At Home in the Universe 1563965003, 9781563965005, 0883188627

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NATIONAL

LIBRARY

UNIVERSITY

SAN DIEGO

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AT HOME IN THE UNIVERSE

Masters of Modern Physics Advisory Board Dale Corson, Cornell University Samuel Devons,

Columbia University

Sidney Drell, Stanford Linear Accelerator, Center Herman Feshbach, Massachusetts Institute of Technology Marvin Goldberger, Institute for Advanced Study, Princeton Wolfgang Panofsky, Stanford Linear Accelerator Center William Press, Harvard University

Series Editor Robert N. Ubell

Published Volumes The Road from Los Alamos by Hans A. Bethe The Charm of Physics by Sheldon L. Glashow

Citizen Scientist by Frank von Hippel Visit to a Small Universe by Virginia Trimble

Nuclear Reactions: Science and Trans-Science

by Alvin M. Weinberg In the Shadow of the Bomb: Physics and Arms Control

by Sidney D. Drell

The Eye of Heaven: Ptolemy,

Copernicus, Kepler

by Owen Gingerich Particles and Policy by Wolfgang Panofsky

At Home in the Universe by John Archibald Wheeler

NATIONAL UNIV LIBRARY SAN DIES

AT HOME IN THE UNIVERSE

JOHN ARCHIBALD WHEELER

AIP PRESS The American Institute of Physics

Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to AIP Press, American Institute of Physics. This book is printed on long-life, acid-free paper.

©1994 by American Institute of Physics. All rights reserved. Printed in the United States of America. AIP Press American Institute of Physics 500 Sunnyside Boulevard Woodbury, NY 11797-2999 Library of Congress Cataloging-in-Publication Data Wheeler, John Archibald,

1911-—

At home in the universe/John A. Wheeler. p. cm.—(Masters

of modern physics)

Includes bibliographical references and index. ISBN 0-88318-862-7 1. Science. 2. Physics. I. Title. II. Series. Q158.5.W44 1992 500-dc20 This book is volume nine of the Masters of Modern Physics series.

Contents

About the Series

Vii

SCIENCE SMILES A Septet of Sibyls: Aids in the Search for Truth Genesis and Observership Our Universe: The Known and the Unknown

23 47

ELAN AND MORALE The Morale of Research People Be the Best to Give the Most To Nicolaus Copernicus To Joseph Henry The Spirit of Colleagueship at Princeton

73 76 81 84 86

BOHR AND EINSTEIN Niels Bohr and Nuclear Physics

Delayed-Choice Experiments and the Bohr-Einstein Dialogue

The Outsider

93 ys 132

vi

CONTENTS

135 138 144

To Albert Einstein

No Fugitive and Cloistered Virtue Einstein and Other Seekers of the Wider View

MORE GREATS 161 ili 192 197,

Maria Sklodowska Curie and the World of the Small

Hermann Weyl and the Unity of Knowledge Hendrik Anthony Kramers Hideki Yukawa as Uniquely Ecumenical

FROM HALF-LIFE TO HUMAN

LIFE

Dealing with Risk

201

To Benjamin Franklin Science and Survival

223; 226

The Place of Science in Modern Life

252

BEYOND THE BLACK HOLE Beyond the Black Hole It from Bit

271 295

References

313

Acknowledgments

363

Index

367

About the Series

asters of Modern Physics introduces the work and thought of some of the most celebrated physicists of our day. These collected essays offer a panoramic tour of the way science works, how it affects our lives, and what it means to those who practice

it. Authors report from the horizons of modern research, provide engaging sketches of friends and colleagues, and reflect on the social, economic, and political consequences of the scientific and technical enterprise. Authors have been selected for their contributions to science and for

their keen ability to communicate to the general reader—often with wit,

frequently in fine literary style. All have been honored by their peers and most have been prominent in shaping debates in science, technology, and public policy. Some have achieved distinction in social and cultural spheres outside the laboratory. Many essays are drawn from popular and scientific magazines, newspapers, and journals. Still others—written for the series or drawn from notes for other occasions—appear for the first time. Authors have provided introductions and, where appropriate, annotations. Once selected for inclusion, the essays are carefully edited and updated so that each volume emerges as a finely shaped work. Masters of Modern Physics is edited by Robert N. Ubell and overseen by an advisory panel of distinguished physicists. Sponsored by the American Institute of Physics, a consortium of major physics societies,

the series serves as an authoritative survey of the people and ideas that

have shaped twentieth-century science and society.

A Septet of Sibyls, montage assembled 1992 out of drawings selected from Cesare Ripa's Iconologia of 1603. Clockwise from lower left: 1. Knowable (reproduced from Intrepidita et Costanza, p. 241), 2. Err to Learn (from Pertinacia, p. 396), 3. Measure (from Parsimonia,

p. 385), 4. Analogy Gives Insight (from Armonia “come dipinta in Firenze dal gran Duca

Ferdinando”, p. 26), 5. New and Old Connect (from Filosophia “come depinta da Boetio in

consolatione philosophica,” p. 164), 6. Complementarity (from Poesia,

p. 406), 7. The High and the Low (from Carita, p. 64). Figures reproduced by kind permission of William L. Joyce, Librarian in charge of Rare Books and Special Collections, Princeton

University Library.

2. PERTINACIA

4. ARMONIA

5. FILOSOPHIA

7. CARITA 6. POESIA

J

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ee

a

;

2d JIMé SOVEIOe a

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=

A Septet of Sibyls: Aids in the Search for Truth

have great hesitation in trying to formulate some unifying concepts out of my own field, and still more reluctance in speaking about their application to other fields of human knowledge. I am as far

from being an expert as anyone could well be. It helps to recall the definition of an expert as a man

who, through his own bitter experience,

knows almost all the mistakes possible in his field. Our whole problem is to make the mistakes as fast as possible and recognize them. Can a unifying concept in one field be applied in another? Let me call

on a septet of sibyls to say yes if they will.

Sayings of the Seven Sibyls 1. The Unknown Is Knowable 2. Advance by Trial and Error 3. Measurement and Theory

me

Are Inseparable . Analogy Gives Insight New Truth Connects with Old Truth 6. Complementarity Guards against Contradiction 7. Great Consequences Spring from Lowly Sources

But without the message of the first, “The unknown

other six would speak Without the motive point. If there are any man knowledge, what be lighted”?

is knowable,” the

in vain. for struggle the stratagems of struggle have little unifying concepts applicable in every field of huone stands higher than this: “Every darkness can

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Faith That Nature Is Understandable “Raffiniert ist der Herr Gott, aber Boshaft ist er nicht.” These words of

Einstein are carved over the fireplace of the professors’ meeting room in

Fine Hall. “God is deep, but he is not malicious.” Narrowly interpreted, Einstein tells us his faith that the mysteries of space and time, of matter and energy, subtle as they seem today, can someday be unraveled. But in a broader sense he denies the existence in any sphere of nature or human knowledge of a Pied Piper leading us on to a mystery of wheels within wheels within wheels, through never ending cycles and caverns measure-

less to man, world without end. In the historical sense he is one more

prophet reminding us of our heritage from the age of enlightenment: faith in the power of man’s reason to understand both man and nature.

Arguments That Neither Nature Nor Man Are Knowable However widely these words may meet favor in our times, they are not so obvious that they constitute a minor truth, as Niels Bohr calls a statement

whose opposite is plainly false. The knowability of the unknown is rather what he would call a great truth in the sense that its opposite is also true:

There is much we shall never know! But this is very different from saying there is any limit to the rule of reason. It is not difficult to imagine ourselves in a day when the origin of man was regarded as a sacred mystery forever unknowable. It is harder to conceive the age when the operation of the heavens required intervention from without. But we are still living in a time when human behavior is widely regarded as beyond rational analysis. Griinbaum! has recently carefully refuted the arguments against causality in human behavior. Let me quote the arguments themselves, for they come from many sources and typify the belief of some men in all

times and in all countries that the unknown is not knowable:

1. Human behavior is not amenable to causal description and therefore not predictable, since each individual is unique and not exactly like

anyone else.

2. Even if there is a causal order in the phenomena of human behavior, it is so complex as to elude discovery permanently.

3. In the physical sciences, a present fact is always determined by past

facts, but in human behavior present behavior is oriented toward future goals and thus “determined” by these future goals.

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4. If human behavior were part of the causal order of events and thereby in principle predictable, it would be futile to attempt to make a choice between good and evil, (and) . .. meaningless to hold men re-

sponsible for their deeds... .

Let us forego the refutations. Let the arguments themselves remind us

that the idea of rationalism has not yet been communicated to all minds, however swift its spread from field to field following Newton’s great discovery of the utterly simple machinery of the planets. That the rule of reason applies to all fields of knowledge our Japanese colleagues recognize in one way better than we. Going back to an older and truer version of the word science, they include in their National

Academy of Sciences not only psychology, as do we, but also history, literature, and art. More generally, shall we agree to include in science in this larger sense all activities concerned with “extending the range of human experience and reducing it to order” (Niels Bohr)?

The Struggle for Survival as Compulsion to Find Out That every mystery can be unveiled is not of course a theorem to be established by logic, but an article of faith, to be justified by its consequences. The idea works, we know—that is its proof, and all we shall ever have for evidence. Seen to operate in one field after another, the

principle of knowability becomes a factor in the rise of men and nations. No one finds he can overlook it. Not inherited merit, not ability to reason better than other men, establishes in one’s heart the compulsion to conquer the unknown. Does not the faith in reason come to us instead from a thousand incidents of upbringing, of schooling and everyday life? Where

does the drive to find out come from if it is not a part of the survival

equipment deeded to us—through our civilization—by generations past who have fought for life? I wonder whether a Darwinian would distinguish between

us and the beasts who are born into.the forest, and,

warned by parents, must find the woodland ways. Know the truth or per-

ish! Compulsion enough.

The Thermonuclear Crisis That the urge to know derives from sources deeper than books, deeper

than logic, from the struggle for existence itself, is witnessed by the hy-

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drogen bomb crisis of late 1949 and early 1950. The controversy revolved in many circles, some moral, some

political, some scientific.

However, the division I saw was simpler. It lay between those who said it will take years and years to set off a thermonuclear explosion and it probably won’t be worthwhile anyway and those who said we don’t know how to make one but there must be some way to get the energy out and we can’t afford not to find out the truth and let’s go full steam ahead. At one level the disagreement resolved itself into the question whether there was to be an all-out search into the truth about thermonuclear reactions. At a higher level—if we agree with Lord Tweedsmuir that politics is the highest form of human activity—the issue took many forms, among them the question whether the western world was to disown the policy of peace through strength. It took a courageous political leader to give the answer. His position, paraphrased, was simple enough: As a matter of survival the truth about thermonuclear explosions must be known. Some months later, reviewing problems and progress in the thermonuclear program with the brilliant director of the A. E. C. Division of Military Applications, General James McCormack, and noting the connection between the speed of investigation at Los Alamos and the drive and support coming from Washington, I asked what would happen were the life to go out of the leadership in his office and in the Commission. The reply was quick and simple: The American people would throw us out of office. The survival motive in search for truth does not often show so clearly as in these two incidents. It is not truth for truth’s sake, we are reminded,

but truth for the sake of life—life of a man, an industry, or a people. In-

vestigators have salaries because civilizations demand to know, not be-

cause the investigator demands to know. Or is it because the investigator demands to be paid!

“Truth for Truth’s Sake” More Palatable Than “Truth for Survival” Fortunately the human heart has the power to seize on the hard rock of

“truth for survival” and jewel it over into a pearl, “truth for truth’s

sake.” The pearl attracts more minds to its service than the ungarnished

stone, and civilization often wins by the change of slogan. But great as

is this cause of pure truth as motivation it often seems to take second

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place to survival—survival of one’s patients, of one’s career, or of one’s country. The intensity of motivation to know the unknown varies between indi-

viduals as much, one would say, as the will to live. The differences, like

differences of character, are easily stated in the simple phrase: he cares; or he does not care; or he cares, but not enough.

Fermi’s Drive to Find Out Of the drive to find out let me give one example: The man, Enrico Fermi; the time, a Sunday afternoon in the summer of 1944; the scene, an irrigation canal three-fourths full of racing Columbia river water hemmed in by steep concrete walls; friends swimming in it for escape from the heat of Hanford; ropes stretched across downstream so one could catch hold, pull himself out, and escape being carried miles downstream. Fermi’s question: Suppose the ropes broke, could one save himself? No was the answer of all, after repeated trials to climb out before being carried down

to the ropes. Then came Fermi’s reply, “We shall see.” Plunging in, he

turned to fight the current, headed for the wet sloping concrete, tried with

hands and arms to gain a purchase, was torn loose by the current and car-

ried down, fought his way again to the wall, and with desperate activity struggled on the slippery slope, sometimes gaining, sometimes losing, until at last he escaped the water’s grasp and emerged, arms and legs bloody, but a smile on his face. To describe Fermi’s drive to know, how he searched for the answer to a mystery, and in some sense how every

man has to search for the answer to a mystery, I know no better answer than this incident of the irrigation canal.

Art as Search for Truth Our subject is not irrigation canals but the power of one unifying concept in many fields—just now the concept and the faith that the unknown can be found out. This faith made possible the first escape from the canal; any later escape was altogether different because it was founded on knowledge. Equal faith looked at light shimmering on the water of the Seine and declared that a way to record this sight must be discoverable, struggle as one might to find it. The followers of Seurat did not need the concept that the unknown is knowable. Faith that one could understand

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the equivalence of gravitational and inertial mass gave Einstein general relativity, but the student can get it all from a book with never a touch of

militant faith in the knowability of the unknown. Colonizing is very different from pioneering! One of the most beautiful revelations of the poetic spirit at work arose

from meditations “all intent on the discovery of the nature of soul and spirit.” “The deepest things in my life,” A. E. tells us, “came to me in the

form of poetry, and I brooded upon every circumstance in its uprising

that I might discover its ancestral fountain.” Here, too, he urges, the

seeker must struggle,

“And wrestle with the chaos till the Auuich to the light to be bowed.”

If it is true, as he suggests, that the searchers “receive according to the quality of their desire,” then his own book, Song and Its Fountains, is a

witness to that truth. In poetry, in painting, in physics, and in all knowledge there is at least one unifying principle, an article of faith: “In every field one can extend the range of human experience and reduce that experience to order”; or to summarize in a cryptogram: “The unknown is knowable, the impossible is possible”; or finally in a single word: “Conquest!” This is the dynamic of the quest for truth; now what of the methods?

“Grapple”: Trial and Error I have a suspicion that many of us might be willing to accept trial and error as the first among methods—the first universal concept. We remember the words of the engine inventor, John Cris: “Start her up and see why she don’t run,” as summarizing the boldness and empiricism that are so often needed; or the words of Faust: “Where is the path? No path; into the unknown!”—*Wohin der Weg? Kein Weg; ins Unbetretene!” We recall Pasteur, summoned

to save the silkworm industry of

France, asking to see his first cocoon, holding it up to his ear, shaking it, and asking if it rattled. Through all one sees the spirit of catch as catch can, trial and error, progress by making almost all possible mistakes, the great point being only to make them as quickly as possible and to learn from them. One recalls the instances of great writers, the scientists of life, trying over and over and over again to record sharply and clearly some nuance of human personality; and struggles to record the truth by artists, the scientists of shape, form, and color. Jacques Maréchal, the young French painter, took me to visit the Ecole des

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Beaux Arts, pointed out to me one-by-one his colleagues, impressed on me their sharp eyes and sharp minds, but emphasized to me above all their insistence on integrity and accuracy. He confided: “We have observed and studied each other more accurately than our own families

know us. With this passion for the truth one can develop the technique

to recognize and record it; without that ideal, technique is nothing.”

With such drive to motivate it, how can trial and error not lead to great

discoveries of method?

Alternation between Optimism and Skepticism The skepticism of science is famous, but not so widely known is its optimism. One might even suggest that creative work spans a wider spec-

trum than most activities between the hopeful and the critical, between proliferation and selection. This ranging along the spectrum shows itself differently in different men according to their personalities and ways of work. The greatest thinker I know alternates between up days and down days. One is a day of boiling discussion when new ideas arise or old ones are revived and exploited with the greatest optimism, when an analysis gets put together and told over lovingly with the ear tuned

hopefully for every subtle overtone and inner whispering of new truth. The other is a day of destruction of everything that will not stand the test of searching criticism. One needs a new L’ Allegro and I! Penseroso to describe the contrast. Out of the many times repeated cycle come great results. To trigger off and motivate the machinery in this instance, a paradox proves best: a question as to the logical consistency of present ideas. Sad the week without a paradox, a difficulty, an apparent contradiction! For how can one then make progress? Design for a Brain is the subject matter of a fascinating new book by

F. Mosteller and by Robert Bush? in his day here one of the outstanding

graduate students in physics at Princeton. What should a mechanism look

like that will start blank and learn from the situations in which it finds itself? Two principles of design prove essential: a continual probing out and poking into the environment; and a means to discriminate between reactions of the environment on the device that are favorable or unfavorable to it. Bush and Mosteller show how one can design a system of electronic circuits that will develop by a process of trial and error rational re-

sponses to whatever the environment is in which it happens to find itself, and even relearn if put into a new environment.

