Simply Quantum Physics [1 ed.] 0744028485, 9780744028485

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S I M P L Y

QUANTUM PHYSICS

CONTENTS DK LONDON Project Editor Miezan van Zyl US Editor Karyn Gerhard Art Editor Mik Gates Designer Clare Joyce Managing Editor Angeles Gavira Managing Art Editor Michael Duffy Production Editor Gillian Reid Senior Production Controller Meskerem Berhane Jacket Design Development Manager Sophia M.T.T. Jacket Designer Akiko Kato Associate Publishing Director Liz Wheeler Art Director Karen Self Publishing Director Jonathan Metcalf First American Edition, 2021 Published in the United States by DK Publishing 1450 Broadway, Suite 801, New York, NY 10018 Copyright © 2021 Dorling Kindersley Limited DK, a Division of Penguin Random House LLC 21 22 23 24 25 10 9 8 7 6 5 4 3 2 1 001–322079–Feb/2021 All rights reserved. Without limiting the rights under the copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. Published in Great Britain by Dorling Kindersley Limited A catalog record for this book is available from the Library of Congress. ISBN 978-0-7440-2848-5 Printed and bound in China

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THE QUANTUM WORLD 8

VANISHINGLY SMALL The subatomic scale

10

THREE TINY PIECES The structure of the atom

12

PARTICLE ZOO Subatomic particles

14

WHAT IS LIGHT? Electromagnetic radiation 

15

QUANTUM CONSTANT Planck’s constant

16

RIPPLES IN SPACE Waves

18

WAVE OR PARTICLE Particle-wave duality

20

HOLDING IT TOGETHER The strong nuclear force

21

THE FORCE OF DECAY The weak nuclear force

22

OPPOSITES ATTRACT The electromagnetic force

23

DRAWN TOGETHER Gravity

PRE-QUANTUM PUZZLES 26

IDEAL BODIES Black-body radiation

27

UV CATASTROPHE The Rayleigh-Jeans law

28

PACKETS OF ENERGY Energy quantization

30

ENERGETIC STATES Atomic energy states

55

INFINITE REPETITION The cosmological interpretations

31

CLOUDS OF PROBABILITIES Electron orbitals

56

UNSEEN INFLUENCE Hidden-variable interpretations

32

PHOTON ENERGY The photoelectric effect

58

A QUANTUM HANDSHAKE The transactional interpretation

59

SPONTANEOUS COLLAPSE Objective-collapse hypothesis

60

SURVIVAL OF THE FITTEST Quantum Darwinism

61

THE OBSERVER’S BELIEF Quantum Bayesianism

THE WAVE FUNCTION 36

DESCRIBING A QUANTUM STATE The wave function 

62

38

IN TWO PLACES AT ONCE Superposition

THROUGH THE MAZE Consistent histories 

63

40

SQUARED WAVE The Born rule

DIFFERENT VIEWS The relational interpretation

41

WAVE TRANSFORMATIONS Fourier transforms

42

NOT ALL IS KNOWABLE Heisenberg’s uncertainty principle

QUANTUM PHENOMENA

44

PREDICTING CHANGE Schrödinger’s equation

66

46

EVADING MEASUREMENT The measurement problem 

“SPIN” Intrinsic angular momentum 

67

48

INSTANT COLLAPSE Collapsing the wave function

FIELDS OF ATTRACTION Magnetic moments

68

PARADOX IN A BOX Schrödinger’s cat

THE GREAT DIVIDE Fermions and bosons

69

NO ROOM FOR TWO Pauli exclusion principle

70

WHAT BARRIER? Quantum tunnelling

72

DISTANCE NO OBJECT Quantum entanglement 

74

QUANTUM TELEPORTATION Transferring quantum states

75

UNSTABLE ENVIRONMENT Decoherence

76

INSIDE SOLID OBJECTS Solid-state physics

78

ALTERED STATES Bose-Einstein condensates

49

INTERPRETATIONS OF QUANTUM PHYSICS 52

54

UNDERSTANDING QUANTUM PHYSICS The Copenhagen interpretation EVERYTHING CAN AND DOES HAPPEN The many worlds interpretation 

80

FLOWING WITHOUT FRICTION Superfluidity

81

ENDLESS CHARGE Superconductivity

82

STRANGE QUANTUM ATOMS Cold atom physics

83

UNUSUAL ORBITS Rydberg atoms

QUANTUM TECHNOLOGY

QUANTUM INFORMATION 106 NOT JUST ZEROS AND ONES Qubits 107 SUPERFAST Quantum computing 108 QUANTUM CODES Quantum cryptography 109 SIMULATORS Quantum simulation

NUCLEAR PHYSICS

86

FIRING PHOTONS AT ATOMS Stimulated emission

87

HIGHLY CONCENTRATED Lasers

88

KEEPING TIME Atomic clocks

90

SOLID STATES Band theory of solids

91

SILICON CHIPS Transistors

92

LIGHT RELEASE Light-emitting diodes

93

CAPTURING PHOTONS Charge-coupled devices

94

LEVITATION Superconducting electromagnets

120 ON THE TRAIL OF ELUSIVE PARTICLES Particle detectors

95

TUNNELING PAIRS Josephson junctions

121 SIMPLY SMASHING Particle accelerators

96

SQUIDS Superconducting quantum interference devices

122 SMALLER THAN AN ATOM Quarks

98

LOOKING INSIDE Magnetic resonance imaging

112 SEEKING STABILITY Radioactivity 114 SPLITTING ATOMS Nuclear fission 116 COMBINING NUCLEI Nuclear fusion

PARTICLE PHYSICS

123 NO STRONG INTERACTIONS Leptons

100 SEEING WITHOUT LIGHT Electron microscopes

124 THE QUANTUM WORLD EXPLAINED The Standard Model

102 ATOMIC PROBE Atomic force microscopy

126 FORCE CARRIERS Gauge bosons

127 WHY PARTICLES HAVE MASS The Higgs boson 128 THE OPPOSITE OF MATTER Antimatter 130 NOT SO STANDARD Beyond the Standard Model  132 UNIVERSAL FIELDS Quantum field theory 134 THE JEWEL OF PHYSICS Quantum electrodynamics 135 THREE-COLOR QUARK Quantum chromodyamics

150 IT’S IN OUR DNA A quantum theory of cell mutation 151 TUNNELING FOR A REACTION Enzymes and quantum physics 152 MAGNETIC PERCEPTION Quantum navigation 154 OUR SENSE OF SMELL The quantum nose 155 QUANTUM CONSCIOUSNESS? The quantum mind 156 INDEX

QUANTUM GRAVITY 138 COMBINED FORCES A theory of everything 140 QUANTUM FOAM Planck length and time 142 TINY VIBRATING STRINGS String theories 143 TYING IT TOGETHER M-theory 144 THE FABRIC OF SPACE Loop quantum gravity

QUANTUM BIOLOGY 148 PHOTONS AND FOLIAGE Photosynthesis

CONSULTANT EDITOR Dr. Ben Still is a prizewinning science communicator, particle physicist, and author. He teaches high school physics and is also a visiting research fellow at Queen Mary University of London. He is the author of a growing collection of popular science books and travels the world teaching particle physics using LEGO®.

CONTRIBUTORS Hilary Lamb is an award-winning journalist and author, covering science and technology. She has written for previous DK titles, including The Visual Encyclopedia, How Technology Works, and The Physics Book. Giles Sparrow is a popular-science author specializing in physics and astronomy. He has written and contributed to bestselling DK titles, including The Physics Book, Spaceflight, Universe, and Science.

T H E Q U A N W O R L

T U M D Quantum physics describes the way the universe behaves on the very smallest scales. Far below the limits of even the most powerful microscopes, it governs the behaviors and interactions of atoms and the particles from which they are made—the fundamental building blocks of matter. Scientists only confirmed the existence of subatomic particles with J.J. Thomson’s discovery of the electron in 1897, but the possibility that these tiny particles can sometimes behave like waves, which is key to the strange behavior of the quantum world, was only suggested by Louis Victor de Broglie in 1924.

QUARK 10 -18M

NUCLEONS 10 -15M

Quarks are one type of elementary particle and are building blocks for matter.

The electron particles that orbit in the outer shells of atoms are elementary particles on a similar scale to quarks.

8

THE SUBATOMIC SCALE

ELECTRON ~10 -18M

At the center of the atom is the nucleus—a dense region that contains nearly all of its mass.

The nucleus of hydrogen is a single subatomic proton particle with a diameter of 1.8 million billionths of a meter.

NUCLEUS 10 -14M–10 -15M

ATOM 10 -10M

Atoms are about 100,000 times smaller than any object that can be resolved with the naked eye. Most of the atom is “empty” space.

ed siz na m me . tu a n e n o e nt s

n t ca me an t ss s i c e m e i c l e s ey c th a y h h t r t r t ts c ts . p ex pa en ut tu m r a t m i c tl y b e r i m e f f e n a r u o Q u t o c c u b a t d i r e c h e x p th e i e S a g d v h e u r t v o e s e r th r o b s ob ie d d s tu

PLANCK LENGTH 10 -35M

Q u e s p h re m t b e i no be asu ud

This is the smallest unit of length possible in current physics theories. At lengths at or below the Planck length, current theories of physics break down and can no longer make sensible predictions.

VANISHINGLY SMALL While the largest atoms have a diameter of about half a nanometer (billionth of a meter)—less than 1/100,000 th the width of a human hair—most of their volume is a sparse cloud filled with electrons around a dense central nucleus. Diameters of atomic nuclei are typically a few femtometers (million billionths of a meter), and it is usually at around these scales (and even smaller ones) that strange quantum behaviors become apparent. The smallest distance that makes physical sense is a Planck unit of length (see pp.140–41).

THE SUBATOMIC SCALE

9

Experimental evidence led Ernest Rutherford in 1911 to propose that the entire positive electric charge in an atom lay in a small, dense core and the electrons were imagined to orbit around this nucleus, like moons around a planet.

BOHR MODEL

In J.J. Thomson’s model, negatively charged electrons are dotted randomly throughout a sphere, which has a positive charge.

RUTHERFORD MODEL

PLUM PUDDING MODEL

SOLID SPHERE MODEL

In 1803, John Dalton presented his theory that all matter is made from atoms— indivisible spheres that cannot be created or destroyed. However, atoms can be bonded or broken apart from other atoms to form new substances.

To explain light absorption and emission by atoms, Niels Bohr developed a model in which electrons could orbit only in particular energy “shells.”

THREE TINY PIECES Atoms are the fundamental building blocks of large-scale matter—particles that were first thought indivisible and whose collective chemical and physical properties make them representative of one or another specific element. On a deeper level, however, all atoms are made up of a combination of three subatomic particles: positively charged protons and uncharged neutrons in a central nucleus, and negatively charged electrons orbiting in more distant clouds (see p.31), which allow atoms to bond with other atoms.

10

THE STRUCTURE OF THE ATOM

In modern models of the atom, electrons are not solid spheres orbiting a nucleus at a fixed distance. Instead, they are represented as clouds in which electrons are most likely to be found if looked for.

There is an electromagnetic attraction between negatively charged electrons and negatively charged protons in the nucleus.

ATTRACTION

Electron clouds

QUANTUM MODEL

NUCLEUS PROTON

Clouds of various shapes represent the orbitals in which electrons are most likely to be found.

ELECTRON CLOUD

In the atom, the number of negatively charged electrons balances out the number of positive protons in the nucleus.

ELECTRONS

NEUTRON

THE STRUCTURE OF THE ATOM

11

PARTICLE ZOO NS QUARKS UP DOWN CHARM

ENTARY FERMION ELEM S

FERMIONS

STRANGE TOP BOTTOM

LEPTONS ELECTRON ELECTRON NEUTRINO MUON MUON NEUTRINO TAU PARTICLE

SU

The elementary (indivisible) particles that make up matter fall into two groups: leptons and quarks. Only a few of each family are widespread in today’s universe.

IO

FE

RM

While electrons are truly elementary particles, which cannot be divided any further (and part of a family of particles called the leptons), protons and neutrons are made up of three even smaller particles called quarks (see p.122). Particles formed by groups of quarks are collectively known as hadrons, which are subdivided into baryons (made up of triplets of quarks) and mesons (made up of a paired quark and antiquark particle).

TAU NEUTRINO

TO BA

12

SUBATOMIC PARTICLES

C

I

Using particle accelerators (see p.121) to break apart atoms and create short-lived and unstable particles, physicists have assembled the so-called Standard Model (see pp.124–125) of particle physics.

M

The subatomic world

PA R

TI

CL

ES

These composite particles are made of quarks. Baryons are themselves fermionic in nature, while mesons behave as bosons (see p.68)

HADRONS

COMPOSITE PARTICLES

BO S

BARYONS

O

PROTON

NS

NEUTRON LAMBDA PARTICLE OTHERS

EM EL

GLUON W+ BOSON

MESONS POSITIVE PION

Z BOSON HIGGS BOSON

RY BOS O

W- BOSON

ENTA

PHOTON

NS

NEGATIVE KAON

BOSONS

OTHERS

Elementary bosons mostly act as “messengers,” transmitting forces between particles of matter. They behave very differently from fermions.

SUBATOMIC PARTICLES

13

ELECTROMAGNETIC RADIATION

RADIO WAVES

E

INFRARED

M

N AG

C TI

EL

D

VISIBLE LIGHT

FI

ELECTRIC FIELD UV

ELECTROMAGNETIC SPECTRUM

MICROWAVES

Scientists classify electromagnetic waves according to their wavelength and frequency, from long-wavelength, low-frequency radio waves, through microwaves, infrared, and visible light, to shorter wavelength and higher frequency ultraviolet, X-rays, and gamma rays.

Particles with electric charge can exchange forces between each other by emitting electromagnetic radiation. These moving waves consist of oscillating electric and magnetic fields aligned at right angles so that changes in one reinforce the other. The properties and effects of these waves are determined by the frequency at which they repeat, giving rise to different forms of radiation such as X-rays, radio waves, and visible light.

WHAT IS LIGHT?

THE SPECTRUM

14 OSCILLATING FIELDS

X-RAYS

GAMMA RAYS

Light consists of electrical and magnetic waves that are at right angles to each other and perpendicular to its direction of motion.

DIRE C O F M TI O N OTI O N

As the electric and magnetic fields in an electromagnetic wave vary, they reinforce each other, allowing the wave to travel for very long distances.

Self-propagating wave

PLANCK’S CONSTANT

15

This fundamental constant of quantum physics defines the relationship between a photon’s energy and its frequency or wavelength. It means that energy is only delivered in discrete units.

