not, why not? 27. What is the significance of the Planck length and time? 28. What is the string hypothesis? 1

2

Position

Position

1

Time 2 Time (a)

(b)

Figure 3

(a) A Feynman diagram for a series of interactions between two weakly interacting (i.e. only low-energy photons are exchanged) electrons. The electrons’ paths approach smooth Newtonian paths. (b) At stronger interactions (high-energy photons), the paths deviate considerably from smooth paths, and Newtonian physics is no longer a good approximation. From Chapter 17 of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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Quantum Fields: Problem Set

Conceptual Exercises

Problems

QUANTUM ELECTRODYNAMICS AND ANTIMATTER

QUANTUM ELECTRODYNAMICS AND ANTIMATTER

1. In Figure 6(a), what is the evidence that each pair consists of two oppositely charged particles? 2. In Figure 6(a), which of the two pairs has the fastermoving particles? How do you know? 3. In Figure 6(a), why don’t we see the tracks of the two photons that created the two pairs? 4. Each of the two photons created when an electron–positron pair annihilates has a frequency of about 1020 Hertz. To what region of the EM spectrum do these photons belong? If the electron and positron were moving instead of at rest, would it make this photon frequency higher or lower? 5. How would the photograph of Figure 4 be altered if the particle track had been made by an electron moving upward instead of a positron moving downward?

ELECTROWEAK UNIFICATION 6. Of the 10 electroweak particles (Table 1), which ones travel at or near lightspeed? 7. Of the 10 electroweak particles (Table 1), which ones can feel the electric force? Which can exchange photons? 8. Into which one of the boxes of Figure 10 should the discovery of beta decay be placed? 9. In what ways are the W and Z particles similar to photons? In what ways are they different?

THE STRONG FORCE 10. According to the standard model, which of the following are elementary: neutrino, neutron, quark, muon, photon, antiproton? 11. In what ways are gluons similar to photons? In what ways are they different? 12. In what ways are quarks similar to electrons? In what ways are they different? 13. Give at least one specific reason (other than a general belief in unity) why scientists believe there is probably a single theory that can unite the electroweak and the strong force into a single grand unified force. 14. According to Table 2, the total rest-mass of the two u-quarks and one d-quark that make up a proton seems to be only 0.003 + 0.003 + 0.008 = 0.014 proton mass! Where does the remaining mass of the proton come from?

QUANTUM GRAVITY 15. In the past, it was assumed that the fundamental particles occupied only isolated geometrical points. Why does the string hypothesis assume that they are shaped like tiny loops of string? 16. Explain how a garden hose illustrates the notion of small, curled-up dimensions.

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(You’ll need to use the formula E = hf for some of these.) 1. Each of the two photons created when an electron–positron pair annihilates has a frequency of about 1020 Hertz. Find the energy of each photon. 2. A proton–antiproton pair, at rest, annihilates and creates two photons. Using the information in the preceding problem, and the fact that a proton is 1800 times more massive than an electron, find the frequency of each photon. 3. A proton–antiproton pair, at rest, annihilate and create two photons. Find the energy of each photon from the fact that a proton’s mass is 1.7 * 10 - 27 kg. Use this energy to find the frequency of each photon, and compare your answer with the preceding problem. 4. MAKING ESTIMATES A large electric power plant generates 1000 MW of electricity. If the energy came from matterantimatter annihilation, estimate the total mass of matter and of antimatter that would be required each year, assuming that the electricity is generated at an energy efficiency of 50%. 5. MAKING ESTIMATES Suppose 1 gram of matter is annihilated with 1 gram of antimatter. Show that the resulting energy could lift the entire U.S. population of about 300 million by about 1 km.

Answers to Concept Checks 1. (b), (d), (e) 2. Twenty percent of 400 is 80 pairs, or 160 particles. However 3. 4. 5. 6. 7.

this is only approximate, due to quantum uncertainties, (a). All four. (a), (c), (e) 2>3 - 1>3 - 1>3 = 0, (a) (b), (c), (e) (b)

Answers to Odd-Numbered Conceptual Exercises and Problems Conceptual Exercises 1. Both the upper pair of tracks and the lower pair of tracks curve in opposite directions, indicating the forces on the pair of charged particles are in opposite directions, so the particles must have opposite charges. 3. Photons are not charged, and only charged particles make tracks in bubble chambers. 5. The portion of the track below the barrier would have been straighter than the portion above the barrier. 7. The charged particles: electron, muon, tau, W + and W - . These are also the particles that can exchange photons, because microscopically “exchanging photons” is what we mean by “feeling the electric force.”

Figure 6

(a) A bubble-chamber photograph of electron–positron pair creations, caused by gamma-ray photons. In the event at the top, a photon has struck an atomic electron and knocked it out of its atom (long curving line), and it simultaneously created an electron–positron pair (tightly curling spirals). Why can’t you see the path of the photon? Toward the bottom, a different photon creates an electron–positron pair. How can you tell that each pair has two particles of opposite charge? Of the two pairs, which pair has the highest energy and speed?

Ernest Orlando Lawrence Berkeley National Laboratory

Quantum Fields: Problem Set

Ernest Orlando Lawrence Berkeley National Laboratory Figure 4

The photo that won a Nobel Prize. This photo alone established the existence of a positive electron. (a)

Figure 10 Space

Some of the unifications in physics. The dashed lines represent unifications not yet established. Time runs from top to bottom. Electricity

Time

Heavenly motions

Earthly motions

Newton’s mechanics

Newton’s gravity

Magnetism Light

Electromagnetism

Electromagnetic field theory

Quantum theory

Special relativity General relativity

Quantum electrodynamics

Electroweak theory

Weak force

Strong force

Grand unification Theory of everything

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Quantum Fields: Problem Set Table 1 The theory of the electroweak force. Two fundamental electroweak fields pervade the universe: an electroweak force field whose quanta are the four exchange particles listed below, and an electroweak matter field whose quanta are the electron and the electron-neutrino. In addition, there are “second-generation” and “third-generation” matter fields whose quanta are listed below. Generation

Particle type

Mass (proton = 1)

1

electron

1

electron-neutrino

2

muon (mu electron)

2

muon-neutrino

3

tau (tau electron)

3

tau-neutrino

Charge (proton = +1)

0.0005

–1 0

a a

0.11

–1

a

0

1.90

–1 0

a

Exchange particles: photon

0

0

+

86

+1

W-

86

–1

Z

98

0

W

a

The three types of neutrinos have small but nonzero rest-masses, although the values are uncertain. The sum of the three masses of all three types of neutrinos is known to be less than 1 millionth of an electron’s mass.

Table 2 The theory of the strong force. Throughout the universe there is a strong force field whose quanta are gluons and a strong matter field whose quanta are u-quarks and d-quarks. In addition, there are “second-generation” and “third-generation” matter fields whose quanta are listed below. Only the first-generation particles are stable and play a role in ordinary matter. Protons are made of u-u-d, and neutrons of u-d-d, bound together by the strong force acting between quarks. The unstable second- and third-generation particles decayed during the early moments of the big bang and exist today only during brief high-energy microscopic events. Generation

Particle type

Charge (proton = 1)

u-quark

0.003

+2/3

1

d-quark

0.008

–1/3

2

c-quark

1.4

+2/3

2

s-quark

0.1

–1/3

3

t-quark

3

b-quark Exchange particles: gluons

508

Mass (proton = 1)

1

185

+2/3

5.0 0

–1/3 0

Quantum Fields: Problem Set 9. Similarities: the W and Z are exchange particles; the Z is

uncharged. Differences: the W and Z have rest-mass; the W is charged; the W and Z move at less than lightspeed. 11. Similarities: both are exchange particles; both are uncharged and massless and move at lightspeed. Differences: gluons exchange the strong force, and photons exchange the electric force; gluons feel the strong force (the same force that they exchange), but photons do not feel the electric force (the force that they exchange). 13. Tables 1 and 2 show considerable similarity between the two forces: There are three “generations” of weak particles, and three generations of strong particles; the weak force operates by means of exchange particles, and so does the strong force. Another reason is that it was possible to unify the electric and magnetic forces into a single electromagnetic force, and it was possible to unify the electromagnetic and the weak forces into a single electroweak force, so it is plausible that the electroweak and strong forces might be unified into a single force. 15. The string hypothesis seems plausible because strings aren’t concentrated at a single point as point particles are. Thus, we expect this hypothesis to smoothe out the extreme fluctuations, shown in Figure 16, that are the source of the problem of unifying gravity with quantum theory.

Problems 1. E = hf = (6.6 * 10 - 34 J-s) * (1020 Hz) = 6.6 * 10 - 14 J. 3. Each photon’s energy is mc2, where m represents the mass of either a proton or antiproton (they have the same mass). Thus, E = mc2 = (1.7 * 10 - 27 kg) * (3 * 108 m>s)2 = 1.5 * 10 - 10 J. From E = hf, each photon’s frequency is f = E>h = 1.5 * 10 - 10 J>(6.6 * 10 - 34 J>Hz) = 2.3 * 1023 Hz. 5. 2 g, or 0.002 kg, of rest-mass is annihilated. The energy of this mass is E = mc2 = (0.002) * (3 * 108)2 = 1.8 * 1014 J. Assume that the average weight of a U.S. citizen is 600 N (about 130 pounds). Then the weight of the U.S. population is 300 * 106 * 600 N = 1.8 * 1011 N. Since GravE = weight * height: height = energy>weight = 1.8 * 1014 J>1.8 * 1011 N = 1000 m = 1 kilometer!

509

510

EPILOGUE: SUMMING UP

From Epilogue of Physics: Concepts & Connections, Fifth Edition, Art Hobson. Copyright © 2010 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved.

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EPILOGUE: SUMMING UP Science is much less a body of knowledge than it is a way of thinking, and that way of thinking, with its characteristic mix of rigorous skepticism and openness to new ideas, is desperately needed in every area of our lives—including social, economic, political, and religious arenas. Carl Sagan

Tree Souls, by U.S. sculptor Alison Saar, portrays humankind’s dependence on Earth for physical and spiritual survival.

512

We have come some distance together, you and I, since we started this text. Now we are at journey’s end. Let’s step back and view the landscape through which we have passed. The details were connected by four recurring themes: the scientific process, modern physics and its significance, energy, and the social context of physics. Occasionally when I talk with groups on the social context of physics, I ask them to name some significant contemporary social issues. It doesn’t take long to accumulate quite a list: terrorism, overpopulation, extinction of species, drug abuse, global warming, AIDS, poverty, and so forth. As we search for common themes among them, it becomes apparent that each has a significant science and technology component. Science confers great power, power that is often both helpful and harmful. For instance, because medical science has extended our lives (that’s good), we now have an overpopulation problem (that’s bad). We have accepted science’s help in solving the death problem but have not taken responsibility for the birth problem. For another example, when you start your automobile you bring great power to bear on yourself and on the planet. The speed is exhilarating, but global warming and other problems testify to the dark side of the equation. The problems of science and society come down to this: Humankind is not paying its dues for the fruits of the scientific age. We are quick to accept the convenience of cars and the miracles of medicine, but slow to solve our fossil-fuel problem or to control our birthrate. We dare not accept science’s benefits without also taking on its responsibilities. Speaking as a science teacher who is doubtless prejudiced in the matter, my first suggestion is that all of us learn much more science. Humankind commands enormous power today, with little knowledge. We had better try harder to understand what we are doing, for power without knowledge is a prescription for disaster. Energy unifies all physics and can organize our thinking about every physical process. I hope you have picked up the habit of visualizing physical processes as transformations of energy. It’s a fundamental principle of physics that energy, not matter, is the “stuff ” of the universe. Modern physics tells us the processes of the universe are not simply mechanical motions of matter, but are more appropriately viewed as transformations of various sorts of energy fields that fill the universe. Socially, our culture must get a grip on our use of energy resources if we are to fashion a prosperous future. We will soon face the end of the fossil-fuel age—a challenging but exciting prospect. You can help. Modern physics and its significance touches deeply upon the cultural roots of industrial civilization. Modern culture still assumes that the Newtonian clockwork universe represents science’s view of reality. This materialistic worldview leaves little room for freedom, chance, creativity, or spiritual values.

EP I LO GU E

But modern physics paints a non-Newtonian picture of fields and energy structured by relativity and quantum theory. Many nonmechanical forms of energy operate in the modern universe, and reality emerges not as a predictable clockwork but as a dynamic and unpredictable network of energy. This is nearly the opposite of a clock. It’s not clear what worldview will emerge from this. Our Newtonian culture is only beginning to absorb the impact of relativity and quantum theory. After all, more than a century elapsed after Copernicus’s death before Europe began to absorb the cultural impact of postmedieval science. So it’s not surprising that the first postNewtonian century was not the twentieth, but will probably be the twenty-first. One practical example of the importance of transcending the Newtonian worldview is the ongoing reaction, in the United States at least, against the theory and observed fact of biological evolution. The reaction comes from a perceived threat to religious beliefs. Religious fundamentalists typically view evolution as deterministic and materialistic, with no room for spiritual values. This appears to be a reaction to evolution as interpreted through Newtonian physics rather than a reaction to evolution itself. A post-Newtonian culture might relieve us of such religious anxieties about science. I hope that the main message you’ve gathered from this text concerns the scientific process. We have often inquired: How do we know? Science’s answer is surprisingly simple: We know by experience, as interpreted by rational thought. It’s a simple but demanding code: Take nothing for granted, form conclusions on the basis of careful observation and honest thinking, and be willing to modify those conclusions in the light of new experience. In other words: Trust the universe. With today’s powerful technologies, we could all be living like kings and queens if we had played our cards right. But we’re not living like kings and queens. In fact, large parts of the globe, including millions in the United States, live in poor and miserable conditions. What’s wrong? Perhaps the answer is that most ideologies are not arrived at by anything resembling careful observation or honest thinking and are seldom open to doubt in the light of new experience. Yet most believers of those ideologies are absolutely convinced they are right. The results of their dogmatism are all around us: fanaticism, war, terror, persecution, prejudice, and suffering. Science’s view of this is that the danger lies not so much in the beliefs themselves as in their absolute nature. Even wrong or harmful beliefs can be corrected if one is willing to trust experience and be intellectually honest. Even correct and healthy beliefs can become dangerous if accepted as absolute truth. In thinking about how we might do better in the twenty-first century than we did in the twentieth, we should perhaps ponder science’s most basic value: All ideas are subject to testing by experience and to challenge by critical rational thought. It is a code that has worked surprisingly well for science. It might be science’s most important benefit.

Only by the fusion of science and the humanities can we hope to reach the wisdom appropriate to our day and generation. I. I. Rabi, Physicist

For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world. Max Born, Physicist

513

514

515

#

1

Ra Radium

Fr Francium

89–103†

58 Ce Cerium

90 Th Thorium

57 LA Lanthanum

89 Ac Actinium

105 Db Dubnium

104 Rf Rutherfordium

24

Pa Protactinium

91

Pr Praseodymium

59

Sg Seaburgium

106

W Tungsten

74

Mo Molybdenum

42

Cr Chromium

These elements have been discovered but not yet named.

Actinides

†

*Lanthanides (Rare Earth Metals)

88

87

Ta Tantalum

73

72 Hf Hafnium

57–71*

56

Ba Barium

55

Cs Cesium

41 Nb Niobium

40 Zr Zirconium

39

Y Yttrium

38

23 V Vanadium

22 Ti Titanium

21

Sc Scandium

Sr Strontium

Ca Calcium

K Potassium

37

20

19

Rb Rubidium

12

Mg Magnesium

11

Na Sodium

4

Be Beryllium

3

Li Lithium

H Hydrogen

U Uranium

92

Nd Neodymium

60

Bh Bohrium

107

Re Rhenium

75

Tc Technetium

43

Mn Manganese

25

Np Neptunium

93

Pm Promethium

61

Hs Hassium

108

Os Osmium

76

Ru Ruthenium

44

Fe Iron

26

Transition Metals

METALS

Pu Plutonium

94

Sm Samarium

62

Mt Meitnerium

109

Ir Iridium

77

Rh Rhodium

45

Co Cobalt

27

Am Americium

95

Eu Europium

63

Ds Darmstadtium

110

Pt Platinum

78

Pd Palladium

46

Ni Nickel

28

Cm Curium

96

Gd Gadolinium

64

Rg Roentgenium

111

Au Gold

79

Ag Silver

47

Cu Copper

29

30

48

Zn Zinc

Bk Berkelium

97

Tb Terbium

Cf Californium

98

Dy Dysprosium

66

113#

112#

65

Tl Thallium

81

In Indium

49

Ga Gallium

31

Es Einsteinium

99

Ho Holmium

67

114#

Pb Lead

82

Sn Tin

50

Ge Germanium

32

14 Si Silicon

13 Al Aluminum

6 C Carbon

5

Fm Fermium

100

Er Erbium

68

115#

Bi Bismuth

83

Sb Antimony

51

As Arsenic

33

P Phosphorus

15

N Nitrogen

7

Md Mendelevium

101

Tm Thulium

69

116#

Po Polonium

84

Te Tellurium

52

Se Selenium

34

S Sulfur

16

O Oxygen

8

9

No Nobelium

102

Yb Ytterbium

70

At Astatine

85

I Iodine

53

Br Bromine

35

Cl Chlorine

17

F Fluorine

Metalloids and Non-metals

B Boron

Hg Mercury

80

Cd Cadmium

Periodic table of the elements 2

Lw Lawrencium

103

Lu Lutetium

71

118#

Rn Radon

86

Xe Xenon

54

Kr Krypton

36

Ar Argon

18

Ne Neon

10

He Helium

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FLOW CHART OF TOPICS This chart shows the text’s main topics and connections between them. It organizes three topical categories—Newtonian, modern, and societal physics. These topics can then be used to create several different course structures: general physics (all three categories), Newtonian emphasis, modern emphasis, and societal emphasis. For further details on alternative course structures, see the Instructor Resource Manual.

Societal

Newtonian

Modern, philosophical

Invitation to science

Atoms and molecules

Inertia Motion Newtonian mechanics Newtonian gravity Energy for transportation Electric power plant Energy Thermodynamics

Scientific method Pseudoscience

Newtonian worldview

The law of entropy

Exponential growth

Ozone depletion

EM force Planetary atom EM fields

Waves EM waves

Special relativity

General relativity Cosmology

Global warming Quantum physics Uncertainty Nonlocality Radioactive dating and geological ages

Biological effects of radiation Technological risk

Modern worldview

Quantum atom

The nucleus Radioactivity

Fusion and fission Nuclear weapons Nuclear terrorism The energy future Nuclear and fossil Renewables Efficiency

Quantum fields and standard model

Quantum gravity

517

518

Index Page references followed by "f" indicate illustrated figures or photographs; followed by "t" indicates a table.