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“Measure”; Dependence of Measurement on Theory So much for trial and error as a familiar organizing principle valid in

many fields of knowledge; now for measurement as another unifying concept. Lord Kelvin declared, if you can’t measure it you don’t know what you are talking about. We recall Taylor’s famous measurements on productivity of labor as affected by amount of load and length of rest periods and their consequences for the rationalization of industry. But we recall also the studies at the Hawthorne plant of the Western Electric Company near Chicago on output in its dependence upon lighting and other working conditions, and the striking conclusions. Production scores turned out the same for groups with quite different lighting, and different for groups with the same lighting. There was no reliable correlation between output and any reasonable change in physical environment. Even more remarkable, the further the analysts studied any given group with

any given set of conditions, the more the productivity of that group in-

creased. Ultimately it became clear that lighting and other physical vari-

ables were quite secondary to that mysterious factor known as group morale. Being studied helped group morale. Being appreciated as individuals helped it more. The investigation of this human factor of morale

demanded a complete change in the plan of the study and in the philosophy of measurement. The results of the Hawthorne studies today contin-

ue to work a revolution in plant management. But to us the lesson is

more general: measurement does not make sense until one has a rational theory of what it is he is measuring. That measurement depends upon theory was stressed long ago by Henri Poincaré in his beautiful little book, La Valeur de la Science3

where he takes as example the concept of momentum. The early workers defined this quantity as mass times velocity, mv. Definitely second in their minds came the law of conservation of momentum—the observation that the sum of the momenta of two objects, as so defined, is con-

served in the collision between them. Trouble came for objects moving with a velocity comparable to the speed of light, c. Momentum as previously defined was not conserved. The concept had to be changed. Mo-

mentum has now to be defined as my[1 — (v2/c?)]-"/. The new outlook

starts with the law of conservation of momentum and from it derives the definition of momentum as that directed quantity which is conserved. One asks, how can the law of conservation of momentum

be worth-

while if momentum is so defined as to make the law hold true. Poincaré

answers by asking us to look at an object which like a billiard ball bats

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about colliding with one body after another. In the first collisions we use the conservation law to find out or define the unknown momenta of the several objects. The situation is quite different in the subsequent

collisions. There the momenta are already known. There the law of

conservation of momentum

comes true, not by definition, but by the in-

ner workings of the world’s machinery. All the laws and theories of physics have this deep and subtle character, Poincaré stresses, in that they both define for us the needful concepts, and make statements about these concepts. Contrariwise, the absence of some body of theory, law and principle deprives one of a means properly to define or even to use concepts. Both the Hawthorne productivity studies and Poincaré’s analysis of momentum remind us how far out of date is that

view of science which used to say, “Define your terms before you proceed.” They also remind us more clearly than ever of the truly creative

nature of any forward step in human knowledge, where theory, concept,

law, and method of measurement—forever inseparable—are born into

the world in union.

Theory and Principles of

Measurement Form an Indivisible Unity One of the great papers of modern physics owes its origin to claims by several able physicists of inconsistency in electromagnetic theory. They argued that the theory itself denies the possibility of measuring the central quantities of the theory. In contrast, the deep 1935 paper of Bohr and Rosenfeld4 emphasizes that the principles of measurement would not

make sense without the theory, nor would the theory be acceptable if the

possibilities of quantitative check did not fully measure up to it. They resolve one of the apparent paradoxes after the other. They end by showing quantum electromagnetism, within the well specified limits of its subject matter, is a logically self-consistent body of ideas, measurements, and

measurement possibilities. Their analysis is a perfect pattern for the logical structure we hope someday to see in every branch of science. To look at the other side of the picture, to examine

some of the

pseudoscience that has been based on artificial concepts and defini-

tions and masses of meaningless measurements, is a task that we can

spare ourselves.

To make one’s case, whether good or bad, whether for a new tooth-

paste or a new budget, is motive enough in this day and age for tying

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numbers to ideas. Numbers speed one on his way! That unifying concept now spans all fields from science to salesmanship! When not reassured by number, man is naturally skeptical, made so by daily encounters with distortions, half truths, and fuzziness.

Could one not say that the language of number sometimes provides a certain minimum standard of integrity in communication, without which

cooperation of human beings on subjects of some kinds is almost fruitless?

No one mindful of the history of land measuring and astronomy and physics can pass over the lessons they taught, how to associate numbers with the world about. What marvellous good fortune we have had in penetrating nature along these lines! How remarkable that today we can measure the strength of an invisible radio wave passing through an equally invisible space and give its strength as 1.7 microvolts per meter, or predict in advance the fantastic explosion history of a nuclear device never before seen.

How Far Can a Wild Goose Fly? This idea of pinning numbers to ideas and things around and forces is

such a new one that we haven’t found out how to pass on the pure delight and wonder of it. A major university has made a good try with a special course on analysis. I am told by my friend Charles Cooper that the final examination consisted of a single question: “How far cana wild goose fly?” One had to draw on nothing more than one’s fund of common knowledge. One might for example start with a guess for the weight of the goose, but the rules of the game demanded that one also

set limits of error for one’s guesses. From that one might go to an esti-

mate of the fat content of the bird (10 percent? 25 percent?) and from

there—knowing the mechanical equivalent of heat—to upper and lower limits for its energy resources. The energy demand, on the other hand,

one might estimate from the angle of glide in unpowered flight. In this

or another way one comes to an estimated flight distance without refueling of the order of one or two thousand miles, in reasonable accord with the observations.

One company now seeks staff who win satisfaction and make urgently

needed estimates by such thinking. It has tested potential new employees by a similar question: “How many drugstores are there in the United

States?” (One member of the audience organized a pool on this number af-

ter this talk. The speaker lost his nickel, but evidently in a popular cause.)

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That chance events are also subject to estimation along these lines, that the probability to be killed crossing the street can be calculated from common knowledge as well as the reach of a goose, is too obvious to

need mention. Neither do we have to recall operations analysis, that ever-

growing application of quantitative methods to the tactics of war, of busi-

ness, and of almost every other human activity. Without more ado, let us

conclude that the slogan”Measure!” is one of the great unifying concepts.

Analogy as Stimulus to Creativity “Analogize!” If one ever sews a flag for this fourth sibyl, let it be three squares joined together. The missing square symbolizes the challenge. Let nuclear physics supply the illustration (Figure 1). The core of the atom has a shape and is held together by forces, two features that recall a

droplet of liquid. Around this fluid surface tiny wavelets can make their way. Do nuclei show any effect of this kind, and if so, what? The study

of this problem has marked one of the most important parts of nuclear physics in recent years. Spectroscopists have discovered that some nuclei have substantial departures from sphericity. Thus the analogy to a liquid can be used only with caution. However, it has also proved fruitful.

A TYPICAL ANALOGY A known field

The field under study

Waterdrop—nearly spherical;

Nucleus—not far from spherical

endowed with a surface

Capillary wavelets on surface of drop

FIGURE |

ANOTHER ANTHOLOGY Polyatomic molecule—a system that

vibrates much more slowly than

its swift constituent electrons Clean division between electronic and vibrational excitation

Nucleus—a system much heavier

than the individual neutrons and protons of which it is composed

FIGURE 2

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A polyatomic molecule has shape. Does it provide any kind of reasonable analogue to the nucleus (Figure 2)? In molecules there is a sharp division between the rapid motions of the electrons and the slow vibrations of the atomic centers of force that govern the electronic motion. Do the types of motion in the nucleus analogously divide themselves into rapid motions of the individual particles and slow collective vibrations of the boundaries that define the nucleus? It is difficult to name a part of nuclear physics that is more actively studied today than this analogy.

Semiconductor Physics and Electron Pair Physics Other analogies enrich other parts of physics. Compare a semiconductor to a vacuum. In both the absorption of electromagnetic energy produces a pair of oppositely charged objects, in the one case a free electron and a hole, in the other case a positive and a negative electron. One can do wonderful things technically with semiconductors, as witness the new look in pocket radios and hearing aids. What can one do with the vacuum of comparable interest? Fascinating question, of which one does not know one-tenth the answer.

Instability in Liquids and Stellar Atmospheres Let a great sheet of liquid mercury lie on top of a pool of water. The situ-

ation is not stable. The mercury wants to be at the bottom. The interface

between the two liquids, no matter how smooth and horizontal it may be originally, commences to develop irregularities. Bulges from the mercury soon reach downward. They develop into prongs and spikes. With a rush,

these projections transport the heavy liquid from the top to the bottom.

Has this famous Rayleigh-Taylor instability any analogue among the

stars, where we know there exist both heavy and light gases? Lyman Spitzer posed for himself this challenge. He found there are cases of

stars, the hot light bright gases from which produce just this turnover ef-

fect in pushing on cold dense dark gas. Hydrodynamic instability on this enormous scale gives patterns of light and dark, of cataclysmic but lawful chaos, in full accord with the analogy.

On a more philosophical level, we recall Irving Langmuir’s suggestive

analogy between various kinds of physical and social processes that he calls

convergent on the one hand, and between others that he calls divergent.

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The Challenge of Confucius Passing from one analogy to another, saying always X is to A as B is to C, asking always what this implies for X, we suddenly realize what Confucius meant when he said, “I show the student three corners of the subject,

and if he cannot find the fourth, I do not repeat the lesson.” Not an easy

taskmaster! But what principle can guide one more quickly than analogy into the first trial ideas of a new subject? This is for today, the day of optimism and creation. Forget that there will be a tomorrow of criticism and revaluation!

The Road to Xanadu Do analogies form themselves out of thin air? Does one’s own problem click by magic into parallelism with another idea from one’s own area, or with a thought from quite another field? Not by magic alone, but magic plus the prepared mind, Flexner reminds us. We recall the industrial leader who went to Arthur D. Little for something in writing on the proper organization of a research laboratory and came away with John Livingstone Lowe’s Road to Xanadu. And where could one see better than in that study of Coleridge how the storehouses of the imagination are stocked by conversation, story, book, and observation? Apparently trivial circumstances make all the difference—an hour free for chosen reading;

20 minutes of relaxation at tea time regularly free for conversation with good people from neighboring fields, “explaining to each other what we

don’t understand,” as Oppenheimer puts it, and in return listening eagerly for miracles from afar; or membership in a literary group that maintains a high level of discussion.

Man Selects What Makes the Man We descendants of the fishes bathe ourselves from within by that saline environment that once also lay all around us, Homer Smith reminds us

in his fascinating book on the evolution of the kidney. On that organ’s delicate control of the blood’s constituents our life and health depend. But what agency selects the nourishment of our minds: the conversation

we have, the thoughts we record, the books we read and the very issues

we embrace? The richness of this nutrient stream can vary far more

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widely than the composition of the blood, and with far greater consequences. Man selects what makes the man. No wonder that wealth of association is subject to such variations, nor that analogy springs forth in very different measure from different humans.

Compulsions to the Search for Analogy Analogies flow to best advantage when we are confronted with a quite unfamiliar problem, of a kind no one ever saw before. That also is often

the time when one can use to best purpose a dash of adrenalin, a touch of

pressure from the outside to push one into the most vigorous possible grapple with the unknown. It may be the visitation of a student troubled about his thesis. One may have been called in as advisor on a problem in another institution, in industry, or in government. One may have arranged for himself a deadline for a paper summarizing his own work. Or one

may have to give a lecture on a chaotic subject. It often adds to the stimulus—human nature being what it is—to be caught in a situation where one is counted an “expert,” expected without fail to produce the answers!

Students in some parts of the world see their professors decked out in a panoply designed, so they think, to impress them. That is perhaps one side of a great truth, but isn’t the other side more relevant here? Does not

the formality put the professor under yet one more pressure to reach out into chaos, to lay hold on something both new and true? But however motivated, the grapple with the brand new problem begins. What an adventure! How important never to let oneself get stopped! How stimulating to try one analogy after another, to trace out the line of attack that each suggests, to analyze for each in turn the similarities and differences to the problem under discussion! How rewarding to see the new features of the problem come out of the mist and to map out a campaign of conquest! In such a problem analogy comes into its own.

Correspondence of New to Old; Bohr’s Atom Analogy we need to make the wheels of thought go round, but for better

judgement on what route to take we ask the fifth sibyl. She replies, the present and the future are children of the past; her motto, in a word,

“Correspondence.” New sound views must have a rich texture of connec-

tion with sound old views. Exploration of the connecting fabric leads to

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still more progress. We are reminded of Bohr’s approach to the mystery of atomic stability. Nothing was further from his approach than the free play with ideas that one finds in the Philosophical Magazine of the

1910s. There one author treated atoms as electric fluids, another made a hydrodynamic model, others changed the laws of electrostatics, and still

others altered the laws of electromagnetic radiation to account for the absence of radiation from stable atoms. In contrast, Bohr accepted the well-

founded law of force between point charges, made use of the usual principles of mechanics, and recognized that the laws of electromagnetic radiation are of far-reaching application. The very firmness with which he held these principles made it far easier for him than for the inventors of new ideas to recognize that the stability of atoms required for its understanding a new concept which, relative to what was already known, had to be not basically contradictory, but supplementary. The new idea was not to be pulled from the air. Bohr’s perpetual search for a larger

unity, for a harmonious view of the whole sweep of physics, had already made clear to him the fundamental character of Planck’s quantum. No concept so deep going could fail to have consequences for every branch of physics. The obligation became inescapable to Bohr to trace out these consequences in the atomic domain. His judgment and courage, his daring conservatism, carried him to wonderful conclusions of a kind that free invention has not strength to reach, nor conviction to maintain.

The parallelism between the old science and the new became so important as a guide that physicists gave it a well-defined mathematical for-

mulation, named it the correspondence principle, and use it every day as

a working tool.

History as Tracer of the Correspondence of Present with Past The principle of correspondence of past and present ideas is not a sibyl that speaks only mathematics, however; hear her ina wider context through the mouth of Benedetto Crocce: “We are products of the past and we live immersed in the past which encompasses us. How can we move toward new life, create new activities without getting out of the past—without placing ourselves above it? There is no other way out except through thought which does not break off relations with the past but rises ideally above it and converts it into knowledge. . . . Only historical judgment liberates the spirit from the pressure of the past; it maintains its neutrality and seeks only to furnish light—it alone makes

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possible the fixing of a practical purpose; opens a way to the development of action.” That human truth is defined, not by textbooks, but by the battles of men and ideas that have brought us where we are, is a lesson appreciated least of all by those we call cranks and nuts, knowing well that we are all in some measure cranks and nuts. Overturn all truth, or at least half of it; what happens in the process to the correspondence between new and old ideas is the last issue to be considered! How remind one of these ardent minds that one has to establish the inescapability of a new idea, that one has to carry his fellows with him on a line leading straight out of the past? What a wonderful sorter out of ideas is the principle that new ideas must correspond to old ones, must include them, but must transcend them!

Complementarity: Powerful Guard against Contradictions Complementarity, the sixth of our sibyls, represents in one sense the most revolutionary philosophical conception of our day. With a slight rewording of Bohr’s formulation,> we say, “The use of certain concepts in the description of nature automatically excludes the use of other concepts, which however, in another connection are equally necessary for the description of the phenomenon.” For illustration, look at a large-scale version (Figure 3, page 20) of the University of Copenhagen’s exhibit at the 1939 New York World Fair. One can find the value of the momentum of an electron by one kind of experiment (symbolized in the model by pulling the drawer to the right) or the position of the electron with another type of observing apparatus (symbolized by the left-hand position of the drawer). But nature is such that one cannot build and operate both pieces of experimental equipment (neither shown here!) to discover at the same time both properties of the electron; the two sets of equipment simply won’t fit into the same place at the same time. Even more, it has no meaning even to speak of the electron as possessing at the same time both position and velocity. Witness the unpredictable consequences for the one property due to the observation of the other. These consequences show in the model as a random throw of one die produced by looking at the other. We come to quite a new view of nature. The interaction of the

measuring device with the object under study is never nil. With its qualities of unpredictability, this coupling maintains forever inviolate the dis-

tinction between complementary features of the activity under analysis.

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Spread of Complementarity Concept Slow But Irresistible With its subtleties, the idea of complementarity has been slow to spread.

One still finds textbooks of physics that speak of “the crisis of indeterminism” or stress “the fundamental inconsistency between the wave and

particle pictures of matter” or look forward to a day when one will

“straighten out the quantum mess.” Quite the contrary! Complementarity is battle-tested. No one knows an acceptable alternative. The new viewpoint is part of the working attitude of the great majority of physicists of this generation. It would be hard to name a part of science better established than the quantum principle, more thoroughly analyzed for selfconsistency, or able to account for a more fantastic range of experience. There is no going back on complementarity!

Exploration of Complementarity in Its Extended Meaning What about going forward? How far outside of the physical sciences can one apply the principle of complementarity as worded by Bohr? He has given a number of illustrations of the far-reaching usefulness of this idea in resolving what would otherwise appear to be logical paradoxes. Of the examples collected in the caption of Figure 3, take the dilemma of free will and causality. There is no dilemma, Bohr stresses. The experimental conditions that permit a subject to exercise his free will are physically incompatible with the experimental conditions required for a causality

analysis. In such an analysis one says the future is completely determined by the past. There one’s approach makes sense only if one can measure all the electrochemical potentials in the brain, and make throughout a thoroughgoing biochemical assay. That type of dissection is perfectly conceivable in principle—but it is altogether inconsistent with the normal existence of the subject, and rules out the exercise of free will on his part. Free will and determinism, in others words, are’;complementary concepts, not contradictory; the two can never come into use at the same

time. The idea of complementarity as illustrated in this fashion is evidently appropriate for use in every field of thought. Indeed, as application after application comes up, one discovers in how many situations there is no reasonable alternative to the language of complementarity.