PLANCK’S CONSTANT

-34

JOULE SECONDS

=

PHOTON’S ENERGY

 = 6.62607015 x 10

At the level of individual atoms and subatomic particles, electrically charged matter emits and absorbs electromagnetic radiation as small packets called photons. These tiny objects are “quanta” (discrete, selfcontained bundles) of electromagnetic energy. The amount of energy a photon contains is determined by a simple calculation involving its frequency, the speed of light, and a number known as Planck’s constant.

The frequency of a photon is the number of waves that would pass a point in a single second if the wave was continuous—as the photon’s wavelength shrinks, its frequency increases.

PLANCK'S CONSTANT

QUANTUM CONSTANT

The energy carried by a single photon is greater for higher frequencies and shorter wavelengths of light. FREQUENCY

RIPPLES IN SPACE

ENERGY TRANSFERENCE

Wavelike behavior is fundamental not just to electromagnetic radiation (see p.14) but also to the quantum behavior of particles. Unlike particles, waves can pass through each other to boost the overall disturbance in some places and decrease it in others (an effect called interference) and also spread into the “shadows” cast by barriers (diffraction). When they encounter a boundary between two different materials, waves can be bounced back (reflection) or slowed down and deflected onto new paths (refraction).

16

Waves are repeated oscillations (fluctuations) around a fixed midpoint. While waves transfer energy, they do not carry matter from one place to another.

WAVES

WAVELENGTH

AMPLITUDE The amplitude of a wave is the maximum displacement (distance) a field or particle oscillates from its central equilibrium position. DISTANCE

Wave essentials A wave’s frequency is the number of times it oscillates per second, while wavelength is the distance covered by one complete oscillation.

Interference When the crests of two waves of the same frequency line up, they form a wave with greater amplitude (called constructive interference). Destructive interference occurs when the troughs of one wave partially or entirely cancel out the peaks of another.

COMBINED WAVE

WAVES CANCEL OUT

WAVES

17

At quantum scales, the dividing line between particles and waves (see pp.16–17) becomes blurred, with strange results. It is possible to design experiments that detect individual particlelike packets of energy, such as photons (quanta of electromagnetic radiation; see p.14), and at the same time demonstrate their wavelike behavior. Photons may arrive one at a time at a detector on the opposite side of two small slits, yet the pattern they build up can only be explained by each photon deciding on its location based upon wavelike interference (see pp.16–17).

The effect of measurements One of the strangest aspects of quantum theory is that wave or particle behavior can be determined by the process of measurement.

PARTICLE DETECTOR If we measure which slit each photon or electron passes through, they behave as particles at that slit and lose the wavelike behavior that existed prior to the slits.

18

PARTICLE-WAVE DUALITY

Double slit experiment A famous experiment conducted in 1800 to prove the wave nature of light can be adapted to show the wavelike nature of electrons and other particles.

ELECTRON SOURCE

WAVE OR PARTICLE

Electrons emerge in a stream from an “electron gun”. Each particle can be treated as an advancing wave. The individual electron wave functions interfere with themselves to produce the probability pattern.

ELECTRON GUN

DISTRIBUTION

DIFFRACTED WAVES

As the electron waves pass through two thin, narrowly spaced slits, their waves are diffracted. The wavefronts become curved and begin to overlap and interfere.

This curve shows the probable distribution of the electrons hitting the screen.

SCREEN WITH 2 SLITS OPTICAL SCREEN FRONT VIEW

INTERFERENCE PATTERN

OPTICAL SCREEN A screen of sensitive material detects electron impacts, recording a complex interference pattern of light and dark areas.

PARTICLE-WAVE DUALITY

19

PROTON

Nuclear force The nuclear force binds quarks (and protons and neutrons) together, opposing electromagnetic repulsion (see p.22).

Protons repel each other, but this repulsion is overcome by the stronger nuclear force.

NUCLEUS OF AN ATOM

NEUTRON A neutron has no charge, so is unaffected by electromagnetic repulsion.

HOLDING IT TOGETHER Four fundamental forces are responsible for binding the matter particles in the universe together, and each is governed by quantum physics to some extent. The most powerful of these forces, known as the strong force, only works on tiny scales of about one millionbillionth of a yard. This force bonds quark particles together to form protons and neutrons, and produces a nuclear force that binds these to form atomic nuclei. The strong force is carried by particles called gluons.

20

THE STRONG NUCLEAR FORCE

DURING BETA DECAY

Weak force The weak force causes some types of radioactive decay (where particles transform from one type to another). The weak force is carried by W and Z bosons.

The particle emitted from the nucleus in beta minus decay (see pp.112–13) is a fast-moving electron.

TO

N

UNSTABLE NUCLEUS

PR

O

NUCLEUS OF AN ATOM

NE UT

RO

In beta minus decay, a neutron transforms into a proton in the nucleus, emitting an electron in the process.

N

THE FORCE OF DECAY The weak force, as its name suggests, is less powerful than the strong and electromagnetic forces, and it operates over even smaller scales, only making itself felt at ranges below the diameter of a proton. However, weak interactions are hugely important as they can influence matter particles of all types (both quarks and leptons), and the weak force is the only one of the fundamental forces that can turn one type of particle into another type.

THE WEAK NUCLEAR FORCE

21

On the atomic scale, electromagnetism is the attractive force between protons and electrons. Electromagnetic radiation is carried by massless particles called photons (see p.14).

Electrons and protons in the nucleus are attracted to each other, keeping them together in the atom.

HELD IN ORBIT

Infinite range

EL

N

PR

O

TR O N

TO

EC

NUCLEUS OF AN ATOM

NE UT

RO

N

OPPOSITES ATTRACT It is the force of electromagnetism that attracts particles of opposite electric charge and also repels particles with the same electric charge. Electromagnetism has an infinite range, not only binding atoms together but also shining as light across vast distances in the cosmos, although its strength decreases rapidly with distance.

22

THE ELECTROMAGNETIC FORCE

DRAWN TOGETHER

Gravitational force keeps planets orbiting the sun.

PLANET IN ORBIT

The sun‘s greater mass cause space-time to warp, drawing other bodies in the solar system toward it.

SUN

Gravitation is an attractive force between objects with mass. It is extremely weak and only becomes apparent between objects of large mass, yet, like electromagnetism, it has an infinite range. The best model for understanding gravitation is Einstein’s General Relativity, a theory that seems completely separate from quantum physics. Understanding how gravity works on the level of particles poses many baffling questions (see pp.136–45).

Space-time Einstein described the three dimensions of space and the dimension of time as a fourdimensional grid called space-time. General Relativity explains gravity as arising from distortions in space-time by massive objects.

GRAVITY

23

PRE-QU P U ZZ L E

A N T U M S Quantum physics began as an attempt by scientists to explain a number of apparently separate puzzles in early 20th-century physics. These puzzles affected the nature of light emitted by objects heated to different temperatures, the internal structure of the atom, and the interaction between light and matter. Together, they led to the realization that electromagnetic waves are emitted and delivered in small, discrete packets of energy known as photons, and hinted at deeper mysteries in the behavior of subatomic particles.

M A L R A D I AT I O

BL A

N

INCOMING LIGHT

THE R

A black body absorbs all radiation incident upon it, and then very efficiently reemits that absorbed radiation as thermal energy.

C K B O DY

IDEAL BODIES In order to understand how objects emit electromagnetic radiation when they are heated, scientists use an idealized object called a “black body.” All but the coldest objects emit some form of radiation, but because most will also reflect radiation from their surroundings, it can be hard to measure how much radiation is actually being released. A black body has a pitch-black, completely nonreflective surface whose radiation is dependent only on its temperature.

26

BLACK-BODY RADIATION

Radiation distribution

LONG WAVELENGTH

TA CA

Radiation declines at shorter wavelengths, even for the hottest sources.

V EU

SHORT WAVELENGTH

TH

INTENSITY OF RADIATION

The Rayleigh-Jeans law failed to describe the ranges of wavelength emitted at all but the longest wavelengths, with energy increasing infinitely at smaller and smaller wavelengths.

Experiments have shown that black bodies emit radiation across a spread of wavelengths that becomes narrower in range, with a shorter peak wavelength, as their temperature increases. Cool objects emit primarily long infrared waves, then glow red, white, and eventually blue and ultraviolet as they get hotter. An equation called the Rayleigh-Jeans law predicted the pattern of radiation for cooler objects, but also suggested that emission would increase exponentially toward higher temperatures and eventually become infinite, which was called the “ultraviolet catastrophe.”

ST

Classical physics describes radiation distribution, but predicts infinite output at hotter temperatures and shorter wavelengths.

RO

PH

E

WAVELENGTH

THE RAYLEIGH-JEANS LAW

27

PACKETS OF ENERGY

G

RA

D

U AL

IN

CR

EA

SE

In 1900, Max Planck showed a way to avoid the ultraviolet catastrophe (see p.27) and make the theoretical emissions of black bodies (see p.26) match with their measured behavior. What if energy was being released not in a continuous stream, but as small, discrete bursts (or packets of energy), each with a distinct wavelength? Planck called these bursts “light quanta,” and assumed that their production had something to do with the emission process rather than being a property of light itself (see p.14).

Classical physics In the pre-quantum view, properties of particles, such as the energy they hold, vary continuously and may have any value.

28

ENERGY QUANTIZATION

QUANTUM LEAPS

Particle energies, and other properties, jump from one value to the next.

Quantum physics In the quantum world, the properties of particles are limited to distinct quantized values, which are multiples of Planck’s constant (see p.15).

ENERGY QUANTIZATION

29

ELECTRON JUMPS Electrons jump to the highest state possible by absorbing high-energy photons, then cascade back to the ground state, releasing several lower-energy photons.

E LE C TRO N O R B IT

COLOR AND ENERGY

VIOLET

Different energy transitions involve the absorption or release of photons with different wavelengths and energies—the greater the change in energy, the bluer the photon.

GROUND STATE N1 B LU

RE

D

EG

REE

N

1ST EXCITED STATE N2

2ND EXCITED STATE N3

3RD EXCITED STATE N4

Energy shells Electrons can move between energy states by absorbing or releasing photons with the right energy. The lowest energy state is known as the ground state— states with higher energy are said to be “excited.”

ENERGETIC STATES Early 20th-century physicists wrestled with how the structure of atoms (see pp.10–11) related to the way they emitted or absorbed radiation. In 1913, Niels Bohr proposed a model in which electrons orbited in shells at various distances from the nucleus, giving each a distinctive energy state. Atoms absorbed or emitted quanta of electromagnetic energy whose wavelengths corresponded to the difference between these states.

30

ATOMIC ENERGY STATES

CLOUDS OF PROBABILITIES Discoveries in the 1920s revealed that atomic structure is more complex than the simple Bohr model. The modern model shows that electrons occupy a series of “orbitals”—shells and subshells with a variety of shapes. As it is impossible to know all of their properties at a single instant (see pp.42–43), it is more accurate to think of these orbitals as fuzzy regions where the electrons are likely to be found—for some purposes, the electron’s properties are effectively “smeared out” across the orbital.

P-ORBITALS ORBITAL ARRANGEMENT

These are dumbbell-shaped orbitals in each of the three spatial dimensions. Each dumbbell can hold up to two electrons, so a p-orbital holds a total of six electrons.

The three p-orbitals are arranged at rightangles to each other.

S-ORBITALS Spherical s-orbitals can contain up to two electrons each.

NUCLEUS

Orbiting a fluorine atom A fluorine atom contains nine electrons, two each in its inner two S-orbitals and five in the first p-orbital.

ELECTRON ORBITALS

31

32

THE PHOTOELECTRIC EFFECT

LOW ENERGY

The photoelectric effect causes electric current to flow from the surface of certain metals when they are bombarded with light. However, it only works when that light is shorter than a certain wavelength; even intense bombardment with longer-wavelength light cannot trigger it. In 1905, Albert Einstein determined that this was because the effect depends on electrons being struck by individual light quanta. Based on his discovery, Einstein argued that all radiation takes the form of quanta or “photons.”

PHOTON ENERGY Albert Einstein won his only Nobel Prize for describing the photoelectric effect, not for his theories of relativity.

Each photon of red light does not possess enough energy to liberate individual electrons. Making the light brighter just increases the number of low-energy photons.

Red light

METAL SURFACE

Green light

Ultraviolet light

Individual photons that have higher energy than those of red light can deliver enough energy for some electrons to escape from the metal’s surface atoms.

Each ultraviolet photon has a short wavelength and can deliver enough energy to individual electrons to liberate them from the surface of the metal.

HIGH-ENERGY ELECTRON

HIGHEST ENERGY

HIGHER ENERGY

LOW-ENERGY ELECTRON

THE PHOTOELECTRIC EFFECT

33

T H E W F U N C

A V E T I O N In classical physics, the nature of a system at any point in time can be precisely calculated using deterministic rules, such as Isaac Newton’s laws of mechanics. In the quantum world, however, systems unravel unpredictably. A quantum system is best described with mathematical “wave function,” which gives the probability of finding it in a certain state at a certain time. Quantum systems that could be in one of several states can be described with a superposition of all these possible states, although this superposition always “collapses” into a single state when a measurement is taken. It is this collapse of the wave function that creates unpredictability.

— de al i tu tr p l c e n th e m e t a h e to e r e s m t o int w h li t y t a ro p nt b i e . e f r i a cl e g c e i u m p o o b ti th s t a n l i b r th e t p r p a r t i i s A d qu is e he e e k— igh g t th a h in p e th e i n d i s of f re e th

36

THE WAVE FUNCTION

Y

Objects on the quantum scale behave in unpredictable ways; for instance, it is impossible to calculate with certainty a particle’s state at a given time. Instead, its state is described mathematically with a wave function that varies in space and time. The probability that the particle will be found at a certain place and time is related to the amplitude of the wave function multiplied by itself (see p.40).

IT

DESCRIBING A QUANTUM STATE

IL

This image is an example of a wave function for a particle moving in one dimension.

GH AB HI OB PR

Basic wave function

LY KE N LI I O SS AT LE O C L

n io c t ly un like e f ve u n i l l b . wa i t i s l e w a re a e t h e , ti c i s r e v a l u p a r i n th e h e W l ow t t h u n d s a th a f o a h

“If you know the wave function of the universe, why aren’t you rich?“ Murray Gell-Mann

THE WAVE FUNCTION

37

”Causality applies only to a system which is left undisturbed.“ Paul Dirac

SPIN STATES An electron can exist in a superposition of different states, such as spin up or spin down.

IN TWO PLACES AT ONCE In classical physics, waves can be added together to form another wave (superposition). Similarly, quantum states— described by wave functions—can be combined to form another quantum state. This is known as quantum superposition. A quantum system that could be found in one of multiple states (e.g. an electron could have spin up or spin down, see p.66) can be described with a superposition of all these possible states.