A A ring, 254 Absolute zero, 74, 171, 306, 318 Absorption, 480 Accelerating reference frames, 323 accelerating universe, 1, 300, 313, 321-322 Acceleration, 5-6, 8, 72, 81-85, 87, 89-91, 94-105, 107, 109, 113-117, 121, 123, 127, 141-144, 164, 177, 275, 285-287, 293-294, 299-301, 314-315, 464, 497 and air resistance, 89 and mass, 94, 100, 287, 293 average, 6, 87, 89-91, 177, 287 cosmic, 8, 299, 314-315, 321-323 due to gravity, 83, 87, 100, 116-117, 294, 323 force and, 6, 94-95, 114, 224 instantaneous, 1, 6, 81 straight-line motion, 121 Acceleration due to gravity, 83, 87, 116, 294 acid rain, 186, 424-425, 437 Acidity, 256 acids, 394 actinides, 515 Action, 1, 5, 76, 94, 246, 249-251, 258, 357, 385, 467, 469 Action at a distance, 357 Addition, 12, 68, 73, 110, 117, 170, 237, 256, 289, 339, 369, 380, 389, 436, 488-490, 496, 503 aerosols, 263 Air, 17, 40, 53-56, 59-60, 63-66, 67-70, 73-79, 82-84, 87-91, 95-97, 100-101, 105-107, 109, 114-117, 123, 137, 141-142, 150, 152, 158, 170, 173, 175, 181, 183-184, 186, 194, 196-198, 235-236, 246-248, 252-253, 261, 310, 314, 364, 389-390, 399-401, 403, 433, 439, 481-482 density, 5, 55 Air conditioners, 158, 246, 439 air pressure, 63, 68, 165, 399 air resistance, 1, 74-77, 79, 83-84, 89-91, 95, 100-101, 105-107, 114-117, 123, 141-142, 150, 152, 155-156, 161-165, 173, 178, 181, 183 alloy, 41 Alpha Centauri, 263 Alpha decay, 1, 5, 389-392, 405-406, 488 Alpha particle, 1, 204-205, 389-392, 406, 460, 473-474 Alpha particles, 204-205, 392, 399, 406, 457-458, 460, 473, 484 Alpha rays, 5-6, 389, 400, 405 Alternating current, 1, 208, 245 altitude, 40, 77, 122, 125-126, 128, 142, 247 altitudes, 32, 77, 407 Aluminum, 98, 215, 457, 460, 515 Amino acid, 394 amino acids, 394 Ampere, 210-211, 221 Amplitude, 229-230, 261, 265, 326, 340 of waves, 229 Andromeda, 37, 299 Andromeda galaxy, 37 angular distance, 303 Angular momentum, 128, 153 conservation of, 128, 153 rotational, 128, 153 Angular position, 27, 32 Animals, 40, 65-66, 156, 176, 184, 188, 243, 263, 319, 395-396, 412-413, 435 annihilation, 3, 7, 289-290, 474, 477, 482-483, 486 Antarctic ozone hole, 250 Antennas, 142 antielectron, 1, 291, 295-296

Antimatter, 7, 289, 474, 477, 482-485, 487, 496, 505-506 Antimony, 515 antineutron, 1, 482 Antiparticle, 3-4, 7, 10, 13, 482, 484, 486-487, 491, 505 Antiparticles, 290, 295, 482-483, 487, 494, 505 antiproton, 1, 290, 482, 487, 506, 509 Antiprotons, 1, 289, 483 antiquark, 495 Aquifers, 426 arcminutes, 31 Area, 24, 183, 196, 198, 207, 234, 246, 248, 255, 257, 296-297, 446-447, 471-472, 512 Aristarchus, 1-2, 25, 29, 34, 36 Aristotle, 24, 38, 47, 60, 72-76, 87, 91, 120-121, 135 asteroid, 107 asteroids, 106, 402 Astrologer, 31 astrology, 18, 40-42, 45, 47 Astronomical unit, 47 astronomical unit (AU), 47 astronomy, 17-18, 28, 30, 33, 37-39, 42, 45, 74, 78-79, 121, 132-135, 395 ancient, 18, 28, 45, 135 defined, 1 history of, 18, 30 study of, 18, 135, 299 astrophysics, 303 atmosphere, 9, 12-13, 40, 53, 59, 68-70, 77-78, 88, 90, 105, 115, 132, 177-178, 185-186, 245, 247-255, 257, 262-263, 267, 399, 416, 426, 432, 486, 491 composition of, 247, 394 gravity and, 13, 77 heat and, 2 of Earth, 77, 250-251, 254-255, 265, 393, 407, 446 origin of, 2, 59, 407 ozone hole, 248, 250 ozone in, 248 primary, 247, 253 secondary, 12 solar, 9, 12-13, 245, 247-248, 250, 263, 267, 296, 394, 416, 432, 491 structure of, 9, 59, 394 Atmospheric pressure, 246 atomic hydrogen gas, 371 atomic mass, 474 Atomic model, 10-11 atomic nucleus, 58, 202, 204, 289, 316, 477, 484 Atomic number, 52, 205, 221, 386-387, 389-391, 405-406, 410, 459-460, 462, 474-475 Atomic physics, 387, 483 atomic spectra, 364, 371, 376 Atomic structure, 348 Atom(s), 4 atoms, 8-10, 13-14, 16, 21, 43, 49-66, 67-70, 74, 97, 101, 128-131, 133-134, 136-137, 152, 178, 198, 202-208, 212, 215, 221-222, 236, 239-244, 246-247, 251, 253, 263, 265-267, 286, 290, 309, 311, 318, 363-364, 369-371, 384-387, 409-410, 424-425, 434, 438, 474-475, 483-484, 517 atomic mass, 474 atomic number, 1-2, 52, 205, 221, 386-387, 390, 406, 410, 474-475 characteristics of, 53 electricity and, 236, 270, 424, 438 electrons, 1-4, 8-10, 13-14, 50, 58-59, 63, 101, 129, 131, 202-208, 212, 215, 221-222, 224, 236, 242-244, 266, 290, 336, 345, 351, 367, 370, 381, 385-386, 390, 438, 483-484, 493-494 elements, 13, 52-54, 63-64, 67-70, 202, 205, 221, 307, 386-387, 474, 493 Atom(s) first, 4

atoms isotopes, 307, 387, 390, 394, 400, 406, 409-410 kinds of, 52-54, 63, 202, 212, 221, 240-241, 263, 307, 311, 366, 385-386, 478, 493 neutrons, 8-9, 50, 63, 152, 203-204, 242, 266, 290, 307, 311, 318, 336, 341, 381, 385, 387, 474-475, 493-494 periodic table, 9, 52, 66, 67-69, 198, 386-387, 406, 409, 493 planetary model of, 10, 63, 202-204, 221-222, 366, 369, 376 properties of, 13, 205, 241, 386, 493 protons, 1-2, 8-9, 50, 63, 152, 203-206, 224, 242, 266, 290, 307, 309, 311, 318, 336, 338, 345, 351, 381, 483-484, 486, 493-494 size of, 2, 60, 131, 202, 241, 243-244, 265, 333, 353 structure of, 9, 59, 152, 241, 270, 386, 394 subatomic particles, 21, 133-134, 203, 221, 263, 493 AU, 47-48, 515 Average power, 163 Average speed, 6, 80, 87, 89-92, 287, 386, 498

B background radiation, 60, 244, 307, 309, 315, 318, 322 cosmic, 60, 307, 309, 315, 318, 322 bacteria, 66, 188 balloon analogy, 314 bar, 214-217, 221, 223-224, 288, 481 Bar magnets, 215-216, 221, 288 bars, 223-224, 255 Batteries, 179-182, 195, 206, 208 recharging, 181 Beam, 3, 7, 58-59, 90, 101, 152, 203, 236, 243, 270, 273-280, 287-288, 293-294, 302-304, 330, 333-337, 364-365, 398, 484-485, 494 spread, 330, 333, 335-337 width, 59, 285, 303-304 Bell, Jocelyn, 133 Beryllium, 454, 456-457, 474, 515 Beta decay, 5, 14, 154, 385, 390-391, 405-406, 410, 473, 488-489, 506 Beta particle, 1, 390, 462, 488-489 Beta particles, 390-391, 488 Beta rays, 1, 5-6, 389-390, 398, 400 Betelgeuse, 132 Big Bang, 42-43, 59, 175, 244, 300, 306-311, 313-314, 316-319, 321-323, 352, 452, 455-456, 473, 481, 483, 486-487, 489, 491, 496-497 evidence for, 43, 237, 306-308, 323 Big Bang model, 318 Big Bang theory, 306-307 Big Crunch, 313 Big Dipper, 18-19 Biological evolution, 16, 42, 176, 398, 513 biology, 12, 17, 38, 42-43, 45, 65, 282, 326, 395, 470 biomass, 1-2, 413-417, 431-432, 438, 441, 443-444, 446-447 birds, 25, 29, 78 black hole, 132-135, 139, 141, 143, 305, 311, 456, 487, 499-500 Black holes, 1, 3, 54, 133-135, 138, 153, 305, 309, 311, 314, 485-486, 502 geometry, 309, 314 mass of, 133-135, 305, 311, 314 size of, 485 bladder, 60 blood, 53, 65, 398-399 blood vessels, 398 Bohr, Niels, 62, 154, 325, 339, 363, 370, 459, 461 Boiling, 55, 91, 169, 184, 193-194, 296, 421, 498 of water, 91, 169, 296 Boiling point, 91 Bone, 397-399 bone marrow, 398-399

519

Boron, 420, 454, 515 boson, 299 Bosons, 485 Boyle, Robert, 136 Brahe, Tycho, 31, 33, 395 brain, 60, 102, 137, 243, 271 Breeder reactor, 1, 422, 424, 442, 446 bremsstrahlung, 154 brightness, 26, 313-314, 340, 343 bromine, 53, 69, 515 Brown, Robert, 51 Brownian motion, 1, 51, 54, 58, 63, 68 Brushes, 218 Bubble chamber, 1-2, 481, 484 bulge, 47, 93 stars in, 47

C Calculations, 2, 10, 32, 51, 250, 254, 290, 307, 315, 361, 459-460, 468 calendar, 42 calorie, 2, 4, 155-156, 161 Camera, 76, 227-228, 263, 331 Cancellation, 230, 327 cancer, 249-250, 398-403, 405, 407-408, 410, 430 carbohydrates, 66 Carbon, 1-3, 9, 12-13, 43, 54, 63-66, 67-70, 178, 186, 202-203, 222, 227, 249-254, 256, 258-260, 263, 265, 267, 392-394, 396-397, 400, 405-406, 408-410, 424-427, 431-432, 437, 444, 456 forms of, 1, 9, 475 Carbon atom, 67, 222, 393, 409 Carbon dating, 2, 254, 393-394, 396-397, 405-406, 408 Carbon dioxide, 9, 12-13, 43, 54, 64-65, 67-69, 186, 251-253, 256, 424, 431, 444 on Mars, 251 carbon monoxide, 65, 67, 178 Carbon-12, 387 carbon-13, 387 Carbon-14, 387 Cars, 91, 105, 116, 176-178, 180-184, 260, 270, 407, 410, 418 Cathode, 203 Cathode rays, 203 cells, 9, 179, 181-182, 243-244, 246, 397-400, 416-417, 427, 432-435, 438, 442, 444, 446 animal, 397, 416 plant, 9, 181, 399, 416, 432-433, 435, 438, 442, 444 types of, 9, 398, 435 Celsius scale, 169 CFCs, 2, 9, 246-250, 256, 261, 263, 267 Chain reaction, 2-3, 5, 401, 419, 421-422, 444, 451, 458, 460-461, 463, 465, 468, 471, 473-475 changes, 6, 24, 48, 65, 69, 80-83, 87, 91, 107, 146-147, 200, 236-237, 256-258, 289, 360, 394, 397-398, 416-418, 500 chemical, 52, 65, 69, 289, 376, 416, 453, 500 physical, 6, 52, 146, 289, 360, 398, 500 Charged particles, 3, 7, 9, 202-203, 206-207, 215, 221, 366, 480-482, 484, 488, 506 interactions, 7, 480-481, 488 Charges, 3-4, 165, 201, 205-206, 213-216, 222, 224, 237, 319 conservation of charge, 206 like, 201, 216, 224, 506 moving, 3-4, 165, 215-216, 224, 237, 506 opposite, 201, 203, 205, 213-214, 224, 506 source, 3, 203, 205, 213, 237 Charging, 4, 200, 205 chemical composition, 67, 259, 365, 376 chemical compounds, 1-2, 56, 64, 68 Chemical elements, 13, 52, 221, 307, 322, 487 atomic number, 52, 221 periodic table, 52, 473 spectra, 307 chemical energy, 1-2, 8, 109, 152-153, 156, 158, 162-163, 165, 173, 176-179, 181-182, 186, 194, 416, 432, 486, 500 chemical formula, 54, 68-69 chemical properties, 1, 205, 386-387, 391, 493 chemical reactions, 2, 49, 64, 67-68, 152, 175, 202, 208-209, 248, 251, 289, 364, 386-387, 430 combustion, 289 electrons, 2, 202, 208-209, 289 energy, 2, 49, 152, 175, 202, 208-209, 248, 251, 289, 364, 430

520

entropy, 175 protons, 2, 152, 209, 289, 387 chemistry, 17, 40, 42, 64, 67, 247, 249, 326, 366, 371, 386, 388, 395, 397, 470 compounds, 2, 64, 69, 247 elements, 2, 64, 67, 69, 386 Chinese, 41, 47, 72 Chips, 326 Chlorine, 2, 53-54, 66, 68-69, 205, 246-248, 250, 264, 515 Chlorofluorocarbons (CFCs), 2, 246 Circuits, 199, 201, 208-211, 221-223, 243-245, 326, 439 diagrams, 222 elements, 209, 211, 221 short circuit, 221 Circular motion, 13, 28, 33, 45-46, 127, 305 orbits, 28, 33, 45 uniform circular motion, 13, 28, 33, 45 Circular orbits, 10, 135, 311 Circular waves, 232, 262 climate, 2, 6, 57, 227-260, 261-267, 396, 411, 426-427 Moon and, 263 clocks, 11, 13, 87, 96, 273, 279-281, 283-285, 293-294, 304 Closed universe, 2, 5, 309-310 Cloud chamber, 1-2, 481-482 clouds, 12, 25, 29, 40, 128, 131, 248, 318, 360 Cluster, 312 galaxy, 312 cluster of galaxies, 312 Clusters, 59-60, 306, 318-319, 352 coal, 5, 12, 68-69, 146, 161, 173, 179, 184-187, 195-196, 198, 260, 295, 403, 408, 412-417, 423-427, 430-433, 435-438, 441-444, 446-447 Coils, 224 collision, 107-110, 116, 244, 305, 438, 457, 486, 497 Collisions, 74, 107, 109, 389, 486 Color, 42, 53, 61, 158, 163, 234, 243, 250, 328, 343-345, 365 of stars, 365 colors, 13, 243, 344, 364-365, 367 Columbus, Christopher, 28 Combustion, 4, 6, 9, 12, 65, 106, 173, 177-179, 184, 193, 252, 289, 366, 413, 425-426, 446-447, 453, 474-475 Comets, 93, 130, 402 communications satellites, 142, 265 community, 57, 172, 176, 314 Compass needle, 216 Compasses, 215 Components of, 136, 212, 442 compounds, 1-2, 53, 56, 63-64, 68-69, 186, 247-248, 424 Compression, 228 Computers, 146, 154, 352, 360-361 Concentration, 47, 247-248, 251, 253, 264-265, 307, 406-407, 416, 424, 426 Concrete, 9, 114, 117, 215, 328, 400-401, 421, 437 Conduction, 2, 207-209, 212 electrical, 2, 207-209 heat, 2, 207, 209 model of, 212 conduction electrons, 2, 207-209, 212 Conductor, 2-3 Conductors, 12, 207, 434 current, 12, 207 semiconductors, 434 cones, 281-282, 294 conservation, 2, 7, 64, 67, 108-111, 117-118, 128, 145-160, 161-165, 168-169, 174, 211, 240, 260, 288-289, 296, 371, 415-418, 427, 440, 446-447 of angular momentum, 128 of energy, 2, 7, 111, 145-160, 161-165, 168-169, 174, 240, 288-289, 296, 371, 415-416, 446, 486, 489 of momentum, 2, 7, 108-111, 113, 117-118, 128, 153, 206, 211 Conservation laws, 111 Conservation of angular momentum, 128 Conservation of charge, 2, 7, 206, 211 Conservation of energy, 2, 7, 111, 145-160, 161-165, 168-169, 174, 240, 288, 296, 371, 415, 446, 486 machines, 146 relativity and, 288 Conservation of momentum, 2, 7, 108-111, 113,

117-118, 128, 153, 206, 211 law of, 2, 7, 108-109, 111, 113, 117, 153, 206 Constellation, 38 constellations, 19 Constructive interference, 230-232, 262, 335, 359 consumers, 158, 177, 439 Contact forces, 95, 206 continental drift, 42 Continuous spectra, 366, 380 continuous spectrum, 2, 365-367, 379 contraction, 7, 129, 132, 285-287, 295, 322 gravitational, 7, 322 Coordinate, 20, 359-360 coordinates, 359, 378 Copernican revolution, 2, 31, 37, 39, 45, 47, 308 Copernicus, Nicolaus, 28 Copper, 206-207, 211-212, 216, 515 core, 63, 130, 132-133, 146, 258, 420-421, 429-430, 445, 447, 456, 493 Earth, 130, 132-133, 258, 456 Correlation, 248, 359 cosmic background radiation, 60, 315, 318, 322 Cosmic inflation, 2, 315-319, 321-323 Cosmic microwave background, 3, 299, 306-310, 314, 319 map of, 306 Cosmic rays, 3, 312, 393, 400, 406, 482, 484, 486, 491 Cosmology, 3, 43, 135, 299-320, 321-323, 488, 517 Big Bang, 3, 43, 300, 306-311, 313-314, 316-319, 321-323 cosmic microwave background, 3, 299, 306-310, 314, 319 dark energy and, 315 defined, 302 Newtonian, 135, 304-305, 517 Coulomb, 1-3, 200-202, 210, 214, 224-225 Coulomb, Charles, 200 Couples, 169, 178 Crab Nebula, 47, 133-134 creationism, 3, 40, 42-44, 45 Crescent Moon, 45 crests, 231-232, 262, 266, 327 critical mass, 3, 5, 465-466, 469, 473 crust, 464 Crystals, 55, 317, 319 Cultural evolution, 395 Curie, Marie, 388, 457 Curie, Pierre, 237, 388 Current, 3-5, 8-9, 12, 37, 41, 133, 190, 199, 204, 207-212, 217-218, 221-224, 239, 254, 279, 307, 322, 366, 411-412, 422-424, 427, 435, 438-439, 462 conservation of, 211 creating, 4, 210, 439, 462 currents, 3, 237, 252, 257, 274, 423, 485 electric, 3, 237, 274, 423, 485 ocean, 257 surface, 252 Curved space, 3, 303, 305 cycles per second, 208 Cyclotron, 458 Cygnus, 134 Cygnus X-1, 134