One can never relinquish possession of this new means to think and

speak clearly. To me, the most miraculous part of it all is man’s ability to discover this one kind of limit on what man can ever know!

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DETAILS

OF DIE FLIPPER

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MECHANISM

AGE RBEER.F100R, | This MeGeanon JAviacheo To (OF STATIONNRYcewten BASE SECTION CF ORAWER ‘kD TUNNEL

‘SELF FOSTIONNG SUDES FASTENED To (ORAWER TO ACTUATE TRIP HAMNER MANOLE

Ficure 3. Model to illustrate complementarity. The sliding drawer has a transparent front and top and contains two dice symbolizing complementary aspects of nature. Only one die is visible at a time. By grasping the handle at the right one can move the drawer in the wooden tunnel to any one of three positions: to the right, as shown, with die R visible; to the center position, with neither die in sight; or to the left, where one sees only die L. Let the number on the face of the left-hand die stand for a measurement of the position of an electron; the one on the right, for the numerical value of the electron’s momentum. One can pull out the drawer from the neutral position as often as one pleases to look at the “momentum die,” and always find the same number. However, let the drawer be pushed through so “position” is observed then pulled back to neutral. This crossing of the neutral location cocks a trip hammer under the rub-

ber floor and suddenly releases it. The blow sends die R tumbling in its

chamber. When the drawer is now drawn to the right for a “momentum” observation, an unpredictable value will be found. In other words, the “position” observation has led to an unfollowable change, as a consequence of which one’s previous information about momentum has completely lost its value. Analogously, nature denies all possibility whatsoeyer to observe simultaneously two complementary properties of a

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“The High and Low” Let me pass to the seventh sibyl, with the message that great effects and complex phenomena can be explained in terms of lowly causes and simple reasoning; or more briefly, the theme of “The High and the Low.” Ex-

plain mountains and valleys, not by original creation, but by the long ac-

cumulation of gradual changes? The idea was too audacious in its simplicity to win acceptance without years of battles. Yet what could be

more magnificent than the true history of the earth’s features? We know

how it appealed to Darwin. Was it surprising that he went on to find the secret of man’s origin? I can never put out of my mind the thrill he must

have had as he looked about this miraculous world, with the mists

cleared away, and first saw it in its true glory. How marvellous this explanation of the complexity of nature from simple causes! Why look for an origin any more wonderful! Temperature and that burning sensation as one puts his hand ina flame, are clearly like nothing else between heaven and earth. How can one blame anyone for advancing a phlogiston theory of heat? Nor could

one blame anyone for surprise when all these strange effects could be laid to the dynamics of large numbers of small particles in rapid mophenomenon. To say that the electron “really has” both position and momentum, but that we can’t measure them, is equally unacceptable—contrary to what one might expect from the model, and from the possibility to tear away the wooden tunnel that covers what goes on. In nature there is no wooden cover, nor anything to be seen beneath. The labels at left and right can be replaced by other pairs of complementary concepts: L.1 Position L.2 Time L.3 Observation of wave aspect of matter L4 Use of aword to communicate information L.S Free will L.6 Justice

R.1_ R2 R.3 R4_ RS R.6

Momentum Energy Observation of particle aspect of matter. Analysis of the meaning of the word Determinism Love

This demonstration-scale model was designed and assembled by Harold

Waage in 1955 on the basis of a matchbox scale model shown in the University of Copenhagen exhibit at the New York World Fair, 1939.

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tion—and nothing more! Yet who does not now appreciate the identity in nature between heat and energy of motion! That the abstraction to large numbers leads to qualitatively new features we are beginning to learn from new advances in the theory of games. When many players take part, optimum strategy dictates quite mathematically the necessity to join up in groups; one even begins to see hierarchies of groups. Is it foolish to believe that we will gain out of such studies a new understanding of group loyalties—not a belittling of their

importance, but on the contrary a heightened appreciation of their indispensable place in a complex world? It is not an accident that a recent inaugural lecture at Cambridge University has the title, “Theory of Games as a Tool for the Moral Philosopher”!® These examples of geological change, of evolution, of heat, and of

group combinations remind us how simple ideas lead to wonderfully rich consequences, and how the most noble aspects of our world come from the most lowly sources.

Any Community between the Seven Sibyls? Now we have finished with our septet of sibyls. It may be asked, is there any general principle that will systematize these great concepts that unify our multifarious search for truth? Perhaps yes, perhaps no. Might it not be more useful to use the principles that we know than to impose upon them some artificial classification? As we go about the world, we are ex-

ploring a marvellous jungle, full of strange birds, sights, and sounds. We find that there are a few paths that allow us to go about from one part of

the jungle to another. It is perhaps too early to look for a law of these paths. Let us only be happy that there we indeed have for paths some great unifying concepts and that we can communicate with one another.

Adapted from a report presented before the Symposium on Communication held by the Fifth Annual Conference of Graduate Alumni, Princeton University, December 30, 1955, in the session dealing with the question: “Can a unifying concept from one field be applied in another?”

Genesis and Observership

Is Genesis Unfathomable? Less than four years after the November 24, 1859, publication of The Origin of Species, Charles Darwin! (1863) wrote to Joseph Dalton Hooker, “It is mere rubbish, thinking at present of the origin of life; one might as well think of the origin of matter.” Today, thanks not least to Darwin

himself, we possess an attractive and actively investigated scenario? for

the origin of life. Will we ever know anything about the still deeper issue, what is the origin of matter? Leibniz put it in his famous words, “Why is there something rather than nothing?” William James,’ translated the “why” to the more meaningful “how”: “How comes the world to be here. . . ?” We ask today, “How did the universe come into being?” realizing full well that how properly to ask the question is also a part of the question. One can even believe that one can only then state the issue in the right words when one knows the answer. Or is there an answer? Is the mys-

tery of genesis forever beyond explanation?

The investigator of today is not content to let a major question remain

forever in the air, the football of endless indecisive games. Either it can

be ruled out or it must be answered: that is his credo. Something may rule out the question as meaningless, as quantum mechanics rules out any possibility to find out simultaneous values for the position and momentum of an electron. Or something may establish the issue to be undecid-

able, as Gédel has proved certain propositions to be undecidable. But in

the absence, as here, of some clear indication that the question is meaningless or undecidable, the question must be faced and the relevant evi-

dence sought out.

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Four Lines of Evidence If no two detectives turn up the same clues in a murder case, perhaps no two investigators regard the same pieces of evidence as relevant to a major issue that is still far from resolution. However, one inquirer’s search

of the literature and questioning of many colleagues ends up, at least today, always with the same four points at the center of consideration: 1. Einstein’s general relativity theory of cosmology leads to big bang

or big crunch or both—not periodicity, not big bang, big crunch and reexpansion, not big bang, big crunch and “reprocessing,” but big bang and big crunch; and big bang or big crunch or both argue for the mutability of the laws of physics. 2. There is no law of physics that does not lend itself to most economical derivation from a symmetry principle. However, a symmetry principle hides from view any sight of the deeper structure that underpins that law and therefore also prevents any immediate sight of how in each case that mutability comes about. Moreover, no search has ever disclosed any ultimate underpinning, either of physics or of mathematics, that shows the slightest prospect of providing the rationale for the many-storied tower of physical law. One therefore suspects it is wrong to think that as one penetrates deeper and deeper into the structure of physics he will find it terminating at some nth level. One fears it is also wrong to think of the structure going on and on, layer after layer, ad infinitum. One finds himself in desperation asking if the structure, rather than terminating in some smallest object or in some most basic field, or going on and on, does not

lead back in the end to the observer himself, in some kind of closed cir-

cuit of interdependences. The final two points fuel this thought:

3. A book of Henderson‘ and papers of Dicke,® of Carter,” and of

Collins and Hawking® give evidence that substantial changes in certain

of the constants or initial data of physics would rule out, not only life and consciousness as we know them, but even the planets and elements-

heavier-than-hydrogen that would be needed for almost any other imaginable form of life. This line of reasoning raises a central question.

Could the universe only then come into being, when it could guarantee

to produce “observership” in some locality and for some period of time

in its history-to-be? Is “observership” the link that closes the circle of interdependences?

4. David Hume? asked, “What peculiar privilege has this little agita-

tion of the brain that we call thought that we must make it a model for

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25

the entire universe?” In conformity with this assessment it was long

natural to regard the observer as in effect looking at and protected from

contact with existence by a 10 cm slab of plate glass. In contrast, quantum mechanics teaches the direct opposite. It is impossible to observe even so minuscule an object as an electron without in effect smashing that slab and reaching in with the appropriate measuring equipment. Moreover, the installation of apparatus to measure the position coordi-

nate, x, of the electron automatically prevents the insertion in the same

region at the same time of the equipment that would be required to measure its velocity or its momentum, p; and conversely. The act of measurement typically produces an unpredictable change in the state of

the electron. This change is different according as one measures the po-

sition or the momentum. This is the strange feature of quantum mechanics that led Niels Bohr to say,!® “If a man does not feel dizzy when he first learns about the quantum of action, he has not understood a word.” The choice one makes about what he observes makes an irretrievable difference in what he finds. The observer is elevated from “observer” to “participator.” What philosophy suggested in times past, the central feature of quantum mechanics tells us today with impressive force: In some strange sense this is a participatory universe. If “participation” is the strangest feature of the universe, is it possible that it is also the most important clue we have to the genesis of the uni-

verse (Point 4)? The position (or momentum) of an object only acquires

a useful meaning through the participatory act of observation. Does also the object itself only acquire a useful meaning through observership? What is the fuller lesson of the quantum, and how is “observership” to be spelled out? Spell out, too, we must, the first three points: 1. Gravitational big bang or big crunch or both lend support to the view that every physical law is transcended by the application of sufficiently extreme conditions (“mutability”).

2. Each law, mutable though it is, is derived most compactly on first analysis from an immutable symmetry principle—that hides the machinery that makes it mutable. No source is evident, either in physics or mathematics, for any “ultimate underpinning” at the bottom of it all. Is this a clue that the structure of physics, rather than having any “bottom,” returns in the end full-circle to the observer with which it began? 3.

No reason has ever offered itself why certain of the constants

and initial conditions have the values they do except that otherwise anything like observership as we know it would be impossible.

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The Four Theses In Four Phrases;

and One Central Theme and Thesis

Look again in a moment

at (1) “mutability,” (2) “no ultimate underpin-

ning,” (3) “observership as prerequisite for genesis,” also to be known in what follows as the “anthropic principle” of Dicke and Carter, and (4) “observer-participator as definer of reality.” However, pause here to ask if these four central points together suggest any still more central theme and question. If so, question though it were and must for long remain, it could bind the points together and bring a certain helpful unity to the discussion. No other way has disclosed itself to bring the four assortments of evidence into tight connection except to ask, is the universe a “self-excited circuit”? Does the universe bring into being the observership, and the observership give useful meaning (substance, reality) to the universe? Can one only hope some day to understand “genesis” via a proper appreciation of the role of the “observer”? Is the architecture of existence such that only through “observership” does the universe have a way to come into being? The collective knowledge of mankind makes an overwhelming pyramid but it is not evident that any of it bears more directly than physics on the question “how the universe came into being.” Even physics itself is a gigantic structure of observation, theory, and experiment; but out of it all it is not clear that any evidence lays more claim to attention

in connection with genesis than what we have out of the four named areas and out of the active work going on today in every one of them. To bind these results and this work together into any coherence demands a

central theme and thesis. The search for such an architectural plan can and will continue. Up to now, however, no pattern suggests itself from the available clues except this, to interpret quantum mechanics as evidence for the tie between genesis and observership.

Exploration As First Step Towards Revision and Advance To advocate the thesis “genesis through observership” is not the pur-

pose here; nor is it the purpose to criticize the thesis. It is too frail a reed to stand either advocacy or criticism. The purpose here is rather to explore the thesis. At least four objections offer themselves against investigating the

GENESIS

AND

OBSERVERSHIP.

oy

question “How did the universe come into being?” along lines such as

these: (1) the question is meaningless, therefore is beyond answer, and therefore should be rejected; (2) thinkers have debated for centuries be-

fore and after Leibniz and Berkeley between “realist” and “idealist” views of existence and the debate is as far as ever from being ended to-

day, so what profit is there in re-raking these stale issues? (3) the laws of physics persist forever—so it makes no sense to ask how they “came into being”; (4) any exploration of the concept of “observer” and the closely associated notion of “consciousness” is destined to come to a bad end in an infinite mystical morass. Every one of these objections has the same counsel about the present exploration: “Drop it!” Moreover, we have to be open to the possibility that any one of them may be

right—or all of them. However, it is not the way of science to sit inac-

tive in the face of mystery. More acceptable to the many active in this field today is a continuing search for more evidence and a continuing attempt to bring it into order. Nothing better suggests the outlook of science in the search for a plan than the motto of the engine inventor John Cris, “Start ‘er up and see why she don’t run.” That “start-up” is beyond

our power here because we are not even sure we have before us all the

parts of the “engine,” still less a plan of how they fit together. Handicapped though we are by these circumstances, it is not obvious that we are in any worse position than any engine inventor. He does not know that his engine will ever go. We know that ours “runs.” No better way is evident to get on with the exploration of this “engine” than to review again the four central points in greater detail. THESIS 1. Gravitational Collapse Argues Physical Law

for the Mutability of all

About the conditions of extraordinary density and temperature that pre-

vailed in the first few minutes of the universe we have today a wealth

of evidence that one would hardly have dared hope for 20 years ago. Radiotelescopes less than a meter long operating in the range of wavelengths of a few centimeters have brought evidence of the so-called pri-

mordial cosmic fireball radiation, or “relic radiation” from the time when the universe was enormously smaller than it is today and enor-

mously hotter. Measurements of the abundances of the elements and their isotopes and analysis of the mechanism of formation of these nuclear species reveal more about what went on around ~10 x 10° yr ago

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than we know about the biochemistry in our own interiors in the here

and the now. The prediction of a big bang at the hands of Friedmann out of Einstein’s 1915 and now standard geometrical theory of gravitation is now strongly supported by the evidence. Estimates of galactic distances as they stood 20 years ago were wrong, we realize today, by a factor of the order of 6. With the correction of this error interest has dwindled in such alternative views of cosmology as “the continuous creation of matter” and a “steady state universe.”

The simplest cosmology compatible with Einstein’s theory of gravitation is characterized by a “big crunch” as well as by a “big bang.” In this model the fluctuations in density from galaxy to galaxy are idealized as smoothed out and the geometry of space is treated as homogeneous and isotropic, curved equally in all directions and everywhere by the same amount. Einstein gave arguments! that this bending should be great enough to curve space up into closure, making the geometry that of a “3-

sphere,” the three-dimensional analog of the 2-sphere of the familiar geo-

graphic globe. If he had stated this requirement for closure as an equation, “closure” could have been regarded then and thereafter as a built-in boundary condition and necessary part of general relativity. Instead he left it in the form of words and the alternative view that the universe is “open” is often explored. Space bending is proportional to matter density. However, the amount of matter seen in galaxies today falls short by a factor of the

order of 30 compared to that required by Einstein’s theory for closure.!? Therefore it is a remarkable development that Ostriker and Peebles! find reason to believe that galaxies contain in their outer

fringes three to 20 times as much matter as one had previously attributed to the visible parts of the galaxies. An intense search is now underway for direct observational evidence of faint stars or other objects in galactic halos. It is conceivable that insufficient matter is present; that the universe is open; and that the universe goes on expand-

ing forever. However, if the searches now under way reveal the

“missing matter” and the conditions for closure are verified this will

be another impressive confirmation of Einstein’s conception of general relativity. In this event Figure | gives a quantitative impression of the

predicted variation with time of the radius of the universe. Collapse or “big crunch” is symmetric to the big bang. Extreme models of the singularity and big bang and big crunch have

been proposed, including a so-called “whimper” singularity!4 and “closed-in-space to closed-in-time transition”!> very different in char-

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29

PPlmariatsatstatenei islets ey

(Se een; actual time since start

Se

Hubble time

Illustrative values all derived from

Time from start to now

Hubble time now

Hubble expansion rate now Rate of increase of radius now

Radius now Radius at maximum

Time, start to end

Density now Amount of matter Equivalent number of baryons

10

20.

x 10% yr

x 10% yr

peekiuises

megaparsec

0.66 lyr/yr

13.19 x 109 lyr 18.94 x 109 lyr

59.52 x 109 yr

14.8 x 10°80 g/cm3 5.68 x 10° g 3.39 x 1080

Ficure 1. Sample figures for Friedmann model of homogeneous insotropic “stardust-filled” universe.! The last eight numbers are derived, via Einstein’s standard gravitation theory, from the first two numbers treated as 100% accurate, although the present uncertainty in each is of the order of 30%: (1) the actual age of the universe as estimated from the rate of evolution of stars and star clusters; and (2) the extrapolated or “would-be”

or “Hubble” age of the universe; that is, the time it would have taken for galaxies to get to their presently observed separations at their presently observed rates of recession (slower today by reason of the continued pull of gravity than their speeds of recession in the intervening time).

acter from the singularity of simple Friedmann cosmology. However,

all available evidence!® suggests that the Friedmann description of singularity is closer to describing the extreme conditions encountered in

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the generic case.!7 Moreover, when a cloud of matter collapses to a black hole and gives rise to a singularity in the here and now, this singularity is not topologically distinct from the final cosmological singularity but!® part and parcel of it (see Figure 2). Thus if the universe is closed—as Einstein argued, and as available evidence allows one to be-

lieve or disbelieve—one has a choice whether to rocket in to the nearest black hole and encounter the singularity in the near future or wait some tens of 10? years down the road to encounter the singularity. But

COLLAPSE

COLLAPSE VOUV OT UNUSCUCE ey

DUTY

1 ' i !