38

SUPERPOSITION

PARTICLE POSITIONS An unobserved particle can be conceived as existing in every possible position at the same time.

Supporting waves Any two quantum states can be added together to create another valid quantum state. When the waves are identical, as in this example, they reinforce one another in superposition. ELECTRON

ELECTRON

SUPERPOSITION

39

40

BORN RULE

SQUARED

ENERGY

PROBABILITY AMPLITUDE

ENERGY

The Born rule, named after the German physicist Max Born, is used to calculate the probability of finding a system in a certain state, based on the wave function (see pp.36–37) that is used to describe the system. For any enclosed system, the probability of finding a particle in a certain location is proportional to the square of the wave function’s magnitude at that location. The wave function, and therefore the probability, is dependent upon the energy of a particle (see p.30).

WAVE

PROBABILITY Probability is found from the square of the wave function’s amplitude. It is always positive.

P = ²

POSITION

The wave function contains all information about the state of a particle and how it differs through space and time. It is given the mathematical symbol psi ().

POSITION

WAVE TRANSFORMATIONS Fourier transforms are mathematical operations that represent any function as a composition of basic waves with various frequencies. This allows for switching between “domains” such as time and frequency. In quantum mechanics, they are used to switch between position and momentum. This means that a quantum state represented by a wave function of position can be switched to being represented by a wave function of momentum, and vice versa.

U FO

MOMENTUM SPACE A particle can be described in terms of its movement as a wave function in the momentum domain.

RIE R

TR A N S F

OR

M

POSITION SPACE The same particle can be described with a wave function in the position domain.

FOURIER TRANSFORMS

41

NOT ALL IS KNOWABLE Unlike in classical mechanics, in the quantum world some pairs of physical quantities cannot be calculated with certainty. For example, it is impossible to know the exact position and momentum of a particle at the same time; the more precisely one of these quantities is determined, the less precisely the other can be determined. This is known as the uncertainty principle or Heisenberg’s uncertainty principle, after German physicist Werner Heisenberg, who discovered the law along with his early framework of quantum mechanics (known as matrix mechanics).

POSITION

”We can never know anything.“

The more certain the position of a particle becomes, the less is known about its momentum.

Werner Heisenberg

42

HEISENBERG’S UNCERTAINTY PRINCIPLE

K N OW N

MOMENTUM The more certain the momentum of a particle becomes, the less is known about its position.

One or the other

UNKNOWN

There are some pairs of properties of a particle that cannot be known at the same time. These paired properties are known as conjugate variables.

HEISENBERG’S UNCERTAINTY PRINCIPLE

43

The equation uses complex numbers that contain the imaginary number “i,” which is equivalent to the square root of minus one (√–1).

The wave function is represented by the Greek letter psi.

QUANTUM WAVE FUNCTION

RATE OF CHANGE IMAGINARY NUMBER

This part of the equation gives the rate of change of the wave function with respect to time.

The reduced Planck constant is the quantum of variables such as spin, momentum, energy, space, and time.

Time dependent Schrödinger's equation can be written in many different forms. The time-dependent equation shown here describes a system evolving as time passes.

44

SCHRÖDINGER’S EQUATION

HAMILTONIAN OPERATOR

PLANCK'S CONSTANT

 iħ— = Ĥ t The Hamiltonian is a function that, when applied to the wave function, represents the sum of kinetic and potential energies for all particles described by the wave function.

IC

E

PR

NG

ED

HA

NG C I T

The Schrödinger equation determines the evolution of a wave function (se pp.36–37), predicting the future behavior of the system of superposed states it describes. It can be considered the quantum equivalent of Newton’s laws of motion, which predict changes to a classical system over time. The future behavior of a system cannot be determined with certainty, but the equation allows us to calculate the probability of finding a system in a certain state at some later time.

”Where did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.“ Richard Feynman

SCHRÖDINGER’S EQUATION

45

MEASUREMENT TAKEN

MEASURING POSITION

PHOTON

Some measurement can influence what is being measured, such as when a photon is used to measure the position of an electron.

EVADING MEASUREMENT The Schrödinger equation (see pp.44–45) describes the evolution of a wave function— giving the probability of finding the system in various states in a superposition at any given time—but when the system is measured, it is always found in a single state. It is impossible to observe the wave function of superposed states and say which will be seen when the system is measured; this mystery has led to different interpretations of quantum mechanics.

46

THE MEASUREMENT PROBLEM

AFTER MEASUREMENT

PHOTON The interaction with the electron has also altered the photon.

ELECTRON MOVES Having absorbed energy from the photon, the electron’s wave function has changed because of changes to its energy and position.

”The problem of measurement … is the problem of where the measurement begins and ends, and where the observer begins and ends.“ John Stewart Bell

THE MEASUREMENT PROBLEM

47

INSTANT COLLAPSE When a quantum system is measured, the wave function (see pp.36–37) representing the superposition of states, with probabilities assigned to different states, stops evolving and is reduced to a single definite state. This process is known as wave function collapse. The evolution of the wave function is determined by the Schrödinger wave equation (see pp.44–45); at any specific point in time, wave function collapse leaves only one possible outcome.

BEFORE MEASUREMENT A superposition of states evolves over time. This diagram shows the probabilities of finding a particle in various places in a box.

AFTER MEASUREMENT The instant a measurement is taken, the superposition of states is reduced to a single, definite state. In this example, the particle’s location in the box is revealed.

48

COLLAPSING THE WAVE FUNCTION

BOX INTERNAL VIEW

ALIVE CAT

The random and unpredictable nature of radioactive decay means that, until an observation is made, it is uncertain whether or not the poison has been released.

CAT CONUNDRUM

RADIOACTIVE DECAY

DEAD CAT

Without looking inside the box, it is impossible to know if the cat is alive or dead, so it can be thought to be in a superposition of being alive and dead at the same time.

PARADOX IN A BOX The mystery of what occurs before wave function collapse inspired a famous thought experiment known as “Schrödinger’s cat.” In this thought experiment, a cat in a box could be killed at any time by poison released via nuclear decay. In one interpretation of quantum mechanics (see pp.52–53), the superposed states of dead and alive exist until an observer opens the box. Erwin Schrödinger devised this thought experiment to highlight the absurdity of a cat being both dead and alive until someone checks on it.

SCHRÖDINGER’S CAT

49

i nt e r p r o f QUA N T ME C HA N I

e tat i o n s UM CS The wavelike evolution and unpredictable wave function collapse of quantum physics is hard to reconcile with more familiar classical physics in which outcomes, positions, and behaviors are well defined. In order to explain why quantum uncertainty is not seen in the everyday world, scientists and philosophers have devised many different “interpretations” of quantum physics. Some attempt to simply get rid of uncertainty above a certain scale by forcing the wave function to collapse, while others take more ingenious routes to explain why we never come across uncollapsed wave functions “in the wild.”

UNOBSERVED

• Events follow quantum rules • Systems are described by wave functions • Wave functions obey the Schrödinger equation (see pp.44–45).

”I think that a particle must have a separate reality independent of measurements. ... I like to think the moon is there even if I am not looking at it.“ Albert Einstein

52

THE COPENHAGEN INTERPRETATION

OBSERVED

• Events follow rules of classical mechanics • Wave function collapses to a definite value • Probability of any outcome is the wave function squared (see p.40).

UNDERSTANDING QUANTUM PHYSICS The Copenhagen interpretation was the earliest attempt to bridge the gap between the quantum world and classical physics. In this view, the act of an observer measuring the state of a quantum system causes it to resolve instantaneously to a single value—a phenomenon called the collapse of the wave function (see p.48). The wave equation itself is treated as merely offering a measure of the probability that different values will be detected when the observation takes place (see pp.36–37).

THE COPENHAGEN INTERPRETATION

53

SIMILAR BUT DIFFERENT NO CONNECTION

At every measurement, each possible outcome is realized in a separate universe. These multiple universes remain separate.

Each universe follows its own course and may be indistinguishable from parallel universes in many ways.

EVERYTHING CAN AND DOES HAPPEN This quantum interpretation, developed by physicist Hugh Everett III, considers the wave function to be a particle’s true nature, and wave function collapse (see p.48) to be impossible. Instead, measurement creates a multitude of parallel universes—one for each possible outcome of the measurement process. The wave function remains uncollapsed as a whole, but an observer ends up in one of these parallel universes where it appears to have collapsed.

54

THE MANY WORLDS INTERPRETATION

INFINITE REPETITION The cosmological interpretation is one way of understanding the parallel realities of the many worlds theory. It suggests that our universe has a truly infinite extent in space, within which every event is repeated an infinite number of times. The wave function links these remote events, so that while we may observe one outcome of a measurement at our point in space, elsewhere other versions of us are making the same observations with different results.

OBSERVABLE UNIVERSES Each point in the multiverse is surrounded by a bubble of observable space, limited by how far light has traveled since the Big Bang.

DIFFERENT OUTCOMES An event’s wave function extends across the multiverse—measurements depend on its values within a particular observable universe.

An infinite multiverse In a multiverse that is infinite in extent, every possible event must play out somewhere in the infinite extent of space.

THE COSMOLOGICAL INTERPRETATION

55

STEERING WAVE

UNSEEN INFLUENCE

In pilot wave theory, results of quantum measurements are guided by undetectable matter waves steering collections of particles.

The Copenhagen interpretation assumes that entangled particles (see pp.52–53) somehow share information instantaneously. Hidden-variable interpretations suggest one way to avoid this apparently faster-than-light transfer of information—a particle has undetected properties that guide the wave function’s collapse. Pilot wave theories propose the existence of unseen quantum waves that do a similar job of “steering” wave functions to collapse toward certain properties.

”We are not sufficiently astonished by the fact that any science may be possible.“ Louis de Broglie

56

HIDDEN-VARIABLE INTERPRETATIONS

RIDING THE WAVE

The actual relationship arising from quantum mechanics.

QUANTUM REALITY

Expected outcome if entanglement relies on hidden variables carried locally by particles.

CLASSICAL PREDICTION

Particles may appear to have individual wave functions and uncertain properties, but the pilot wave will determine their positions when measured.

Bell’s theorem In 1964, John Stewart Bell ruled out the possibility of locally held hidden variables by showing that they would produce incorrect measurements when comparing the spin of two entangled particles.

HIDDEN-VARIABLE INTERPRETATIONS

57

WHERE THE WAVES MEET

Interference between waves moving forward and backward in time produces an appearance of instantaneous wave-function collapse.

A QUANTUM HANDSHAKE The transactional interpretation offers a possible explanation for the way that interactions between quantum systems actually take place. It suggests that the wave function generates waves that move out into the surroundings and both forward and backward in time. Other systems (including observers) generate similar waves. When the forward-moving wave from a quantum system encounters a backward-moving wave from another source, the “handshake” process that occurs resolves the properties of the quantum system.

OBSERVER Chance encounter The measured position, momentum, and other properties of a quantum particle are determined by the interaction between its wave function and the observer’s wave.

58

THE TRANSACTIONAL INTERPRETATION

Wave function half-life

When particles are in groups, the collapse of one particle can trigger the collapse of other particles.

COLLAPSE LIKELY

The wave function of a single particle has a small probability (e.g. 1 in a million years) of collapsing.

MEDIUM CHANCE

SMALL CHANGE

Though initially uncertain, a wave function has a certain probability of collapsing spontaneously, somewhat like the half-life of radioactive decay. Collapse may be accelerated by interactions with the collapsing wave functions of other particles.

Large objects are made up of lots of particles, many of which are likely to be in a collapsed state.

SPONTANEOUS COLLAPSE The Copenhagen interpretation’s suggestion that measurement or observation trigger the collapse of the wave function raises the troubling question: what happens when no measurements are taken? Alternative or spontaneous collapse theories get around this by suggesting that the collapse happens automatically and randomly, without a trigger from the outside world. A wave function’s likelihood of collapse can still be influenced by the wave functions of particles surrounding it.

OBJECTIVE-COLLAPSE HYPOTHESIS

59

PARTICLE WILDERNESS The less interaction a quantum particle has with its environment, the wider the range of its possible states. Due to decoherence—the entangling of the particle state and that of the world around it— eventually there will be only one outcome.

Eventually one wave function proves itself fittest for the environment—it is this one that will determine the results of classical measurements. LONE SURVIVOR

SURVIVAL OF THE FITTEST If hidden variables (see pp.56–57) do not guide the wave function to collapse into a certain state, perhaps something else does? Quantum Darwinism, as its name suggests, involves an idea similar to Charles Darwin’s evolutionary “survival of the fittest.” According to this interpretation, interactions between a particle and factors in its environment gradually filter the possible end states of its wave function until it settles on a single outcome known as a “pointer state.”

60

QUANTUM DARWINISM

THE OBSERVER’S BELIEF

The wave function is simply information about the likelihood of different outcomes when a measurement is made. For QBism, quantum states are “degrees of belief.”

All in the mind Quantum Bayesianism relies on arguments that the entire concept of probability is a mental construct rather than an objective property of reality.

The observer’s information about a quantum system allows them to update their beliefs and ultimately determine a “measurement.”

PERCEIVED REALITY

ENCODED PROBABILITIES

Named after 18th-century statistician Thomas Bayes, and also known as QBism (pronounced “cubism”), this interpretation of quantum physics puts the observer at the center of the theory. In the same way that Bayesian statistics allow people to adjust their ideas about the likelihood of events as more information becomes available, so according to QBism, the wave function is merely a representation of the observer’s subjective information and beliefs about possible different outcomes.

OBSERVER

QUANTUM BAYESIANISM

61

WAVE FUNCTION The wave function’s properties may evolve in many different ways, following different histories prior to its measurement.

Sifting outcomes The consistent histories approach can be likened to a maze where the wave function can take several routes to the measured outcome.

PARTICLE The observed properties arise from the unseen histories of a quantum object.

THROUGH THE MAZE Sometimes referred to as “Copenhagen done right,” the consistent histories approach attempts to marry quantum mechanics with the “classical” rules of mathematical probability.In this approach, the wave function never collapses, but instead decoheres (see p.75) to reveal the properties of the quantum system at that moment in time. A set of potential “histories” describing the possible evolution of the system can be mapped out, with a certain probability assigned to each.

62

CONSISTENT HISTORIES

DIFFERENT VIEWS Albert Einstein’s famous theory of Special Relativity explains how observers in different “frames of reference” (for instance, moving at different speeds) can differ in their interpretation of events. The relational interpretation applies a similar idea to the wave function, suggesting that it may simultaneously display different states of collapse (or remain uncollapsed) for different observers depending on their location, motion, and other properties; the quantum system and its observers are, in fact, described together by a combined wave function.