D Dalton, John, 51 Dark energy, 3, 299-300, 313-315, 321-323 Dark matter, 3, 299-300, 311-315, 321-323, 485 evidence for, 312, 323 extraordinary, 315 structure of, 323 Darwin, Charles, 38 Daughter nuclei, 399, 408 Daughter nucleus, 3, 390-391, 399, 410 day, 22, 24, 29, 34, 39, 48, 60, 72, 124, 155, 157-158, 162-163, 169, 186-188, 193-196, 199-200, 245, 271-272, 282, 291, 299, 305-306, 395, 399, 409, 419, 446-447 solar, 60, 124, 146, 181, 196, 199, 245, 263, 395, 446-447 Decay, 9-11, 17, 59, 154, 175, 312, 339, 352, 364, 384-385, 388-394, 399-400, 405-406, 409-410, 427, 456-457, 473, 487-489, 506 exponential, 3, 6 nuclear, 5-6, 9-11, 154, 175, 312, 352, 384-385, 388-391, 397, 399-400, 405-406, 427, 456-457, 459, 473, 475, 488-489 rate, 6, 10, 389, 394, 397

series, 10 Deceleration, 82, 181, 244 deciduous trees, 437 Deep space, 97 Deferent, 26, 28 deforestation, 6, 256, 258, 260, 262-264 degrees, 3, 27, 56, 171, 194, 196, 198, 248, 251, 255, 306-307, 316, 318, 322-323, 422-423 delta, 349 Democritus, 50-51, 59, 61, 69, 136, 152, 240, 483 Density, 5, 55 average, 55 critical, 5 infinite, 5 Derivative, 477 desert, 464, 466 Destructive interference, 3, 230-232, 234-235, 262 detector, 21, 236, 243, 354-357, 362, 375, 378, 380, 485, 490-491, 494 Detectors, 11, 243, 310, 353, 355-357, 361-362, 375-376, 485, 490-491, 493-494 determinism, 93, 348 Deuteron, 345 development, 5, 33, 37, 41, 45, 74, 120, 172, 179, 241, 271, 427, 430, 458, 466, 483 human, 41, 146 Diamond, 263 Dinosaurs, 402 Direct current, 3, 208 direction, 5-8, 11-14, 17, 19, 21, 25, 38, 46, 80-82, 98-101, 105-110, 113-118, 141-143, 147-148, 174-175, 193, 208-209, 213-214, 216, 243, 258, 276, 284-285, 293-294, 296, 307, 319, 369, 422, 439, 481-482 diseases, 257 Disorder, 175, 194 entropy, 175, 194 Displacement, 26, 122, 261 dissolving, 162 Distance, 7-8, 11-14, 23, 25, 47-48, 49, 51, 56-60, 67-68, 74, 76-77, 79-80, 83-85, 89-92, 124-129, 132-133, 139, 141-144, 159, 164-165, 182, 184, 200-203, 208, 212, 221-223, 237-241, 243, 265, 267, 279-280, 288, 303-305, 310, 322-323, 359, 369, 495, 499-501, 512 angular, 128, 303 cosmological, 315 measurement of, 284, 295 distortion, 43, 213, 230, 310 Disturbance, 1, 4, 13-14, 206, 212-213, 229, 237-239, 242, 310, 389 DNA, 53, 69, 242-243, 266, 344-345, 381, 394, 397-398, 495 Double-slit interference, 234, 325, 328, 335, 339, 358 down quark, 12 Drag, 59, 77, 89 Drift, 42, 51, 208, 247, 384 drift speed, 208 Drift velocity, 3, 208 Driving force, 128 Dust, 1, 11, 22, 36, 38, 51, 58, 60, 69-70, 128-131, 202, 242-243, 266, 311, 316-318, 351, 376, 380-381, 399, 401 interplanetary, 36 interstellar, 129-130 Dust grain, 51, 317, 500 Dynamics, 291 Dyson, Freeman, 289

E Eagle Nebula, 129, 131 Early universe, 306, 310, 316-317, 322 Big Bang, 306, 310, 316-317, 322 evolution of, 306 Earth, 5-6, 9-10, 12-14, 16, 18-19, 21-31, 33-44, 45-48, 52-55, 57, 59-60, 64, 66, 67-68, 72-73, 76-79, 84, 87-91, 98, 100-107, 120-135, 139, 147, 149, 151, 161, 164, 176, 181, 212-213, 215, 238-239, 242-247, 250-252, 254-258, 263-267, 278-279, 283-284, 304-306, 308-314, 318-319, 321-323, 354, 370, 393, 395-396, 402, 423, 432-433, 486-488, 499, 502-503 atmosphere of, 251 composition of, 247 core, 130, 132-133, 258, 456 core of, 456 density, 5, 55

diameter of, 38, 57, 305, 312 features of, 24, 41 formation of, 67, 130, 456 gravitational attraction, 122, 124-125 greenhouse effect on, 251 interior of, 244 life on, 16, 43, 131, 176, 246-247 mass of, 10, 12, 14, 100-102, 113-114, 116, 124, 132-135, 143, 203, 293, 295-296, 305, 311, 314, 318, 466, 474, 487 measuring, 27, 79, 89, 96, 250, 284, 354 properties of, 13, 279, 319, 503 radius of, 47, 78, 88, 265, 318 rotation of, 24, 30 structure of, 5, 9, 59, 323, 384 surface of, 22, 84, 105-106, 133, 143, 251-252, 261, 265, 305-306, 308, 319, 322-323 velocity of, 14, 87, 115, 273 Echo, 307 eclipse, 24, 302-303 solar, 303 eclipses, 19 ecology, 259 ecosystems, 251 Efficiency, 3-6, 13, 147, 156, 158-159, 161, 168, 170-173, 181-182, 184-186, 193-196, 198, 246, 254, 258, 260, 414-419, 423-424, 431, 435, 438-439, 446-447 Einstein, Albert, 16, 34, 51, 137, 202, 241, 271-272, 388 theories of relativity, 271 Electric charge, 3, 111, 153, 201-202, 213, 215, 221-223, 237-239, 261, 338, 386, 389, 482, 486 electric forces, 3, 10, 202, 215, 221-222 of an electron, 223 quantization of, 10 electric circuits, 199, 209, 221-223, 243-244, 439 Electric current, 3-5, 199, 204, 207, 209, 211, 217-218, 223, 246, 422, 427, 433, 435, 438 electric currents, 3, 237, 274, 423, 485 Electric field, 213-214, 216-218, 221, 223-224, 236, 389, 434 Electric field lines, 213-214, 216 Electric field strength, 214 Electric fields, 213-214, 216, 221, 236 Coulomb, 214 Electric force, 2-3, 7, 101, 199-203, 205-206, 208, 213-216, 218, 221-224, 385-386, 390, 406, 409, 452, 487-488, 492, 494-495, 500-501, 505-506 Electric motors, 208 electric power, 3-4, 9-10, 12, 158, 168, 171-172, 177, 184-186, 189, 193-196, 203, 208, 217-218, 246, 264, 419, 432-434, 441, 463 Electric power generation, 217-218, 264, 415, 419, 441 Electrical charge, 389 Electrical power, 172 electrical resistance, 3, 9, 207-208, 211 Electricity, 5, 9-10, 14, 52, 63, 152, 163, 171-172, 177, 179, 181-182, 184-186, 194-196, 198, 199, 214-215, 217-218, 236-237, 260, 267, 270, 412-413, 415-417, 419-425, 427, 431-436, 438-439, 441-442, 444-446, 488, 492 atoms and, 152, 270 charges, 3, 214-215, 237, 506 conductor, 2-3 conservation of charge, 2 coulomb, 2-3, 214 direct current, 3 electric charge, 3, 10, 215, 217, 237, 239 electric circuits, 199, 209, 439 electric current, 3, 5, 199, 209, 217-218, 239, 422, 427, 433, 435, 438 electric power, 3, 9-10, 12, 171-172, 177, 184-186, 194-196, 217-218, 264, 415, 419, 432-434, 441, 506 generation of, 172, 415, 422, 427, 444 insulators, 9, 12, 434 microwave oven, 163 Electrode, 181, 207, 367 Electrodes, 367 Electromagnetic fields, 5, 217, 227, 236, 240-241, 276, 316, 328, 338 forces and, 217, 240-241 Electromagnetic force, 3-5, 9, 199, 206, 217-218, 236, 241, 317, 409, 474 Electromagnetic radiation, 3-4, 12, 41, 237, 242-243,

245-246, 250, 276, 278, 311, 313, 315, 386, 410, 433 Electromagnetic spectrum, 4, 239, 241-242, 244-245, 266, 313, 365, 381 electromagnetic wave, 4, 11, 235, 237-240, 244, 261, 263, 267, 273 Electromagnetic waves, 4, 237-245, 261, 263, 265, 276, 278 energy of, 4, 345 momentum of, 8 speed of, 237, 239, 265, 276, 278, 345 Electromagnetism, 4, 199-219, 221-225, 236-237, 271, 335, 450, 488, 492 Electromagnets, 485 Electron, 1, 7-8, 10-13, 58-59, 63, 69, 132-133, 139, 154, 202-206, 210-211, 215, 218, 222-223, 244, 288-289, 291, 295-296, 326, 332-340, 343-346, 351-353, 355-356, 361-362, 366-370, 386-387, 389-391, 394, 434, 486-494, 498, 501, 506-508 production of, 10, 434 Electron beam, 3, 58-59, 288, 333-337, 344, 494 Electron microscope, 4, 58-59, 338, 343-344 electron microscopes, 338 Electron spin, 394 Electronic devices, 326 computers, 326 Electron-positron pairs, 1, 482-483 Electrons, 6-11, 13-14, 50, 58-59, 63, 101, 129, 131, 201-212, 215-217, 221-224, 236, 238, 242-244, 266, 289-291, 325-326, 331, 333-341, 343-345, 349, 351, 354-356, 361-362, 367, 370, 380-381, 385-386, 390, 405, 433-435, 438-439, 478-484, 487-488, 493-494, 496-498, 503 acceleration of, 1, 8 charge of, 201, 203, 206, 223-224, 493 conduction, 2, 207-209, 212 discovery of, 63, 326, 483, 487, 493-494, 503 drift speed of, 208 electric charge of, 493 energy levels of, 7, 380 energy of, 1, 4, 6-7, 13-14, 210, 289-291, 326, 331, 345, 367, 370, 433, 438, 482, 487 magnetic force on, 215-216 mass of, 7, 10, 14, 101, 133, 203, 289-290, 311, 336-337, 345, 487, 497, 506 nature of, 11, 50, 58, 63, 224, 338, 361-362, 370 orbits, 10, 63, 202-203, 205, 215, 238, 289, 311 path of, 2, 484 reduction, 2, 439 velocity of, 14, 349, 380 wavelengths of, 266, 333 Electroweak force, 4-6, 477, 488-490, 496, 500, 508-509 Electroweak theory, 489-490 Element, 50, 52, 63-64, 66, 67, 69, 130, 175, 181, 205, 208, 210-212, 266, 289, 351, 386-389, 391-392, 458-462, 464, 473-474 formation of, 67, 130 elements, 2, 52-54, 63-64, 67-70, 181, 202, 205, 209, 211, 221, 289, 307-308, 321-322, 386-387, 455-457, 459-460, 462, 493 heavy, 181, 322, 452, 455-456, 459 in Earth, 68 ellipse, 33, 47 foci, 33 Elliptical orbits, 35-36 emission, 1, 11, 182, 330, 337, 371, 437, 452 spontaneous, 1, 11 Energy, 1-14, 17-18, 49, 52, 65-66, 79, 104-105, 109, 111, 130, 138, 145-160, 161-165, 168-179, 181-187, 189-190, 193-196, 198, 206, 208-212, 228-230, 240-248, 251-255, 257-260, 262-266, 270-271, 282, 286, 288-291, 295-297, 299-300, 312-319, 321-323, 328-333, 336-339, 353, 357, 360-362, 366-367, 369-372, 378-381, 390-391, 397-398, 411-440, 441-447, 450-458, 466-469, 471, 477-484, 486-487, 489-491, 495-497, 500-501 and chemical reactions, 364 conservation of, 2, 7, 109, 111, 145-160, 161-165, 168-169, 174, 211, 240, 288-289, 296, 371, 415, 446, 486 conservation of energy, 2, 7, 111, 145-160, 161-165, 168-169, 174, 240, 288, 296, 371, 415, 446, 486 dark, 3, 248, 262-263, 266, 299-300, 312-315,

521

321-323, 339, 366-367, 434, 450 dark energy, 3, 299-300, 313-315, 321-323 internal, 8-9, 147, 151, 177-179, 193, 204 kinetic, 5, 7-8, 13-14, 109, 149-153, 155-156, 161-165, 173-175, 181, 193-194, 210, 246, 290, 295, 317, 386, 391, 433, 484 kinetic energy, 5, 7-8, 14, 109, 149-152, 155-156, 161-165, 181, 194, 246, 290, 295, 336, 386, 391, 433, 484 law of conservation of energy, 7, 149, 153, 161, 168, 174, 288, 446, 486 mass-energy equivalence, 3, 10, 290, 453, 473-474, 500 nuclear energy, 5, 11, 152, 154, 184, 246, 386, 391, 405, 423, 427, 431, 450-458, 460, 463, 467, 473-475 of electromagnetic waves, 4, 241, 243-244 of photon, 331, 338, 480 of photons, 332, 343, 362, 376 potential, 151, 247, 432, 443, 457, 461 potential energy, 151 quantization of, 10, 206, 325, 434 relativistic, 282, 286, 288, 386, 479, 481, 486-487 relativity and, 5, 11-12, 271, 288, 291, 293, 477-478, 480, 497 rest, 4-7, 11-12, 65, 105, 130, 149, 151, 161-162, 164-165, 209, 218, 223-224, 282, 286, 289-291, 293, 300, 314, 323, 328, 330, 332, 367, 391, 401, 474-475, 486, 489-490, 500 rotational, 12, 153, 208 solar, 3, 8-9, 11-13, 66, 130, 135, 146, 153, 172, 176, 179, 181-182, 190, 196, 199, 245-248, 258, 260, 263-264, 416-417, 432-433, 435-438, 442-444, 456, 491 sources of, 184, 241, 258, 262, 405, 411-412, 423 stored, 149, 151, 156, 179, 181, 195, 427-428, 431, 442 thermal, 2, 12-13, 65, 148, 150-156, 161-162, 164-165, 168-178, 184-186, 193-196, 198, 210, 242-243, 246, 257, 265-266, 288-289, 295-296, 381, 391, 401, 415-417, 421-422, 424, 432-433, 435-438, 446-447, 452-454, 475, 486 transfer of, 480 transformation of, 7, 11, 147, 202, 415, 491 transitions, 151, 379 uncertainty principle, 6, 11, 13, 306, 316, 348-349, 353, 375-376, 378-380, 386, 486, 500 units of, 10, 161, 289, 329 vacuum, 4, 7, 13, 147, 185, 218, 244, 314, 316-317, 333, 393, 486-487 work, 6-10, 14, 109, 147-159, 161-165, 168, 170-171, 173, 176-178, 182-183, 185-187, 194-196, 198, 208-209, 241, 246-248, 296, 317, 323, 369, 405, 415, 420, 422, 443-444, 460-462, 473-474, 489, 500-501 Energy levels, 4, 7, 10, 370-372, 378-381, 487 Energy transfer, 14, 154, 362 diagrams, 154 Energy transformations, 147, 155-156, 161-162, 164, 193, 210 Engines, 12, 69-70, 77, 101, 106, 116, 136, 157, 163, 168, 170-171, 177, 181-182, 193-194, 246, 415, 438 Entropy, 1, 4, 6-7, 12, 168, 173-176, 193-194, 198 environment, 14, 16-17, 64, 99-101, 104-106, 158-159, 176, 188, 203, 206, 247-248, 255, 258, 264, 391, 405, 423-425, 427, 429-430, 436 epicycle, 26-28, 30-31 Epicycles, 26-29, 34-35, 46-47 Equations, 84, 90, 237, 469 equator, 47, 265, 306, 322-323 equivalence principle, 4, 301-302, 321-322, 464 eras, 5 Ethanol, 179, 194, 260, 264, 267, 416-417, 432 Ether, 4, 73, 241, 261, 278 Euclid, 199 Euclidean geometry, 309 European Southern Observatory, 20 eV, 3, 181, 484, 486 Evaporation, 155, 164, 178, 257, 431 Evaporative cooling, 185-186 Events, 11, 19, 41-42, 48, 64, 175, 256-257, 290, 304, 339-340, 353, 359, 364, 456-457, 486, 491, 496-497, 499-500, 505 time of, 175, 304

522

evolution, 16, 42-43, 47, 128, 175-176, 299, 306, 395, 398 biological, 1, 16, 42-43, 176, 395, 398, 513 chemical, 1, 175-176, 395 cosmic, 3, 299, 306 cultural, 395, 513 evidence of, 395 evolution of life on Earth, 395 exchange particle, 4, 6, 505 excitation, 367 excited state, 4, 6, 370, 376, 462 Excited states, 370, 376 exercise, 47, 81, 89-90, 165, 221, 376 Expanding universe, 308, 313 Expansion, 11, 56, 93, 131, 169-170, 189, 256, 300, 307-308, 313-316, 318-319, 321-322, 352, 422, 424, 430-432 Experiment, 33-34, 47-48, 50, 52, 54, 59, 63, 67-68, 83, 96-97, 153, 158, 171, 205, 215, 232-238, 246, 254, 261, 263, 274-279, 300-304, 317, 327-331, 333-341, 343-345, 354-355, 358-362, 482-484, 489-491, 493-494, 500 Explosions, 1, 3, 129-131, 315-316, 386, 416, 455 exponential growth, 6, 168, 187, 189-190, 193, 195-196, 316 exposure time, 328-329, 335, 343 External forces, 1, 7, 76, 81, 108, 110, 117 extinction, 249, 251, 512 atmospheric, 251 extinctions, 256 extraterrestrial life, 244 Eye, 6-8, 27, 31, 37, 45-46, 69, 72, 132, 235, 243-244, 250, 266, 456 lens, 243 myopia, 31