'

wy Ha

t that a normal galaxy at such a distance has the power to take two light rays, spread apart by 50,000 light

years on their way out from the quasar, and bring them back together at the Earth. This circumstance, and evidence for a new case of gravita-

tional lensing,>® make it reasonable to promote the split-beam experiment in the delayed-choice version from the laboratory level to the cosmological scale as illustrated in Figure 4.

We get up in the morning and spend the day in meditation whether to

observe by “which route” or to observe interference between “both routes.”

When night comes and the telescope is at last usable we leave the half-sil-

vered mirror out or put it in, according to our choice. The monochromatizing filter placed over the telescope makes the counting rate low. We may have to wait an hour for the first photon. When it triggers a counter, we discover “by which route” it came with the one arrangement; or by the other, what the relative phase is of the waves associated with the passage of the photon from source to receptor “by both routes”—perhaps 50,000 light years apart as they pass the lensing galaxy G-1. But the photon has already passed that galaxy billions of years before we made our decision. This is

the sense in which, in a loose way of speaking, we decide what the photon

shall have done after it has already done it. In actuality it is wrong to talk of the phenomenon until it has been brought to a close by an irreversible act of amplification: “No elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon.”

DELAYED-CHOICE

EXPERIMENTS

Ficure 3. Left, the double quasistellar object (“quasar”’ : red shift z = 1.41), identified by its right ascension and declination as 0957 + 561 A,B, and suspected to be the two images—produced by gravitational lens action—of one and the same quasar. This photograph, made at the University of Hawaii telescope by Alan Stockton and kindly communicated and discussed by Derek Wills of the University of Texas at Austin, is the digital sum of five one-minute exposures in red light (5700 to 7000 A). The stellar images appear elongated because of a telescope tracking problem. Right, the same digital photographic record after a stellar profile has been subtracted from the southern image (B), the residual being compatible with the existence near B of a lensing galaxy (G-1). Evidence has been found by Young, Gunn, Kristian, Oke, and Westphal at Caltech for such a galaxy (0.02" to the west and 0.8" north of B; red shift z = 0.39), much closer to B than to A (which is 1.2" to the west and 6" north of B), and for its membership in a cluster of perhaps 1000 to 10,000 galaxies (centered 2" to the west and 15" north of B).

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The “Past” in the Light of the Dealyed-Choice Experiment To use other language, we are dealing with an elementary act of cre-

ation. It reaches into the present from billions of years in the past. It is

wrong to think of that past as “already existing” in all detail. The “past” is theory. The past has no existence except as it is recorded in the present. By deciding what questions our quantum registering equipment shall put in the present we have an undeniable choice in what we have the right to say about the past. What we call reality consists of a few iron posts of observation between which we fill in by an elaborate papier-maché construction of

imagination and theory.>7

Spacetime in the prequantum dispensation was a great record

parchment. This sheet, this continuum, this carrier of all that is, was and shall be, had its definite structure with its curves, waves, and rip-

ples; and on this great page every event, like a glued-down grain of sand, had its determinate place. In this frozen picture a far-reaching modification is forced by the quantum. What we have the right to say of past spacetime, and past events, is decided by choices—of what measurements to carry out—made in the near past and now. The phenomena called into being by these decisions reach backward in time in their consequences

as indicated in Figure 5, back even to the earli-

est days of the universe. Registering equipment operating in the hereand-now has an undeniable part in bringing about that which appears to have happened. Useful as it is under everyday circumstances to say

that the world exists “out there” independent of us, that view can no

longer be upheld. There is a strange sense in which this is a “participatory universe.”

From Measurement to Meaning We cannot speak in these terms without a caution and a question. The caution: “Consciousness” has nothing whatsoever to do with the quan-

tum process. We are dealing with an event that makes itself known by an irreversible act of amplification, by an indelible record,*® an act of registration. Does that record subsequently enter into the “consciousness” of some person, some animal, or some computer? Is that the first step in translating the measurement into “meaning”—meaning regarded as “the joint product of all the evidence that is available to those who communi-

DELAYED-CHOICE

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ty

>

ter i

2a

Ficure 4. Proposed delayed-choice experiment extending over a cosmological reach of space and time. Left, quasar Q recorded at receptor as two quasars by reason of the gravitational lens action of the intervening galaxy G-1. Middle, schematic design of the receptor for delayed-choice experiment: (i) filter to pass only wave lengths in a narrow interval, corresponding to a long wave train, suitable for interference experiments; (ii) lens to focus the two apparent sources onto the acceptor faces of two optic fibers; (iii) delay loop in one of these fibers of such length, and of such rate of change of length with time, as to bring together the waves traveling the two very different routes with the same, or close to the same, phase. Right, the choice. Upper diagram, nothing is interposed in the path of two waves at the crossing of the optic fibers. Wave 4a goes into counter 1, and 4b into counter II. Whichever of these photodetectors goes off, that—in a bad way of speaking—signals “by which route, a or b, the photon in question traveled from the quasar to the receptor.” Lower diagram, a half-silvered mirror, !/2 S is interposed as indicated at the crossing of the two fibers. Let the delay loop be so adjusted that the two arriving waves have the same phase. Then there is never a count in I. All photons are recorded in II. This result, again in a misleading phraseology, says that “the pho-

tons in question come by both routes.” However, at the time the choice

was made whether to put in !/2 S or leave it out, the photon in question had already been on its way for billions of years. It is not right to attribute to it a route. No elementary phenomenon is a phenomenon until it is a registered phenomenon.

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cate’”?3® Then that is a separate part of the story, important but not to be confused with “quantum phenomenon.”

Is the Universe Constructed Out of Elementary Phenomena? From this caution we turn to the question: If the elementary quantum process is an act of creation, is an act of creation of any other kind required to bring into being all that is? At first sight no question could seem more ridiculous. How fantastic the disproportion seems between the microscopic scale of the typical quantum phenomenon and the gigantic reach of the universe! Disproportion, however, we have learned, does not give us the right to dismiss.

Else how would we have discovered that the heat of the carload of molten pig iron goes back for its explanation to the random motions of billions of microscopic atoms and the shape of the elephant to the message on a microscopic strand of DNA? Is the term “big bang” merely a shorthand way to describe the cumulative consequence of billions upon billions of elementary acts of observer-participancy reaching back into the past as symbolized in Figure 5? An old legend describes a dialogue between Abraham and Jehovah. Jehovah chides Abraham, “You would not even exist if it were not for me!” “Yes, Lord, that I know,” Abraham replies, “but also You would not

be known if it were not for me.”4°

In our time the participants in the dialogue have changed. They are the

universe and man. The universe, in the words of some who would aspire to speak for it, says, “I am a giant machine. I supply the space and time for your existence. There was no before before I came into being, and there will be no after after I cease to exist. You are an unimportant bit of matter located in an unimportant galaxy.” How shall we reply? Shall we say. “Yes, oh universe, without you I would not have been able to come into being. Yet you, great system, are made of phenomena; and every phenomenon rests on an act of observation. You could never even exist without elementary acts of registration such as mine”?

Are elementary quantum phenomena, those untouchable, indivisible acts of creation, indeed the building material of all that is? Beyond particles, beyond fields of force, beyond geometry, beyond space and time

themselves, is the ultimate constituent, the still more ethereal act of ob-

server-participancy? For Dr. Samuel Johnson the stone was real enough

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when he kicked it. The subsequent discovery that the matter in that rock is made of positive and negative electric charges and more than 99.99

percent empty space does not diminish the pain that it inflicts on one’s toe. If the stone is someday revealed to be altogether emptiness, “reality” will be none the worse for the finding.

Roland M. Frye, in reminding us‘! of Shakespeare and of ways of see-

ing, gives us opportunity to recall those words of almost 400 years ago,

FicurE 5. Symbolic description how all that “has happened” in the past is influenced by choices made in the present as to what to observe. The upper tip of each “leaf” stands for the elementary act of registration. The lower end of each leaf stands for the beginning of the elementary phenomenon being investigated by the observational means at hand. Is anything else required to make up space and time and all their burden of physical content except the information carried in the elementary quantum acts thus symbolized?

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And as imagination bodies forth The form of things unknown, the poet’s pen Turns them to shapes, and gives to airy nothing A local habitation and a name. Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as far as we can be today from knowing enough about the deeper machinery of the universe to answer this question. Increasing knowledge about detail has brought an increasing ignorance about plan. The very fact that we can ask such a strange question shows how uncertain we are about the deeper foundations of the quantum and its ultimate implications.

The Quantum: Its Uses—And Its Use To encounter the quantum is to feel like an explorer from a faraway land who has come for the first time upon an automobile. It is obviously meant for use, and an important use, but what use? One opens the door, cranks the window up and down, flashes the lights on and off, and perhaps even turns over the starter, all the time without knowing the central point of the thing. The quantum is the automobile. We use the quantum in a transistor to control machinery, in a molecule to design an anesthetic,

in a superconductor to make a magnet. Could it be that all the time we have been missing the central point, the use of the quantum phenomenon in the construction of the universe itself? We have turned over the starter. We haven’t got the engine going. Electricity in the days of Benjamin Franklin was a strange mixture of sparks and lightning, Leiden jars and wire, cat’s fur, and wax. He had the remarkable combination of adventurous spirit and solid common sense4? that let him penetrate deep into the subject. Not otherwise would he have gone so far in explaining with a minimum of mathematics so many of the central points including positive and negative electricity and a simple and still useful picture of how charge distributes itself over the surface of a conductor. How far the science of electricity grew in his hands and how far it has grown since! How far the concept of the quantum grew in the hands of Bohr and Einstein! How far has it yet to grow? In the work of exploration and judgement we can perhaps gain some

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encouragement from the words of Einstein, “In my opinion there is the

correct path and . .. it is in our power to find it.”43

Report presented at joint meeting of the American Philosophical Society and the Royal Society, London, June 5, 1980.

The Outsider

66

his huge world,” Einstein exclaimed, “stands before us like

a great eternal riddle.” What is its secret central principle of construction? That is the unscaled Everest of all knowledge. Mere way stations on the laborious climb toward that highest outlook— that was Einstein’s assessment of his discoveries about space and time,

about the strange quantum nature of light and matter, and about gravitation

and the universe. For him, these findings were not goals. He had only one

goal: the distant peak. It will surely be reached someday by someone, he declared: “The most incomprehensible thing about the world is that it is comprehensible. . . Today we have less ground than ever before for allowing ourselves to be forced away from this wonderful belief.” Which means more to us today—the goal he was climbing toward, or how he tried to reach it? “How” for him meant catch-as-catch-can, try-

and-try-again—explanation enough for his definition of a “unscrupulous opportunist.” There were three additional stein’s work that stand out for use in our times. First, out simplicity. Second, from discord make harmony. Third, in difficulty lies opportunity.

scientist as an rules of Einof clutter find the middle of

Simple Central Point Many not close to his work think of Einstein as a man who could only make headway by dint of pages of complicated mathematics. The truth is the direct opposite. As the great mathematician of the time, David Hilbert, put it, “Every schoolboy in the streets of Géttingen understands more about four-dimensional geometry than Einstein. Yet .. . Einstein did the work and not the mathematicians.” The amateur grasped the simple central point that had eluded the expert. Where did Einstein acquire

this ability to sift the essential from the nonessential?

THE The management-consultant

has a works thing many,

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firm of Booz, Allen & Hamilton, Inc.,

word of advice: “What a young person does and who he or she with in the first job has more effect on his or her future than anyelse anyone can easily analyze.” What was Einstein’s first job? To clerk in the Swiss patent office was no proper job at all. But it was

the best job available to anyone with his unpromising record of resisting

all required learning. Einstein served in the Bern patent office for seven years. Every morning he faced his quota of applications, each accompanied by the inventor’s working model. Over and above the papers and the models was the boss, Friedrich Haller, a kind man, a firm man, and a wise man. He gave

strict instructions: explain briefly why the device will work or why it won't, why the application should be granted or denied. Day after day, Einstein had to distill the central lesson out of objects

of the greatest variety. Who knows and how it works? It is no wonder machinery of the world—from the of a river. Was it a miracle for the obscure

a greater way to learn what physics is that Einstein always delighted in the action of a compass to the meandering clerk rather than the experts to discov-

er in 1905 that “space by itself, and time by itself are... mere shadows,

and only [spacetime], a kind of union of the two, preserve[s] an indepen-

dent reality”? And to derive from this concept of spacetime the famous

E=mc?, with all its consequences? From all the clutter of facts, who else

could better distill the central point—spacetime—than someone whose job it was over and over to extract simplicity out of complexity? Bern does honor to the bears from which its gets its name by having a

great open bear pit. There one can watch the bears go round and round

on all fours with their heads to the ground. The young Albert Einstein liked to take his visitors there. Only very rarely, he pointed out, does one

rear on its hind legs and look around for a wider view. For Einstein, that

bear symbolized the thinker. For us, let the bear symbolize the outsider who by virtue of being an outsider understands the situation of the insid-

er better than any insider.

:

What do we mean by the word “outsider”? Someone alienated from the world is the last thing we want the term “outsider” to mean, and the last description that could ever be applied to Einstein. He had the optimistic outlook of all great investigators. He rarely grumbled. Once he spoke of autograph hunting as the last vestige of cannibalism. Another time he described hell as the devil approaching menacingly every halfhour with his pitchfork loaded with a fresh bale of letters to be answered.

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But if Abraham Lincoln was right when he said that people are generally as happy as they make up their minds to be, then Einstein had made up his mind to be happy.

Dream and Drive To one who discussed physics with him from time to time over a span of 21 years, studied his writings, and worked with his great theme, Einstein will always mean an outsider with a vision in his early days above the vi-

sion of all insiders, united with a try- and- -try-again drive. This combination of dream and drive makes an uncommon outsider. Still more uncom-

mon, and still more needed today, is the outsider-generalist who, like

Einstein can lead the way surefootedly through the complex world of science and technology to goals that were overlooked or deemed impossible by most experts. I am afraid I shall have no lesson to offer about this. I

don’t know how to manufacture such treasures, and I don’t know anyone who does. I can only say, when you see one, treasure him or her.

Newsweek condensation (1979) from the author’s paper, “Albert Einstein, March 14, 1879-April

18, 1955,” in C. K. McKuen, ed., Biographical Memoirs, National Academy

of Sciences (1980).

To Albert Einstein

ow can one most clearly say that science reaches beyond all na-

tional boundaries, and belongs to mankind? How else than by commemorating one who was born in Germany, studied in Italy

and Switzerland, taught in Prague and Berlin, and lived 22 years in

America, one who by belonging to five countries belonged to no one people—and to all people? How can one most strongly testify that science throws its shoulder— and its heart—behind the wheel of the world’s work? How better than by remembering the contributions of the man whose concepts are the heart of electronic devices in home and factories all over the world. . . ? How can one most movingly say that science—and the application of science to the needs of society—is a work for the young in heart. . . ? Not by a pompous figure on a pedestal. . . (rather by) a figure of one

who said, “The ideals which have lighted my way, and time after time

have given me new courage to face life cheerfully have been Kindness, Beauty and Truth.” Professor Einstein,

You showed us that an ordinary human

Speaking clear sentences in childhood As the first step to thinking clearly, Reading great men in youth As the first step to being great,

Taught by one’s first job

Day after day for seven years

To distill simplicity out of complexity, Taking a star to guide one’s course Can achieve beyond imagination. Remind us by your example

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That the young person Inspired by heroes and guided by a star Is the hope of science—and of the world. From address, April 22, 1979, at the unveiling of the Robert Berks bronze and granite monument to Einstein, National Academy of Sciences lawn, 2101 Constitution Avenue,

Washington, D.C.