SIZE DOES NOT MATTER

SOLUTION 1 In this interpretation, a system retains quantum uncertainty regardless of its scale.

Observer 1 measures the system in one particular state, but this measurement has no special privilege.

OBSERVER 1

SOLUTION 2 Observer 2 may experience the system in a different state. This is another partial description of the system.

PARTICLE

OBSERVER 2

UNCOLLAPSED WAVE FUNCTION Observer 3 measures no collapse, but again there is no special privilege to their point of view—or, in fact, to any other in the universe.

Everything is connected According to the relational interpretation, the true state of a quantum system cannot be described without including the observer in the system.

OBSERVER 3

THE RELATIONAL INTERPRETATION

63

QU A N T p h e n o

U M m e n a When put into practice, the strange rules of quantum physics produces a wide variety of unusual phenomena. The quantum revolution of the 1920s helped to resolve some of the biggest outstanding mysteries in the physics of the time (such as what forces governed the internal structure of atoms, and how some unstable atomic nuclei decay). However, it also made predictions of strange behaviors and unusual states of matter that troubled many physicists at the time, but which were demonstrated through ingenious experiments later in the 20th century.

”But then the discovery of electron spin changed this picture considerably. The electron was not symmetrical. … They are not simple, not so elementary as we had thought before.“ Werner Heisenberg

66

INTRINSIC ANGULAR MOMENTUM

SPIN UP

In large-scale physics, spinning objects naturally possess a form of momentum due to a combination of their mass and rotation. Quantum particles possess a property (called intrinsic angular momentum, or spin) that was initially thought to be them spinning on the spot, but later turned out to be something much more curious. Spin does not refer to an actual physical rotation of particles, but shares many of the same characteristics as classical rotation and produces some similar effects.

The spin of a particle is measured against one of three dimensions, most often the dimension defined as the z-axis. When cast on this axis, the spin points in one of two directions: positive spin up or negative spin down.

SPIN DOWN

“SPIN”

Rotating a “spin-up” 1 ⁄ 2 electron through 360° results in its spin being reversed to “spin-down” or -1 ⁄ 2 .

Field lines

BAGNETIC DIPOLES In this familiar bar magnet, countless dipoles (molecules with a positively and a negatively charged side) are aligned to produce a strong magnetic field.

Magnetic fields are often depicted using lines that indicate the strength and direction of their influence.

N

S

FIELDS OF ATTRACTION While electric charge is a fundamental property of many particles, magnetism is not—instead it is an effect that arises from electric charges in motion. Charged subatomic particles such as electrons and quarks develop their own weak magnetic fields, known as magnetic moments, as a consequence of their intrinsic angular momentum, or spin. Like spin and charge themselves, magnetic moments are quantized—only capable of taking on certain discrete values.

S

I C FIE L D LIN E S

PARTICLE

GNET

An effect called electromagnetic induction means that any spinning electrically charged particle induces (creates) a magnetic field similar to that of a bar magnet.

N

MA

HAVING A MOMENT

MAGNETIC MOMENTS

67

THE GREAT DIVIDE

FERMIONS

The property of spin defines a fundamental division between elementary subatomic particles. Particles associated with the structure of matter all have spin values of either +1 ⁄2 or -1 ⁄2, while those with a spin of 1 carry the forces between these matter particles, and the spin-0 Higgs boson provides them with mass. Particles with half-integer spins follow a mathematical model called Fermi-Dirac statistics and are known as fermions. Those with integer or zero spin follow BoseEinstein statistics and are called bosons.

SPIN = 1 ⁄₂,3 ⁄₂,5 ⁄₂ ...

Matter particles The + or - sign on a particle’s spin simply indicates whether its direction is up or down. When fermions join together their spins add up.

BOSONS

SPIN = 1,2,3,...

SPIN = 0

Integer spin particles Force-carrying bosons have a spin of 1, but larger bosons can be made by adding together fermions. The unique Higgs boson has zero spin (see p.127).

68

FERMIONS AND BOSONS

REJECTED PAIRING

SPIN DOWN

Particles with identical spin cannot share the same state— one must always go somewhere else.

Particle pairs

SPIN UP

Two otherwise identical particles can have the same energy, momentum, and position if their spins are complementary.

NO ROOM FOR TWO One of the most important rules underlying the structure of matter, the Pauli exclusion principle prevents fermions from falling into completely identical quantum states. This generates a form of pressure that keeps particles apart even when other repulsive forces such as electromagnetism fail (for instance, inside superdense collapsed stars known as white dwarfs and neutron stars). It also explains why only two electrons (with up and down spins) can occupy the same orbital subshell within an atom (see p.31).

PAULI EXCLUSION PRINCIPLE

69

APPROACHING A BARRIER In terms of classical physics, the forces binding an atomic nucleus create an energy barrier or “potential well.” Classically, a particle could only escape a well if it had enough kinetic energy to overcome the potential energy deficit. Energy below this value would mean that the particle was trapped forever.

WHAT BARRIER? An effect known as tunneling explains how subatomic particles can sometimes cross apparently insurmountable barriers. During radioactive alpha decay (see p.113), for example, a cluster of protons and neutrons spontaneously breaks free from a larger atomic nucleus by overcoming the binding energy that holds the nucleus together. Such a leap is impossible in classical physics, but the edges of a quantum wave function can reach beyond the barrier, allowing for a small chance of the particle being found there.

70

QUANTUM TUNNELING

A possible outcome Over time there is a finite probability that a radioactive particle will decay, but the decay event itself is impossible to predict. Tunneling may provide a solution as to why particles sometimes, but not always, escape from an atomic nucleus. TUNNELING THROUGH The amplitude of a wave function decreases exponentially across a potential barrier, but it can still end up with a nonzero value on the other side of the barrier, and therefore there is a nonzero chance of the particle being found on the other side of the barrier.

BARRIER

OPPOSING FORCES

NUCLEI IN THE SUN

The sun’s core has lightweight hydrogen nuclei, which are subject to electromagnetic coulomb forces: similarly charged particles repel each other and differently charged particles attract.

Temperatures of millions of degrees give nuclei huge kinetic energy, but conditions inside the sun are not hot enough to account for the vast number of particles that overcome repulsion.

NUCLEAR FUSION

COULOMB FORCE

COULOMB FORCE

There are many more fusion reactions in the sun than would be expected given the coulomb barrier in place, and so quantum tunneling must play a key role.

QUANTUM TUNNELING

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DISTANCE NO OBJECT One of the strangest quantum effects, entanglement arises from the nature of the quantum wave function itself. Pairs of particles produced in a single interaction share a common origin and cannot be described independently of one another. The particles can be separated by a vast distance, yet when the properties of one particle are measured, its entangled partner somehow instantaneously “knows,” and itself collapses to the appropriate state.

SPIN UP

PARTICLE A

72

QUANTUM ENTANGLEMENT

The properties of the entangled particle pair are described by a shared wave function.

PARTICLE B

PARTICLE A

A measurement of physical properties— such as spin, position, momentum, or polarization—of one particle in an entangled pair will correlate with the measurement in the second.

Particles can be widely separated, yet measuring one resolves the properties of the other instantaneously.

SPIN DOWN

PARTICLE B Entangled properties remain in a state of quantum uncertainty, but measuring one particle also resolves the properties of the other.

QUANTUM CONNECTION

Correlation

QUANTUM ENTANGLEMENT

73

SENDER

Bob has the other half of the entangled photon pair. Information about Alice’s system, sent by conventional means, allows him to recreate Alice’s encoded photon and read its information. RECEIVER

74

TRANSFERRING QUANTUM STATES

ENTANGLED PHOTONS

CONVENTIONAL SIGNAL

The strange physics of entanglement (see pp.72–73) can be put to work in quantum teleportation—the reconstruction of quantum information from one system in another system. Teleportation involves the creation of an entangled pair of quantum states (qubits; see p.106), which are then separated. The system to be teleported interacts with one qubit, resulting in a “classical” measurement that is then transmitted to the location of the other qubit at the speed of light, and used to reconstruct the interacting system.

PHOTON

TELEPORTED PHOTON

QUANTUM TELEPORTATION

BELL-STATE ANALYZER

Alice encodes information into a photon, which is then made to interact with one of a pair of entangled particles in a device called a “Bell-state analyzer.”

0 1

COHERENCE A quantum particle in complete isolation can retain an indeterminate state indefinitely.

ENVIRONMENTAL IMPACT In a complex system, such as an atom, interference with wave functions from other particles causes indeterminate systems to lose coherence.

ATOM

LE B A T UNS ENT M N RO I ate V N ate st n i E m r ndete o be

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DECOHERENCE

75

INSIDE SOLID OBJECTS Individual atoms consist of positively charged nuclei surrounded by negatively charged electrons (see pp.10–11). In order to form large-scale solid materials, such as crystals, however, atoms surrender some of their electrons, allowing them to float freely (to a certain degree) within a fixed geometric lattice of positively charged ions. Quantum effects govern where electrons can reside—modeling the electrons as a “gas” of fermions provides insights into phenomena such as electrical and heat conduction and insulation.

SOLID OBJECT

76

SOLID-STATE PHYSICS

FREE ELECTRON

–

Early models of solids attempted to model the movement of free electrons as a “Fermi gas” obeying pure Fermi-Dirac statistics.

+ ION

SECTION OF LATTICE

NEARLY FREE ELECTRONS

Modern theories rewrite the wave equation to take interactions between electrons and the positively charged ions of the crystal lattice into account, describing energy levels inside the solid in terms of “electronic bands” (see p.90).

CRYSTALLINE STRUCTURE

SOLID-STATE PHYSICS

77

OVERLAPPING WAVES

As a sparse gas of bosonic atoms is cooled to very low temperatures, their wave functions expand and begin to overlap with each other.

ENERGY LEVEL TEMPERATURE

ENERGY LEVEL

TEMPERATURE

BOSONIC GAS

Because of the way the quantum spin property adds up (see p.68), atoms containing the right number of fermion particles (spin 1 ⁄ 2) can behave as bosons with whole-number spins.

78

Normal temperatures

Extreme cooling

At high temperatures, the boson gas seems outwardly normal, with particles at a wide range of energy levels— although some levels are shared.

As temperatures fall and the particles lose kinetic energy, their range of possible energy states is reduced. More particles start to share the same state.

BOSE-EINSTEIN CONDENSATES

ALTERED STATES When a large collection of bosons is cooled to a very low temperature, the range of possible energy states available to the particles is greatly diminished, producing a strange form of matter called a Bose-Einstein condensate (BEC). Because the Pauli exclusion principle (see p.69) does not apply to bosons, the particles are not forced to maintain separate states—instead they fall into a shared low-energy state described by a single wave equation.

Critical temperature Below a certain critical temperature, all the particles fall into the lowest possible energy state, described by a single quantum wave function.

BOSE-EINSTEIN CONDENSATE

TEMPERATURE

ENERGY LEVEL

As the temperature is reduced toward absolute zero (−459.67°F/ −273.15°C), the wave functions expand still further and merge to form a BEC that behaves as a single giant particle.

BOSE-EINSTEIN CONDENSATES

79

The strange behavior of helium-4 at temperatures less than 35.9°F (2.17°C) above absolute zero was discovered in 1938.

CLIMBING UP THE WALLS

Superfluidity is a strange phenomenon in which a liquefied gas cooled to an extremely low temperature flows without internal friction between its atoms. Superfluids arise when atoms fall into states where they are governed by Bose-Einstein statistics (see pp.78–79). Their frictionless flow allows them to “creep” up container walls, form curious wave patterns, and even to slow the speed of light.

With no internal friction, other forces such as surface tension (attractions to atoms in the container) dominate, causing the fluid to climb the walls of an open container and equalize its levels inside and out.

Even in isolation, the superfluid will continue to climb out of its container, forming droplets that eventually fall under gravity until the container is empty.

HELIUM-4 SUPERFLUID

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SUPERFLUIDITY

HARD TO HANG ON TO

THE FIRST SUPERFLUID

FLOWING

WITHOUT FRICTION

As an electron moves through a superconductor at low temperatures it attracts positive ions toward it.

ELECTRON ONE

ELECTRON TWO

A second electron with opposite spin is attracted by the deformation. The two electrons form a pair that, with others, can create a Bose-Einstein condensate (see pp.78–79).

BCS model The Bardeen-CooperSchrieffer model is a long-standing and powerful way of explaining most types of superconductivity.

POSITIVELY CHARGED ION LATTICE

ENDLESS CHARGE In normal electrical conductors, energy is lost to resistance— interactions between the electron particles that transmit current and their surroundings. However, at very low temperatures quantum behavior leads to an effect called superconductivity, in which current flows without resistance through certain materials. Electrons in a superconductor travel in Cooper pairs that exhibit the properties of bosons (see pp.78–79) rather than fermion particles, allowing them to flow without friction in a similar way to superfluids.

SUPERCONDUCTIVITY

81

STRANGE QUANTUM ATOMS Most atoms are in a state of constant motion, which makes their properties hard to measure precisely. To get the most accurate measurements, physicists cool them to extremely low temperatures, where the random movement of particles due to excess kinetic (motion) energy is minimized. This can be done by using laser beams to slow down the atoms, ultimately reaching temperatures close to absolute zero (–459.67°F/–273.15°C), where strange quantum properties can develop. COOLING LASERS

Atoms are fed into the trap at low pressure, gradually accumulating into a cloud whose properties can be studied (see pp.78–79). COOLED ATOM CLOUD

VA C

Lasers are “tuned” so that they will interact only with atoms moving toward them. Each collision with a photon from these lasers drains more momentum from the atom. U

UM

CH

AM

BER

BOSE-EINSTEIN CONDENSATE

A varying magnetic field is designed to channel the atoms in directions that ensure the cooling lasers have maximum effect. ANTI-HELMHOLTZ COILS

Slowing down atoms Cooling atoms close to absolute zero involves using a complex apparatus to bring their motion to a near-complete stop in a magneto-optical trap.

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COLD ATOM PHYSICS

MAGNETOOPTICAL TRAP

RYDBERG ELECTRON The wave function of the outer electron has very little overlap with those of the inner electrons and so it is fairly immune to interference from within.

NUCLEUS

Excited atom The inner electrons of a Rydberg atom shield the outermost electrons from most of the influence of the nucleus, from their distant position the electric forces they experience are similar to those in a hydrogen atom.

RYDBERG ATOM

UNUSUAL ORBITS Rydberg atoms are a form of matter in which at least one of an atom’s electrons is boosted into a large orbit with a very high “principal quantum number.” The great distance between the electron and the atom’s inner core produces curious effects. Some properties of Rydberg atoms mirror those of hydrogen, but the atom’s loose grip on the outer electron means it is easily ionized, and highly sensitive to electric and magnetic fields.