F fact, 8-10, 16, 18, 29-30, 36, 41, 43, 45, 47-48, 58-59, 63, 69, 76, 80, 110, 125, 127, 136-137, 152-153, 170-171, 189-190, 206, 211, 214-215, 233-234, 243, 253-254, 265, 358-359, 362-364, 398, 401-403, 424, 434, 459-460, 471, 500-502 Fahrenheit scale, 169, 194 Falling objects, 83-84, 90, 93 Faraday, Michael, 199, 217 Fermi, Enrico, 458, 464, 488 Fever, 257, 398 Feynman, Richard, 49, 54, 123, 175, 339, 366, 479-480 Field lines, 213-214, 216 Fields, 10-13, 62, 199, 212-214, 216-217, 223, 236-237, 240-241, 266, 276, 288-291, 304-305, 316, 328-329, 336, 348-350, 353, 357-358, 397, 432, 452, 477-504, 505-509, 512-513 gravitational, 5, 212-213, 221, 223, 240, 288, 304-305, 316, 336, 452, 483, 486, 492, 498-502 Film, 234, 263, 331, 365, 379, 388 interference, 234, 263, 331 Final velocity, 99, 109 First law of thermodynamics, 154, 168 Fission, 1-2, 5-7, 59, 244, 289, 419, 422-423, 427, 429-431, 449-472, 473-475, 517 Fission fragments, 427, 460 Floating, 68, 96, 127, 257 fluorine, 2, 53, 69, 246, 515 Flux, 154, 411 focus, 7, 17, 28, 33, 50, 60, 74, 83, 136, 235, 435-436 Newtonian, 7, 136, 338 Force, 1-10, 12-14, 25, 32, 40, 61, 76, 79, 94-109, 113-118, 120-128, 133, 135, 141-144, 147-148, 161-162, 164-165, 199-206, 208, 212-218, 228, 236-237, 285-288, 290, 293, 305, 313-314, 316-319, 321-323, 327, 369-370, 383-404, 409, 450-452, 464, 477-481, 487-490, 492-503 acceleration and, 96, 109, 116-117, 300 and interactions, 478 and motion, 101, 147, 278, 290, 317 combining, 1 definition of, 107, 147, 398 electric, 1-7, 9-10, 12, 101, 161-162, 165, 199-206, 208, 213-218, 221-224, 236-237, 286, 385-386, 389-390, 450, 452, 487-488, 492-495, 498, 500-501, 517 electric force, 2-3, 7, 101, 199-203, 205-206, 208, 213-216, 218, 221-224, 385-386, 390,

406, 409, 452, 487-488, 492, 494-495, 500-501, 505-506 external, 1, 4, 12, 76, 94, 99, 108, 115, 117, 212, 218 external forces, 1, 7, 76, 108, 117 friction, 5, 76, 95-96, 99-100, 104-106, 114-117, 162, 164 gravitational, 5-9, 12, 14, 95, 97, 100-101, 103, 105-106, 113, 120-126, 128, 131, 133, 141-144, 161-162, 164-165, 175, 200-202, 206, 212-213, 223-224, 288, 300, 305, 313-314, 316-318, 322-323, 370, 385-387, 464, 498-502 gravitational force, 6, 12, 14, 95, 100-101, 103, 105-106, 113, 117, 121-122, 124-126, 131, 141-144, 162, 200-202, 206, 212-213, 224, 313, 316-317, 464, 499-502 in nature, 237, 316, 385, 399, 406, 479-480 internal forces, 108 magnetic, 4, 114-115, 133, 135, 199, 201, 203, 208, 214-218, 223-224, 236-237, 286, 288, 290, 389 magnetic force, 7, 114, 203, 215-218, 223-224, 236-237, 477, 493 measuring, 32, 79, 96, 237, 394, 500 misconceptions about, 94, 290 net, 7-8, 14, 99-102, 104-105, 107, 113-117, 123, 128, 142-143, 148, 201, 203-204, 206, 285, 317, 394 normal, 25, 40, 101, 105-106, 113-114, 117, 125-126, 128, 131, 143, 286, 314, 318-319, 390, 394, 403, 405, 501-502 normal force, 101, 105-106, 113-114, 117 nuclear force, 14, 290, 385, 389, 406, 450-452 polarization, 215 support, 32, 131, 141 total force, 96 types, 6-9, 141, 164, 175, 203, 316, 389, 398, 478, 490 units of, 10, 161 work, 4, 6-10, 12, 98, 102, 106, 109, 113, 120, 126, 147-148, 161-162, 164-165, 237, 241, 288, 290, 317, 323, 369, 389, 395, 403, 488-489, 500-501 Force pair, 103-104, 113, 115, 117 Forces, 3-8, 76, 81, 87, 94-96, 98-111, 113-117, 120-124, 126, 128, 131-132, 137-139, 143, 151-153, 175, 199-202, 206-208, 210, 212-217, 221-222, 224, 240-241, 244, 270, 289-291, 305, 314, 316-319, 361, 384-387, 391-392, 434, 459-460, 462, 488-489, 496, 498-501, 509 forests, 432 Forward direction, 91, 99, 175, 293 fossil fuels, 3, 5, 146, 164, 181-182, 253, 255, 258, 411-417, 423-425, 431, 441, 443-444 fossils, 394-395, 407 Fourier analysis, 349 Frame of reference, 286 Free fall, 5, 83-84, 126 acceleration, 5, 83-84 acceleration of, 84 weightlessness, 5, 126 Freely falling objects, 84, 90 freezing, 169, 194, 198, 296, 319 Frequency, 3, 5-6, 42, 208, 229-230, 234, 238-244, 256, 261-267, 311, 327-330, 343, 365-366, 371-372, 379-381, 439-440, 478, 487, 509 fundamental, 5-6, 371, 478, 487 natural, 3, 5, 11, 243, 256, 264 wave, 5, 11, 229-230, 234, 238-240, 242, 244, 261-265, 267, 345, 380 fresh water, 251, 394 Friction, 65, 74-76, 89, 91, 95-96, 99-100, 104-106, 110, 114-117, 155, 162, 164, 173, 178, 193 kinetic, 5, 155, 162, 164, 173, 193 rolling, 75-76, 100, 105-106, 114, 116-117, 178 Frictionless surface, 105, 110 Frisch, Otto, 459 Front, 47, 57-58, 94, 96, 98-99, 106, 109, 127, 184, 204, 272-273, 284, 287, 293-294 fruit, 184 Fuel, 5-6, 8-9, 11-14, 65-66, 69, 106, 114, 130-133, 141, 153-154, 164, 172, 177-179, 181-183, 185, 193-194, 197, 252-254, 258, 260, 400-401, 415-417, 419-422, 424-425, 427-432, 438-439, 442-443, 455, 468-471 fuel cells, 179, 182, 427

full Moon, 30, 38, 45 Fundamental forces, 5, 12, 14, 175, 202, 316, 319, 322, 385-387, 405, 473-474, 479, 488-489, 492, 498, 500-501 Fundamental particles, 4, 6, 8, 10, 237, 319, 489, 493-494, 498, 501, 505-506 Fuse, 307, 423, 451-454, 456, 468 Fusion, 5-6, 8-9, 59, 129-131, 244, 416, 422-423, 442, 444, 449-472, 473-475, 513, 517 carbon, 9, 12-13, 416, 444, 456, 473, 475 helium, 130, 423, 453-456, 468, 474 nuclear, 5-6, 8-9, 129-131, 244, 416, 422-423, 442, 444, 450-467, 469-471, 473-475, 517 proton, 451-452, 454, 460, 473-474

G g, 57, 184, 289, 368, 376-377, 410, 458, 460, 475, 509 Galaxies, 1, 4-5, 38-39, 47, 55, 59-60, 110, 132, 134-135, 306, 308-309, 311-314, 318-319, 321-323, 352, 365, 502 active, 1, 308 centers of, 1, 47, 134-135, 311, 502 colliding, 1, 55 defined, 1 evolution of, 1, 306 giant, 1, 38, 134-135, 312 irregular, 55 life in, 483 masses of, 135, 314 normal, 5, 55, 134, 309, 318-319, 502 properties of, 319, 365 radio, 4, 306, 365 receding, 306, 314, 323 spiral, 312 visible, 4, 38, 132, 134, 306, 311-312, 365 galaxy, 5, 37-39, 47, 60, 68, 79, 129-132, 134-135, 141, 176, 244, 305, 308-309, 311-313, 322-323, 456, 503 active, 308 radio, 8, 244, 305 spiral, 305, 312 Galilean relativity, 5, 272-274, 276-278, 293-294, 296 defined, 293 reference frames, 5 Galilei, Galileo, 61, 74 force, 5, 61, 76, 94, 101, 121, 135, 224, 237 inertia, 72, 74-76, 87, 91, 93-94 Galileo Galilei, 61, 74 Gamma, 4-6, 152, 242, 244-245, 261, 266, 288, 296, 345, 381, 389-391, 397-398, 400, 405-406, 487, 489-490 gamma radiation, 244, 296, 345, 406 Gamma ray, 5, 242, 244, 266, 288, 381 Gamma rays, 4-6, 244-245, 261, 389-390, 397-398, 400, 405-406, 410 applications of, 261 medical uses, 398 Gamma-ray photon, 5, 390 gaps, 52, 136, 369 Gas, 3-6, 11-13, 53-56, 59, 65, 67-69, 78, 105-106, 128-131, 134-135, 141, 146-147, 170, 172-174, 179, 181-182, 184, 186, 245-247, 249, 251, 253-254, 257, 260, 267, 338, 364-367, 376, 379, 401, 412-417, 422, 424-427, 430-431, 434-435, 438-439, 443-444, 464, 500 greenhouse, 6, 130, 251, 253-254, 257, 260, 267, 424, 438 interstellar, 129-130 pressure in, 68 Gases, 6, 9, 52, 55-56, 64, 67-68, 133-134, 177-178, 185, 227, 246-247, 251-252, 255-256, 261-263, 267, 360, 365-366, 379, 423, 438 density, 55 expansion, 1, 56, 256 greenhouse, 6, 251-252, 255-256, 262, 267, 438 ideal, 178 pressure, 55-56, 68, 177, 185, 246, 425-426 Gell-Mann, Murray, 493 General relativity, 7, 12, 123, 137-139, 270, 304-306, 308-309, 315-316, 319, 322-323, 479, 492, 497-499, 501-503, 517 General theory of relativity, 4-6, 12, 278, 293, 299-300, 303-304, 306, 312, 479, 498-499 Generators, 172, 433 genome, 395 human, 395 geology, 17, 42, 395 Geometry, 2, 24, 32, 235, 303, 309-310, 314, 319,

321-323, 503 Euclidean, 309 of space, 314, 323 Geosynchronous orbits, 142 Geothermal power plant, 194, 438, 446 Giant planet, 142 giant star, 13, 133-134 Giants, 61, 121 glaciers, 256 Glass, 60, 68, 76, 169, 203, 251, 257, 267, 287, 338, 364-365, 436-438 Glasses, 55, 60 global climate change, 258, 427 Global positioning system (GPS), 304 global warming, 6, 17, 42, 90, 159, 178, 181-182, 186, 190, 199, 253-258, 262, 264-265, 267, 411-413, 415-417, 421-425, 427, 431-432, 436-437, 440, 443-444 glucose, 9, 12, 54, 65-66, 67, 69-70, 176, 376 Gluon, 6, 317 Gluons, 6, 12, 477, 495-498, 506, 508-509 Gold, 7, 50, 67, 69, 117, 308, 333, 359-360, 386, 456, 496-497 GPS, 304 Grand unified theory, 6, 237, 496, 498 Granite, 433 granules, 493 Graph, 125-126, 162, 187-188, 190, 193, 196, 258-260, 281, 286-287, 307, 339-340, 396, 413, 418-419 Gravitational attraction, 97, 122, 124-125, 498 Gravitational constant, 499 Gravitational field, 6, 212-213, 223-224, 316, 483, 486, 498-499 Gravitational force, 6, 12, 14, 95, 100-101, 103, 105-106, 113, 117, 121-122, 124-126, 131, 141-144, 162, 200-202, 206, 212-213, 224, 313, 316-317, 464, 499-502 weight and, 100 Gravitational forces, 6-8, 95, 100, 110, 120, 124, 128, 137-139, 151, 153, 202, 213, 318, 499-500 Gravitational lensing, 312 Gravitational potential energy, 151 Graviton, 6, 499, 503, 505 gravitons, 499, 503 Gravity, 3-6, 13-14, 35-36, 47, 61, 75-79, 87, 94-95, 98, 100-101, 104, 116-118, 120-126, 128, 131-133, 135, 138, 141-143, 149, 153, 199-202, 212-213, 216, 294, 299-305, 309, 313-314, 316-319, 385-386, 456, 464, 487-488, 497-499, 501-503 acceleration of, 1, 8, 89, 104, 116-117, 300, 305, 314 and distance, 3, 5, 200 and speed, 386, 507 center of, 79, 128, 135, 142, 305, 309, 313, 464 in general relativity, 304, 499 on Jupiter, 142 particles and, 501 quantum, 3-6, 8, 13-14, 131, 133, 138, 199, 202, 270-271, 316, 318-319, 385-386, 391, 479, 487-488, 492, 497-499, 501-503, 505-507, 509 sensation of, 126 solar, 35, 47, 87, 124, 128, 131, 133, 135, 153, 202, 303, 309, 456 strength of, 117, 499, 501 theory of, 4-6, 13-14, 35, 78, 95, 98, 120-121, 123-126, 128, 133, 138, 141-143, 212, 294, 299-300, 303-305, 477, 488, 492, 497-499, 502 zero, 3, 98, 101, 104, 116-118, 123, 125-126, 128, 138, 216, 317-318, 322, 464, 499 green light, 243, 265 Greene, Brian, 306, 502 greenhouse effect, 6, 130, 251-253, 255, 262 runaway, 130 Greenhouse gas, 6, 251, 253-254, 257, 260, 267, 424 greenhouse gases, 251-252, 256, 262, 438 Greenland ice sheet, 257 ground state, 4, 370, 376, 380 GUT, 255 Guth, Alan, 315, 317 GUTs, 432

H Hadrons, 484 Hahn, Otto, 459 Half-life, 384, 391-393, 397, 399, 404, 405-407, 410,

471 Half-lives, 392-394, 406, 409-410, 488 Hawking, Stephen, 303, 339, 364 health, 176, 257, 264, 391, 401, 405, 424-425 Hearing, 263 heart, 43, 165, 212, 333, 352, 403, 408, 466, 471 Heat, 2-4, 12, 55, 65, 69, 129, 157, 168, 170-173, 175-177, 182-186, 193-196, 198, 207, 246, 257, 296, 415, 421-422, 432, 438-439, 443-444, 446-447, 469, 471 and temperature, 193 calorie, 2, 4 death, 175 defined, 12 measuring, 193 quantity, 12, 173, 194 quantity of, 12, 173, 194 solar energy, 3, 176, 184, 196, 198, 246 thermal energy, 12, 65, 168, 170-173, 175-177, 184-186, 193-194, 196, 198, 246, 257, 415, 421-422, 432, 438, 446-447 work and, 415 Heat death, 175 Heat engines, 12, 157, 168, 170-171, 177, 182, 193-194, 196, 246, 415, 438, 443, 447 internal combustion engines, 177 perfect, 171 refrigerators, 157, 246 heavy elements, 452 Heisenberg uncertainty principle, 6 Heisenberg, Werner, 137, 348-351, 353 Helium, 1, 18, 52-54, 63-64, 67-69, 130, 154, 222-224, 307-308, 311, 344-345, 352, 366, 376, 379-380, 389-390, 421, 453-456, 491 discovery of, 63, 389 in stars, 54, 455-456 helium atom, 222, 344-345, 352 helium fusion, 474 helium-burning star, 130 hemoglobin, 53, 69-70 Hertz, 6, 229, 238-241, 243, 261, 265, 267, 506 Hertz, Heinrich, 238-239, 241 hertz (Hz), 6, 229 Hewitt, Paul, 103 High-energy physics, 52, 206, 282, 286, 290, 457, 497 History graph, 193 hominids, 396, 405-406 Homo erectus, 395, 407 Homo sapiens, 395-396, 407, 428 horizon, 18, 24-25, 30, 248 Hot spring, 406 hour, 7, 18, 60, 68-69, 79-82, 158-159, 161, 163, 177, 188, 198, 208, 273, 395, 403, 407-408, 412, 446-447 Hubble Space Telescope, 20, 38, 129, 131, 134, 306, 312 human behavior, 136, 254 Human body, 165, 244, 399-400 eye, 244 radiation and, 244 humans, 8-9, 11, 19, 34, 39, 41-42, 60, 120, 135, 137, 184, 227, 243-244, 256, 284, 361-362, 394-395, 407, 412-413, 432 and global warming, 246, 432 evolution of, 3, 299, 395 hurricanes, 256 Huygens, Christian, 199 Hydrocarbon, 5, 65, 69, 178 hydrocarbons, 70, 178 hydroelectric power, 152, 190, 194, 198, 217, 263-264, 438, 447 Hydrogen, 1, 5-7, 9, 51-54, 64-65, 67-70, 106, 128-132, 178-179, 181-182, 202, 204, 223-224, 260, 307-309, 311, 322, 366-372, 376-380, 385, 422-427, 447, 450-455, 468-469, 473-474, 487, 491, 498 energy levels of, 7, 372, 378-380 energy-level diagram, 370-371 in stars, 54, 455 isotopes, 11, 307, 406, 427, 454, 468 spectrum of, 371, 380 Hydrogen atom, 7, 67-69, 202, 204, 367-372, 376-378, 422, 487, 498 mass, 7, 202, 204, 376, 487, 498 Hydrogen bomb, 5-6, 468, 474 hydrogen fusion, 450 Hydrogen isotopes, 468 Hydrogen spectrum, 487 Hypothesis, 12, 18, 22, 24-26, 29, 34-36, 41, 43, 45,

523

47, 50-51, 54, 127, 215, 248, 300, 315-316, 318-319, 395, 497, 499, 501-503, 505-506, 509 Hz, 5-6, 11, 229, 238-239, 241-244, 262, 265-267, 328, 331-333, 345-346, 372, 379, 381, 439

I Ice, 7, 50, 54-55, 89, 105-106, 116, 138, 174, 193-194, 248, 254, 256-257, 317, 319, 394, 426 density, 55 melting, 138, 256, 281, 426 ice ages, 257, 426 ice sheets, 256 Image, 20, 32, 38, 59, 299-300, 310 immune system, 250 Inertia, 6-7, 11-12, 72, 74-81, 87, 89, 91, 93-94, 96-97, 100, 106, 122, 124, 183-184, 286, 289-290, 336, 381 and acceleration, 72, 100 law of inertia, 7, 72, 74-77, 79-81, 87, 89, 91, 93-94, 106, 124, 183-184 thermal, 6, 12, 74, 184, 289, 381 Inertial mass, 337, 349, 486 Infrared radiation, 6, 227, 243, 251-252, 255, 331, 366 inheritance, 352, 364 Inner core, 132 insects, 40, 115 Instantaneous speed, 1, 6, 12-13, 80-81 Insulators, 12, 207, 434 Intelligence, 271, 319, 470 intelligent design, 6, 40, 42-43 Intensity, 314, 335, 337, 343-344, 348, 355, 369 of waves, 344 Interaction, 102-103, 110, 115, 227, 336, 340, 353, 357-358, 479-480, 482, 488-489, 497, 500 interactions, 7, 111, 153, 244, 290-291, 335, 338, 362, 478, 480-481, 487-489, 491, 505 Interference, 2-3, 14, 227, 230-235, 261-263, 307, 327-328, 331, 334-336, 338-339, 354-359, 362, 376, 378 constructive, 14, 230-235, 262, 335, 359 constructive interference, 230-232, 262, 335, 359 destructive, 3, 14, 230-235, 262 destructive interference, 3, 230-232, 234-235, 262 of light, 227, 233-235, 263, 327-328, 331, 336 of matter, 2-3, 14, 336, 362 Interference patterns, 235, 354 Internal combustion engines, 177 Internal energy, 151 Internal forces, 108 interstellar travel, 154 Iodine, 53, 69, 391-392, 399, 402, 406, 456, 515 isotopes, 391-392, 399, 406 Ion, 6, 180, 203, 221-222, 224, 361, 483 Ionization, 397 Ionizing radiation, 6, 8, 11-14, 244, 397-398, 403, 405, 408 Ions, 10, 203, 360, 439 Iridium, 515 Iron, 9, 114, 132-133, 141, 143, 215-217, 438, 454-456 Isolated system, 43, 198 Isotope, 4-7, 11, 253, 387, 389-390, 392-394, 398-400, 404, 405-407, 422, 451-452, 454, 457, 459-461, 464, 468, 473, 475 Isotopes, 11, 307, 387, 389-394, 399-401, 405-407, 409-410, 427-428, 454, 457-459, 461-462, 464, 468, 472, 474 of carbon, 387, 389, 400, 410 of helium, 307, 389-390, 474 radioactive, 6, 11, 389-394, 399-401, 405-407, 409-410, 427-428, 457-459, 461-462, 468, 472, 474