No Fugitive and Cloistered Virtue

n Denmark’s wartime darkest days those who had taken her liberty were trying to snuff out her soul. To overwhelming force, the people of the country and their king presented unbending moral resistance. At the center of their spiritual unity stood Denmark’s men of

learning under the leadership of Niels Bohr. What does it mean to preserve a nation’s soul? What makes a nation—or a man? In time of trouble the answer becomes clear: mankind is formless clay; his spirit he derives from his heroes, from his traditions, from well-accepted thoughts and ways of life, from storied legends, and from firmly held standards of value. To hold high Denmark’s values Bohr and other leaders created and disseminated at their peril a great book entitled Danish Culture. Warned of a plot to seize him, Bohr had to flee for his life in a small

boat across open waters to Sweden in November 1943, but the work went on and Danish resistance stood fast another year and a half. Many times before and since those days Bohr has stressed that a man, like a nation, derives his identity and inward quality not from the genes that he inherits, not from the color of his skin, but from the traditions and the sense of values imparted by his family and by the civilization in

which he lives. We will not deny that great causes make great men. We

will wholeheartedly agree, and remind the world of what he has stood for in his scientific achievements, in his way of thought, and in his work for

understanding between nations. Bohr’s principle of complementarity is the most revolutionary scien-

tific concept of this century and the heart of his 50-year search for the

full significance of the quantum idea. It states that “any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of the phenomena.” Beginning students sometimes find

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themselves explaining this principle with the words of the Abbé of Galiana (1728-1787), “One cannot bow in front of somebody without showing one’s back to somebody else.” In the description of nature at the quantum level, Bohr stresses, the interaction between the observer, or the observing equipment, and thé object under study is significant and cannot be predicted. On this question of indeterminism one of the great debates of all science took place over the years between Einstein and Bohr. Bohr summarized Einstein’s criticisms of quantum theory in 1949 in a tactful and charming chapter in the book Albert Einstein: Philosopher-Scientist and answered them one by one in a great exposition of the logical foundations of quantum physics. Attempts by others to replace classical concepts of space and time and other physical quantities by proposed quantum concepts so as to preserve determinism have been the

target of Bohr’s vigorous analysis. He repels every sort of mysticism. In his November 1954 lecture on The Unity of Knowledge, he emphasizes

that, however “far the phenomena transcend the scope of classical physi-

cal theories, the account of the experimental arrangement and the

recording of the observations must be given in plain language, suitably

supplemented by technical physical terminology. This is a clear logical demand, since the very word “experiment” refers to a situation where we can tell others what we have done and what we have learned.” In this report and in his latest work Bohr has analyzed how typical observation processes are brought to a close by essentially irreversible mechanisms of amplification. Among the many applications of complementarity to bring consistency into science, two concern the theory of measurement of electromagnetic fields and electron fields, as reported in a pair of the deepest and richest papers in the literature of physics, both by Bohr and Rosenfeld, the most recent in 1950. Besides complementarity, the principle of correspondence is one of Bohr’s fundamental contributions to modern physics—the principle that the predictions of quantum theory agree with those of classical physics in the limiting case where one deals with large numbers of quanta. Bohr has used this principle to deal with many problems over the years, most recently with the theory of the stopping of swift charged particles in matter. His comprehensive 1948 treatise on this subject provides at the same time a wonderful survey of the elementary processes of atomic physics in action. We cannot examine in this much too brief survey the fertile applica-

tions that Bohr conceives for complementarity in every branch of

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thought. Instead, let us inquire about the way of work of a man who is the leading citizen of his country, subject to every kind of call, both public and private, from helping in the negotiation of a treaty to speaking on

a great anniversary.

The center of Bohr’s scientific life is his unique institute, an international clearinghouse of ideas. There able young people come from all over the world to work in an atmosphere free of envy and jealousy, one that could be described in the words of Sir William Rowan Hamilton’s

poem:

Yet with an equal joy let me behold Thy truth’s chariot o’er that way by others rolled.

Here the climate of ideas opens the way to new advances in physics. The discussions at the institute establish in the minds of the members firm conclusions and points of view which become the foundation for future fruitful work and influence, not only in Copenhagen, but all over the world. Among this changing group the definition of an expert is well accepted, as someone who knows from his own bitter experience

almost all possible mistakes in his field. Most characteristic of Bohr in these discussions is his energy and concentration on the central issue.

His energy is famous from the days when he was a football hero of

Denmark. From Schiller he quotes the principle of concentrating on the smallest point the great force. He has been known to define a workroom as “a room where no one can keep you from working.” However,

the periods of intense meeting of minds and struggle over issues are not

for Bohr the interruption of his work but the very means by which he accomplishes his work. For this reason he seeks to interact with the most able young thinkers from every country, and on the most impor-

tant issues.

Whoever has told the story of Plato’s school, let him tell of the way of

life at this international exchange of ideas, of the humor, of the happy

balance between the amateur and the professional spirit, of the walks and

talks about the deepest human problems, and of the family spirit with which Margrethe Bohr blesses all the members. From

1935 onwards, a darkening shadow fell over the institute, then

military occupation, then the attempt to seize Bohr himself. Following his escape to Sweden, Bohr was flown first to England, then to the United States. Even before he renewed contacts with leading

men in both countries, he was informed of the fantastic scale of the joint

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atomic project, and was asked to take part. He decided on a division of his time between Los Alamos and Washington. In Los Alamos he saw the dedication to the task of shortening the war and saving lives on both sides. There he contributed on the physics of fission. In Washington Bohr

devoted himself to larger issues: (1) How to secure an agreed-upon system by which nations can live together? (2) How to prevent atomic weapons from being used for aggression? His recognized position as the world’s most responsible man of science forced him to search for ‘a way to make the best out of the situation,” to use the words in which he describes his work in physics. Bohr undertook this task in early 1944 with characteristic energy. As in physics, so here he worked back and forth through the problem with those who represented the most solid current thinking. Each important stage of the discussions was followed by a new draft memorandum of firm conclusions, and of problems, principles, hopes, and difficulties. In this work Niels Bohr had the close collaboration of his young son Aage,

who has since made a distinguished record of scientific accomplishment of his own. The first stage of the intense analysis culminated in a memorandum to President Roosevelt on the third of July, 1944. He urged that America and Britain inform other allied nations about the new weapon before it was used, and consult with them on measures of control. In

time, bombs were bound to be widespread. The possibility of surprise

use would make them a perpetual menace to human security. Only con-

trol could prevent fear and mistrust from enveloping the world. No con-

trol would be effective, Bohr emphasized, without unprecedented free-

dom to look into industrial and military enterprises in every country. This openness would be difficult to secure between nations with very different views on social and economic problems. This difficulty should be regarded as an argument, not against openness, but for it, Bohr point-

ed out. Not only control of weapons but also the even greater rewards of

understanding and confidence between different branches of humanity

would be secured by full freedom to travel and to exchange information

and ideas. Bohr reviewed his thinking in a long discussion with President Roosevelt in August 1944. The subject was complex. Secrecy blocked public discussion. It also prevented discussions between allies about international control at the most favorable time, before the weapon was used. Intensely convinced of the importance of such early agreement, Bohr proposed that a new channel of communication be called into being to start preliminary and noncommittal discussions. Let a small group of dis-

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creet and dedicated scientists be authorized to talk together around the fringes of the subject—men bound in ties of friendship and trust through years of close collaboration. Bohr’s urgent discussions with leaders in Washington continued through the fall and winter on frequent visits from Los Alamos. They culminated in a second memorandum to President Roosevelt in the early spring. There Bohr outlined his ideas still more clearly, ideas which form the foundation of present-day thinking about control. The same day that Bohr completed this document to the President, the 24th of March,

1945, Roosevelt was working on his last speech, never to

be delivered. Aware of the imminence of the atomic age, he wrote, “To-

day we are faced with the preeminent fact that, if civilization is to sur-

vive, we must cultivate the science of human relationships—the ability of all peoples, of all kinds, to live together and work together in the same world, at peace.” In accordance with Bohr’s concept of scientists as the surest channel of communication between peoples of very different outlooks, Roosevelt quoted Thomas Jefferson on the “brotherly spirit of science, which unites into one family all its votaries of whatever grade, and

however widely dispersed throughout the different quarters of the world.” Nineteen days later the careworn President was dead. There was not time to bring a new set of discussions to fruition. Bohr remained in this country until the end of the war in the West and then returned to Europe. In August all the problems that Bohr had prophesied broke upon an unprepared world. The subsequent public history of the control issue is well known. Eventually a United Nations committee was created to examine the problem. Kramers of the Netherlands, one of Bohr’s closest colleagues, wore out many of the last months of his life in persevering diplomacy as chairman. He won agreement that an international check system is technically feasible. But control proved politically unacceptable. In 1948 after this setback Bohr recognized that no progress could take

place without an atmosphere of greater confidence. Therefore the proposed approach had to be reversed. Not first an international control system, and then increasing openness between countries must be the order, but the reverse.

Few men have the vision and courage to try to induce all mankind to

accept a new moral concept of such scope—the principle of the open

world. But Bohr’s is “no fugitive and cloistered virtue.” He has worked

intensively for the past ten years to promote a stand for an open world as the absolute necessity for a peaceful world. He has urged this stand not

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only in earnest and fruitful private discussions with scientists and states-

men, but also publicly, as in his Open Letter to the United Nations of

June 1950, and his message at the International Conference of Peaceful Uses of Atomic Energy at Geneva in August 1955. Good will between two peoples cannot endure, Bohr emphasizes, unless each has full opportunity to find out about the other.

Not peace alone, but also the advance of civilization depends upon openness, Bohr stresses. “The goal to be put above everything else,” he urges, is “an open world where each nation can assert itself solely by the

extent to which it can contribute to the common culture and help others

with experience and resources... . Such a stand would . . . appeal to people all over the world, fighting for fundamental human rights, and would

greatly strengthen the moral position of all supporters of genuine interna-

tional collaboration.

At the same time, those reluctant to enter on the

course proposed would have been brought into a position difficult to maintain since such opposition would amount to a confession of lack in their own cause when laid open to the world.” Bohr asks our help. He says, “The efforts of all supporters of international cooperation, individuals as well as nations, will be needed to create in all countries an opinion to voice, with ever-increasing clarity and strength, the demand for an open world.” Many have already committed themselves to the cause of openness. On encouraging days the slow leaven of his message can be seen working between the lines of foreign policy. Would that Benjamin Franklin were here today to join in the enterprise. Before one great philosopher, scientist, and statesman the other could utter his famous prayer: “God grant that not only the love of Liberty but a thorough Knowledge of the Rights of Man may pervade all Nations of the Earth, so that a Philosopher may set his Foot anywhere on its

Surface, and say ‘This is my Country’.”

Address on the occasion of President Dwight David Eisenhower’s presentation of the first Atoms for Peace Award to Niels Bohr, National Academy of Sciences, Washington,

D.C. on October 24, 1957.

‘i

Einstein and Other Seekers

of the Wider View

The Bear of Bern Bern, the capitol city of Switzerland, remembers those great creatures

from which it gets its name by having an open-air bear pit. There, one can watch the bears go round and round on all fours with heads to the ground. In the early years of this century, a young patent office clerk named Albert Einstein liked to take his visitors there. Only very rarely, he pointed out,

does one of the animals rear up on its hind legs and look around for the wider view. To Einstein, that bear represented the thinker. To us, let it symbolize, by extension, one who rises to the larger view and, from that

vantage point, recognizes what is missing, and fills the gap.

Hutton, Darwin, Mendeleev, Bohr, and Einstein:

“Discover Unity”

In 1795, James Hutton opened out a great new perspective on geology, as a dynamic process going on everywhere and all the time. This view made that consideration stand out which had been missing from all previous thinking, namely, the enormous time scale of the history of the earth. Charles Darwin, as a result of observations made during the voyage of

the Beagle (December 1831 to October 1836), and subsequently at home,

won his way to a comprehensive picture of variations in plants and animals, and of the seeming favor granted to some of these variations by na-

ture. This bird’s eye view exposed to him in October 1838 the missing el-

ement: “The result of [enough such variations] would be the formation of

a new species.”

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Dmitri Ivanovitch Mendeleev developed the periodic system of the ele-

ments to try to display chemistry to his students as a harmonious whole.

By 1871, his system was so well developed that it forced him to recognize the existence of three gaps in his tables. It also gave him clear predictions of the properties of those three hitherto unknown elements and their compounds. These predictions were verified with the discovery of gallium in

the same year, of scandium in 1879, and of germanium in 1886.

By 1905, classical mechanics had developed from the foundations laid by Newton into a harmonious conceptual whole, capable of describing the motion of the moon as well as a simple pendulum. Furthermore,

thanks to the labors of James Clerk Maxwell and his successors, electro-

magnetic theory had also reached an advanced state. Yet, there were puzzling disagreements between them: the two systems, mechanics and electromagnetics, seemed incompatible. Struggling to get a view of the unity

that had to be there, the patent clerk discovered the missing idea, one that

reached far beyond electricity and magnetism to the nature of space and

time themselves. As Einstein’s former teacher, Hermann Minkowski, was

later to phrase the young man’s discovery, “space by itself, and time by itself, are .

. mere shadows, and only [spacetime,] a kind of union of the

two, . . . preserve[s] an independent reality.”

In 1908, striving for a still larger view that would include gravity, Einstein came to recognize the missing concept: gravitation is not something foreign and physical acting through space but a manifestation of the curvature of space. In November 1915 Einstein, by now professor at the Kaiser Wilhelm Institute in Berlin, discovered the law governing the response of spacetime geometry to matter. Today we know how to state the content of Einstein’s “general relativity” in a single simple sentence:

Space tells matter how to move and matter tells space how to curve.

In the last 30 years of his life Einstein sought a unified geometric the-

ory of all the forces of nature. He did not succeed. However, physics to-

day, adopting a new and wider concept of what geometry is, in the sense of a so-called “gauge theory,” is making marvellous new progress toward this dream of unification. I first saw and heard Einstein in Princeton in the fall of 1933, some

days after he had taken up his long-term residence there. Our last time together came 21 years later when he kindly accepted an invitation to speak at my relativity seminar, the last talk he ever gave, April 14, 1954, almost exactly a year before his death. The most extraordinary feature of the man I glimpsed the first day, and came to see ever more clearly each time I visited his house and climbed to his upstairs study and we ex-

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plained to each other what we did not understand. Over and above his

warmth and considerateness, I came to see, he had a unique sense of the

world of man and nature as one harmonious and someday understandable whole, with all of us feeling our way forward through the darkness together towards that harmony, that larger view, that sense of the unity of all things, great and small. Not only to his visitor but in his writings Einstein expressed this lifelong yearning for the larger view. “Out yonder,” he exclaimed, lies “this

huge world, which exists independently of us human beings and which stands before us like a great eternal riddle.” No one has ever affirmed more vividly than he the faith that the mystery will someday be unravelled: “The most incomprehensible thing about the world is that it is comprehensible”; and again, “All of these endeavors are based on the belief that existence should have a completely harmonious structure. Today we have less ground than ever before for allowing ourselves to be forced away from that wonderful belief.” What did Einstein mean by “harmony”? Who does not know who has seen his words of admiration for Niels Bohr and for Bohr’s ability to see amid a maze of distracting evidence the quantum nature of the atom: “He

has the highest form of musicality in the sphere of science”? What did

Einstein mean by “harmonious structure”? He meant what his mentor,

model and hero, Benedict de Spinoza meant: a universe that is beautiful, simple, and understandable—even if not yet understood. As Josiah Royce puts it, speaking of Spinoza, but for us speaking also of Einstein, he is one who “sees everywhere an all-pervading law, an all-conquering truth, a supreme and irresistible perfection” and, even if he himself does not yet have it, nevertheless envisages us all as someday having “‘a clear vision of the supreme and necessary laws of the eternal world.” Discover new unity! That is how

Hutton, Darwin, Mendeleev, Ein-

stein, and Bohr made their contributions. That is not the only way to mount that trilogy of actions, to “rise to the larger view—and from that vantage point recognize what is missing, and fill the gap.” The bear of Bern knows only one way to realize and use his wider

view. But man, working as he does with other men and ideas, knows

more ways—more than seven; but seven will suffice for our survey. For examples we might, but we shall not, turn to the great lawyers and lead-

ers of finance and industry of past and present days, perceptive policy

makers and statesmen, not those who merely keep the world operating as

it is, but those men of the larger view who by their imagination, judgment, and force raise the level of life and hope of all the rest of us.

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Among those who deal with science and technology, there is already enough human variety, enough individuality of thought and action, to more than occupy us here. What are these seven versions of

our trilogy, to “seek the larger

view—and from that vantage point recognize what is missing, and fill the gap?” (1) Discover unity. (2) Draw together pieces of science and technology to create a system, whether that system is xerography or telegra-

phy or steam navigation. (3) Find economic feasibility for a new technology by virtue of a wider grasp of the worlds of man and matter. (4)

Reach harmony through intuition; by meditating on the base of a wide and deep knowledge of the field, arrive at a new result. (5) Build a model, a simplified representation of the problem at issue, subject to experi-

mental or mathematical analysis. (6) Serve as a science-technology generalist who, not once or twice in his life, but many times in a year, and

generally in the service of others, extracts the single, simple missing point out of a complicated situation. (7) Make decisions, or help others make decisions, by imaginative interaction with alternative scenarios

calculated as consequent on those decisions. Under what one name shall we summarize such apparently different activities? The patient may not complain if he receives no cure from his physician, but he is unhappy indeed if he does not at least receive a name for his disease. Yet who can find one word to stand for the trilogy of climbing to the higher view, recognizing from that view what is missing, and filling the gap? The classical scholar might propose the Greek-based adjective “deictic” for the nature of this activity, meaning “showing, pointing out, or proving directly,” and, by extension, the same word “deictic” for those who engage in it. However, no one who believes in the importance of enterprise of this kind in the world of today will want to shackle it with such a word. Will it not be better for us to use the first phrase in our trilogy, “larger view,” or “seek the larger view,” or “seekers of the larger view,” and in that way imply also the other two parts of the trilogy: “recognize what is missing” and “fill the gap”? Shall this then be our understanding when we speak of “seekers of the larger view”?