RYDBERG ATOMS

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QU A N T T E C H N

U M O L O G Y Quantum physics is at the heart of many established and emerging technologies. Applications that harness quantum principles in their design—ranging from everyday electronics to satellite timekeepers—can be broadly described as quantum technologies. The devices that laid the foundation of the Information Age are built on quantum physics—for instance, semiconductor devices are designed around the quantization of electron energy levels, which restrict the movement of charge in a lattice. In the near future, similarly transformative new technologies could be built on other quantum phenomena, such as entanglement.

FIRING PHOTONS AT ATOMS When an electron falls from an excited state to its ground state (see p.30), it releases the energy difference as a photon. Stimulated emission involves firing photons at atoms, causing excited electrons to fall to their ground states and release new photons with wavelength and phase identical to the incident photons. These stimulate other atoms, resulting in a cascade of coherent light (see opposite).

ELECTRON

EXCITED STATE LEVEL

PHOTON

GROUND STATE LEVEL

Absorption of light When an electron absorbs energy from an incident photon, it may be excited (also referred to as being “pumped”) to a higher energy state. An electron in an excited state may then decay to a lower energy state.

86

Spontaneous emission of light

Stimulated emission of light

When an electron falls to a lower state spontaneously, it releases energy in the form of a photon. The phase and direction of photons spontaneously emitted by electrons in a material is random.

An incident photon can cause an electron to fall to a lower energy state. In the process, the electron emits an additional photon, which has the same phase and direction as the incident photon.

STIMULATED EMISSION

LASERS

87

RUBY LASER HIGH-INTENSITY FLASH LAMP

The ruby medium is pumped using a flashtube. Energy emitted from the flashtube is absorbed by electrons in the medium, which then jump to excited states.

The laser emits rapid pulses of visible red light. Due to the photons being produced via stimulated emission, this light is perfectly coherent.

A laser is a device that emits light through the process of optical amplification, based on stimulated emission (see opposite). Unlike light from other sources, laser light is coherent, meaning that the waves are perfectly in step with each other and have the same frequency. The invention of lasers has allowed unprecedented control over light, with applications such as remote-sensing lidar, laser cutting, and spectroscopy. Lasers can also be used to trap and cool small particles, such as atoms and ions.

HIGHLY CONCENTRATED

ALL WAVES IN STEP

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The most precise way of measuring time is based on using the frequency of microwave radiation that excites electrons to jump between energy states in certain atoms.

Cesium atoms are ionized and fired through a magnetic gate that filters out any with a high-energy state. The low-energy-state atoms then continue on to the radio wave oscillator.

The oscillator fires microwaves set to a specific frequency at the atoms, causing them to jump to a higher energy state.

CESIUM–133 ATOMS FIRED

Measuring time

QUANTUM LEAP

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Atomic clocks, which are used in technologies such as satellite navigation, keep precise time using the properties of certain atoms such as those of cesium-133. When atoms are exposed to photons, some electrons jump between energy levels. When the incident photons have precisely the same frequency as a cesium-133 atom, electrons in the atoms resonate and leap between energy levels. One second is defined as 9,192,631,770 oscillations at that frequency.

MAGNET

MAGNET HIGH-ENERGY-STATE ATOMS REMOVED

88

ATOMIC CLOCKS

The definition of a second has been based on this frequency since 1968.

A second magnet filters out low-energy cesium atoms before a detector counts the number of atoms. If the detector counts enough high-energy-state atoms, then the oscillator is at the right frequency. If the number of high-energy atoms is too low, then the oscillator needs adjusting to the correct frequency.

OSCILLATOR

RADIO WAVE SIGNAL SENT AT 9,192,631,770 HZ

9,192,631,770 OSCILLATIONS

FEEDBACK TO OSCILLATOR

FREQUNECY AND TIME

The most accurate atomic clocks will not lose or gain more than 1 second in 15 billion years.

MAGNET

DETECTOR MAGNET LOW-ENERGY-STATE ATOMS REMOVED

ATOMIC CLOCKS

89

ENERGY LEVEL

ENERGY GAP

The ranges of energies where no possible states can exist in a solid are known as band, or energy, gaps. Every solid has a characteristic structure of bands and gaps. The valence band contains the highest energy level that electrons occupy. In a semiconductor, some electrons have enough thermal energy to jump across the gap.

CONDUCTION BAND

OVERLAP

CONDUCTION BAND

Allowed energy states

JUMPING ACROSS

WIDE GAP

In an insulator, no electron has enough energy to jump the wide energy gap between the valence band and the conduction band (which allows electrons to travel within material).

In a conductor, the energies of the valence electrons overlap with the conduction band; there is no gap.

CONDUCTION BAND

ENERGY GAP

VALENCE BAND

VALENCE BAND

VALENCE BAND

INSULATOR

SEMICONDUCTOR

CONDUCTOR

SOLID STATES In order to understand the electric properties of materials, it is necessary to understand how electrons move within them. Band theory is a model that describes the permitted and forbidden energy levels—bands and band gaps—in materials with solid structures (see pp.76–77), which restrict the behavior of electrons. This model explains thermal and electric properties of solid matter and is the basis of solidstate electronic devices, such as transistors (see opposite), diodes (see p.92), and solid-state data storage devices.

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BAND THEORY OF SOLIDS

SILICON CHIPS A transistor is a device that changes electronic signals. It is made from silicon, which is “doped” to give it different properties. For example, when electrons are removed, “holes” are left for electrons to flow into. Putting together layers of silicon, each with either an excess (n-type) or deficit (p-type) of electrons, creates transistors that can amplify or switch a current. Many transistors are integrated onto a single computer chip.

Basic transistor In an n-p-n transistor, a layer with a deficit of electrons (p-type) is sandwiched between layers with excess electrons (n-type). Excess electrons can flow into the p-type region. BASE CONTACT

N-TYPE REGION

P-TYPE REGION

N-TYPE REGION

ELECTRON PATH

SWITCH IS OFF

N-TYPE REGION

When there is a positive bias across the transistor, electrons are pulled from emitter to collector. BASE CONTACT

P-TYPE REGION

N-TYPE REGION

SWITCH IS ON CURRENT IN (EMITTER)

CURRENT OUT (COLLECTOR)

TRANSISTORS

91

LIGHT RELEASE

P-TYPE REGION

ENERGY RELEASE

When the positive terminal is connected to the p-type layer and the negative terminal to the n-type layer, an electric current will flow.

FORWARD BIAS

A light-emitting diode (LED) emits light when a current is applied. In an LED, a p-type and an n-type semiconductor are placed close together, between electrical contacts. When current flows, excess electrons flow from the n-type to the p-type layer, where they fall into “holes” in the semiconductor and release photons (light). The color of the light emitted depends on the energy required for electrons to cross the band gap (see p.90). When electrons and holes recombine, the electrons— which are at a higher energy level—must release some energy. This is emitted in the form of photons.

DEPLETION ZONE

N-TYPE REGION

CURRENT FLOW POWER SOURCE

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LIGHT-EMITTING DIODES

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PHOTON COLLECTION CIRCUIT

Each capacitor accumulates a charge, which is proportional to the intensity of light at that point.

The control circuit forces each capacitor to transfer its charge to its neighbor. The final capacitor in a column then transfers its charge to the horizontal shift register, which moves it to a processor.

PIXEL Each pixel is represented by a capacitor. HORIZONTAL SHIFT REGISTER Transfers charge to processor for output.

DIGITAL OUTPUT

CHARGE-COUPLED DEVICE

A charge-coupled device (CCD) is a circuit of linked capacitors, which store and transfer electrical charge. CCD image sensors convert light into electrical signals and are important components in digital imaging. Pixels are represented by semiconductor capacitors that free electrons when photons are absorbed, accumulating electrical charge proportional to light intensity at that point. A control circuit transfers charges through a capacitor array, converting them into a readable signal.

CHARGE-COUPLED DEVICES

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The superconductor repels the magnetic fields of the permanent magnets. This can result in stable levitation due to the superconductor being “pinned” by the magnetic fields.

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Superconductors may be used to achieve magnetic levitation: the suspension of an object using magnetic fields.

PINNED IN PLACE

Quantum lift

PERMANENT MAGNETS

LEVITATION Superconductivity is a phenomenon observed in special materials, usually at very cold temperatures near absolute zero (−459.67°F/−273.15°C), in which electrical resistance vanishes (see p.81). Superconducting electromagnets are made from superconducting wire coils that conduct massive currents, generating powerful magnetic fields. When a superconductor is in a magnetic field, small currents are created. These currents then create opposite magnetic fields, expelling the field and preventing the magnetic field from penetrating the superconductor.

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SUPERCONDUCTING ELECTROMAGNETS

TUNNELING PAIRS COOPER PAIR

The Josephson effect is a rare example of a quantum phenomenon observable on a macroscopic scale. It involves an electric current flowing indefinitely, without an applied voltage, across a Josephson junction. A Josephson junction is a pair of superconductors with a thin barrier sandwiched between them. Electrons in Cooper pairs (see p.81) tunnel through the barrier from one superconductor to the other with no resistance. Josephson junctions are used in SQUIDS (see pp.96–97). Across the barrier Pairs of electrons tunnel through the barrier from one superconductor to the other until a critical current is reached and a voltage appears across the junction.

BARRIER

A very thin barrier of insulating or normal conduction material between two superconductors forces the pair to tunnel (see pp.70–71) across.

COOPER PAIR

THIN BARRIER

SUPERCONDUCTOR

JOSEPHSON JUNCTIONS

95

SQUIDS A superconducting quantum interference device (SQUID) is used to detect extremely faint magnetic fields, including signals associated with neural activity. A SQUID is based on a superconducting loop containing two Josephson junctions (see p.95). In a magnetic field, the current in the ring varies to shift the magnetic flux (number of field lines) within it to an energetically preferable value, causing voltage to vary with the magnetic field.

SEMICONDUCTOR

INDUCED CURRENT

96

In the presence of a small magnetic field, a current is created (induced). The current generates a magnetic field. If the field outside the loop changes, the current in the loop increases or decreases the magnetic flux inside the loop to an energetically preferable value (a multiple of the flux quantum). This produces a measurable change in voltage across the junctions.

JOSEP HSON JUNC T ION

CURRENT

SUPERCONDUCTING QUANTUM INTERFERENCE DEVICES

MAGNETIC FIELD

SQUIDs can detect changes in electromagnetic energy up to 100 billion times weaker than the energy needed to move the needle of a compass.

DC SQUID

CURRENT

A direct current SQUID uses two Josephson junctions in parallel in a superconducting loop. Each junction lets a small electric current through. The voltage across a junction is very sensitive to the magnetic field within the ring.

SUPERCONDUCTING QUANTUM INTERFERENCE DEVICES

97

MOSTLY ALIGNED

RANDOM POSITION

With no external magnetic field, protons spin inside the body with the axes of their own magnetic fields randomly aligned.

When a powerful external magnetic field is applied, the axis of each proton’s magnetic field lines up (parallel) with this magnetic field.

MRI SCANNER

Quantum scanner When the spin of a single proton is measured, it can be in one of two states: parallel or antiparallel. During an MRI scan, protons switch from parallel to antiparallel and back again.

”It was eerie. I saw myself in that machine. I never thought my work would come to this.” Isidor Isaac Rabi, whose work led to the MRI

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MAGNETIC RESONANCE IMAGING

RELEASE OF RADIO SIGNAL

RADIO PULSE MOVEMENT

Radio wave pulses of a specific frequency are sent through the body, causing the protons to vibrate and exciting the protons into a different alignment (antiparallel).

When the radio pulses stop, the protons keep vibrating and gradually realign with the magnetic field. Their vibration releases measurable radio waves (energy) in the process.

LOOKING INSIDE Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique. The patient is placed in a powerful magnetic field, forcing the magnetic moments (see p.67) of protons in the body to align. Protons make up the nuclei of atoms of hydrogen, one of the most abundant elements in the body. When a current is applied, the protons become excited and spin (or vibrate) out of position. Measuring the frequency of the vibrations of the protons after the current is switched off allows different tissues to be distinguished.

MAGNETIC RESONANCE IMAGING

99

SEEING WITHOUT LIGHT

SECONDARY DETECTOR

The resolution of a microscope is limited by wavelength. When it comes to observing tiny objects, matter waves (which have shorter wavelengths) can be more helpful than light. The wavelength of an electron is up to 100,000 times shorter than that of visible light, allowing for the imaging of up to 100,000 times smaller objects, such as viruses. Scanning electron microscopes use beams of accelerated electrons to illuminate objects, bent by magnetic fields rather than glass lenses. A secondary electron detector attracts and registers electrons emitted from the sample.

Beaming electrons

REFLECTED BEAMS

A focused electron beam scatters from atoms on an object’s surface, producing signals that allow for a very detailed image to be built.

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ELECTRON MICROSCOPES

Some high-energy electrons are reflected or backscattered from atoms within the specimen.

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DE A detector records the intensity of scattered electrons in each position to build an image of the specimen.

A magnetic field bends the beam of electrons, much like the way a glass lens bends a beam of light.

”In basic research, the use of the electron microscope has revealed to us the complex universe of the cell, the basic unit of life.“ Günter Blobel

ELECTRON MICROSCOPES

101

PHOTODIODE

A light-sensitive diode tracks the change in height of the tip as it scans across the surface, using the reflected laser beam.

PH

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FEEDBACK ELECTRONICS

Deflections detected by the laser are used in a feedback loop to control the position of the tip and keep it close to the sample surface.

CA

The tip of an AFM probe can be 5 to 40 nanometers in diameter— smaller than most viruses.

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ATOMIC FORCE MICROSCOPY

NT

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AF ne d th M g e t a a n e n a i ve s i l p r ima n o s s c ie c ob g n e t e f r a l e w ti s t ra om o s a ve r l i n th e l d . T g l i m ga re h e p s cr s o s p o n y b u e int sa il o s su e s o d r fa f a ce .

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LASER

When the tip of the cantilever is brought very close to the surface, repulsive forces cause it to be deflected.

CANTILEVER AND TIP

Atomic force microscopy (AFM) is a scanning technique that involves “touching” the surfaces of objects. When a cantilever with an extremely sharp probe approaches the sample’s surface, forces between the surface and the probe cause the cantilever to be deflected slightly. This movement is detected with a laser. AFM allows for nanometer-scale resolution, and can be used for imaging and manipulating individual atoms.

A laser beam reflected from the cantilever is used to detect its tiny deflections.