J Jefferson, Thomas, 136 Jet, 106, 113, 115-117, 128, 138, 163, 184, 273-274, 277, 282-283, 403, 407-408, 421-423, 445, 456 joule, 7-8, 10, 14, 148, 152, 155, 157, 161, 210, 297, 398, 446, 478 joule (J), 7, 14, 148 jumping, 238, 371 Junction, 434-435 Jupiter, 23, 27, 29, 35, 46, 76, 237-239 mass of, 124 moons of, 76

524

K Kelvin, Lord, 137 Kepler, Johannes, 31-32 Kilogram, 7-8, 12, 14, 97, 101, 114, 126, 155, 183-184, 286-287, 289, 293, 386, 398 kilogram (kg), 7 kilowatt, 4, 7, 57, 157, 159, 161, 163, 177, 189, 195-196, 412, 446 kilowatt-hour, 4, 7, 159, 161, 163, 412, 446 Kinetic energy, 5, 7-8, 14, 109, 149-152, 155-156, 161-165, 181, 194, 246, 290, 295, 336, 386, 391, 433, 484 falling object, 155 gas molecules, 5 random kinetic energy, 366 relativity of, 7, 295 work and, 8, 149-150, 156

L lanthanides, 515 Large Hadron Collider, 7, 477, 484, 494, 497, 503 Laser, 154, 273, 276, 294, 302, 330 operation, 154 Laser beam, 276, 294 Laser beams, 302 Laser light, 154 Lasers, 154, 237, 326, 360 latitude, 249, 303, 306, 322 lava, 184 law, 1-9, 12-13, 17-18, 34, 38, 42-43, 50, 74-77, 79-82, 87, 89, 91, 93-94, 98, 100-109, 111, 113-117, 120-121, 123-124, 137-138, 152-154, 164-165, 167-191, 193-198, 206, 211, 214, 216-218, 223-225, 236, 249, 285-286, 350 law of conservation of energy, 7, 149, 153, 161, 168, 174, 288, 446, 486 law of conservation of momentum, 2, 7, 111, 153 Law of gravity, 77, 94, 121, 123, 201-202 Law of inertia, 7, 72, 74-77, 79-81, 87, 89, 91, 93-94, 106, 124, 183-184 Law of thermodynamics, 1, 7-8, 12, 42, 147, 154, 167-191, 193-198, 415 Laws of thermodynamics, 168, 271 second law of, 168 Lead, 98, 154, 243, 255, 263, 275, 317, 339, 360, 364, 386, 460, 515 isotopes, 389, 399, 462 Length contraction, 7, 11, 285-287, 295 lens, 243 eye, 243 Lenses, 338 life, 5-6, 9, 16-18, 28, 33-36, 38, 42-43, 53, 56, 64-65, 67-69, 72, 74, 120-121, 130-131, 175-176, 182, 193, 204, 209, 244, 246-248, 252, 258, 271, 282-283, 308, 319, 331-332, 366, 391-393, 395-397, 399, 403-404, 405-410, 439, 455, 458-459, 471 characteristics of, 53 extraterrestrial, 244 history of, 16, 18, 34, 175, 190, 483 on Earth, 16, 28, 43, 64, 67, 120-121, 131, 176, 246-247, 283, 319, 408 origin of, 2, 38, 175, 395, 407, 455 Lifetime, 4, 190, 249, 257, 263-264, 282-284, 294, 417 lift, 102, 113-114, 147-150, 158-159, 161-164, 170, 295, 297, 474 Light, 3-10, 12-13, 17, 20-21, 27-28, 30, 33, 37-38, 43, 47-48, 56, 58-60, 62, 65-66, 67, 74, 76, 110, 120-121, 129, 132-135, 138-139, 152-154, 157, 159, 194, 203-204, 208-209, 227-260, 261-267, 273-281, 284-285, 287-288, 293-294, 302-305, 307, 309-313, 321-323, 325-336, 338-339, 343-346, 353-354, 364-366, 427, 431, 433-435, 438-439, 455, 488, 499 bending of, 302-304, 322-323 color, 163, 231, 234, 243, 250, 328, 343-345, 365 double-slit interference, 234, 325, 328, 335, 339 electromagnetic spectrum, 4, 239, 241-242, 244-245, 266, 313, 365 emission of, 4 energy of, 1, 4-7, 13, 153-154, 164, 262, 288, 316, 329-332, 345-346, 353, 431, 433, 438 frequencies of, 241, 345, 365 interference, 3, 227, 230-235, 261-263, 307, 327-328, 331, 334-336, 338-339, 354,

357, 359 interference of, 262, 327 laser light, 154 models of, 6, 8, 10, 67, 233 nature of, 58, 93, 310, 315, 338 plants and, 65 power of, 4, 10, 17, 60, 159 prism, 120, 364-365 properties of, 13, 241, 262, 279, 319, 365, 435 quanta, 4, 6-7, 10, 12-13, 329-331, 333, 336, 338, 345, 364, 483 radiation and, 129, 244-245, 315, 332-333, 479 scattering, 110 sources of, 234, 241, 258, 262 speed of, 21, 89-90, 110, 133-135, 138-139, 143, 153, 208, 237, 239, 265, 270, 273-274, 276-278, 287, 296, 299, 499 ultraviolet, 4-6, 9, 12-13, 152, 227, 242-247, 250-251, 263-264, 266-267, 366, 438 visible, 6-8, 12-13, 27, 37-38, 48, 58, 69, 132-134, 238, 242-245, 251, 259, 266-267, 311-312, 332, 338, 343, 345-346, 353, 364-366, 427, 438 visible light, 133, 157, 238, 243, 267, 343, 346, 438 white, 132, 203, 222, 235, 250, 257, 332, 334 Light clock, 7, 13, 279-281, 293, 302 light microscopes, 338 Light pipes, 20 Light waves, 4, 58, 234-236, 239, 243, 261, 263, 313, 326-327, 331 Lightbulbs, 157-158, 163, 208, 376, 411 Lightning, 154, 237-238, 366 light-year, 7, 47, 129, 284 Light-years, 129, 132, 154, 284, 294, 305, 309-310, 359, 488 Like charges, 3 Limit, 35, 50, 278, 287, 316, 410, 411, 426 Line spectra, 10, 365-366, 379 Line spectrum, 7, 365 Liquid, 1-2, 4, 51, 53-56, 67, 151, 154, 179, 181, 185, 194, 246, 435-436, 459-460, 463-464, 481, 484 Liquids, 55-56, 67, 106, 385 boiling, 55 density, 55 Lithium ion, 180 Load, 147, 165, 183, 196, 469 Logarithmic scale, 242 longitude, 303, 322-323 determining, 322 zero, 322 Loop, 3-4, 10, 26, 33, 207-208, 217-218, 228, 251, 421, 434, 444, 447, 503 low-mass black holes, 134 Luminous matter, 312, 314-315 lungs, 59, 165, 253, 399

M Machine, 135-136, 184, 326, 366, 398 machines, 40, 146, 184 conservation of energy, 146 macroscopic level, 54, 151, 202, 326 Macroscopic systems, 364 macroscopic world, 72, 339, 351, 488 Magnetic field, 4, 7, 208, 216-218, 223-224, 236-237, 288, 291, 477, 481 Magnetic field lines, 216 Magnetic fields, 214, 216-217, 221, 223, 236-237, 290, 389, 481 energy in, 290 Magnetic force, 7, 114, 203, 215-218, 223-224, 236-237, 477, 493 direction of, 114, 223-224 magnitude of, 114 magnetic forces, 4, 7, 115, 152, 199, 214-217, 237, 286, 509 Magnetic poles, 7, 10, 215-216 Magnetism, 199, 214-216, 236-237, 239, 270, 488, 492, 507 electric currents, 237 gravity and, 488 magnetic force, 215-216, 236-237 magnetic poles, 215-216 solar, 199 Magnets, 102, 110, 203, 214-217, 221, 223-224, 274-275, 288 bar magnets, 215-216, 221, 288 compass needle, 216 permanent magnets, 215, 223-224

Magnification, 498-499 magnitude, 60, 107-108, 110, 113-114, 123, 141, 143, 206 absolute, 110 malaria, 257 mammals, 395-396, 407 Manhattan Project, 7, 458, 462-466 Mars, 23-27, 29-30, 32, 35, 46-48, 57, 85, 91, 124, 143, 240, 251 atmosphere of, 251 features of, 24 mass of, 124, 143 moons of, 124 radius of, 47 surface of, 85, 143, 251 water, 91, 143, 251 Mass, 5-14, 94, 97-98, 100-102, 104, 107-109, 113-117, 124-126, 128, 131-135, 141-144, 164, 184, 200-204, 213, 221, 254, 265, 271, 284-291, 295-297, 305, 307, 311, 314-318, 330, 332-333, 336-337, 345-346, 365, 379-381, 387-391, 418, 424, 431, 452-455, 464-466, 469-470, 473-475, 486-491, 495-501, 508-509 and acceleration, 94, 100 and weight, 7, 102, 114 atomic, 1-2, 7, 10-11, 133, 202, 204, 221, 289-290, 316, 351, 376, 380-381, 387-391, 431, 460, 474-475, 501 center of, 9, 128, 134-135, 142, 305, 311, 464, 466, 469-470 conservation of, 2, 7, 108-109, 113, 117, 128, 149-150, 164, 288-289 force and, 6, 94, 221, 224, 278, 317, 488 gravitational, 5-9, 14, 97, 100-101, 113, 124-126, 128, 131, 133-134, 141-144, 149-150, 164, 200-202, 213, 288, 300, 305, 314, 316-318, 336, 391, 431, 498-501 inertial, 135, 337, 349, 486 mass-energy equivalence, 3, 10, 290, 453, 473-474, 500 measuring, 101, 224, 284, 315, 351, 365, 380, 500 units of, 10, 289 mass increase, 286-288, 295, 486 Mass number, 7, 9, 387, 390-391, 405, 454-455 mass-energy, 3, 10, 290, 453, 473-474, 477, 500 Mass-energy equivalence, 3, 10, 290, 453, 473-474, 500 Mathematics, 17, 24, 125 Matter, 1-8, 10-14, 37, 41, 43, 50-52, 54-56, 58-59, 61-64, 67, 74, 95, 97, 125, 128, 131, 133-134, 136-137, 139, 150, 153-154, 174, 212, 218, 223-224, 241, 244, 270, 275-276, 286-290, 299-300, 306-308, 310-315, 317, 321-323, 332-333, 335-341, 352-353, 355-358, 360-362, 367-370, 375-378, 432, 457, 464, 482-490, 496-498, 501-502 antimatter, 7, 289, 474, 477, 482-485, 487, 496, 505-506 antimatter and, 483 atomic mass, 474 dark matter, 3, 299-300, 311-315, 321-323, 485 luminous matter, 312, 314-315 nature of, 11, 50, 58, 63, 224, 310, 315, 338, 361-362, 370, 501 normal, 5, 54-55, 113, 125, 128, 131, 134, 139, 143, 244, 270, 501-502 organic, 1-2, 432 properties of, 13, 241, 340, 386, 392 superconducting, 485 Matter waves, 4, 59, 333, 336, 338, 341, 356-357, 368, 377 Measurement, 7-9, 13, 34, 54, 56, 97-98, 193, 201, 278, 284, 294-295, 302, 304-305, 353-354, 362-363, 369, 371, 375-376, 394, 453 uncertainties, 13, 375 units, 13, 56, 98 Mechanics, 271, 291, 325-326, 333, 339, 353, 363, 478, 492, 517 Medium, 1, 4-5, 8, 12-14, 32, 229-230, 235-237, 261-263, 278, 333, 344-345, 471 for electromagnetic waves, 8, 237 of waves, 229, 235, 344 megawatt (MW), 157 Meitner, Lise, 459 Melting, 8, 52, 138, 151, 212, 256, 281, 426 of ice, 256 Melting point, 212 Merbold, Ulf, 248

Mercury, 23, 27, 29, 35, 46-48, 67, 138, 169, 376, 379, 438 composition of, 376 expansion, 169 orbit of, 47, 138 radius of, 47 Metals, 52, 181, 207, 434, 515 meteorites, 129, 131, 394, 408 meteoroid, 89 Meteoroids, 87 methane, 5, 65, 67-70, 179, 182, 256-257 methanol, 179, 416-417, 444 metric, 7-8, 13, 49, 56-58, 68, 101, 169, 196, 288, 499 metric system, 13, 56, 58 Microscope, 4, 51, 58-59, 67, 316, 338, 343-344 Microscopes, 58-59, 338, 384 electron, 58-59, 338 electron microscope, 58-59, 338 light, 58-59, 338 scanning electron, 58 scanning tunneling, 59 scanning tunneling microscope, 59 microscopic level, 54-56, 95, 164, 175, 221, 325-326, 492, 496, 498, 502 Microwave oven, 158, 163, 242, 245, 266, 381 Microwaves, 242-243, 245, 263, 265, 309, 321 Milky Way, 5, 8, 37-39, 60, 68, 79, 135, 176, 299, 308-309, 312, 503 Milky Way Galaxy, 37-39, 60, 68, 79, 135, 176, 308-309, 312 center of, 37-39, 79, 135, 308-309, 312, 322 diameter of, 38, 312 formation of, 130 history of, 322 mass, 135 mass of, 135 measuring, 79 size of, 60 structure of, 309 mining, 424-425, 447 minute, 24, 31, 33, 60, 79-80, 164, 188, 251, 281, 294, 344-345, 397, 400 Mirror, 20, 233, 263, 279, 299, 359 Mirrors, 55, 279, 359, 435-436 model, 6, 8, 10-13, 32, 34, 49, 63, 137, 202-205, 212, 221-222, 255-256, 271, 290, 366-367, 369, 376, 460, 493, 496-498, 501, 503 Models, 6, 8, 10-11, 49, 63, 233, 254-256 atomic model, 10-11 Modes, 178, 183-184, 197, 384, 501 Molecular structure, 2, 53, 152 Molecule, 8-9, 51, 53-54, 60, 65, 67-70, 181, 198, 242, 247-248, 251, 266-267, 338, 344-345, 376, 483, 495, 498 kinetic energy, 8, 181 molecules, 1-2, 5-6, 12-13, 49, 51, 53-56, 59-60, 64-65, 67-69, 74, 77, 110, 151-152, 165, 173-176, 178, 181, 198, 228, 242-244, 246-248, 251, 253, 264-267, 333, 338, 390, 399, 420 polar, 248 Moment, 17, 41-42, 54, 132, 153, 283, 353 Momentum, 7-8, 94, 107-111, 113-118, 128, 138, 153, 206, 211, 338, 397, 466 angular, 128, 153 angular momentum, 128, 153 collisions, 107, 109 components, 8 conservation laws, 111 conservation of, 2, 7, 108-111, 113, 117-118, 128, 153, 206, 211 conservation of angular momentum, 128 in two dimensions, 110 increasing, 13 law of conservation of momentum, 2, 7, 111, 153 linear, 7 total, 2, 7-8, 107-108, 110-111, 113-115, 153, 397 total momentum, 7-8, 107-108, 110-111, 113, 115, 153 month, 163, 165, 188, 198, 313, 406 Moon, 17-19, 22-25, 27-31, 34, 38-39, 41, 45-47, 68, 73, 76-78, 84, 87-90, 92, 100-102, 104, 117, 120-123, 131, 212-213, 236-239, 305-306, 362, 499 eclipses, 19 full Moon, 30, 38, 45 new Moon, 30, 45 orbit of, 47, 488 phases of, 30-31

Moon, the, 18, 102 mass of, 102 Motion, 3-8, 10-13, 24-26, 28-30, 32-36, 40, 45-47, 49, 51, 54, 56, 58, 61, 63, 68, 72-77, 79-82, 91, 94-96, 98-99, 101-105, 107-110, 113-117, 120-123, 127, 137-138, 147-149, 151-153, 156, 183, 193-194, 208-209, 215-217, 223-224, 230, 274-276, 284-286, 290-291, 317, 360, 367, 381, 433, 439 acceleration, 5-6, 8, 72, 81-82, 87, 89, 91, 94-96, 98-99, 101-105, 107, 109, 113-117, 127, 224, 275, 285-286, 293-294, 497 apparent, 28, 300 Aristotle, 24, 47, 72-76, 87, 91, 120-121 atomic, 5, 10-11, 49, 51, 54, 56, 58, 61, 63, 290, 341, 381, 457 Brownian, 1, 51, 54, 58, 63, 68 describing, 305 free fall, 5 Galileo, 30, 34-35, 61, 72, 74-76, 82, 87, 91, 101, 121, 224, 237, 274, 276, 279-280 kilogram, 7-8, 12, 101, 114, 183, 286, 293 natural, 3-5, 8, 10-13, 24, 29, 36, 40, 73, 87, 91, 94, 110, 120-121, 175, 243, 305 net force, 8, 99, 101-102, 104-105, 107, 113-117, 123, 142-143, 148, 285 proper, 28, 63, 243 relativity of, 7, 11, 13, 278-279, 284-285, 293-294 retrograde, 12, 24-26, 29-30, 34, 45-46 rotational, 12, 153, 208 speed, 5-6, 8, 10-13, 46, 74, 76, 79-82, 87, 89, 91, 94-95, 98-99, 105, 107, 109-110, 113-117, 138, 147-149, 153, 183, 208, 237-238, 274-276, 278-279, 293-294, 381 types of, 4, 6, 152, 171, 175, 193, 439 uniform, 13, 24, 26, 28, 33, 45-46 velocity, 7-8, 72, 79-82, 87, 89, 91, 96, 99, 102, 105, 107-110, 113-115, 120-121, 183, 274-275, 306 vibrational, 262, 367 violent, 8, 73-75, 87, 109, 120 wave, 3-5, 11-13, 58, 228, 230, 236-238, 261-262, 275-276, 341, 345, 355, 360, 375 Motors, 208, 246 Mount Everest, 78, 88, 125 Multiplication, 57, 60 Muon, 8, 13, 282, 482, 487, 489-492, 505-506, 508 Muons, 282, 487 muscles, 164, 322 Musical tones, 24 mutation, 6, 8, 398-399 Myopia, 31