Fitch, Fulton, Morse, and Carlson: “Create a System” Achieve the larger view? Capture the full panorama? Paint a picture? Are these totally different intellectual activities? Eugene S. Ferguson points out that “the designer and the inventor, who bring elements together in

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new combinations, are each able to assemble and manipulate in their minds devices that as yet do not exist.” Is it any accident then that the

steamboat designer, Robert Fulton, had earlier been a painter of portraits

and landscapes; and that the telegraph perfecter, Samuel Finley Breese Morse, had earlier been a painter and first president of the National Academy of Design; or that John Fitch, a pioneer in steamboat naviga-

tion, had earlier been in turn a clockmaker, brass founder, silversmith, and surveyor? As Brooke Hindle, the historian of science and technolo-

gy, points out, who better than a surveyor, a designer, or an artist could

picture in the mind’s eye the trial placements of critical parts and adjustments of their size and shape, and who better could envisage the resulting device as a system in use by people for their daily purposes? It was not necessary for Chester Carlson to have had a painter’s background to initiate one of the greatest enterprises of our times, known in

one part of the world as Xerox, in another as Rank-Xerox, and in yet an-

other as Fuji-Xerox. He had the equivalent in his previous experience— as an inventor—when he conceived xerography. In his mind’s eye he rose to the larger view, of users and use, of what a simple method of copying would do for a civilization dependent as never before on the easy flow of information. From that vantage point he could see what was missing in the way of system and parts. He could start his long struggle to fill the gap by the marriage of unfamiliar physics and yet-to-be-developed engineering. What followed is well known. Carlson, now in the grip of his greatest conception, went from company to company trying to get one that would

back his idea. All said no. How could any already existing industry possibly put together the necessary constellation of talent? Whoever was tempted to say yes to the idea today knew that tomorrow he would be confronted by an impossible combination of challenges: Start by illuminating the master text with brilliance and reliability. Build an unusual lens inexpensively and accurately. Image the master on a selenium cylinder. Guarantee photoelectric charge-up of that selenium surface. Discover a powder that would seek out unerringly this electric charge. Transfer this powder to the copy paper. Make it stick. Build a mechanism to bring

about all the necessary motions with the right timing. Guarantee that the

mechanism will work over and over again, not hundreds of times, not thousands of times, but hundreds of thousands of times. No one in his senses would touch such a hydra-headed enterprise with a ten-foot pole. Defeated in selling his undeveloped idea to any company, Carlson

took it to the Battelle Memorial Institute of Columbus, Ohio, the largest

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not-for-profit research organization in the world. It offered the wide range of expertise and the interim financial backing that he needed. This is not the place to tell about all the technical problems that had to be overcome or the years of work required. Neither is this the occasion to describe all the judgment it takes, when such a baby is at last alive and well, to find the right foster parent to take it over. The company must not be too large. Otherwise the new development does not receive the urgent attention of the top people. Neither must it be too small. Otherwise the capital and the sales force are lacking. The Haloid Company of Rochester, New York, had the right size and the right management. Moreover, it had the most powerful of all incentives to go into a new enterprise: Haloid’s traditional photographic market was shrinking and it would go out of business unless it could find a promising new field of endeavor. It is no wonder that Haloid looked with the greatest interest at the invention of Carlson and the impressive development of that invention by Battelle.

Joseph Wilson: “Find Economic Feasibility” Why, at this stage, did not everyone leap at the opportunity to pioneer one of the greatest industries of our times? In a private conversation some months ago, the vice-president of one of the world’s largest companies revealed that he and a committee working with him had evaluated xerography for his company at the time when Haloid was considering it. “No, no,” the committee had advised the management.

possibly be interested in buying such probably can make the device operate way to make it economically feasible.” firm, Haloid, could foresee as clearly as

“No one could

an expensive machine. Battelle but we certainly can never find a This problem of price the smaller the larger company.

Joseph Wilson, the leader of Haloid, had the two advantages that Ein-

stein also had: first, unsurpassed motivation; and second, the larger view. In this case “the larger view” meant an appreciation of the worldwide in-

terplay of technology, business, and tax laws, and the potential economic impact of fast and inexpensive copying. From this vantage point the missing element became clear, a proper pricing policy. Joseph Wilson filled the gap. He came up with the winning idea: don’t sell, lease; and add to the lease charge a use charge of so much a page. That second, commercial, invention brought economic feasibility. It was indispensable for the success of Chester Carlson’s first, technological, invention.

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The Well Driller and the Chemist: “Reach Harmony Through Intuition” “Seek the larger view—and from that vantage point, recognize the miss-

ing element, and fill the gap.” Most fields of pioneering endeavor are not

well enough surveyed to be entirely accessible to logical analysis. In such fields, as Charles Kettering, an early director of General Motors Research and Development, once put it, “Beware of logic. Logic is an organized way to go wrong—with confidence.” One would do better to call on another human faculty, judgment, defined by du Pont’s George Graves as “an awareness of all factors in the situation and an appreciation of their relative importance.” For the beginning of that “apprecia-

tion,” judgment generally has to call intuition to its help, intuition defined as “the power of knowing or the knowledge obtained without recourse to inference or reasoning; insight; familiarity, a quick or ready apprehension.” Let us turn for illustration to the humblest “seeker of the wider view” of them all, a most improbable person, the countryside driller of wells. He is no geologist, but he knows something of geology, the folds and

strata of the local rock, which are porous and which are not. He is no

historian, but he knows enough of the history of wells drilled in his county to know which were dry and which gave water; what their depths

were, and what their yields. He is no reader of Einstein, but what Ein-

stein told us of his search for the laws of nature the well driller knows from his own seeking for the right places for his wells: “There is no logical path leading to them. They can only be reached by intuition based upon something like an intellectual love of the objects of experience.” The provider of wells is no psychologist, but as he surveys the land around the farm he realizes that his intuition is blanketed out by the

worried questions of the farmer about the cost, the refrain of worry from the farmer’s wife and children, and the gratuitous but conflicting advice of the neighbors. Einstein sought and found quiet for his meditations. The driller cannot find quiet. He has to create it. For that purpose he uses the invention of a wise man of long ago. He holds up a willow wand, utters some abracadabra, and finds that silence reigns. He can lis-

ten undistracted to the inner voice and seek the wider view: “Over there

to the east on firmer ground I got a good well. Down

that way

is a

brook. From it to and past the farm runs a ledge. Halfway up that hillside another man once drilled a dry well.” From the vantage point of this view he goes on to recognize the previously missed indication of

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water. He feeds all the facts and indications into his mental computer,

picks the spot, lowers the willow wand, finds everyone nodding ap-

proval, and starts to “fill the gap,” to drill. Where more compactly than in this homely example does one see what Einstein called “intuition based upon...

. an intellectual love for the objects of experience”; or

where else the combination of motivation and sense of harmony that we

associate with the “seeker of the larger view”? An able chemist once asked me to suggest a good new material for a fuel cell. I had seen enough of him, and knew enough of his work, to realize that nobody in the world knew more about fuel cells than he. On the physics I knew I couldn’t possibly help; but I think I did on the psychology. I told him to get himself the paraphernalia of a seer, an oracle, a fortune teller; to sit before the table, draw the red velvet curtain shut,

and stare into the great glass ball. Whatever the means chosen to promote intuition, it lets the mind peacefully make its way through the pasture of memory to the larger view—and from that vantage point lets it recognize what is missing.

Norbert Winter and the Insurance Company: “Build a Model” “The seeker of the wider view” has to depend on intuition on some occasions but on others he does better to develop and exploit a mathematical

model. No such model is better known than that given for economy in the famous book of John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Today there is a big business in the making of mathematical models for individual firms, entire industries and such world commodities as copper and oil. What else is “microeconomics” and “macroeconomics”? Historically, physics has been one of the great devel-

opers of models and purveyors of models to other areas of endeavor. The

pendulum, the best known example, is also one of the oldest. Who has not

learned from it to speak of equilibrium, natural period of vibration, damp-

ing, excitation, and resonance? And who has not used these terms, if not

the beautiful and far-reaching mathematical analysis that goes with them, in understanding phenomena where no pendulum is seen, phenomena as diverse as the shaking of a bridge, the rise and fall of tides, the flutter of an airplane wing, and the damage-producing power of an earthquake? Today, no field of physics is more imaginative than elementary parti-

cle physics in conceiving and analyzing models for the interactions going

on in multicomponent systems.

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In 1974, a Munich student of elementary particle physics, especially gifted in the analysis of such mathematical models, and having received his degree, decided to move to new territory. His professor, director of a Max Planck Institute, thereupon recommended to one of Germany’s great insurance companies the young man with this (for them) unprecedented background. Today Norbert Winter occupies an important position in the company. His talent for building simple models and thus capturing central features of elementary particle transformations he put to use, upon arrival in the new organization, to seek and win a wider view by constructing—with a colleague—a “dynamic balance model” of a smaller company in the field. From that vantage point—and after a year of selling experience—he recognized from a further simple model calculation a missing element in the industry. Important tax consequences of a new German pension law were going unappreciated and unexploited by anyone. He saw how to fill the gap. His company offered gap-filling insurance contracts and sold them. Today they make up one of the major segments of its business. His model gave a harmonious view of the whole field that had proved difficult to come by for people accustomed to work with bits and pieces. A good model displays the simple central point of what has seemed a complex situation.

Helmholtz, Kelvin, and Tukey: “Serve as Science-Technology Generalist” “Rise to the larger view—and from that vantage point recognize what is missing, and fill the gap.” Do this not once every several years, but many times a year; and don’t count on one man to do it all; let someone come into the picture who is good at inspiring and guiding others in this

work. He is the scientific generalist described by Bode, Mosteller,

Tukey, and Winsor! or, more appropriately for our present purpose, the science-technology generalist.

It is difficult to say where a generalist cannot contribute. It is easy to

say where he can and does: in innovative industry; in an institutional

group located in a government, a university, or a foundation; in the guidance of work or policy wherever “the problems are broad enough to re-

quire a group instead of a few isolated researchers”; and in fields as widely varied as economics, medicine, and biology, engineering, and so-

cial, military, and political policy.

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No investigators were better known in their day as scientific general-

ists than Hermann

von Helmholtz and William Thomson, Lord Kelvin.

Inspiring and guiding others, the one contributed importantly to fields ranging from physiology to mechanics, and from ophthalmology to electromagnetism; the other, to subjects from thermodynamics to the com-

pass and from the tides to the Atlantic cable. What would these two men think of the combination of talents and the

training recommended? for one who would serve as a science-technology

generalist in our day? It is enough to run through 16 of these items!

1. “Recapture the universalist spirit of the early natural philosophers.” 2. “Learn science and not sciences.” 3. Know in capsule form the dozen central concepts of each of the

major sciences. 4. Learn “the habits of mind of the chemist, psychologist, and geologist.” 5. Use “in each science some of the intellectual equipment of the other sciences.” 6. Be “exceptional in. . . breadth of appreciation.” 7. Be able in “biological and medical science” to “suggest physical explanations or mathematical models for known or conjectured facts.” 8. Be familiar with forging and milling, the function of a turret lathe,

the kinds of heat treating used and their effects, what an industrial still looks like, and how it operates and with industrial processes generally. 9. Deal enough with systems problems to know how to make parts “into a balanced whole,” whether this means “weights that are balanced,

or sizes or complexities of component pieces of mechanism, or expense or efforts or research time applied to different phases of the problem.” 10. Be experienced in design of experiments. 11. Be well practiced in “judging, guessing,” estimating, and predicting. 12. Be practiced in data analysis and in mathematical methods and techniques. 13. Be practiced in the “scientific methods of description and model

construction” as “in many ways the most efficient techniques yet devised

for covering a broad field quickly.”

14. Do not become baffled and uncomfortable—like so many specialists—“when confronted with unfamiliar and ill-defined issues.” 15. Know how to “isolate critical elements, establish the essentials of the logical framework, reduce the problem to a few critical issues.” 16.

Know “‘How To Say What You Mean’ orally and in writing.”

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An impossible course of training for an impossible profession? Perhaps this is the moment to apply to the science-technology generalist

what Einstein said about the work of a scientist, “Don’t listen to what he

says, look at what he does.”

No one is better known in our day as a science-technology generalist than John Wilder Tukey, for many years a colleague of Einstein in Princeton. He has become famous in his role of generalist, pushing experts by his questions to think as they would not otherwise think and act as they would not otherwise act. Statistics is his magic weapon in seeking the larger view. The generalist so armed may not have a single new fact to supply. Like the statistician R. A. Fisher of an older time coming fresh to genetics, the statistician of today may have to start as a child in the new field, convinced however through long experience that out of the clutter of facts that confront him some larger harmony can be seen. Of all generalists none spans a greater range. Tukey, as the chairman of a committee on

impacts of stratospheric change, has exerted a decisive influence on policy on chlorofluoromethane release. Similarly, acting as a generalist, he has strongly affected the policies of more than one country on chemicals and health, on governmental statistics, on environmental pollution, on ed-

ucational testing, on detecting underground nuclear explosions, and on regulating stream pollution by use charges. Also, in science itself, as a science-technology generalist he has altered the direction of work of many experts, inspiring early applications of spectral analysis to oceanography and geophysics and pioneering the concept of the “fast Fourier analysis”

that is so central to so much of the instrumentation in use today in

medicine and industry, as well as in academic and government research.

His unique new book, Exploratory Data Analysis, is the breed of statisticians to whom the whole world beckons deavor, happy hunting ground for all who “seek the wider Generalists are turned out less and less—and are needed

bible of the new as a field of enview.” more and more.

Czech Choose-as-you-go Film and Bruno Ante’s Group: “Make Decisions by Interaction with Alternative Scenarios” “Seek for the wider view” in science, or in conceiving a new technology,

or in finding economic feasibility, or in some other realm. But how is one

to seek for the wider view in making the right decisions about the future?

The future is out of reach. It is at the mercy of the unpredictable decisions of others. Yet the future, as Charles Kettering once put it, is “where

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I expect to spend the rest of my life.” Where is tomorrow made if not by

the decisions of many a today? Of the world’s 21 greatest needs as recently identified and studied by Battelle, one was singled out as “of almost overriding importance: Improve the presently inadequate methods for decision-making in complex situations.” The 20 other problems ranged from hunger to war, overpopulation to nationalism, and from energy to the malfunction of institutions. Every one of these difficulties “would be far less pressing,” the report went on, “if proper decisions had been made before the problem reached crisis proportions.” But how? How is one to scrutinize a future that is inscrutable? How is one to interact with a future that is out of reach? Is there any other solution except imaginatively to bring it within reach—and interact with it? Ina world that is often lacking in imagination and foresight that calls for mag-

ic. Perhaps then a few Czech film makers, or a few German Wirtschafts-

prognostikers might know the beginnings of a little magic.

As we took our seats in the little theatre, we congratulated ourselves that in spite of the long wait in line we had finally got into this

Czechoslovak fantasy, one of the most popular of all the attractions at the 1967 Montreal International Exposition.? As the lights were going out we noticed the green button and the red button installed inside each seat arm for voting “yes” or “no.” The film began, unfolding a charming anima-

tion in the spirit of Little Red Riding Hood. The bad and the good began to reveal themselves, and also the character apparently good but really

bad. The drama rose, and with it came a revelation and a chase. The pur-

suer had almost caught the pursued when the film stopped, the lights went on, and the announcer stepped forward. “What happens next is for you to decide,” he explained. “Vote yes if you want him to escape; otherwise, no. Each of you has one green bulb and one red bulb showing at

the front of the theatre around the border of the proscenium. Push the

button of your choice to make your vote light up.” The border did not

take long to come alive with red and green lights as we onlookers elected

“capture” or “escape” and pushed the appropriate button. We could all see that the vote favored escape. The lights went out and projection resumed. There was an exciting escape, much more, and eventually another point of crisis and another vote. When the film ended, we were offered the possibility to go back to the original point of choice and change our decision from “escape” to “capture.” We accepted. A revised projection began. It started with the capture.

The dramatis personae were unchanged. Their character traits were unal-

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tered. The course of the drama itself, however, had been transformed completely in clear consequence of the one decisive audience-voted change. “See vividly, or let others see vividly, the future consequences of present decision.” Is any point more central to what the decision-making process ought to be and someday will be?