SAMPLE SURFACE

ATOMIC FORCE MICROSCOPY

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QU A N T U I NFORM

M A T I O N In 1980, well before computers became household objects, the American physicist Paul Benioff demonstrated that a computer could theoretically operate under the laws of quantum physics. Today, there are many models of quantum computing. Quantum computers store and manipulate quantum information to perform calculations, potentially carrying out new calculations and algorithms that would offer an exponential time improvement on today’s classical computers. Although serious technical barriers stand in the way of quantum computers entering the mainstream, they are expected to transform computing, communication, and security in the 21st century.

The possible states of a qubit can be represented with a Bloch sphere, with the poles corresponding to the states 0 and 1.

BLOCH SPHERE

In a classical computer, a bit is either 0 or 1, which can also be thought of as a switch being either off or on.

0 1 BIT N=0

SUPERPOSITION

BIT COMPARISON

A qubit can exist in a superposition of the states 0 and 1, represented by an arrow pointing at a location on a Bloch sphere. The probability of measuring a 0 or a 1 depends on the position of the vector representing the qubit.

S=1

NOT JUST ZEROS AND ONES The basic unit of information in classical computing is the bit, which can take one of two states (represented as 0 or 1). The quantum equivalent, known as a “qubit,” is not in one state or the other, but instead in a superposition (see pp.38–39) of these two states. Qubits can be encoded in the properties of particles such as electron spin (up or down) and photon polarization (vertical or horizontal).

106

QUBITS

SUPERFAST

In classical computers calculations are performed by manipulating bits one by one, according to programmed instructions.

EVERYTHING AT ONCE

CLASSICAL COMPUTER

ONE BY ONE

Quantum computers use quantum processes to store and manipulate data. They can perform certain calculations— such as breaking down very large numbers into their prime factors—much faster than classical computers. In theory, quantum computers have the ability to execute tasks that would be practically impossible on a classical computer. However, there are serious technical challenges associated with building quantum computers, most significantly in maintaining the wave function of the qubits (see p.75).

For specific computational problems, quantum computers can exploit superposition and entanglement to execute different algorithms that classical computers cannot.

QUANTUM COMPUTING

107

QUANTUM CODES When data is encrypted, only a person with the key can unscramble and read it. Quantum cryptography uses quantum phenomena such as superposition (see pp.38–39) or entanglement (see pp.72–73) to encrypt and decrypt data. This can make it impossible to snoop on encrypted conversations; an eavesdropper must measure a quantum key to gain information about it, causing the wave functions of the shared quantum keys to collapse, thus revealing the unauthorized access. Secret codes

Bob uses polarizing filters and a detector to obtain information from the photons.

Alice shares a secret message with Bob using a series of polarized photons. Alice and Bob then agree on a “sifted key,” which is based on measurements made with compatible polarization filters.

To create the sifted key, Bob tells Alice the sequence of the filters he used and they discard the measurements that do not match.

Photons are polarized using filters.

1

DETECTOR

TRANSMISSION OF CODED SEQUENCE

0

FILTERS

PHOTON

FILTERS

1

0

ALICE ALICE’S SEQUENCE

BOB 1

1

1

0

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1 BOB’S DETECTION

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BOB’S MEASUREMENTS

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SIFTED KEY

ALICE CHECKS BOB’S FILTERS SIFTED KEY

108 QUANTUM CRYPTOGRAPHY

SIMULATORS Some systems are too complex for even supercomputers to simulate—particularly systems with properties that cannot be classically simulated, such as entanglement. However, these can be simulated with analog systems of real particles with quantum properties, such as ultracold gases. While quantum computers can theoretically one day be programmed to solve any problem, quantum simulators are already used to explore specific problems.

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Ions are arranged in a matrix using magnetic fields and laser beams.

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IONS SUSPENDED IN A MAGNETIC FIELD

LASERS Highly sensitive laser beams are used for measuring the ions’ properties, such as temperatures.

ER L AS

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Electric and magnetic fields trap hundreds of ions in an orderly 2D lattice.

Trapped ion simulator It may be possible to simulate interactions in quantum magnetism using trapped ions that mimic this magnetic behavior. This would not be feasible using a classical computer.

COOLING LASER BEAM

QUANTUM SIMULATION

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N U C L E P H Y S I

A R C S On the eve of the 20th century, the discovery of radiation emerging from within atoms challenged the long-held belief that atoms—which had been named for their seeming indivisibility—were the fundamental building blocks of matter. This led to the discovery of atomic nuclei and marked the beginning of the exploration of the subatomic world. At this scale, quantum physics is required to explain how natural phenomena occur. The field of nuclear physics involves the study of nuclei (the dense, positively charged objects found at the center of atoms), their constituents, and associated phenomena such as radioactivity, fission, and fusion.

NEUTRON EMISSION

A neutron may also be ejected from the atomic nucleus during decay.

UNSTABLE NUCLEUS

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RADIOACTIVITY

In beta minus decay, a neutron transforms into a proton, ejecting an electron and electron antineutrino from the nucleus. In beta plus decay, a proton transforms into a neutron, ejecting a positron and an electron neutrino in the process.

Radioactivity was discovered by the French scientist Henri Becquerel in 1896 during experiments with X-rays and phosphorescent material.

 BETA PARTICLE

A nucleus is radioactive if it spontaneously decays (emits radiation) to become a new, more stable nucleus.

High-energy photons are emitted during gamma decay.

During alpha decay, an alpha particle (a helium nucleus comprising two protons and two neutrons) is emitted from the unstable parent nucleus.

 GAMMA RAYS

 ALPHA PARTICLE

S E E K I NG S TA B I L IT Y Radioactivity is the emission of waves or particles from an unstable atomic nucleus. This occurs when a nucleus spontaneously transforms into a more stable configuration itself by emitting energy. The random nature of the quantum world means it is impossible to predict when an individual nucleus will decay, although the decay of a large group of identical nuclei can be described by their half-life (time taken for half of the nuclei to decay).

RADIOACTIVITY

113

Nuclear reaction

NUCLEUS SPLITS

Nuclear fission is initiated by bombarding radioactive material (most commonly uranium-235 in nuclear reactors) with neutrons.

When a neutron destabilizes the uranium nucleus, the nucleus typically splits into two parts.

ENERGY RELEASED

NEUTRON

URANIUM-235 NUCLEUS

SPLITTING ATOMS Nuclear fission is the splitting of an atomic nucleus into smaller pieces. When added together, all of the lower-mass fragments left after fission weigh less than the original heavy nucleus—the missing mass is released as energy. Neutrons released in fission can go on to collide with other nuclei and can cause them to undergo fission. This is called a chain reaction (such as in a nuclear reactor or an atomic weapon).

114

NUCLEAR FISSION

STARTING A CHAIN REACTION When neutrons released in fission strike further uranium nuclei, this can lead to a chain of nuclear reactions.

NEUTRON

CHAIN REACTION

”The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe.“ Albert Einstein

NUCLEAR FISSION

115

HELIUM The two nuclei merge to produce a helium nucleus. A vast amount of energy is also released.

DEUTERIUM Deuterium is a hydrogen nucleus with an extra neutron.

FUSION

NUCLEUS OF AN ATOM

TRITIUM Tritium is a hydrogen isotope that has two extra neutrons in its nucleus. NEUTRON EMISSION An excess neutron is also emitted during fusion.

116

NUCLEAR FUSION

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CREATING ELEMENTS Stellar fusion is responsible for the variety of elements in the universe. Heavy elements are created as dying stars collapse, in the merging of neutron stars, or during other high-energy astrophysical events.

COMBINING NUCLEI Two or more nuclei combine to form a larger nucleus in a process called nuclear fusion. When light nuclei fuse, they lose a little mass, which is released as energy. The repulsive Coulomb forces between positively charged nuclei make fusion impossible under all but the most extreme conditions, such as inside stars. Under these conditions, nuclei can tunnel (see p.71) through the Coulomb barrier and be brought close enough to fuse.

”I would like nuclear fusion to become a practical power source. It would provide an inexhaustible supply of energy, without pollution or global warming.“ Stephen Hawking

NUCLEAR FUSION

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P A R T I P H Y S I

C L E C S Particle physics involves the study of the most fundamental objects and forces in nature. In the 20th century, the discovery of a “zoo” of elementary and composite particles allowed scientists to build the most successful theory yet for understanding particle physics: the Standard Model. This proposes that matter is made up of 12 fundamental particles (fermions), while the three quantum forces—strong, weak, and electromagnetic—are carried by force-carrying particles (bosons). According to quantum field theory, all these particles are excitations of their underlying quantum fields.

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Objects on the quantum scale are invisible, but particle detectors, such as cloud chambers and bubble chambers, can make their paths visible. In a cloud chamber, ionizing particles speed through a vapor-filled chamber, leaving a trail of ionized atoms, around which condensation forms. Within magnetic and electric fields, the condensation forms uniquely curving trails, which allow characteristics such as charge and mass to be calculated.

120

PARTICLE DETECTORS

Bubble chambers use superheated fluids, and bubbles of gas form around points of ionization to create trails.

SIM

PLY

SMA

ENER G E N C O E TI C U NTE R

Collid At pa in g pa the L a r ticle acce r t ic le lerato rg e H s r s , su a d ro n c h a rg ch as Collid e d pa e r at C r ticle s a re s ER N , each mash o th e r ed int at g re o at s p e ed.

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SHI

NG

PARTICLE ACCELERATORS

121

ATOMIC NUCLEUS

P R OT

ON

N E UT R

ON

GLUON

NEUTRON

Baryons (such as protons and neutrons) are made up of three quarks. A proton consists of two up quarks and one down quark.

PROTON

Gluons hold quarks together.

Neutrons consist of two down quarks and one up quark and have a mass slightly higher than that of a proton.

SMALLER THAN AN ATOM Atoms are built from elementary matter particles, such as quarks. There are six quark flavors: up, down, strange, charm, top, and bottom. Quarks also have a unique property known as “color charge” (see p.135), which is unrelated to color in the everyday sense. Particles with color charge cannot be isolated, so quarks always combine to form “colorless” composite particles such as protons, which are bound together through the strong force.

122

QUARKS

NO STRONG INTERACTIONS Leptons are the other type of elementary matter particle. There are six flavors of leptons, divided into three generations and two classes: charged leptons (electron, muon, and tau), and electrically neutral neutrinos (electron neutrino, muon neutrino, and tau neutrino). All quarks and leptons have half-integer spin. Leptons are unaffected by the strong force. While charged leptons frequently interact with other particles throught the electromagnetic force, neutrinos are considered “ghostlike,” barely interacting with anything as they can influence other particles only through the weak interaction.

N

N RI T EU

OS

JUST PASSING THROUGH About 100 trillion neutrinos pass through your body each second, arriving from the upper atmosphere, fusion processes in the sun, and from many other sources throughout the cosmos.

LEPTONS

123

THE QUANTUM WORLD EXPLAINED

d

The Standard Model is the most successful theory for organizing the quantum world. It describes everything in terms of interactions played out by the set of elementary matter particles (fermions), force-carrying particles (gauge bosons), and the Higgs boson. Despite the success of the theory in predicting experimental results, it is considered a work in progress as there are some phenomena that cannot yet be explained (see pp.130–31). CREATING MATTER Leptons and quarks are fermions (with half-integer spin). They are the smallest building blocks of matter.

LEPTONS Leptons come in three “generations” and two types: charged and neutral. The charged leptons are the electron, muon, and tau. The neutrinos are neutral.

”The Standard Model is so complex it would be hard to put it on a T-shirt—though not impossible; you'd just have to write kind of small.“ Steven Weinberg

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THE STANDARD MODEL

DOWN

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I

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e

ELECTRON NEUTRINO

s

c

STRANGE

CHARM

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I N E R AT I O N I

Quarks are the only matter particles to experience the strong force. Like leptons, they come in three generations.

g

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PHOTON

GLUON

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HIGGS BOSON

BOSONS

t

TAU NEUTRINO

Z BOSON

There are four known gauge bosons (spin 1), which carry fundamental forces.

E R AT I O N

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W BOSON

N GE

TOP

The Higgs boson, which gives particles their mass, is the only confirmed scalar boson (its spin is equal to zero).

HIGGS BOSON

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MUON NEUTRINO

THE STANDARD MODEL

125

FORCE CARRIERS Quantum physics successfully incorporates three of the four fundamental forces: electromagnetic, strong, and weak. When particles interact, they do so by exchanging the gauge (spin 1) bosons, also known as “force carriers,” associated with those forces. The electromagnetic force is mediated by photons, the weak force by W and Z bosons, and the strong force by gluons.

SPIN

1 BOSON S

Photons are the smallest possible packets of light. PHOTON

W+, W –, AND Z BOSONS

GAUGE BOSONS

The W and Z bosons are among the heaviest of the elementary particles. The W bosons possess an electric charge while the electrically neutral Z0 behaves like a photon with mass.

Gluons, which carry the strong force, bind quarks together to form hadrons, such as protons.

The gauge bosons listed here are the ones included in the Standard Model (see pp.124–25). Beyond the Standard Model, it is possible that the fourth fundamental force (gravity) is also carried by a boson (graviton).

GLUON

Fundamental forces

126

GAUGE BOSONS

Higgs interactions

The electron—which is the lightest particle with electric charge— interacts weakly with the Higgs field.

PHOTON

Top quarks are the heaviest type of fermion and interact strongly with the Higgs field.

ELECTRON

QUARK

The interaction of particles with the Higgs field inhibits the particle’s movement, generating their mass. Without it, all particles would zip around at the speed of light.

Photons have no mass and do not interact with the Higgs field.

THE HIGGS FIELD

WHY PARTICLES HAVE MASS The Standard Model includes one scalar (spin zero) boson, which is called the Higgs Boson. This is the particle associated with the Higgs field: a field that permeates throughout all space and gives particles their mass. The more strongly a particle interacts with the Higgs field, the more mass it has. A particle that does not interact with the field at all (such as a photon) has no mass.

THE HIGGS BOSON

127

Matter

HYDROGEN ATOM

Hydrogen is made of “ordinary” matter: a proton containing two up quarks and one down quark, orbited by a single electron.

PROTON ELECTRON

Q U AR

KS

THE OPPOSITE OF MATTER Antimatter is composed of antiparticles, which have the same mass but opposite electric charge (and some other properties) to their corresponding “ordinary” matter particles. For example, a positron has the same mass as an electron; however, it has the same size, but opposite, charge to the electron. When a particle meets its antimatter partner, they annihilate each other with a burst of energy. The dominance of ordinary matter in the universe is an unresolved mystery in physics.

128

ANTIMATTER

Antimatter

ANTIHYDROGEN ATOM

ANTIPROTON

Hydrogen’s antimatter counterpart is called antihydrogen. It is made of an antiproton containing two up antiquarks and one down antiquark, orbited by a positron.

KS

A NTIQ

UA

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POSITRON

Annihilation When a particle collides with its antiparticle counterpart, they annihilate, resulting in pure energy in the form of gauge bosons.