N Nanometer (nm), 57, 59 NASA, 20, 56, 127, 306-307, 312-313 National Academy of Sciences, 43, 398-399 natural motion, 8, 73, 91, 120-121 natural philosophy, 93-94 Nature of science, 18 Navigation, 57 nebula, 47, 129, 131, 133-134 Negative charges, 216 Neptune, 35, 462 discovery of, 462 Net charges, 201 net force, 8, 99-102, 104-105, 107, 113-117, 123, 142-143, 148, 285 neutrino, 21, 154, 311-312, 390, 482, 488-492, 505-506, 508 electron, 154, 390, 482, 488-492, 506, 508 mu, 490, 508 solar, 8, 491 tau, 8, 489-492, 505-506, 508 Neutrino detector, 21, 491 Neutrino telescope, 21 neutrino telescopes, 490 Neutrinos, 3-4, 8, 21, 154, 311, 314-315, 477, 488-491, 496-497, 508 Neutron, 54, 132-134, 138-139, 141, 143, 203-204, 244, 290, 305, 326, 344-345, 390-391, 419-420, 422, 451-452, 456-463, 468, 473-475, 493-494, 497 fusion of, 9, 452, 473-474 neutron star, 132-134, 139, 141, 143, 456 neutron stars, 54, 133, 138, 244, 305, 326 discovery of, 326 Neutrons, 6-9, 50, 63, 152, 203-204, 242, 266, 289-290, 307, 311, 317-318, 335-336, 341,

525

381, 385, 387, 389-391, 405, 420, 422, 451-452, 456-462, 465-466, 473-475, 496, 508 mass of, 133, 203, 289-290, 311, 317-318, 336, 389, 452, 458, 460-461, 466, 474 new Moon, 30, 45 Newton, Isaac, 8, 29, 35-36, 38, 47, 61, 93-94, 121-122, 137, 199, 237 and gravity, 8, 35, 61 law of inertia, 93-94 newton (N), 8 Newtonian mechanics, 271, 325, 363 Nickel, 454, 456, 473 night sky, 18-19, 31, 37, 40, 45 Nitrogen, 1, 53, 64, 69, 178, 186, 247, 251-253, 392-393, 425-426 liquid, 1, 53 molecular, 53, 64 Noise, 244 normal, 25, 30, 40, 54-55, 70, 101, 105-106, 113-114, 117, 125-126, 128-129, 131, 139, 143, 184, 240, 246, 248, 251-252, 263-265, 270-271, 280, 318-319, 390, 405, 483, 486 Normal force, 101, 105-106, 113-114, 117 Normal matter, 483 North Pole, 288, 323 North Star, 18-19, 22, 474 nova, 499 n-type semiconductors, 434 Nuclear decay, 154 Nuclear energy, 5, 11, 152, 154, 184, 246, 386, 391, 405, 423, 427, 431, 450-458, 460, 463, 467, 473-475 Nuclear fission, 289, 451, 457, 459-461, 473 Nuclear force, 14, 290, 385, 389, 406, 450-452 Nuclear fusion, 9, 12, 129-131, 416, 423, 451, 473-475 Nuclear medicine, 400 Nuclear physics, 204, 307, 326, 387, 479, 491 nuclear reactions, 387 radiation, 307, 326, 479 radioactivity, 204, 384, 387 Nuclear power, 5, 8-9, 11, 13, 159, 194-195, 258, 263-264, 267, 289, 295, 326, 399-403, 408, 416, 419, 421-425, 427-428, 430-431, 441-442, 444-447, 470-471, 488 Nuclear power plants, 263-264, 427-428, 430, 447, 470-471 Nuclear reactions, 130, 132, 152, 175, 244, 289, 386-387, 390-391, 405, 450, 453, 459 Nuclear reactors, 386, 391, 399, 416, 463, 466 nuclei, 129, 131, 133, 152, 203-206, 222-224, 242, 244, 266, 289, 307-308, 317-318, 322, 333, 370, 381, 385-390, 392, 394, 399, 405, 408-409, 450-461, 468 atomic, 133, 204-205, 222, 242, 244, 266, 289, 370, 381, 385-390, 405, 457, 459-460 Nucleus, 5-12, 58-60, 63, 154, 202-205, 221, 223-224, 242, 244, 266, 289, 366, 369-370, 381, 383-404, 405-410, 422, 450-451, 453-465, 473-475, 484, 493-495 alpha decay, 1, 5, 389-392, 405-406, 488 atomic, 5, 10-11, 58, 60, 63, 202, 204-205, 221, 242, 244, 266, 289, 370, 381, 385-391, 401, 405-406, 457, 459-460, 462-463, 474-475, 484, 493 beta decay, 5, 154, 385, 390-391, 405-406, 410, 473, 488 cell, 5, 9, 60, 242, 266, 381, 395, 397-398, 407 daughter, 3, 388, 390-391, 399, 408, 457 discovery of, 63, 389, 457, 462, 493-494 parent, 9, 352 properties of, 205, 386, 391-392, 493

O observable universe, 36-38, 135, 138, 143, 305, 313, 322 galaxies in, 38 observatories, 132, 134, 484 ocean currents, 257 ocean water, 171 oceans, 130, 251, 256, 264 seawater, 256 waves, 251, 256, 264 Octave, 24 ohms, 12, 211-212, 224 Open universe, 5, 9, 309-310 Oppenheimer, Robert, 133, 464-465, 468 opposition, 36, 258

526

Optic nerve, 243 Orbital period, 141-142 orbiter, 57 orbits, 10, 12, 28-29, 33, 35-36, 45, 47, 63, 123-124, 135, 142-143, 202-203, 205, 238-239, 289, 294, 311 circular, 10, 28, 33, 45, 47, 135, 311 elliptical, 33, 35-36 geosynchronous, 142 Order-of-magnitude estimates, 60 Ordinary matter, 12, 282, 289-290, 307, 311-312, 314, 321, 455, 496-498, 501, 508 ore, 388, 474 Oscillation, 326 Oscillations, 238, 326 amplitude of, 326 frequency of, 238 Oxygen, 1, 9, 51-54, 60, 64-66, 67-70, 106, 181-182, 186, 198, 247, 251-252, 322, 426, 456 molecular, 53, 64, 68, 424 oxygen gas, 53, 67 ozone, 2, 9, 13, 54, 64, 199, 246-250, 256, 258, 261-265, 267 ozone hole, 248, 250 Ozone layer, 246, 250

P Partial melting, 256 Particle accelerators, 391, 477, 484, 497 Particle, charged, 203 Particle detector, 356, 378 Particle model, 12, 501 Particle physics, 316, 477 Particle-antiparticle pair, 486, 491, 505 Particles, 3-4, 6-13, 21, 49-52, 58, 61, 63, 130, 133-134, 136, 152-153, 175, 186, 199, 202-207, 212, 215-216, 224, 233-237, 240-241, 243, 248, 263, 289-291, 311-312, 317, 319, 330, 332-336, 340-341, 343-345, 349-351, 357-364, 375-376, 384-385, 387, 390-393, 457-458, 477-494, 496-501, 503, 505-509 system of, 8, 153, 289 parts per million (ppm), 248 Path, 16, 18, 26, 51, 78, 286, 301-305, 309, 312, 463-464, 480-482, 498 Pauli, Wolfgang, 154, 488 Peak power, 159 Pendulum, 279 physical, 279 Period, 38, 41, 50, 59, 130, 141-142, 159, 257, 315-316, 367, 392, 413, 426, 428 of wave, 59 orbital, 141-142 wave, 2, 59 Periodic table, 9, 52, 66, 67-69, 198, 386-387, 399, 406, 409, 456, 459, 462, 464, 473 groups, 52 periods, 26, 159, 483 permafrost, 257 Permanent magnets, 215, 223-224 petroleum, 105, 177, 194, 413 Phase, 30-31, 132, 151 phases, 30-31, 46-47, 132 of Venus, 30-31 Phosphor, 5, 438 Photodisintegration, 456 Photoelectric effect, 9, 434 Photography, 243, 328 Photomultiplier, 21 Photon, 4-5, 9-10, 330-333, 338, 343-345, 354, 359-360, 364, 370-372, 376, 378-381, 480, 483-484, 486, 488-492, 495, 498, 501, 505-509 energy of, 4-5, 330-332, 345, 364, 370-371, 478, 486, 509 gamma-ray, 4-5, 390, 507 Photons, 4-5, 9-10, 13, 330-332, 334-336, 338, 341, 343-346, 358-360, 362, 367, 370, 372, 376, 379, 391, 433, 438, 480-484, 487, 489-490, 495-497, 503, 505-507 absorption of, 480 emission of, 4 energy of, 4-5, 13, 330-332, 345-346, 367, 370, 391, 433, 438, 478, 482, 487, 509 gamma-ray photon, 5 wavelength of, 334, 344-345 Photosynthesis, 2, 9, 64, 66, 67, 156, 345 photovoltaic cell, 9

Photovoltaic cells, 246, 432, 434-435, 438, 442, 446 physical change, 360 Physical laws, 62, 169, 503 physical properties, 62, 319 Physical theories, 291 physics, 5, 7-11, 15-18, 28-29, 38, 42-44, 45, 52, 54, 61-63, 71-75, 77, 79-80, 93-94, 97-98, 103, 110, 131, 135-139, 152-153, 202-204, 206, 212, 215, 217, 223, 254, 275-276, 278, 285-288, 290-291, 293-295, 307, 314-316, 330-332, 335-341, 356-358, 360-364, 366-367, 403, 433-434, 457-459, 477-484, 486-487, 490-493, 497-499, 503 Pitch, 311, 462 Planck, Max, 271, 329-330, 500 Planck time, 10, 500 Plane, 90, 115, 117, 128, 274-275, 282, 294, 456 planet, 10, 16, 24-28, 30, 32-34, 36-38, 40, 45-48, 60, 90-91, 95, 124, 133, 138, 142-143, 184, 199, 209, 251-253, 417, 438-439, 462, 498, 503 terrestrial, 251 planetary model, 10, 63, 202-205, 221-222, 366, 369, 376 Planetary system, 284, 294 Planets, 1-3, 7, 10, 12, 19, 22, 25-29, 31-38, 41-42, 45-48, 63, 68, 73, 76, 93, 123-125, 127, 129-131, 135, 137, 251, 311, 318, 364, 487 data on, 31 Earth, 1-3, 10, 12, 19, 22, 25-29, 31, 33-38, 41-42, 45-48, 68, 73, 76, 93, 123-125, 127, 129-131, 251, 311, 318, 487, 491 Jupiter, 27, 29, 35, 46, 76 Mars, 25-27, 29, 32, 35, 46-48, 124, 143, 251 Mercury, 27, 29, 35, 46-48 Neptune, 35 Saturn, 27, 29, 35, 46 Uranus, 35 Venus, 27, 29, 31, 35, 46-48, 130, 143, 251 plankton, 256 plants, 2, 17, 40, 47-48, 65-66, 158-159, 165, 171-172, 176, 184, 186, 189, 217, 250, 260, 419, 421, 425-428, 432-435, 438-440, 444, 447, 470-471 plasma, 54, 317 platelets, 398 plates, 221, 389, 482 Plato, 24-25, 34, 36, 199 Pluto, 462 discovery of, 462 Plutonium, 5, 9, 11, 392, 406, 416, 422-423, 428, 430-431, 444, 446-447, 462-468, 470-471, 473-474, 515 p-n junction, 434-435 Polar, 248, 426 polar ice, 426 Polarization, 215 pollen, 1, 51, 68-69 Pope, Alexander, 93, 270 population, 17, 146, 161, 188, 190-191, 197-198, 247, 254, 258, 297, 395, 400-403, 413-414, 467, 474-475 growth of, 413 Position, 2-3, 27, 32, 34, 37, 41, 48, 55, 59, 79, 83-84, 87, 133, 149, 162, 206, 212, 234-235, 304, 349-351, 362-363, 365, 368-369, 375-377, 379-380, 394, 480-481 Positive charges, 213-214, 216 Positive ion, 483 Positron, 1, 4, 10, 336, 389, 481-484, 487, 493, 498, 506-507 Positrons, 1, 4, 481-483, 487-488 Potential, 151, 188, 247, 443, 457, 461 Potential energy, 151 elastic, 151 gravitational, 151 gravitational potential energy, 151 pounds, 56, 98, 100-101, 114, 117, 143, 158, 400 Power, 2-5, 8-13, 17, 26, 40, 42, 49, 54, 57, 67-68, 83, 107, 152, 157-159, 163-165, 168, 171-172, 177, 180-181, 184-186, 189-190, 193-198, 202-203, 208, 217-218, 242, 246, 258, 260, 263-267, 289, 381, 399-403, 408, 419-436, 438-440, 444-447, 450-451, 453, 467, 470-471 average power, 163 machines, 40, 184 of light, 4, 13, 60, 67, 159, 203, 208, 263, 265-266, 333, 434, 446 of sound, 263

of waves, 333 production of, 2, 10, 434 solar, 8-9, 11-13, 47, 57, 60, 172, 181, 184, 190, 194, 196, 246, 258, 260, 263-264, 267, 427, 432-433, 435-436, 438, 446-447 unit of, 4, 8, 147, 157, 161, 424, 467 units of, 10, 161, 289 Power generation, 217-218, 260, 264, 415, 419, 434, 441 Power lines, 186 powers of 10, 10, 49, 56-58, 68, 317 precipitation, 256 Pressure, 55-56, 63, 68-69, 115, 129, 151, 162, 164-165, 179, 184-185, 217, 246, 399-400, 416, 419-421, 425-426, 432, 445 atmospheric, 55, 69, 246, 399, 425, 432 atmospheric pressure, 246 blood, 165, 399 in liquids, 56 measuring, 365 radiation, 5, 129, 164, 246, 365, 399-400, 425 thermal, 5, 56, 151, 162, 164-165, 177, 184-185, 246, 416, 419, 432 units, 56 primates, 395-396, 407 Princeton University, 259 Principle of equivalence, 5 Principle of relativity, 12, 271, 274-276, 278, 293-294, 300 Prism, 120, 364-365, 379 Probability, 10-11, 13, 340, 344, 355, 368-369, 376-377, 392, 398-399, 410, 430, 478-480, 483, 499 probe, 57, 59, 107, 259, 306, 502 producers, 417 products, 6, 184, 250, 432, 474 Projection, 255 Projectors, 200 Promethium, 515 Proportionality, 9, 84, 96, 98, 100, 201-202, 211 proportionality constant, 9, 202 proportions, 307, 403 Propulsion, 12, 106, 154 Protein, 53 Proton, 1, 10, 69-70, 202-204, 206, 218, 290-291, 315, 344-345, 351-352, 367, 369, 376, 380, 385, 390-391, 460, 473-474, 480, 482-487, 489-490, 493-499, 501, 508-509 mass of, 10, 203, 290, 345, 452, 460, 474, 487, 490, 497, 501 Proton fusion, 452 Protons, 1-2, 6-9, 50, 63, 152, 201, 203-206, 209, 224, 238, 242, 266, 289-290, 307, 311, 317-318, 335-336, 338, 351-352, 381, 387, 389-392, 405, 450-452, 458, 482-484, 493-494, 496, 498, 500-501 charge of, 201, 203, 206, 224, 493 mass of, 14, 133, 203, 289-290, 311, 317-318, 336, 345, 389, 452, 458, 500-501 pseudoscience, 10, 18, 39-43, 45, 47 Ptolemy, 10, 13, 26-31, 34-36, 38, 45-48 p-type semiconductors, 434 pupil, 243, 345 pure substance, 2, 52, 64 Pythagoras, 22-25, 28, 36

Q Quality, 136, 170, 173, 176, 193-194, 415, 439, 464 Quanta, 10-13, 329-331, 333, 336, 338, 345, 349-350, 361-362, 364, 397, 478-480, 482-483, 489-490, 494-497, 500, 505, 508 Quantization, 10, 138, 206, 325, 329, 331-332, 434, 479 atomic, 10, 331 of charge, 10, 206 of energy, 10, 206, 329, 331-332, 434 Quantized, 6-7, 9-11, 13, 138, 206, 316, 325, 327-329, 331-332, 336, 338, 345, 348, 353, 362, 370, 433, 477-478, 480, 497, 501 Quantum computers, 352, 360-361 Quantum gravity, 318, 477, 498-499, 501, 503, 505-506 Quantum jumps, 370-372, 376, 378-379, 381 Quantum mechanics, 291, 325-326, 333, 339, 353, 478 Quantum physics, 7-8, 10-11, 93, 137-138, 202, 241, 270, 315, 325-326, 330-331, 335-341, 343-345, 348-349, 357-358, 360-364, 367, 370, 387, 390-391, 433-434, 503

atomic structure, 348 lasers, 326, 360 photoelectric effect, 434 quantum state, 4, 11, 370-372, 376, 482 Quark, 3, 11-13, 317, 485, 493-496, 501, 505-506, 508 Quark-antiquark pair, 495 Quarks, 10-12, 50, 206, 290, 317-318, 385, 477, 488, 493-497, 503, 505-506, 508 types of, 8, 508 Quarter Moon, 30 quasars, 135