If “imaginative interaction with alternate scenarios of the future” is the

key requirement, and has been explored in one way by the Czech creators of the choose-as-you-go film, it has been reconnoitered in another way through the Abteilung Wirtschaftsprognostik of Battelle-Institut e.V. of Frankfurt, through Bruno Ante and.his colleagues. They have helped a North German community to make up its mind whether or not to implement a new transportation technology and by what route it wants its new rapid transit line to snake through the city. They met evenings over a period of months with working groups of officials and concerned citizens. Two alternative but ever evolving scenarios for the route and for its economic and social consequences provided the backbone of the study sessions. The drawings and prices together with the demographic studies and traffic estimates associated with each alternative led to questions, objections and proposals. These reactions led to much hard work in intervening days and new studies, giving fresh numbers and projections. They led in

turn to further questions, objections and proposals. But then one of the townspeople suddenly conceived a new route that combined most of the

best features of the other two. With further examination and modification

it eventually won approval, and moved ahead to realization. Part of this projection of alternative futures is familiar to every archi-

tect of a major project. The new feature is the early involvement of the community of those affected. To guide this large-scale interactive devel-

opment of scenarios, those skills were essential which the Frankfurters

had acquired by special training: (1) practice in guiding meetings, (2) impartiality, (3) preventing confrontations, (4) eliciting the best thinking of those present; and between conferences (5) digging out quickly themselves, and getting others to dig out or develop, the newly needed facts and figures, (6) testing in advance that their information is bias-free and

battle-proof, and (7) imparting maximum impact to the two alternative scenarios for each new meeting. One of the most important of all ways to “seek the wider view—and

from that standpoint see what is missing and fill the gap” will surely someday be to “make decisions, or help others to make decisions” —as

did our Czech and German friends—“by promoting imaginative interac-

tion with alternative scenarios of the future.” Such a “jump into the fu-

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ture” is no jump if the scenarios are not vivid—prods to the imagination and to action—and truthful guide to correctness of action. Unbelievably rich prospects to “make vivid” lie waiting in today’s technology of sight and sound; to “make truthful,” in today’s power to assemble the best thinking on whatever topic. This audio-visual technology and this information capability make possible the “jump into the future”; but its use is inevitable. What other way offers itself for community, nation, or world intelligently to avert crisis?

What Makes the Seeker? What makes the “seeker of the larger view?” Different aptitudes surely

characterize (7) the one who finds, or helps others to find, the larger view of the future, (6) the science-technology generalist, (5) the one who provides a wider view by building a model, (4) the user of intuition, (3) the

finder of economic feasibility, (2) the creator of an engineering system, and (1) the discoverer of new unity in science. More interesting for us

here than these differences, however, is the faith that drives all these seekers: the faith that the larger view exists, it can be found, “I” can find

it, “I” will see from it what is missing, and “I” will fill the gap. In brief,

each believes in “harmony.” He may not know the word, nor how Einstein and Spinoza used it; but he lays his course with the conviction that

the world—or at least that part of it with which he is occupied—is ruled,

not by chaos, but by understandability.

How did Einstein, or how does anyone, acquire a faith in this larger

view so powerful as to take control of his life? The traditions of the family and the community are important, education counts, but is there anything more central than a role-model? Do not Thomas Mann and Erik

Erikson and other analysts of achievement tell us that each one of us models his or her life consciously or unconsciously on someone who has

gone before? If they are right, can one name anyone closer to being rolecreator for Einstein than Spinoza? The young Einstein had a few close

student colleagues, and those still closer colleagues he met in books,

from Leibniz and Newton to Maxwell and Boltzmann; but closest of all

was Spinoza. No one did Einstein admire more; and no one expressed

more strongly a belief in the harmony, the beauty, and—most of all—the

comprehensibility of nature. In a letter to his close friend, Maurice Solovine, Einstein wrote, “I can understand your aversion to the use of

the term ‘religion’ to describe an emotional and psychological attitude

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which shows itself most clearly in Spinoza. [But] I have not found a bet-

ter expression than ‘religious’ for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason.” Where

else than from a great man animated by a great faith can one better ac-

quire a great vision? What more than anything else do I want to say about the life and work of the “seekers of the wider view,” including Einstein himself? He—and

they—have a happy, and useful, outlook because they feel that the world, or the part of it that they have to deal with, is in some way beautiful and

understandable.

A lecture presented at the Science Policy Foundation, London, Friday, March 2, 1979.

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Maria Sklodowska Curie

and the World of the Small

he month of October 1867 that brought Maria Sklodowska into

the world saw James Clerk Maxwell winning new insight into

the laws of electromagnetism. Four years later, in the same month of October, while she sat pouring water from one bottle to another and asking her childhood questions about how and why, Maxwell was delivering his introductory lecture on experimental physics at Cambridge University. After describing the new facilities and stressing the importance of experimental work for the young man and for society, Maxwell offers his vision of physics: “Two theories of the constitution of bodies have struggled for victory with various fortunes since the earliest ages of speculation: one is the theory of a universal plenum, the other is that of atoms and void.” Maxwell went on to note that “the molecule . . . is a very different body from any of those with which experience has hitherto made us acquainted. “In the first place its mass, and the other constants which define its

properties, are absolutely invariable; the individual molecule can neither grow nor decay, but remains unchanged amid all the changes of bodies of which it may form a constituent. “In the second place it is not the only molecule of its kind, for there

are innumerable other molecules, whose constants are not approximately,

but absolutely identical with those of the first molecule, and this whether they are found on the earth, in the sun, or in the fixed stars.

Lam forced to believe that these molecules must have been made as they are from the beginning of their existence. . . . [The] idea of the ex.

istence of unnumbered individual things, all alike and all unchangeable, is one which cannot enter the human mind and remain without fruit.”

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Maxwell concludes with the question, “But what if these molecules, in-

destructible as they are, turn out not to be substances themselves, but mere affections of some other substance . . . a uniformly dense plenum... ?”

Four themes in Maxwell’s account deserve attention as representative of physics a century ago. First, he was stating his belief in the indestruc-

tibility of the atom at the very time that a little girl in Warsaw had started—without herself yet knowing it—on the road to radium and the transmutation of the atom. Second, Maxwell is modest about electromagnetism. Hardly a word does he say about that branch of physics, and nothing of his own contribution to it. He may have thought of the electromagnetic field as the magic “plenum” out of which every material object is to be constructed, but he does not make this identification in print. Not only Maxwell was modest about electromagnetism a hundred years ago. Everyone was. As

late as 1900, and despite the achievements of Hertz, most German

uni-

versities considered electromagnetism so little important as not to deserve any course of lectures. Even the great Kelvin declared in 1903 that he could not believe Maxwell’s theory.

Third, Maxwell says nothing of the possibility that one simple law

might account for the structure of every molecule and for all of chemistry. Reason enough there was in his day to discount such ideas. In the first half of the nineteenth century the great chemist Berzelius had proposed that all

chemical forces are but manifestations of electric forces. The idea excited

investigations by many workers. Eventually the hypothesis was discredited. The homopolar bond: How can one oxygen atom attract another oxygen atom if identical electric charges repel? Homopolar forces, ionic

forces, Van der Waal’s forces, valence forces; how can all this variety of

magnitudes and particularities possibly be compatible with electric forces,

pure and simple? No wonder that Maxwell had turned from the mystery of the individual molecule to the safer ground of statistical mechanics! To

him the domain of the small had become a crowd of flying molecules, col-

liding with one another, those collisions described by one or another em-

pirical law of force. It was a world of black box machinery. If there was a great principle behind it all, that principle was hidden by a hundred details. Finally, despite all the complexities of phenomena as they appear to the eye, Maxwell held fast to the long-term dream of an underlying unity. Yet to him “unity” meant not so much one law as one substance.

Can we capture in a single word the physics of a hundred years ago as we see it through the eyes of Maxwell? How better can we name it than

the physics of substance? The elementary substances were indestructible.

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In the structure of substances electromagnetism played a minor role or no role at all. The varied substances found in nature might or might not be

made of one common substance.

Law Above Substance From a physics of substance we have moved far in a hundred years towards a physics of law. The study of substance revealed law. Law in turn explained substance. Three laws the great investigators gave us: the relativity principle,

both special and general; the quantum principle; and electromagnetism.

Electromagnetism, already discovered, was in effect rediscovered when

at last it was taken seriously in the world of the small. To that end no one

contributed more than Marie Curie. Without her radium where would Rutherford and Marsden have found their projectiles? How would one have penetrated to the universal electric law at the heart of every substance? To the great discovery of the quantum principle nothing drove Planck

more surely than his determination of many years to study a thermal

property of nature free of all reference to solid state physics and free of unsolved issues about the constitution of atoms and molecules. That each law came to light only by abstracting away from the properties of particular substances shows nowhere more clearly than in the well-known history of relativity. The unbounded dominion of a basic physical law never ceases to be a source of awe. Who a hundred years ago, measuring the attraction be-

tween electric chargers, and testing the Coulomb law at distances from

meters to millimeters, could have predicted that it would be proved valid

in 1911 to 10-!' cm, in 1933 to 10-!3 cm, and in still later times to still

smaller distances? Who expected that the quantum principle would apply to everything from the molecules to nuclei, and from an elementary particle to a superconducting loop a meter in circumference? Who that heard Einstein in 1915 could have anticipated that by 1922 general relativity would predict, and predict correctly, long before it was observed, so fantastic a phenomenon as the expansion of the universe?

Colleagues in the Search for Law If the sad and lonely figure of Mme. Curie touches anyone’s heart, and if he hears from those who knew her that she never smiled, let him read her

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works. A new step forward, by whomever made, captured her admiration. To her the search was one great enterprise; and all searchers, partners. How did she respond to the movement from a physics of substances towards a physics of law? She welcomed the new laws, she followed them,

she preached them. Speaking very early in the 1900s of the law of conservation of mass and the law of conservation of energy she says, “Recently an admirable synthesis has made it possible for us to attain a still higher degree of generalization through the union of these two principles, for it has been proved that the mass of a body is proportional to its internal energy.” In 1933 she expounds the quantum mechanical theory of penetration through a potential barrier. In her last book, the two-volume treatise on radioactivity that appeared only in 1935, the year after her death, she

surveys among other foundation areas of physics both quantum theory and relativity. She emphasizes that “the proper time of a system is the only time that is accessible to experience” and goes on to clarify the distinction between special relativity and general relativity.

Chemistry as Physics and Physics as Chemistry If abstracting from substance led to simple law, then in turn simple law unravelled the hundred puzzling details of substance. Chemistry became physics—and much of the physics of substance became transformed into a new and broader chemistry. What difference in principle was there after all between the bonding of atoms in a molecule and the binding of atoms in a solid? What distinction between the pairing of electrons in a superconductor and the pairing of electrons in a giant dye molecule? What sets off the photoelectric energy of an electron in a metal from the valence

energy of an atomic electron? All of these effects and much besides reduced to the dynamics of fast moving electrons and slow moving nu-

clei—and to nothing more. If, nevertheless, much of chemistry looked complex, how could it be otherwise when the bindings at stake were the

very small residuals of much larger energies! Complex or not, the mystery of chemistry had to yield once J. J. Thomson had discovered the electron in 1897 and once Niels Bohr had shown in 1913 that this electron moves obedient both to electric forces and to the quantum principle. Still it was not easy for the imagination to grasp what organizing power the quantum principle possesses. In en-

counters in the mid 1920s more than one physicist told his colleague from the laboratory across the way, “Your chemistry is now passé. All

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that jumble can now be explained in terms of electrons and quantum

numbers.” In more than one case the then-justified reply came back,

“What makes you think your circular and elliptic orbits have anything to do with chemistry? Have you ever heard of the valence angles of ammo-

nia or the tetrahedral bonds of carbon? Don’t ever forget that electrical forces are electrical forces and chemical forces are chemical forces.” Before Heitler and London could explain valence forces, de Broglie, Heisenberg, and Schrédinger had to clarify the quantum principle. Today no one doubts that the Schrédinger wave equation plus simple electroStatics account in principle for all of chemistry. Yet no surer way could be found to stop the advance of chemistry than to require everyone to calculate the wave function of his new compound before making it. Not the contemplation of 600-dimensional configuration space, but the analysis of the regularities between molecule and molecule, proves the fruitful way to make progress. After all, will not an electron revolving within a molecule always provide us with our cheapest analog computer? What better procedure is there than to use nature’s own computer when the energy of binding is the very small difference between the very much larger total energies of the associated and dissociated states? If during the life of Marie Sklodowska Curie chemistry learned from physical law to master the machinery of molecules and metals, today chemistry has added the nucleus to its domain of interest. Call it nuclear chemistry or nuclear physics as one will, it is remarkably similar to molecular chemistry and atomic physics in its history and way of thought. In both cases the really rapid advance in understanding only began with the identification of the dynamic entity: the electron in 1897, the missing nucleon in 1933. Approximate orbits and quantum numbers we have for nucleons in the nucleus as for electrons in the molecule. The analysis of

the regularities from nucleus to ties from molecule to molecule, understanding than any attempt speak with admiration when we

nucleus, like the analysis of the regularioften provides a better answer and deeper at a calculation from first principles. We speak of nuclear chemistry!

Marie Sklodowska Curie and Nuclear Chemistry Though the great progress in the chemistry of the nucleus took place after her death, Mme. Curie contributed actively during her life. At the famous Solvay Congress of 1913 she calls attention anew to the mystery of

the exponential law of radioactive transformation. She stresses the exper-

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imental evidence that an atom, if it has not yet decayed, has not aged at

all, no matter how long it has lived. She finds physics forced “to look in the interior of the atom for the element of disorder necessary to explain the application of a law of chance.” She brings forward the suggestion of Debierne, first, that in the center of the atom there may exist an effective

temperature much higher than the external temperature; and second, that the mechanism involved may be identical with that of a monomolecular chemical reaction. She ask us to imagine “a molecule which is moving

about in the interior of a box endowed with a tiny hole.” She goes on the

say, “When the molecule in the course of its motion meets the hole it leaves the box and the system is radically changed. If we have a great number of boxes each containing one molecule, and if the initial veloci-

ties and positions of the molecules are random, it may happen that the escape phenomenon is governed by the rule of chance, even though the constitution of the system itself is relatively simple.” Of all those who have read these wonderfully clearly expressed ideas in recent days, none can have been more astonished to see them than I,

who in 1939 had the honor and pleasure in association with Niels Bohr to follow exactly this line of reasoning to its logical conclusion, and end up with the now standard formula for the rate, A, of a spontaneous transfor-

mation in terms of the level spacing D and the effective number of open

channels, N:

T=

ha = (D/2n)N.

Mine. Curie was in advance of her age. She put forward the right idea to describe nuclear fission at an epoch when she had to do with the leakage of alpha particles through a potential barrier! No one had a more active concern than she did to distinguish between the nuclear electrons and the extranuclear electrons. When finally it became necessary to conclude that beta rays are formed at the moment of

transformation rather than existing in advance, no one could cite more

promptly than she the remark of Aston that the smoke does not exist in the pistol until the trigger is pulled!

The Distant Past In distinguishing between extranuclear electrons and nuclear electrons

Marie Sklodowska Curie recognized the proper boundary between molec-

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ular chemistry and nuclear chemistry; but she also knew when an idea from the one field could illuminate the other field. Does the abundance of various molecules on earth today reflect the chemical history of our planet

in the recent past? Then may not the abundance of the various nuclei reflect the history of a hotter and more distant past? She ends her book

L’isotopie et les Eléments Isotopes with these words, “It is important to

continue actively the determination of precise atomic weights, with strict attention to source and purity. If differences appear, they may perhaps give clues to the conditions to which matter was subject in the distant

past.” Prophetic prelude to all we know today of the building of the elements, thanks not least to Gamow, Fowler, the two Burbidges, and Hoyle!

No New Law Physics and chemistry continue together today Puzzles are encountered, then by skilled hands through ceaseless activity new knowledge day minion of old law. Knowledge grows, but the quantum idea flowered into wave mechanics

change in fundamental principle.

their fruitful married life. regularities are found, and by day is added to the dolaws do not. Not since the in 1925 has there been a

Elementary particle physics has given us many beautiful regularities but no new law. Regularities in beta decay, the concept of strangeness and strangeness-conserving currents, marvelous symmetries among the particles, and many another result of recent times excite our imagination. Fascinated as we are, we also ask, are we not seeing simply the unfolding of a third and still more gorgeous branch of chemistry: an “elementary particle chemistry”? We are entranced that the product of charge symmetry and parity mysteriously changes in the decay of the K2 meson, and we are on the alert for something new—with good reason! Did not the mysterious disappearance of energy in the beta decay

of atomic nuclei reveal the neutrino? Or in an earlier day, did not the ro-

tation of the plane of polarization of light lead to the discovery of stereo-chemistry? Chemistry, chemistry, chemistry! The Okubo formula

for the masses of the elementary particles—does it not recall other tri-

umphs: Aage Bohr’s formula for the energy levels of a nucleus, Racah’s formula for the energy levels of an atom, and Bethe’s formula for the

splitting of levels in the field of force of a crystal? Above all details do we not see in the world of the particles as we see in the other two

branches of chemistry the small and complicated residuals of far more

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powerful energies? What other explanation for structure has anyone ever found? In any case: regularities, yes; beautiful symmetries, yes; but new law, no. Not for 42 years! Is there a new law still to be found? How tantalizing, for us, not to know — and how fortunate for society! “I must find out”; how else could

people be brought to bind themselves together in laboratory superorganizations and drive themselves at such a pace? How else build the accelerators, invent the detectors, and develop the particle technology for some thriving new industry of tomorrow?

No one in chemistry or biology feels himself cheated because the rele-

vant physical laws are already known. There is challenge enough, and to spare, in unravelling fresh regularities and in finding new ways to put together old building blocks. So too in physics. And with each passing decade we understand the principles better because we have applied them to more issues. We believe in them all the more firmly because they have never let us down. Neither on earth nor in space do we know of any cloud to darken their light. The formation of new stars and the explosion of old stars and the greatest variety of events, gigantic in scale and in energy, make the universe incomparably more interesting than any fireworks display that anyone could imagine in his wildest dreams. However, in all this wealth of events not one single effect has been discovered which has led to a new law of physics, and not one single finding has ever been obtained which is generally recognized to be incompatible

with existing law.