PHOTONS PRODUCED The electron and positron annihilate each other, producing two photons with the same energy held by the particles before the collision.

ANTIMATTER

129

Particle partners

PARTICLES

In supersymmetry, every boson has an associated massive fermion with spin differing by a half-integer, and vice versa.

Every particle in the Standard Model could have a “superpartner.”

NOT SO STANDARD The Standard Model leaves many mysteries unresolved; for instance, it does not incorporate gravity or dark matter. Supersymmetry is a proposed extension that predicts a supersymmetric partner for every particle, with identical quantum numbers except spin, to resolve some problems with the model (such as by providing a dark matter candidate). Scientists explore beyond the Standard Model through highenergy particle accelerator experiments (see p.121).

130

BEYOND THE STANDARD MODEL

SUPERSYMMETRIC SPARTICLES Hypothetical supersymmetric particles are named after their partners: for example, squarks are the supersymmetric partners of quarks.

”Most gravity has no known origin. Is it some exotic particle? Nobody knows. Is dark energy responsible for expansion of the universe? Nobody knows.“ Neil deGrasse Tyson

BEYOND THE STANDARD MODEL

131

UNIVERSAL FIELDS Quantum field theory (QFT) is a broad framework that treats all particles as ripples in their underlying quantum fields. For instance, an electron emerges when the electron field is excited beyond a certain limit. Due to the uncertainty principle (see pp.42–43), these fields constantly froth with particles and antiparticles appearing from nothingness and vanishing an instant later. This theoretical framework incorporates theories such as the Standard Model (see pp.124–25).

QUANTUM FIELD Every “particle” has an underlying quantum field that reaches throughout all of space.

132

QUANTUM FIELD THEORY

”Quantum field theory, which was born … from the marriage of quantum mechanics with relativity, is a beautiful but not very robust child.“

CONJURING PARTICLES

Steven Weinberg

What we think of as a solid and localized particle is really a disturbance in its quantum field. For example, the Higgs boson (see p.127) is produced by the excitation of the Higgs field.

C PARTI

QUAN

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I E LD

QUANTUM FIELD THEORY

133

ELECTRONS

N

M

EC

TR

CO

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IN

Fermions, such as electrons and quarks, are represented with a straight, solid line.

N

O

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U

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TG

O

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IN

EL

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G

EL

IN

THE JEWEL OF PHYSICS Quantum electrodynamics (QED) is the quantum field theory for the electromagnetic force. It describes how electrically charged particles interact by exchanging photons: the force carrier for the electromagnetic force. As these photons are absorbed or released by charged particles, the energy exchanged by the photon changes the speed and direction of the particles. These processes can be visualized with Feynman diagrams.

SPACE

SINGLE PHOTON EXCHANGE Photons and other gauge bosons are represented with wavy lines, except gluons, which are represented by curly lines (see opposite).

VERTEX

G IN O ON TG TR U O LEC E

IN EL CO EC M TR I N O G N

Vertices represent interactions between particles.

Feynman diagram This Feynman diagram is used to represent the process of electron– electron scattering, with the repulsive electromagnetic force between them mediated, or conveyed, by a photon. TIME

134

QUANTUM ELECTRODYNAMICS

M

ES O N

MESON (PAIR OF QUARKS) A meson is made up of a quark–antiquark pair (see pp.128–129), bound by the strong force. The quarks have opposite color charge, resulting in an overall colorless particle.

BA

GL

RY

UO

N

ON

BARYON (ODD NUMBER OF QUARKS) G LU

ON

A baryon is made up of three quarks. For example, protons are consists of two up quarks and one down quark bound by the strong force. All three primary colors (red, blue, and green) are represented, making it “colorless” overall.

THREE-COLOR QUARK Quantum chromodynamics (QCD) is the quantum field theory for the strong interaction, which involves the exchange of gluons between quarks (see p.122). It has many parallels to QED (see opposite), with color instead of electric charge and gluons instead of photons. However, the strong interaction has some unique characteristics, resulting in behavior such as color confinement (which means that color-charged particles cannot be found on their own) and an extremely limited range of approximately 10 -15 m.

QUANTUM CHROMODYNAMICS

135

Q U A N G R A V

T U M I T Y In the 20th century, two revolutionary theories emerged in physics: General Relativity and quantum mechanics. General Relativity describes physics on astronomical scales and models gravity as a geometric property of space-time, as it warps in the presence of mass and energy. Quantum mechanics describes physics on a scale in which gravity appears insignificant and inexplicable. Physicists hope to reconcile these by describing gravity according to the principles of quantum mechanics. The two most popular quantum gravity theories are string theory and loop quantum gravity (which does not treat gravity like other fundamental forces).

THEORIES OF EVERYTHING

BIG BANG

A quantum explanation of gravity could explain all four fundamental forces in a single framework.

SUPERGRAVITY/ QUANTUM GRAVITY

GRAND UNIFIED THEORIES

All in one A theory of everything predicts that, at exceedingly high energies—such as just after the Big Bang—the four fundamental forces are united into one ”superforce.”

COMBINED FORCES In the 20th century, physics coalesced into two frameworks: quantum mechanics and General Relativity. If these could be unified in a single theory, it would describe all phenomena in the universe: a “theory of everything.” This is a Herculean task because according to General Relativity, gravity is not a force, but a property of space-time (see p.23). All efforts to model gravity as a quantum force (like other fundamental forces) have fallen short.

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A THEORY OF EVERYTHING

GRAVITATIONAL FORCE

ELECTROWEAK THEORY

In this theory, the weak interaction and the electromagnetic force are unified at high energies.

WEAK NUCLEAR FORCE

ELECTROWEAK FORCE

ELECTRICITY AND MAGNETISM

ELECTROMAGNETIC FORCE

James Clerk Maxwell proved that electric and magnetic fields were aspects of the electromagnetic force.

GRAND UNIFIED THEORIES

STRONG NUCLEAR FORCE

These seek to describe how all the forces except gravity can become one force at extremely high energies.

”From time immemorial, man has desired to comprehend the complexity of nature in terms of as few elementary concepts as possible.“ Abdus Salam

A THEORY OF EVERYTHING

139

QUANTUM FOAM Under extreme conditions, such as in the center of a black hole or an instant after the Big Bang, the tried-and-tested laws of physics (General Relativity and quantum physics) break down. It is in this realm—the Planck scale—that physicists expect quantum gravity to emerge. The extreme quantities associated with this scale are measured with Planck units such as Planck length (~10 -35 m). One unit of Planck length in comparison to the size of an atom is similar to the length of a football field relative to the entire visible universe.

140

PLANCK LENGTH AND TIME

On the Planck scale, space-time (see p.23) may not be smooth and empty but instead be full of fluctuations.

NO SUCH THING AS EMPTY SPACE

”In any field, find the strangest thing and then explore it.“ John Wheeler

Space-time bubbles Quantum gravity models predict that space-time is made up of tiny regions where dimensions froth in and out of existence, like bubbles in foam. This may be permitted by the uncertainty principle (see pp.42–43) over distances and intervals on the Planck scale.

PLANCK LENGTH AND TIME

141

Closed vibrating string A closed string is a loop without any end point. Closed loops are included in all string theories.

Open vibrating string An open string has end points that connect to 2D surfaces called d-branes. Not all string theories incorporate the idea of open strings.

TINY VIBRATING STRINGS String theory is a candidate TOE (see pp.138–39), which proposes that all particles are vibrating one-dimensional strings. Different vibrational states cause them to manifest as different particles, including a force carrier for gravity (graviton). In string theory, gravitons escape to higher dimensions, causing gravity to appear very different from the other fundamental forces. There are several different versions of string theory.

142

STRING THEORIES

TYING IT TOGETHER M-theory unifies five versions of string theory—which allow different types of strings—into a single theory. M-theory proposes fundamental building blocks called “branes,” which are multidimensional versions of one-dimensional vibrating strings. The theory requires 11 dimensions (ten of space and one of time), and seven of them are “curled up” so small that they are invisible to us living in the other four dimensions. String theories, including M-theory, have been criticized for being possibly unfalsifiable.

6D CROSS SECTION This image depicts the cross section of a 6D Calabi-Yau manifold.

HIDDEN DIMENSIONS Most dimensions could be imperceivable due to being “curled up” on themselves.

Calabi–Yau manifold It is proposed that the extra dimensions of string theory are curled-up complex multidimensional space, such as this Calabi-Yau manifold.

M-THEORY

143

THE FABRIC OF SPACE Loop quantum gravity is a candidate TOE (see pp.138–39), which—rather than trying to unify the four fundamental forces— models gravity as a property of space-time (see p.23). The theory proposes that spacetime is granular; it is built of Planck scalesized “loops” of gravitational fields. Loops are woven into structures called spin networks, which represent states and interactions, and become a frothing “spin foam” when observed over time.

144

LOOP QUANTUM GRAVITY

”What is most satisfying about the picture of space given by loop quantum gravity is that it is completely relational. The spin networks do not live in space; their structure generates space.“ Lee Smolin

SPIN NETWORK In loop quantum gravity, a spin network represents a state of the gravitational field at one instant in time.

LOOP QUANTUM GRAVITY

145

Q U A N B I O L

T U M O G Y At the most basic level, all the processes that make up what we call life come down to biochemistry—chemical interactions between a variety of complex molecules. Perhaps it should not be surprising, then, to learn that quantum effects have a part to play. Many pioneers in the field, including Erwin Schrödinger and Niels Bohr, predicted that quantum phenomena would play important roles in processes ranging from the harvesting of energy to genetic mutation, but it is only in the past few decades that our understanding of biochemistry has been able to reveal some of the details.

PHOTONS AND FOLIAGE

SUNLIGHT

Photosynthesis is the process by which plants manufacture sugars and other chemicals using energy from sunlight. Its first step involves photons triggering chemical changes to molecules called chromophores. Energy produced by these changes is transferred to other molecules, where it can be put to use with remarkable efficiency, involving synchronized vibration between different energy states. Many biologists believe that photosynthesis has evolved to take advantage of the quantized nature of light energy, and some go further, suggesting that other quantum phenomena, such as superposition (see pp.38–39), may play a role.

Inside the energy factory A leaf is an electrochemical power plant that harnesses sunlight of specific wavelengths to trigger excitation in chromophores, and ultimately chemical changes in its pigment molecules.

148

PHOTOSYNTHESIS

PHOTONS

LIGHT-COLLECTING MOLECULES

Changes to pigments produce separated positive and negative ions, creating an “electrochemical potential” that can trigger other reactions.

REACTION CENTER

LO

NG

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TR

OU

TE

SH

OR

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ST

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Incoming light carries energy corresponding to its color. Chromophores can be excited by high-energy violet and blue photons and low-energy red ones, but midrange green light is reflected back.

Energy is transferred via neighboring chromophores to the reaction center with high efficiency. Each molecule in the chain is always ready to receive the energy in turn, so it is suggested that quantum phenomena aid the cells in finding the most efficient paths.

PHOTOSYNTHESIS

149

IT’S IN OUR DNA The process of mutation plays a vital role in evolution by introducing random changes to DNA, the self-replicating biochemical molecule that carries instructions for making living things. Mutations involve individual chemical units called “bases” (the individual letters of the DNA code) abruptly changing from one form to another. Because bases seem inherently stable, some scientists think that quantum tunneling (see pp.70–71) is needed to leap energy barriers within their structure and allow them to change.

Bases bond in specific pairs—adenine to thymine, and guanine to cytosine.

Quantum change One form of mutation may start with a quantum event in which a proton from one base tunnels to its neighbor. This alters the length of the bond between them and triggers an error when the DNA is replicated.

150

A

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C

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REPLICATION

BASE PAIRS

BASE PAIRS

DOUBLE HELIX

Base pairing ensures that DNA can be replicated by “unzipping” and rebuilding the opposite strand.

A QUANTUM THEORY OF CELL MUTATION

DNA STRAND

DNA consists of a chain of base pairs linked by sugar-phosphate “backbones” that twist into a spiral, or helix, shape.

Catalytic process

SUBSTRATES

Catalysis involves changing the structure of two or more chemicals to allow a reaction between them. In some cases, the barrier to reaction appears to be overcome only through quantum tunneling.

The chemicals involved in the reaction may initially be drawn to separate areas of the enzyme surface by weak attractive forces. ENZYME

ACTIVE SITE

TUNNELING FOR A REACTION Chemicals called enzymes are found throughout our bodies, aiding processes such as digestion (the breaking down of food into useful nutrients). They are thought to work by lowering the energy barrier between molecules called substrates so that they undergo reactions, but the precise way in which they do this remains poorly understood. One theory is that they do this by creating conditions in which electrons are able to bridge the gap between molecules using quantum tunneling (see pp.70–71).

ENZYME-SUBSTRATE COMPLEX

As the substrates bond to the enzyme, chemical changes allow them to overcome the energy barrier that prevents a reaction, forming a product that is then released.

PR

OD

ENZYMES AND QUANTUM PHYSICS

UC

T

151

Radical pairs can only be in one of two states (called singlet or triplet), and the Earth’s magnetic field may affect these states. Each of the states may trigger a different chemical signal being sent to the bird’s brain.

MESSAGES TO THE BRAIN

CHEMICAL REACTION 2

MAGNETIC FIELD

See the force Migrating bird species navigate with great precision, even when flying over terrain or in weather conditions where there are no visual landmarks to guide them.

152

QUANTUM NAVIGATION

CRYPTOCHROME LIGHT

CHEMICAL REACTION 1

RADICAL PAIRS

Photons cause some molecules to split into radical pairs—each with one electron from the previously shared chemical bond.

Molecules of the cryptochrome protein are found on the retina of the birds’s eye. The bonds that form these cryptochrome molecules may be disturbed by incoming photons.

MAGNETIC FIELDS

N

EARTH

S

MAGNETIC PERCEPTION Seasonal migrations see many different bird species fly vast distances between their winter and summer habitats. Experiments have demonstrated that birds rely on some sort of internal “compass” to navigate, and some scientists have proposed explanations that quantum effects are responsible. Proteins called cryptochromes found in the retina of the eye form pairs of molecules with correlated spins (see p.66) in blue light, and these spins can be oriented by magnetic fields, perhaps allowing birds to see Earth’s magnetism.

QUANTUM NAVIGATION

153

OUR SENSE OF SMELL

OLFACTORY BULB

The traditional understanding of our sense of smell, known as the “lock and key” model, involves a scent molecule (odorant) fitting into a receptor cell in the nose and triggering a sensory response. But is that the whole story? The unproven “vibrational” theory of olfaction uses quantum effects to offer a solution to some outstanding questions. It suggests that our odor reception involves a quantum tunneling effect, driven by the vibrations of scent molecules.