R RA, 515 radar, 11, 90, 242-243, 245, 265-266, 304, 381 Radiant, 5, 11, 152, 161, 164-165, 176, 210, 242, 245-246, 251-252, 317, 330, 391, 447 radiant energy, 5, 11, 152, 176, 242, 245-246, 251-252, 330, 391 emission of, 11 types of, 152 Radiation, 3-14, 41, 43, 60, 128-131, 164, 176, 227, 237, 242-247, 250-252, 259, 263-267, 276, 287-288, 290, 304, 306-307, 309-311, 313, 315, 318, 321-322, 325-327, 329-333, 336-337, 360, 364-366, 370-371, 376, 379-381, 388-390, 397-404, 405-410, 424-425, 427-428, 433-435, 447, 471-472, 478-479 alpha, 1, 5-6, 263, 389-390, 397-400, 405-406, 447, 460 as particles, 330, 332, 478 background, 3, 60, 176, 227, 243-244, 304, 306-307, 309-310, 315, 318, 321-322, 428 beta, 1, 5-6, 14, 389-390, 397-398, 400, 405-406, 410, 447 cosmic background, 60, 315, 318, 322 defined, 12-13, 293 doses of, 401 electromagnetic, 3-6, 8-12, 41, 227, 237, 242-246, 250, 263, 265-267, 276, 278, 287-288, 290, 311, 313, 315, 360, 364-366, 381, 386, 400, 409-410, 433, 478-479 environmental, 176, 246-247, 250-251, 428, 433 gamma, 4-6, 242, 244-245, 261, 266, 288, 296, 345, 381, 389-390, 397-398, 400, 405-406, 487 gravitational, 5-9, 14, 41, 128, 131, 164, 288, 304, 306, 313, 322, 336, 370, 447 half-life, 397, 399, 404, 405-407, 410, 471 Hawking, 364 in universe, 318 ionizing, 6, 8, 11-14, 244, 261, 397-398, 403, 408 laws of, 10, 276, 287, 345, 364 light and, 9, 263, 287, 329, 343, 427, 433-434 medical uses of, 398 nonthermal, 12 particle, 1, 6-14, 60, 242-243, 266, 290, 315, 326-327, 329-330, 332-333, 336-337, 345, 360, 381, 386, 389-390, 406 solar, 3, 8-9, 11-13, 60, 128-131, 176, 245-247, 250, 261, 263-264, 267, 296, 309, 364, 427, 433, 435 terrestrial, 251 thermal, 9, 12-13, 164, 176, 242-243, 246, 265-266, 330, 381, 401, 421, 424, 433, 435 types of, 4, 6, 8-9, 307, 326, 389, 398, 405, 435 ultraviolet, 4-6, 9, 12-13, 227, 242-247, 250-251, 263-264, 266-267, 366, 381 units of, 10, 329 Radiation dose, 398, 404 Radiation exposure, 400, 404 radiation zone, 472 Radio radiation, 365 Radio signals, 21, 133 Radio telescope, 21, 133 Radio telescopes, 243 Radio waves, 11, 133, 239, 241-245, 261, 263, 265-266 radioactive dating, 11, 42-43, 384, 391, 393-394, 396, 405-406, 408, 517 radioactive decay, 9-11, 59, 154, 339, 352, 364, 384, 388-391, 393-394, 405-406, 409-410, 457, 473, 475 radioactive isotope, 6, 11, 392-394, 398-400, 406, 409, 422, 457, 461, 468 Radioactive isotopes, 11, 389-392, 399-401, 405-407,

427, 458-459, 472 Radioactivity, 2, 9, 13, 204, 383-404, 405-410, 428-430, 432, 470-471, 517 alpha decay, 389-392, 405-406 alpha particle, 204, 389-392, 406 beta decay, 385, 390-391, 405-406, 410 beta particle, 390 gamma rays, 389-390, 397-398, 400, 405-406, 410 half-life, 384, 391-393, 397, 399, 404, 405-407, 410, 471 Radios, 240 Radium, 389-390, 399, 457, 515 Radius, 23, 47, 78, 88, 125-126, 128, 133, 135, 142-143, 265, 296, 318, 500 of Earth, 47, 125, 128, 142, 265 of Mars, 47 of Mercury, 47 of stars, 135, 318 Radon, 8, 11, 392, 399-404, 405-406, 408, 410, 515 decay, 11, 392, 399-400, 405-406, 410 Rainbow, 365, 380 Rainbows, 365 Random kinetic energy, 366 Randomness, 326, 331, 339, 480 ranges, 244, 256, 350-351 reacting, 264, 419, 422, 464, 473, 475 Reaction, 5, 64-66, 67, 69, 247, 266, 384, 386, 391, 401, 419-422, 451-454, 457-458, 460-461, 463, 465, 468-469, 471, 473-475 recharging, 181 Recoil, 115, 499 red blood cells, 398-399 red light, 263, 288, 331, 343 redshift, 11, 313 gravitational, 313 reduction, 2, 12, 35, 125, 152, 158, 181, 257-259, 439 reference frames, 5, 12, 283, 323 accelerating, 323 time in, 283 Reflection, 233, 265, 299 Refrigerators, 157, 246, 250 Relative motion, 11, 13, 272, 275, 293 velocity, 13, 275 Relativity, 4-7, 10-13, 72, 93, 123, 137-139, 144, 241, 269-291, 293-297, 299-300, 303-306, 308-309, 312, 315-316, 319, 321-323, 330-331, 345, 477-480, 482, 492, 497-499, 501-503 energy and, 199, 271, 288, 296, 306, 315, 478 events, 1, 11, 290, 304, 497, 499 general, 4-7, 12-13, 93, 123, 137-139, 270-271, 278, 299-300, 303-306, 308-309, 312, 315-316, 319, 321-323, 330-331, 479, 492, 497-499, 501-503 general theory of, 4-6, 12, 278, 293, 299-300, 303-304, 306, 312, 479, 498-499 length contraction, 7, 11, 285-287, 295 measurements, 11, 272, 284, 286, 289, 295, 304-305 of motion, 1, 6, 11, 13, 72, 123, 137-138, 144, 284-286, 293-294, 345 of time, 4, 7, 11, 13, 137, 139, 271, 278-282, 284, 293-294, 315 special, 1, 7, 11-12, 137-139, 144, 269-291, 293-297, 299-300, 304, 316, 319, 322-323, 345, 387, 477-480, 492 speed of light, 138-139, 276, 278, 299, 499 theory of, 4-7, 10-13, 72, 123, 137-138, 241, 269-291, 293-297, 299-300, 303-306, 312, 325, 345, 479-480, 492, 497-499, 502 time dilation, 11, 13, 281-282, 284-287, 294-297 reptiles, 395, 407 research, 43, 181, 204, 312, 335, 395, 400, 434, 471, 479 reservoirs, 426 Resistance, 1, 5-6, 28, 74-77, 79, 83-84, 89-91, 95-96, 100-101, 105-107, 114-117, 123, 141-142, 147, 150, 152, 155-156, 161-165, 173, 178, 181, 183, 207-208, 286, 467, 497 equivalent, 12, 155, 163, 183 internal, 6, 9, 107, 147, 178 Resistive force, 1, 12, 113-114 Resolution, 20, 201, 360, 491, 493 angular, 493 telescope, 20 Resonance, 394 respiration, 12, 64-66, 67, 412 Rest mass, 296, 332, 475, 486

527

Retina, 243 retrograde motion, 12, 24-26, 29-30, 34, 45-46 rock, 5, 13, 18, 23, 56, 69, 73-74, 89-91, 96-98, 107, 114-117, 161-164, 173, 193-194, 198, 210, 289, 362, 370, 433, 437 formation, 452 sedimentary, 394 types, 161, 164 Rocket propulsion, 12, 106 rocks, 18, 87, 106-107, 124, 131, 240, 251, 394, 400, 406, 433 sedimentary, 394 rods, 2, 6, 9, 11, 27, 419-421, 425, 427-431, 444-445, 447 Ropes, 235 Rotation, 19, 24, 29-30, 105, 279 of Earth, 30 rate of, 24 Rotational motion, 12, 153 rubber, 105, 151, 162, 164, 207, 236, 288-289, 291, 451, 501 Rubin, Vera, 311 Runaway greenhouse effect, 130 Rutherford, Ernest, 202, 204, 364

S S waves, 239-240, 243 Sagan, Carl, 34, 40, 283, 512 Salam, Abdus, 488-489 satellites, 12, 40, 77, 122-125, 134, 138, 142, 265, 299, 304, 306 communications, 142, 265 orbits, 12, 123-124, 142 Saturn, 23, 27, 29, 35, 46 scanning tunneling microscope (STM), 59 science, 12, 15-44, 45-48, 49, 51, 59, 61-64, 72, 75, 93-94, 132, 134-137, 150, 152-153, 217, 248-251, 278, 290, 307-308, 316, 339, 363, 394-396, 457, 464, 490-491, 496, 501, 503, 512-513 and technology, 17-18, 43, 248, 457, 512 astronomy, 17-18, 28, 30, 33, 37-39, 42, 45, 134-135, 395 chemistry, 2, 17, 40, 42, 64, 249, 388, 395, 405, 470 hypothesis, 1-2, 12, 18, 22, 24-26, 29, 34-36, 41, 43, 45, 47, 248, 316, 395, 482, 501 limitations of, 137 mathematics, 17, 24 nature of, 18, 49, 63, 501 physics, 15-18, 28-29, 38, 42-44, 45, 61-63, 72, 75, 93-94, 135-137, 150, 152-153, 217, 237, 240, 271, 278, 290, 307, 316, 339, 363, 395, 503, 512-513 pseudoscience, 18, 39-43, 45, 47 roots of, 512 Scientific method, 18, 43, 517 stars and, 18 seasons, 196, 245 Seawater, 256 second, 4-8, 12, 17, 24, 37-38, 40-43, 55, 76, 78-79, 81-85, 87, 90-92, 94-95, 99-100, 102-106, 108-110, 114, 117, 132-134, 136, 138, 147-149, 157-159, 167-191, 193-198, 208-211, 213, 215, 232-233, 235-236, 238-240, 245, 247-248, 256, 265-266, 276, 287-288, 307, 312, 318-319, 331-333, 357-360, 394-395, 398, 404, 435, 437, 439, 459-460, 469, 502, 508 Second law of thermodynamics, 1, 7-8, 12, 42, 147, 167-191, 193-198, 415 seeds, 38, 352, 494-495 Seeing, 40, 58, 243, 304 Semiconductors, 434-435, 442 p-n junction, 434-435 senses, 38, 276 shale, 417 shell, 22, 95, 117, 130, 204 Shock wave, 456 Short circuit, 12, 212, 221 silicon, 59, 66, 69, 326, 434, 515 Silver, 52, 314, 359-360, 432, 515 Slip rings, 218 smell, 51, 54, 67 Smog, 247 snow, 168, 256, 307 Sodium, 52, 205, 265, 345, 366, 376, 515 Sodium atom, 345 soil, 7, 47, 50, 400

528

solar eclipse, 303 Solar energy, 3, 9, 11, 66, 146, 176, 190, 196, 198, 199, 245-246, 248, 417, 427, 435 global warming, 190, 199, 246, 417, 427 seasons, 196, 245 solar masses, 8, 134 solar neutrino, 491 problem, 491 Solar neutrino problem, 491 Solar neutrinos, 491 solar power, 260, 264, 267, 427 solar radiation, 9, 12, 176, 245, 250, 261, 263, 296, 433, 435 Solar system, 35, 47, 57-58, 60, 87, 96, 106, 124, 128-131, 133, 135, 153, 222, 309, 364, 394-395, 407-408, 456 age of, 309, 394, 407-408 asteroids, 106 astronomical unit, 47 black holes, 133, 135, 153, 309 comets, 130 cosmology, 135, 309 formation of, 130, 456 meteoroids, 87 Milky Way, 60, 135, 309 Moon, 47, 87, 128, 131 planets, 12, 35, 47, 124, 129-131, 135, 153, 364, 456 properties of, 13 sun, 35, 47, 60, 106, 124, 128-131, 133, 135, 364, 456 Solids, 55-56, 67, 136, 204, 385 molecules, 55-56, 67, 385 solstices, 19 solutions, 17, 258, 432 solvent, 249, 263 Sound, 24, 91, 115, 156, 236-237, 239-240, 244, 267, 361 interference, 263 nature of, 91, 310, 361 origin of, 361 speed of, 91, 115, 237, 239 Sound waves, 236, 240, 263, 310 Sources of energy, 258, 411-412, 423 Space, 3-7, 9-14, 16, 18, 20-21, 24-25, 28, 38, 40, 53, 55, 57, 60-61, 63, 69, 76-78, 87-89, 95-98, 106-107, 126-134, 137-139, 176, 199, 206, 212-214, 216-217, 244, 250-252, 259, 270-271, 284-285, 287-288, 290-291, 300-316, 319, 330, 336, 357, 402, 426, 435, 455-456, 477-478, 484-488, 497-503 at, 3-4, 6-7, 9-14, 16, 18, 21, 24-25, 28, 38, 40, 60, 63, 76-78, 87-89, 95, 97-98, 101, 106-107, 126-134, 137-138, 176, 199, 212-214, 216-217, 234, 241-242, 244, 250-251, 259, 270-271, 284-285, 290-291, 300-302, 304-316, 319, 330, 357, 402, 426, 455-456, 477-478, 484-488, 497-503 black holes, 1, 3, 133-134, 138, 153, 305, 309, 311, 314, 485-486, 502 conservation of momentum, 7, 113, 128, 153, 206 cosmology, 3, 300-316, 319, 321-323, 488 curvature of, 122, 303, 305, 314, 498 geometry of, 5, 9, 310, 314, 319, 321-322, 503 telescopes, 20-21, 237, 306, 313, 490 weightlessness, 5, 14, 126, 305, 322 Space program, 25, 88 Space Shuttle, 106 Space Station, 322 Space travel, 106, 284 spacetime, 5-6, 12, 299-300, 304-305, 315, 492, 498, 500, 502-503 curved, 304-305 geometry of, 5, 492, 503 mass and, 6 time and, 5, 12, 500 Sparks, 366 Special relativity, 1, 7, 11, 137-139, 144, 270-271, 278, 291, 316, 319, 323, 326, 387, 477-480, 492 Special theory of relativity, 5, 12, 269-291, 293-297, 299-300, 322, 325, 345, 479-480 species, 1, 17, 38-40, 249, 251, 256, 395, 428, 462, 512 Spectra, 10, 307, 364-366, 371, 376, 379-380 continuous, 10, 365-366, 379-380 continuous spectra, 366, 380 electromagnetic, 10, 364-366 line spectra, 10, 365-366, 379

types of, 307 spectroscope, 12, 364-365, 371, 376, 379 Spectroscopy, 365 spectrum, 11-12, 239, 241-245, 250, 261, 263, 266, 306-307, 313, 365-367, 371, 379-381, 386, 483, 487, 506 emission, 4, 11, 371 Speed, 1-3, 8-14, 21, 46, 74, 76, 78-85, 87, 89-92, 94-95, 97-99, 105, 107, 109-110, 113-117, 133-135, 138-139, 147-149, 153, 177-180, 183, 208, 229, 237-239, 265-266, 272-279, 281-282, 285-287, 293-296, 318, 321-322, 386-387, 464, 481, 484, 498-499 and air resistance, 76, 89 and gravity, 8, 299 average, 6, 13, 80, 87, 89-92, 139, 163, 173, 177, 287, 316, 386, 419, 498 average speed, 6, 80, 87, 89-92, 287, 386, 498 escape, 1, 9, 133-134, 183 in units, 12-13 instantaneous, 1-2, 6, 9, 11-13, 80-81 instantaneous speed, 1, 6, 12-13, 80-81 kinetic energy and, 149 molecular, 138, 175, 194 of light, 21, 90, 110, 133-135, 138-139, 143, 153, 208, 237, 239, 265-266, 273, 276, 278-279, 299, 315, 322, 330, 499 of sound, 115 terminal, 164, 208 units of, 10, 161 wave, 1-3, 8, 11-14, 229, 237-239, 265, 275-276, 278, 344-345 Speed of light, 21, 90, 110, 133-135, 138-139, 143, 153, 208, 237, 239, 265, 276, 299, 499 in a vacuum, 239 relativity, 138-139, 276, 278, 299, 499 Speed of sound, 115 speedometer, 79-80, 83 sperm, 398 Spherical surface, 303 spin, 29, 91, 275, 394 Spiral galaxy, 312 Spontaneous emission, 1 Springs, 101, 279 stability, 130 Stable isotopes, 391, 409 Stadium, 229 Standard model, 6, 10, 12, 212, 290, 477, 496-498, 503, 506 standing wave, 12 Stanford Linear Accelerator, 315, 494 star, 12-14, 18-19, 22, 27, 29, 35, 37, 39, 46-47, 123-124, 128-134, 141, 143, 245, 283-284, 294, 302, 305, 309, 394, 455-456, 468, 498 star formation, 130 Starlight, 302 stars, 5, 12-14, 16-25, 27-30, 32, 34, 37-39, 45-48, 49, 54, 59-60, 68-69, 73, 100, 120, 124-125, 127-135, 175, 236, 243-244, 284, 302, 305, 307-309, 311, 315, 365, 394, 450-452, 455-456, 502 constellations, 19 neutron, 54, 132-134, 138, 141, 244, 305, 326, 385, 451-452, 456 neutron star, 132-134, 141, 456 supernova, 13, 130, 132-134, 315, 456, 473 white dwarfs, 14, 131-132, 456 Steam, 3-5, 7, 12, 54, 67, 69, 106, 146, 157, 170-172, 177, 184-186, 193-196, 217-218, 419-422, 426, 429, 432, 435-436, 438 Steel, 105, 183, 401, 421 Stellar evolution, 128 theory of, 128 stomach, 38 Stonehenge, 19 Straight-line motion, 121 acceleration, 121 velocity, 121 Strain, 188 Strangeness, 271, 276 strata, 394 stratosphere, 9, 12, 247-250, 264 streams, 1, 203, 390, 426 Stress, 439, 477 stresses, 93 string theory, 501, 503 Strings, 12, 94, 501-502, 509 strong force, 3, 6, 12-13, 202, 316-318, 385-386, 392, 405, 409, 488, 492-497, 500, 505-506,

508-509 quarks and, 494, 496-497, 506, 508 strong nuclear force, 385, 389, 406, 450-451 Subatomic particle, 7, 277, 282, 286, 481 Subatomic particles, 21, 133-134, 153, 203, 221, 263, 282, 319, 450, 493 Sulfur, 51, 53, 68-69, 186, 424-426, 431, 437, 439, 446, 515 sulfur dioxide, 51, 68, 431, 439 sulfuric acid, 67 Sun, 1-2, 9-10, 18-19, 21-25, 27-37, 39, 41, 43, 45-48, 60, 63, 65-66, 73, 77-79, 84, 90, 100, 120, 123-125, 128-135, 138, 141, 143-144, 176, 179, 238-239, 244-248, 250-252, 259, 265-266, 278-279, 284, 295-297, 302-305, 364-366, 417, 431, 433, 446-447, 455-456, 466, 474-475, 490-491 active, 1, 304, 435 atmosphere of, 251 composition of, 247, 259 constellations and, 19 diameter of, 305 evolution of, 1, 43, 128 features of, 24, 41 interior of, 244 mass of, 10, 12, 100, 124, 132-135, 143, 164, 265, 295-296, 305, 311, 318, 452-453, 466, 474, 490 neutrinos of, 491 nuclear fusion in, 130 orbit of, 47, 138 oscillations, 238 path of, 2, 144, 302-303 radius of, 47, 78, 265, 318 regions of, 129, 244 rotation of, 24, 30 spectrum of, 244, 365 structure of, 9, 152 temperature of, 2, 176, 250-251, 259, 296, 366 visible surface of, 259 weight of, 14, 100, 133, 143, 297, 474-475 Sunlight, 9, 12, 40, 152, 161-162, 172, 176, 227, 245, 247-248, 257, 296, 436-437, 447 superclusters, 318 superconductors, 54, 154, 326 supernatural, 42-43 supernova, 1, 13, 130, 132-134, 294, 313, 315, 456, 473-474 white dwarf, 456 Supernova explosion, 13, 130, 132-134, 313 Supernovae, 13, 452, 456 Superposition, 349 Supersymmetry, 240, 503 surface area, 196 surface temperature, 176, 251, 254-255 surface waves, 231-232, 262 Symmetry, 37, 55, 153, 237, 317, 332-333, 336, 480, 503 System, 7-8, 10, 22, 26, 28, 32, 35, 38, 43, 47, 56-58, 87, 96, 98, 101, 106-111, 117-118, 128-131, 133, 135-137, 149-154, 161-162, 171, 173-175, 182, 194, 246, 250-251, 288-291, 304-306, 309, 361-362, 394-395, 407-408, 427, 437, 452-453, 482-483 Systems, 10-11, 43, 68, 138, 150, 155, 171-173, 175-176, 296, 360, 364, 385, 417, 438, 456, 471, 482-483 energy of, 173, 364, 438, 456, 482 isolated, 6, 43, 438 ordered, 482

T Technetium, 515 technology, 17-18, 41-43, 97, 105, 161, 182, 184, 194, 237, 243, 248-249, 259-260, 263, 267, 425, 430-434, 457, 468 telescope, 19-21, 30, 35, 37-38, 76, 129, 131, 133-134, 263, 306, 311-312, 316, 365 Hale, 311 high-energy, 266, 312 infrared, 263, 266 neutrino, 21, 311-312 Newtonian, 38, 131 optical, 134 radio, 21, 133, 263, 266, 306, 365 resolution, 20 size of, 131 ultraviolet, 263, 266 Telescopes, 20-21, 27, 29, 45, 237, 243, 306, 384, 490

Hubble Space Telescope, 20, 306 resolution of, 20 Temperature, 2-4, 56, 74, 106, 151, 154-155, 169, 171-177, 179, 181, 184-185, 193, 198, 246, 250-251, 254-259, 306-310, 316, 365-366, 376, 419, 422, 429, 438, 453-455, 468-469 absolute, 74, 171, 306 atmospheric, 6, 246, 250-251, 257-258, 264 body, 6, 106, 193, 255, 267, 308, 474 energy and, 151, 154, 169, 193, 296, 306, 454-455 mass and, 2, 6, 296 of stars, 365 on Mars, 251 Tension, 340 terminal speed, 164 Terminals, 206-207, 209 Theory, 4-14, 18, 22, 26-36, 38-39, 43, 45-48, 50-51, 54, 61, 63-64, 67, 69, 72-75, 123-128, 137-138, 212, 235-239, 241, 247-248, 258, 269-291, 293-297, 299-300, 302-307, 329-332, 336, 338-339, 353-354, 357, 363-364, 387, 477-482, 486-490, 492, 494, 496-503 Theory of relativity, 4-6, 12-13, 269-291, 293-297, 299-300, 303-304, 306, 312, 325, 345, 479-480, 498-499 thermal energy, 2, 12-13, 65, 148, 150-156, 161-162, 168-178, 184-186, 198, 210, 246, 257, 265-266, 288-289, 295-296, 391, 401, 415, 417, 421-422, 424, 432-433, 435-438, 446-447, 452-454, 475, 486 absolute zero, 171 heat, 12, 65, 168, 170-173, 175-177, 184-186, 193-194, 196, 198, 246, 257, 415, 421-422, 432, 438, 446-447 microscopic, 13, 151-155, 161-162, 169, 171, 174-175, 198, 202, 391, 435, 486 of gases, 174 temperature, 2, 13, 151, 154-155, 169, 171-177, 184-185, 193, 198, 246, 257, 296, 419, 422, 438, 453-454 Thermal expansion, 256 water, 256 Thermodynamics, 1, 7-8, 12-13, 42, 147, 154, 167-191, 193-198, 415 energy resources, 172-173, 195, 415 entropy, 1, 7, 12, 168, 173-176, 193-194, 198 first law of, 154, 168 heat engines, 7, 12, 168, 170-171, 177, 182, 193-194, 196, 415 internal combustion engines, 177 laws of, 168, 173, 193, 271, 481 second law of, 1, 7-8, 12, 42, 147, 167-191, 193-198, 415 Thermometers, 56, 254 Fahrenheit, 56 thermonuclear fusion, 468-469 Thomson, J.J., 203 Thorium, 391, 423, 515 Thrust, 37, 39, 101-102, 114, 116, 163 thyroid gland, 398 tide, 61 Tides, 41, 93 Time, 3-7, 9-14, 16, 18, 22, 25-26, 30-31, 33-34, 38, 42, 45-47, 54, 59-61, 69, 72-76, 79-85, 87, 89-92, 97, 103, 107, 109-111, 116-117, 120-123, 127, 135, 137-139, 141-142, 147-149, 156-158, 163-164, 174-175, 184, 187-190, 196-198, 212, 236-240, 246, 248, 253-254, 264-267, 270-272, 278-287, 293-297, 304-309, 312-313, 315-319, 338-340, 353-354, 392-394, 403-404, 422-423, 426-429, 439, 446-447, 455, 467, 486, 488, 492, 494-495, 497, 502-503 beginning of, 33, 47, 82 dilation, 11, 13, 281-282, 284-287, 294-297 gravity and, 5-6, 13, 76, 121, 299-300, 488 in different reference frames, 283 measurement of, 9, 284, 295, 302 of events, 353 Planck, 9-12, 271, 329, 332, 343, 500 relativity and, 5, 11-12, 72, 271, 278, 293, 480, 497 relativity of, 7, 11, 13, 271, 278-279, 281-282, 284-285, 293-295 uncertainty principle, 6, 11, 13, 139, 306, 316, 351, 353, 486, 500 units of, 10, 329 Time delay, 237, 265 Time dilation, 11, 13, 281-282, 284-287, 294-297

tissue, 200, 204-205, 215-216, 221-222, 224, 353 titanium, 515 Total angular momentum, 153 Total electric charge, 482 Total energy, 150, 153, 164, 173-174, 182, 289, 329, 336, 349, 418-419, 424, 438, 441-442, 447, 486 Total force, 96 Total mass, 142, 184, 288-290, 295-296, 311, 321 Total momentum, 7-8, 107-108, 110-111, 113, 115, 153 touch, 54, 103, 169, 206 Tracers, 399 Transformers, 157 Transistors, 326 transit, 184, 418 Transitions, 151, 379 Transmission, 178, 186, 195, 237, 239, 243, 330, 415, 433, 441 Transparency, 200, 204-205, 213, 215-216, 221-222, 224, 236 transportation, 13, 171-172, 176-178, 182-184, 193-194, 196-198, 264, 412, 415, 427, 431-432, 441, 443, 446-447 tree of life, 395 troughs, 231-232, 262 Tungsten, 59, 207, 334, 515 Turbulence, 128, 498 gas, 128 Tycho Brahe, 31, 33, 395

U UFOs, 13, 40 Ultraviolet radiation, 5, 9, 13, 227, 243, 246-247, 250, 264, 267, 366 Uncertainty, 6, 10-11, 13, 139, 254-256, 305-306, 316, 325, 331, 339-340, 343-344, 348-353, 357, 359-363, 369, 378-380, 385-386, 390, 486, 498, 500 Uncertainty principle, 6, 11, 139, 306, 316, 348-349, 351-353, 359, 375-376, 378-380, 386, 486, 498, 500 Uniform circular motion, 13, 28, 33, 45 Uniform motion, 28 Units, 10, 12-13, 49, 56-58, 82, 84, 98, 100, 157, 202, 251, 288-289, 307, 329, 438, 483, 499 astronomical, 12, 98, 100 of charge, 10, 202 of radiation, 4, 10, 307, 329, 483 Universal constant, 329 universe, 1-6, 8-9, 11, 16, 22-25, 27-29, 31-34, 36-39, 43, 46-47, 53-54, 58-62, 66, 74, 76, 93-94, 110-111, 119-140, 141-144, 147, 154, 175-176, 181, 199, 240-241, 243-244, 275-276, 278-280, 290-291, 321-323, 331, 347-373, 375-381, 384-386, 391, 394, 427, 454-456, 477-481, 485-487, 496-497, 500, 502-503 acceleration of, 1, 8, 127, 300, 305, 314, 323 age of, 53, 299, 306, 309, 394 big bang, 43, 59, 175, 244, 300, 306-311, 313-314, 316-319, 321-323, 352, 452, 455-456, 481, 483, 486-487, 491, 496-497 birth of, 326 black holes, 1, 3, 54, 133-135, 138, 305, 309, 311, 314, 485-486, 502 closed, 2-5, 54, 121, 309-310, 319, 326, 355 composition of, 307, 376, 394 critical, 5, 427, 513 expansion of, 1, 4, 11, 300, 307-308, 313-314, 316, 318, 321-322, 352 fate of, 168, 175 flat, 5, 9, 23-24, 33, 47, 74, 303-304, 308-310, 319, 321-323 galaxies, 1, 4-5, 38-39, 47, 59-60, 110, 132, 134-135, 306, 308-309, 311-314, 318-319, 321-323, 352, 365, 483, 502 geocentric, 37 geometry of, 2, 5, 9, 310, 314, 319, 321-322, 503 night sky, 31, 37 open, 5, 76, 309-310, 319, 355, 361, 513 quasars, 135 radiation in, 243 relativity and, 5, 11, 93, 144, 276, 278, 291, 477-478, 497, 513 stars, 5, 8, 16, 22-25, 27-29, 32, 34, 37-39, 46-47, 54, 59-60, 124-125, 127-135, 141, 175, 243-244, 302, 305, 307-309, 311, 315, 365, 385, 394, 455-456, 502 Unlike charges, 3

529

up quark, 12 Uranium, 5-7, 9, 13, 289, 296, 385, 388-390, 392, 396-397, 406, 416, 419-423, 430-431, 442-444, 446-447, 456, 459-462, 464-472, 473-475, 515 isotopes, 6, 389-390, 392, 406, 459, 461-462, 464, 468, 472 uranium dating, 397 Uranium isotopes, 461-462 Uranus, 35, 462 discovery of, 462

V Vacuum, 55, 67, 74, 147, 185, 216, 218, 239, 314, 316-317, 333, 393, 486-487 perfect, 55, 67, 147 vacuum energy, 7, 487 vapor, 13, 54, 64-65, 251-253, 255-257, 265, 366, 376, 424, 438 variation, 239 Vector, 110 Vector addition, 110 Vectors, 8, 110, 257 area, 257 force, 8 unit, 8 velocity, 8, 110 Vega, 284 Velocity, 7-8, 13-14, 69, 72, 79-83, 87, 89-91, 96, 99, 102, 105-110, 113-115, 117, 120-121, 183, 212, 273-275, 306, 333-334, 349-353, 362-363, 375-376, 379-380 acceleration and, 96, 109, 117 and acceleration, 72, 82 average, 13, 69, 80, 87, 89-91, 351 escape, 1, 183 in two dimensions, 110 instantaneous, 1, 13, 80-81, 353 of Earth, 87, 91, 141-142 relative, 7, 13, 164, 183, 273-275, 294, 301 straight-line motion, 121 terminal, 164, 208, 212 wave, 1, 7-8, 13-14, 273, 275, 333-334, 345, 349-350, 352-353, 362, 375-376, 380 Venus, 23, 27, 29-31, 35, 40, 46-48, 130, 133, 143, 251-252 atmosphere of, 251 distance from Earth to, 47 greenhouse effect on, 251 mass of, 133, 143 orbit of, 47 phases of, 30-31 radius of, 47 surface of, 133, 143, 251-252 vertebrates, 395, 407 vibrations, 5, 228-229, 234, 242, 266, 278, 381, 439, 501, 503 violent motion, 73-74 violet light, 243 Visible galaxy, 312 Visible light, 133, 157, 238, 243, 267, 343, 346, 438 frequency of green, 243 Vision, 17, 31, 136-137, 458 void, 152 volcanoes, 407 Voltage, 9, 12-13, 210-212, 221, 224, 244, 486 peak, 9 terminal, 210, 212, 486 Volts, 7, 13, 210-211, 224, 484, 486 Volume, 10, 41, 54-56, 67-69, 114, 131, 174, 204, 207, 309, 329, 331, 369, 424, 426, 439, 465-466, 493, 498, 500, 502 units of, 10, 329

W walking, 59, 157, 164, 182-184, 194, 197 Waste heat, 446 Wastewater treatment, 411 Water, 5-9, 12-13, 21, 41, 43, 50-55, 58, 60, 62, 64-66, 67-70, 73, 91, 104-106, 120, 151-152, 155-156, 162-164, 174-179, 181-182, 184-186, 198, 207-209, 217, 232-235, 237, 251-253, 255-257, 261-262, 264, 329-330, 364, 403, 411, 419-422, 426-427, 429-433, 435, 444-447, 471, 489, 498 boiling, 55, 91, 169, 184, 193-194, 296, 421, 498 cycle of, 1, 194 density, 5, 55

530

drinking, 403, 408 forms, 1-2, 8-9, 12, 53, 55, 64, 151-152, 155-156, 163-164, 184, 207, 264, 287, 380, 432, 435 fresh, 251, 394 heavy, 1, 9, 91, 104, 181, 184, 256, 322, 459 in chemical reactions, 2, 64 life and, 406, 459, 471 ocean, 171, 194-195, 198, 251, 256-257, 426 on Earth, 1-2, 41, 43, 52, 54-55, 60, 64, 67, 73, 91, 120, 176, 181, 251, 427, 432 on Mars, 251 thermal expansion, 256 wastewater treatment, 411 waves of, 230, 235 water vapor, 2, 6, 13, 64-65, 251-253, 255-257, 424, 481 watershed, 32, 415 Watt, 10, 57, 157, 161, 164, 201, 297, 412, 446 Watt, James, 157 watt (W), 157 watts, 57, 157-158, 163, 177, 196, 245-246, 446, 453 Wave function, 7, 336 Wave packets, 350, 357-359, 375 uncertainty and, 357 Wavelength, 11, 14, 58-60, 67, 222, 229-230, 235, 239, 242, 244-245, 263-267, 313, 333-334, 343-346, 349, 365, 371, 379, 381 of electrons, 14, 333-334, 344 of radio waves, 261 rest, 11, 334, 343, 349 Wavelengths, 13, 59, 235, 241-245, 261, 263, 265-267, 338, 349-350, 364, 366, 372, 379, 381 of electromagnetic waves, 241, 243-244 of sound waves, 263 Waves, 4-5, 11, 58-59, 133, 227-260, 261-267, 276, 278, 288, 310, 326-327, 330-336, 338, 341, 343-345, 349, 368, 381, 405, 423 amplitude, 229-230, 261, 265, 326 body, 5, 244, 255, 267 circular, 232, 262 compression, 228 disturbance of, 229 electromagnetic, 4-5, 11, 227, 235-246, 250, 263, 265-267, 276, 278, 288, 313, 338, 381 electron, 4, 8, 11, 58-59, 133, 244, 288, 326, 332-336, 338, 343-345, 349, 356, 368, 381 frequency, 5, 11, 229-230, 234, 238-244, 256, 261-267, 327, 330, 343, 381 hertz, 229, 238-241, 243, 261, 265, 267 infrared, 4, 227, 242-245, 250-252, 255, 263-264, 266-267, 331 intensity, 335, 343-344 interference, 227, 230-235, 261-263, 327, 331, 334-336, 338, 356-357 motion, 4-5, 11, 58, 228, 230, 236-238, 243, 261-262, 276, 345, 381, 517 motion of, 228, 230, 243, 261, 276, 278 ocean, 248, 250-251, 256-257 power of, 4 radio, 4, 8, 133, 237, 239-245, 261, 263, 265-267, 381, 423 sound, 236-237, 239-240, 244, 263, 267, 310 sound waves, 236, 240, 263, 310 speed, 5, 11, 14, 133, 229, 237-239, 265-266, 276, 278, 330, 343-345, 381 speed of, 133, 237, 239, 265, 276, 278, 345, 381 surface, 5, 58-59, 133, 228, 230-236, 245-246, 250-252, 254-255, 259, 261-262, 264-267, 345 types of, 4, 8, 59, 253, 258, 326, 405 vibrations, 5, 228-229, 234, 242, 266, 278, 381 wavelength, 11, 14, 58-59, 229-230, 235, 239, 242, 244-245, 261, 263-267, 313, 333-334, 343-345, 349, 381 weak force, 6, 14, 175, 316-317, 385, 390, 488, 492, 500, 509 Weak nuclear force, 385 Weather, 193, 245, 256, 437 and climate, 245, 256 hurricanes, 256 solar radiation, 245 week, 19, 388, 403, 408, 411, 460 Weight, 6-7, 13-14, 32, 51-52, 54, 56, 58, 62, 64, 67-69, 73, 93, 96-97, 100-102, 105, 113-117, 124-126, 133, 135, 141-144, 148-150, 155, 158-159, 181-182, 194, 289, 297, 474-475

and mass, 7, 100, 128, 289 in an elevator, 126, 300 true, 52, 56, 62, 67, 115, 150 Weightlessness, 5, 14, 126, 305, 322 Weinberg, Steven, 212, 291, 326, 363, 477-478, 482, 488-489, 500 Wheeler, John, 486, 498-500 white blood cells, 398 white dwarf, 14, 54, 131, 456 helium, 54, 456 white dwarfs, 14, 131-132, 456 Wilkinson Microwave Anisotropy Probe (WMAP), 306 wind power, 260 winds, 146, 156 trade, 146 Wires, 201, 203, 207-209, 221-223, 434 WMAP, 306 Wood, 50, 141, 152, 179, 190, 207, 396, 416-417, 432, 438, 443-444, 447 Work, 6-10, 28, 45, 51, 75, 98, 102, 109, 120, 126, 147-159, 161-165, 170-171, 173, 176-178, 182-183, 185-188, 194-196, 208-209, 237, 239, 241, 246-248, 296, 317, 369, 403, 422, 443-444, 459-462, 473-474, 488-489, 498, 500-501 and kinetic energy, 150 electric circuits, 209 heat and, 2 kinetic energy and, 149, 156 relativity and, 12, 93, 276, 288 units of, 10, 161, 289

X x-axis, 107-109, 348, 350, 353, 367, 375 X-ray radiation, 244

Y y-axis, 367 year, 19, 28, 31, 37, 47-48, 49, 60, 90, 129-130, 157-158, 180-181, 187-191, 195-198, 248-250, 253-258, 260, 267, 271, 283-284, 304, 306-307, 392, 398-403, 405-410, 418, 426, 428, 430-431, 438-439, 442-443, 450, 459, 501 tropical, 257 Young, Thomas, 234

Z zero, 3, 6-7, 59, 74, 81-82, 91, 98, 101, 104-105, 107, 113, 115-118, 125-126, 128, 138, 216, 233, 251, 287, 306, 317-318, 322, 328-331, 369, 403, 432, 464, 489-491 absolute, 74, 171, 306, 318 longitude, 322 zinc, 456, 515