The molecular structure of odorants is not static, but instead vibrates rapidly, emitting infrared energy in different “modes” akin to musical harmonics. ODORANT MOLECULES

Quantum-tuned for smell? According to one model, signals to our brain are triggered when electrons from an odorant molecule tunnel into our receptor proteins, boosting these complex molecules from one energy level to another.

154

THE QUANTUM NOSE

QUANTUM CONSCIOUSNESS? Conscious thought appears to be a uniquely human ability—but could our ability to reason, imagine, and assess problems be rooted in quantum physics? Several renowned physicists have argued that the unique aspects of our brains might arise from the harnessing of quantum phenomena such as entanglement (see pp.72–73) and superposition (see pp.38–39), but others doubt that quantum uncertainty could be sustained for long enough in our warm, wet bodies for any brain function to take advantage of it, due to decoherence (see p.75).

Quantum thinking? The brain’s ability to solve problems that are not solvable by traditional computing methods could mean that it is harnessing superpositions and acting as a quantum computer (see p.107).

THE QUANTUM MIND

155

INDEX Page numbers in bold refer to main entries.

A absolute zero 82, 94 alpha decay 70, 113 alpha particles 113 amplitude wave function 36–37, 40 waves 14, 17 antimatter 128–29 antiparticles 128, 132 atomic clocks 88–89 atomic energy states 30, 40 atomic force microscopy (AFM) 102–103 atoms cold atom physics 82 quantum model 11 Rydberg 83 solid-state physics 76–77 splitting 114–15 stimulated emission 86 structure of 10–11, 25, 30, 31, 65 see also nuclei, atomic

B band theory of solids 90, 92 baryons 12, 135 Bell, John Stewart 47, 57 Bell-state analyzer 74 Bell’s theorem 57 beta decay 21, 113 beta particles 21 Big Bang 55, 121, 138, 140 biochemistry 147 birds, migrations 152–53 bits 106, 107 black-body radiation 26, 27, 28

156

INDEX

Bloch spheres 106 Bohr, Niels 10, 30, 147 Bohr model 10, 30, 31 Born, Max 40 Born rule 40, 53 Bose-Einstein condensates 78–79, 82 Bose-Einstein statistics 68, 80 bosons 13, 21, 68, 79, 81, 119, 130, 134 Bose-Einstein condensates 78–79 brain function 155 branes 142, 143 bubble chambers 120

C Calabi-Yau manifold 143 capacitors 93 cell mutation 150 chain reactions 114–15 change, predicting 44–45 charge-coupled devices (CCDs) 93 classical physics 28, 38, 51, 53 closed vibrating strings 142 cloud chambers 120 coherence 75 cold atom physics 82 color charge 122, 135 composite particles 119, 122 computer chips 91 computers, classical 107 conduction 76, 81 conjugate variables 43 consciousness 155 consistent histories 62

constructive waves 17 Cooper pairs 81, 94, 95 Copenhagen interpretation 52–53, 56, 59 cosmological interpretation 55 coulomb forces 71, 117 cryptochromes 152, 153 cryptography 108 crystalline structure 76–77

D dark energy 131 dark matter 130 data storage, solid state 90 de Broglie, Louis Victor 7, 56 decoherence 75 degrees of belief 61 destructive waves 17 diffraction 16, 18 digestion 151 digital imaging 93 dimensions, hidden 143 diodes, light-emitting 90, 92 DNA 150 doping 91 double slit experiment 18–19

E Einstein, Albert 23, 32, 52, 63, 115 electric charge atoms 10–11 particles 67 electrical current 81 electromagnetic attraction 11, 22 electromagnetic energy 97

electromagnetic fields 14, 121 electromagnetic force 20, 22, 119, 123, 126, 134, 139 electromagnetic radiation 14, 16, 26–27 electromagnetic repulsion 20, 22, 69 electromagnetic spectrum 14 electromagnetic waves 25 electron detectors 100, 101 electron microscopes 100–101 electron orbitals 31 electronics 85, 90–91 electrons 12, 22, 46–47, 112 accelerated 100 antimatter 128–29 atomic clocks 88 atomic structure 10–11 band theory of solids 90 clouds 11 Cooper pairs 81, 94, 95 energy states 30, 31, 69, 83, 94 Higgs field 127 jumping between energy levels 30, 88 LEDs 92 magnetic moments 67 photoelectric effect 32–33 quantum electrodynamics 134 quantum field theory 132 Rydberg 83 size 8 solid-state physics 76–77 spin state 38, 106 stimulated emission 88 superconductivity 81 superposition 38–39 transistors 91 wavelike properties 18–19 wavelength 100 electroweak force/theory 139

elementary particles 12, 68, 119, 122, 123, 124–25 elements atoms 10 creating 116–17 energy antimatter 128–29 nuclear fission 114–15 nuclear fusion 116–17 photosynthesis 148–49 energy quantization 28–29 energy shells 10, 30, 31, 69 energy states 30, 78, 86, 88, 90, 94, 148 entanglement see quantum entanglement environmental factors 60, 75 enzymes 151 equilibrium point 36 Everett, Hugh III 54 excited states 30, 86, 87

F feedback electronics 102 fermions 12, 68, 69, 76, 81, 119, 124–25, 130, 134 Feynman diagrams 134 fission, nuclear 114–15 force carrying particles 119, 124–25, 126 Fourier transforms 41 frequency microwave radiation 88, 89 wave function 41 fundamental forces 20–23, 125, 126, 137, 138–9, 142, 144 fusion, nuclear 116–17

General Relativity 23, 133, 137, 138, 140 genetic mutations 147, 150 gluons 13, 20, 122, 125, 126, 135 grand unified theories 138–39 gravitational fields 144, 145 gravitons 23, 142 gravity 23, 130, 131, 140–41 theories of everything 138–39, 142–45 green light 33 ground states 30, 86

H hadrons 12, 13, 122 half-life 113 Hamiltonian operator 44 Heisenberg, Werner 42–43 helium 116 hidden variables 56–57, 60 Higgs bosons 13, 66, 124–25, 127, 133 Higgs field 127, 133 hydrogen 83, 99, 116, 128–29

IJK infrared radiation 14, 27 insulation 76 interference 16, 18–19, 58 intrinsic angular momentum 66, 67 ions 76, 81, 83, 87, 109 Josephson junctions 95, 96, 97 kinetic energy 82

G

L

gamma decay 113 gamma rays 113 gauge bosons 68, 124, 125, 126

Large Hadron Collider 121 lasers 82, 87, 102, 103, 109 lattice, geometric 76–77, 81, 94, 109

INDEX

157

leptons 12, 21, 123, 124–25 levitation, magnetic 94 light absorption 86 charge-coupled devices 93 coherent 86, 87 electromagnetic radiation 14, 22 lasers 87 light-emitting diodes (LEDs) 90, 92 photoelectric effect 32–33 photosynthesis 148–49 speed of 15, 74, 80 stimulated emission 86 light energy 148 light quanta 28, 30, 32 loop quantum gravity 144–45

M M-theory 143 Maglev transport systems 94 magnetic fields electromagnetic radiation 14 electron microscopes 100, 101 MRI 98–99 quantum navigation 152–53 SQUIDs 96–97 subatomic particles 67 superconductors 94 magnetic flux 96 magnetic moments 67, 99 magnetic resonance imaging 94, 98–99 magneto-optical traps 82 magnets, superconductors 94 many worlds interpretation 54 mass, particles 127

158

INDEX

matter and antimatter 128–29 atoms 10 electromagnetic radiation 14, 15 and light 25 unusual states of 65 matter particles 14, 20, 21, 68, 122, 124–25, 128 matter waves 56, 100 measurement problem 46–47 mesons 12, 13, 135 metals, photoelectric effect 32–33 microwaves 14, 88 migrations, seasonal 152–53 momentum 41, 42–43 MRI scanners see magnetic resonance imaging multidimensional space 143 multiple states 38 multiple universes 54, 55 muon neutrinos 12, 123, 125 muons 12, 124

N nanoscale 102–103 neutrinos 123, 124–25 neutron stars 117 neutrons 8, 10, 12, 13, 20, 21, 70, 112–13, 122 nuclear fission 114–15 nuclear fusion 116 Newton, Isaac 35, 45 nuclear fission 111, 114–15 nuclear fusion 71, 111, 116–17 nuclear physics 111–19 nuclei, atomic 20, 111 nuclear fission 114–15 nuclear fusion 116–17 size 8, 9 unstable 21, 65, 112–13 nucleons 8

O objective collapse hypothesis 59 observable universes 55 observed/unobserved events 52–53, 59, 61, 63 olfaction 154 open vibrating strings 142 optical amplification 87 oscillations 14, 88–9

P p-orbitals 31 parallel universes 54, 55 particle accelerators 121, 130 particle detectors 18, 120, 121 particle physics 119–35 particle-wave duality 18–19 Pauli exclusion principle 69, 79 photodiodes 102 photoelectric effect 32–33 photons 13, 18, 22, 25, 46–47, 108, 113, 124, 126, 127, 152 charge-coupled devices 93 color and energy 30 LEDs 92 photoelectric effect 32–33 photosynthesis 148–49 Planck’s constant 15 polarization 106 quantum electrodynamics 134 stimulated emission 86 photosynthesis 148–49 pilot wave theory 56–57 pions 13 pixels 93 Planck, Max 28 Planck length 9, 140–41 Planck scale 9, 140–41, 144

Planck time 140–41 Planck’s constant 15, 44 plum pudding model 10 pointer state 60 position measuring 46–7 uncertainty principle 42–43 positrons 128–9 possibility waves 58 prime factors 107 principal quantum number 83 probability 35, 36–37, 40, 48, 53, 61, 62 protons 8, 10, 11, 12, 13, 20, 21, 22, 70, 112–13, 122, 128 MRI 98–9

Q QBism 63 quantum Bayesianism 61 quantum biology 147–55 quantum chromodynamics (QCD) 135 quantum computers 75, 105, 107, 109 quantum cryptography 108 quantum Darwinism 60 quantum electrodynamics (QED) 134 quantum entanglement 56, 57, 72–73, 74, 85, 107, 155 quantum field theory 119, 132–33, 134 quantum foam 140–41 quantum gravity 137–45 quantum information 105–109 quantum leaps 29 quantum magnetism 109 quantum mechanics 29, 41, 42, 46, 49, 133, 137, 138, 140

interpretations of 51–63 quantum mind 155 quantum navigation 152–53 quantum numbers 83, 130 quantum phenomena 65–83 quantum physics, interpretations of 51–63 quantum revolution 65 quantum simulation 109 quantum states 36–37 quantum superposition see superposition quantum technology 85–103 quantum teleportation 74 quantum tunneling 70–71, 95, 150, 151 quantum uncertainty see uncertainty principle quarks 8, 12, 20, 21, 67, 122, 124–25, 126, 127, 128, 131, 135 qubits 74, 106, 107

R radiation 14, 26–27 radical pairs 152 radio waves 14, 99 radioactive decay 21, 49, 65, 112–13 radioactivity 111, 112–13 Rayleigh-Jeans law 27 red light 32 reflection 16, 26 refraction 16 relational interpretation 63 resistance, electrical 81, 94 Rutherford model 10 Rydberg atoms 83

S s-orbitals 31 satellite navigation 88 satellite timekeepers 85

scalar bosons 125 Schrödinger’s cat 49 Schrödinger, Erwin 44–45, 49, 147 Schrödinger’s equation 44–45, 46, 48, 52 semiconductors 85, 92, 93, 96 sifted key 108 silicon chips 91 simulators 109 single state 39 smell, sense of 154 solid state physics 76–77, 90 solids, band theory 90 space-time 23, 137, 138, 141, 144 sparticles 131 Special Relativity 63 spectroscopy 87 spin 57, 66, 67, 72–73 electrons 38, 130 fermions and bosons 68 protons 98, 99 radical pairs 153 spin down 66, 68, 73 spin foam 144 spin networks 144, 145 spin up 66, 68, 72 squarks 131 SQUIDs 95, 96–97 Standard Model 119, 124–25, 127, 132 beyond the 130–31 stellar fusion 71, 117 stimulated emission 86, 87 string theories 137, 142, 143 strong nuclear force 20, 119, 122, 126, 139 subatomic particles 12–13 atomic structure 10 discovery of 7, 111 fermions and bosons 68 leptons 123 Pauli exclusion principle 69 quantum tunnelling 70–71 quarks 122

INDEX

159

subatomic scale 8–9 sun 23 sunlight 148–49 superconducting loops 96, 97 superconducting quantum interference devices see SQUIDs superconductivity 81, 94–97 superfluidity 80, 81 superforce 138–29 superposition 35, 38–39, 46–47, 48, 49, 106, 107, 108, 148, 155 supersymmetry 130–31

T teleportation see quantum teleportation temperature Bose-Einstein condensates 78–79 cold atom physics 82 and electromagnetic radiation 26–27 superconductivity 81 superfluidity 80 theories of everything 138–39, 142–45 thermal radiation 26

time 23, 44–45, 58, 88–89 transactional interpretation 58 transistors 90, 91 trapped ions 109

U ultraviolet catastrophe 27, 28 ultraviolet radiation 15, 27, 33 uncertainty principle, Heisenberg’s 42–43, 51, 132, 141, 155 universe cosmological interpretation 55 many worlds interpretation 54 theory of everything 138–39 unobserved events 52

V vibrating strings 142 vibrational theory of olfaction 154 viruses 100, 102 visible light 14

W W bosons 13, 21, 124, 126 wave function 35, 36–37, 52, 54, 55, 56, 60, 61, 62, 63, 70, 72, 75 Born rule 40 Fourier transforms 41 measurement problem 46–47 Schrödinger’s equation 44–45 spontaneous collapse 59 squared 40, 53 superposition 38–39, 46–47 transactional interpretation 58 uncertainty principle 42–3 wave-function collapse 35, 48, 49, 51, 53, 54, 56, 58, 59, 62, 63 waves 16–17 particle-wave duality 18–19 weak force 21, 119, 126, 139

XYZ X-rays 14, 112 Z bosons 13, 21, 125, 126

ACKNOWLEDGMENTS DK would like to thank the following for their help with this book: Dominic Walliman for work on the contents list; Mik Gates, Dan Crisp, and Dominic Clifford for illustrations; Katie John for proofreading; Helen Peters for the index; Senior Jacket Designer Suhita Dharamjit; Senior DTP Designer Harish Aggarwal; Jackets Editorial

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INDEX

Coordinator Priyanka Sharma; Managing Jackets Editor Saloni Singh.

All images © Dorling Kindersley For further information see: www.dkimages.com