A Time For Reassessment In Kelvin’s laboratory in Glasgow I saw a great rock, and a wire urged

to work left the sor of a of rock.

its way down through that rock by mighty weights. Kelvin had wire in tensed duel with its opponent in the hope that the succesdistant day would see some progress and measure the viscosity The new director spoke of the laboratory’s desperate need for

more space. He asked an associate, “How

long has this rock sat here?

“Forty years,” he was told. “Forty years?” came his response. “We will give it one more week!” If one laboratory director can reexamine the experiment that he inherited from another, may not one generation of investigators reexamine the “plan” of physics handed down by an earlier generation? Who among us has sworn eternal allegiance to the doctrine that there are endless great new laws around the corner? Or six? Or even

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one? No, our thinking has been locked to the “around-the-corner plan”

of physics, not by any attractions of an endless search, but by bewilder-

ment about the alternative. And what a bewildering and even stupefying alternative it is! (1) All the overarching principles are already in hand. (2) Relativity, electromagnetism, and the quantum principle supply the entire backbone of physics. (3) Einstein’s vision is to be taken seriously that particles, rather than being foreign objects immersed in geometry, are manufactured out of geometry—no other building material being available. (4) A particle is a quantum state of excitation of space, a “ge-

ometrodynamical exciton.” (5) Elementary particle couplings in all their variety, strong, intermediate, and weak, and with all their specificities,

are geometrodynamical in origin, as chemical forces of the most diverse intensities, and most marvelous directivities, are electrical in origin. In

brief, Einstein’s vision in today’s translation—the only alternative that we know to the “‘around-the-comer plan” of physics—is of unprecedented scope. No wonder it is fascinating to contemplate, supremely challenging to translate into calculations, and premature to assess!! Theory, no; vision, yes; a geometrodynamical

vision.

Marie Sklodowska Curie as

Copernicus of the World of the Small As we weigh the one plan the days and years ahead, main in our thoughts. We with such happiness for a

of physics and then the other, over and over, in may the face of Marie Sklodowska Curie resee her in her later years, packing her suitcase Solvay Congress, where she would walk and

talk again with Lorentz, Planck, Einstein, Ehrenfest, and Bohr.

We see the magic circle and see Planck speaking. He repeats his great and familiar message: there is only one truly fundamental length in na-

ture, a length free of all reference to the dimensions and rate of rotation of the planet on which we happen to live; free of any appeal to the complex properties of any solid, liquid, or gas; free of every teference to the mysterious properties of any elementary particle; what we call today the Planck length,

L = (hG/c3)"2 = 1.6 x 10-3 cm, and what we identify with the characteristic scale of the quantum fluctuations in the geometry of space.

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The light shifts, the figures are regrouped, and Einstein is giving his famous account of the quantum fluctuations that pervade the electromagnetic field in every part of space, forerunner of modern quantum electrodynamics—the greatest triumph of theoretical physics since World War 1l—and happy guide to the meaning of quantum fluctuations in the geometry of space at the Planck scale of distances. The Solvay Congress fades away, we are in an old shed in Paris, and we see a young woman working intently at her radium. She did more than anyone to open the door to 107 cm, as her countryman Copernicus did more than anyone to alert us to movement and meaning at the previously unimaginable distance of 10+!3 cm. Today, thanks not least to these great investigators, we see in our mind’s eye each decade of the distance

scale alive with its own special activities, from the expansion of the uni-

verse at 1078 cm to the form factor of the proton at 10-!© cm. Copernicus

directed our gaze out to the domain of the unbelievably remote, and to-

day we have come close to plumbing the greatest distances that we know how to conceive. The discoverer of radium by her life and work directs our gaze down to the world of the small. There many new decades of the distance scale still wait to spring into life and meaning, all the way from

101° cm to Planck’s 1093 cm. Marie Sklowdowska Curie is our Coper-

nicus in the still continuing voyage of exploration into the world of the unbelievably small. Address given at Warsaw October 16, 1967 on the celebration of the centenary of Marie Sklodowska Curie (November 7, 1867—July 4, 1934), as revised for publication.

Hermann Weyl and the Unity of Knowledge

ermann Weyl was—is—for many of us, and for me, a friend, a

teacher, and hero.

A North German who became an enthusiastic

American, he was a mathematical master figure to mathemati-

cians, and to physicists a pioneer in quantum theory and relativity and discoverer of gauge theory. He lives for us today, and will live in time to come, in his great findings, his papers and books, and his human influence. Among Weyl’s papers is his Columbia University bicentennial lecture, “The Unity of Knowledge.”! Unity? This world in which we live and have our being: What was it to Hermann Wey!1? Not to him did the poet’s

words apply,

Heaven wheels above you,

Displaying to you her eternal glories, And still your eyes are on the ground. The world to him was no dreary cavern; no, a miraculous panorama, exciting in him a passionate desire to capture its beauty, its order, and its unity. What can we learn from his search for unity? Remarkable issues connected with the puzzle of existence confront us today in Hermann Weyi’s domain of thought. Four among them I bring before you here as especially interesting: (1) What is the machinery of existence? (2) What is deeper foundation of the quantum principle? (3) What is the proper position to take about the existence of the “continuum” of the natural numbers? And (4) what can we do to understand time

as an entity, not precise and supplied free of charge from outside physics, but approximate and yet to be derived from within a new and deeper

time-free physics? In brief, how come time? What about the continuum?

How come the quantum? What is existence?

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Between four issues of such different flavor, can we hope at the end to

see the glimmerings of a linkage? Let me anticipate. Let me propose that we shall find the unity-bringing theme in Weyl’s own 1954 address on

the unity of knowledge: “the realm of Being is not closed, but open.”

Let us plot our course backward from our theme. The unity of knowledge? At the end. Just before the theme? Our consideration of those four great questions. Before the four questions? Some developments in

knowledge relevant to those questions: contributions of Weyl; further

findings since his day; and the driving force, straight out of the age of enlightenment, that impelled Weyl—and thinkers before and since—to apply reason to, and hope to make progress with, such great issues. And before this brief survey of some Weyl-related issues? A glimpse of Weyl himself.

The Man I last knew Wey] after I last knew him. Day after day in Zurich in late

1955 he had been answering letters of congratulation and good wishes

received on his seventieth birthday, walking to the mailbox, posting them, and returning home. December eighth, thus making his way home-

ward, he collapsed on the sidewalk and, murmuring “Ellen,” died. News

of his unexpected death reached Princeton by the morning New York Times. Some days later our postman brought my wife and me Weyl’s

warm note of thanks. I like to think he sent it in the last mailing.

I first knew Weyl before I first knew him. Picture a youth of 19 seated

in a Vermont hillside pasture, at his family’s summer place, with grazing

cows around, studying Weyl’s great book, Theory of Groups and Quan-

tum Mechanics,” sentence by sentence, in the original German edition,

day after day, week after week. That was one student’s introduction to

quantum theory. And what an introduction it was! His style is that of a

smiling figure on horseback, cutting a clean way through, on a beautiful

path, with a swift bright sword.

Some years ago I was asked, like others, I am sure, to present to the Li-

brary of the American Philosophical Society the four books that had most

influenced me. Theory of Groups and Quantum Mechanics was not last on

my list. That book has, each time I read it, some great new message. Erect, bright-eyed, smiling Hermann Wey I first saw in the flesh when 1937 brought me to Princeton. There I attended his lectures on the

Elie Cartan calculus of differential forms and their application to electro-

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magnetism—eloquent, simple, full of insights. Little did I dream that in 35 years I would be writing, in collaboration with Charles Misner and Kip Thorne, a book on gravitation, in which two chapters would be de-

voted to exactly that topic. At another time Wey] arranged to give a

course at Princeton University on the history of mathematics. He ex-

plained to me one day that it was for him an absolute necessity to review, by lecturing, his subject of concern in all its length and breadth. Only so, he remarked, could he see the great lacunae, the places where deeper understanding is needed, where work should focus. If I had to come up with a single word to characterize Hermann Weyl, the man, as I saw and knew him then and in the years to come, it would

be that old-fashioned word, so rarely heard in our day, “nobility.” I use it

here not only in the dictionary sense of “showing qualities of high moral character, as courage, generosity, honor,” but also in the sense of showing exceptional vision. Weyl’s eloquence in pointing out the peaks of the past in the world of learning and his aptitude in discerning new peaks in newly developing fields of thought surely were part and parcel of his lifelong passion for everything that is high in nature and man.

Weyl in the Larger Community of Learning Weyl belonged to the community of learning. He felt at home in the great wide world of thought. What that community is and what it means I first

fully felt in Sunday morning walks through the woods around the Insti-

tute for Advanced Study with Hermann Weyl, Oswald Veblen, and two or three other colleagues from other disciplines. Topics ranged from art to the history of the Renaissance, from Helen Porter Lowe’s current translation of Thomas Mann to Hella Weyl’s putting Ortega y Gasset’s Spanish into German and English, from mathematical logic to Europe’s nightmare, from movements to men, and from ideologies to ideas. To his computer pass the place where John von Neumann was developing was to see Weyl’s face light up with the delight of a small boy within

touching distance of fireworks.

Weyl’s new house was being built. Sometimes the walks took us there

to inspect the progress and note the architecture. Outside, its shape and flavor were new to the Princeton community.

Inside, when it was fin-

ished, order, calm, and beauty were the themes. From this place of happy

reading, reflection, and writing Weyl’s thought ranged out over Minerva’s many meadows.

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Not least for Hermann Wey! among the green pastures of the mind was art. His Vanuxem Lectures at Princeton University appear in that widely read and many times reprinted book, Symmetry.3 Nowhere more explicitly than here, in examples taken out of painting, symbolism, and the decorative arts, do we see the rich connections that his mind was forever making among art, history, science, and mathematics. Art was for Weyl not only an activity practiced by others. Art charac-

terized also his own way of thinking, writing, and speaking: art in the

sense of bringing disparate themes into harmonious unity. The chapters in Theory of Groups and Quantum Mechanics masterfully alternate between group theory and quantum mechanics, between mathematical methods and their applications, between the ideas basic for groups and the concepts fundamental for physics. Space Time Matter‘ skillfully

weaves together the deepest concepts of geometry with the physics of

matter and motion. And did anyone ever bring together philosophy, mathematics, and physics into a happier unity than Weyl does in his famous book Philosophy of Mathematics and Natural Science?® The grace and sense of style characteristic of the whole book is epitomized in one of its best-known passages: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along

the life line of my body, does a section of this world come to life as a

fleeting image in space which continuously changes in time.” If the painter-inventor moves things around on the screen of the mind

to make a new and greater thing, if Henry Moore mentally abstracts a

beautiful new form out of the whitened bones, ebony

carvings, and

rounded stones he chooses and lays before him each morning on his little

worktable, so—we can believe—Hermann Wey] by like artistry knew how to select from his rich storehouse the ideas needed at the moment

and push them about, this way and that, until they fell together in a new,

greater, and more wonderful idea. Art for him was ever green.

Literature for him was another nourishing pasture of the mind, from Goethe and Gottfried Keller to Rilke and Mann and from Shakespeare and Coleridge to Ortega y Gasset and T. S. Eliot.

Through the green fields of history Weyl walked, too, with the greats, from Thucydides and Pliny to Vico and Ranke, Burckhardt, and

Hesse. Surely it was from Wey] that I learnt that wonderful statement

of Burckhardt, in The Civilization of the Renaissance in Italy, about the

age-old human passion for superstition and astrology: “It is profoundly

instructive to observe how powerless culture and enlightenment were against this delusion, since the latter had its support in the ardentiimag-

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ination of the people, in the passionate wish to penetrate and determine the future.” Weyl knew as well as anyone that we cannot know who we are and where we are going unless we know how we got here. “All history in the proper sense,” he reminded us, “is concerned with the development of one

singular phenomenon: human civilization on earth.”® What it takes to do history, he adds, is not science, not mathematics, not a measuring device, but interpretation. Interpretation “springs from the inner awareness and knowledge of myself. Therefore the work of a great historian depends on

the richness and depth of his own inner experience.” How he would have applauded the motto of the distinguished historian Jack Hexter: “If you would read history, write history.” Participation is as necessary for understanding, Weyl recognized, as understanding is for participation.

In the field of economics it was enough, to satisfy Weyl’s wish for un-

derstanding, to know Winfield Riefler and Oskar Morgenstern. The scene comes vividly to mind of a cocktail party where Wey! was a guest, and guests, too, were Morgenstern and von Neumann,

working at that time

on their great investigation, embodied in their book Theory of Games and Economic Behavior. Lively as was their participation in separate knots of guests, one or the other would sometimes break off, draw his fellow investigator aside, and report some new idea that had just bubbled up out of his subconscious. Then back to the party. Weyl himself, in such close touch with this newly developing realm of knowledge, found his own imagination caught up in it. He even published a paper on the subject, beginning with this sentence: “J. von Neumann’s minimax problem in the theory of games belongs to the theory of linear inequalities and can be approached in the same elementary way in which I proved the funda-

mental facts about convex pyramids.”7 Colleagues? Wey! knew that nobody can be anybody without somebodies around. Teatime was for him a central point of the day, an opportunity, as Oppenheimer later put it, to “explain to each other what we do not understand.” And cocktail parties? None do I remember as richer in interesting colleagues and lively conversation about fascinating subjects than those given by Hermann Wey] and his wife, Hella. Weyl himself, so universally respected and beloved, at home in so many fields of thought, made one think of the words of Frederick II about Leibniz, in effect: “Founder of the Prussian Academy? He already was an academy!” Weyl was an academy. For Weyl to update in 1947 his great 1927 survey of philosophy, mathematics, and natural science was an enormous undertaking, understand-

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able only in the light of his passion for truth and unity. The marvelous

discoveries in the 30 years since his death would surely have filled him

with joy and reanimated his wish, harder now than ever for anyone to achieve, to capture for us all the larger unity of these findings.

Electricity and Geometry Before and After Weyl What is the role of electricity in the geometry of spacetime? Weyl came back to this topic in paper after paper and book after book. The perspec-

tives that he and his successors opened up are probably explored today, under the names of “gauge field theory” and “grand unified field theory,” by more investigators than there were in the entire physics community at the time of Weyl’s first paper in the field. Weyl invented the gauge con-

cept in 1918. By 1928 he had reformulated and restated the idea in the way it is still understood today: “Gauge invariance corresponds to the conservation of charge as a coordinate invariance corresponds to the con-

servation of energy-and-momentum.”®

In 1950 Wey] referred to the 1921 idea of T. F. E. Kaluza that gauge

invariance might be connected with the possible presence in the nature of

a fifth dimension.? He noted that O. Klein added to Kaluza’s idea the further conception, arising out of quantum theory, that the fifth dimensional part of the geometry is curled up into a very tight radius of curvature. This pregnant idea, students of modern particle theory know, has itself

taken 50 years to bloom. Today the gauge field at each point in spacetime

is envisaged as running, not around the one-dimensional rim of a tiny cir-

cle, but around an ultra-small cavity of much higher—perhaps six units

higher—dimension. The variations of the field in the several directions

describe not only the electromagnetic field but also the fields associated with neutrinos and all the rest of elementary particle physics. A particle

mass itself corresponds in effect to an organ-pipe resonance of the geometry in this tiny world—or, in mathematical terms,” fiber”—attached to each point of spacetime. Weyl, were he still living, would rejoice in the rich modern development of elementary particle physics and be contributing himself, surely, to putting the theory of gauge fields and fiber bundles into a wider and deeper mathematical and physical framework. Another insight Weyl gave us on the nature of electricity is topological in character and dates from 1924.19 We still do not know how to assess it properly or how to fit it into the scheme of physics, although with each passing decade it receives more attention. The idea is simple. Wormholes

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thread through space as air channels through Swiss cheese. Electricity is not electricity. Electricity is electric lines of force trapped in the topology of space. Niels Bohr, presented at one point with this thought, immediately

asked, “But will not any wormhole pinch itself off?” Subsequent calcula-

tions showed that, in the context of classical theory, indeed it will.!! Further consideration, however, has made it clear that one should deal not

with classical wormholes but with quantum fluctuations in the geometry of space, wormholes at the unbelievably small Planck scale of distances (on the order of 10-33 cm), giving a “foamlike” structure to space with these microscopic wormholes all the time and everywhere being created and annihilated, annihilated and created.!?

How are we to assess Weyl’s proposal, thus updated? That is a question not for today but for tomorrow. To deal with it is to work at the fron-

tier between quantum theory and general relativity, in that realm often called “quantum geometrodynamics,” one of the most challenging fields of research of our day.

General Relativity and Gravitation It is sometimes said today that no progress has been made in uniting gen-

eral relativity and quantum theory. No statement could be further from the

truth. We have possessed for years the appropriate wave equation. We have also known, through the work of Ulrich Gerlach,}5 that the predictions of this wave equation go over, in the so-called correspondence-prin-

ciple limit, into those of classical geometrodynamics. Recently we have seen applications of this wave equation, by James Hartle and Stephen Hawking,!4 to important issues of cosmology. But this whole field of investigation is so new and strange that we have still some way to go before

we have a proper notion what to make of Weyl’s idea that “electricity is a field trapped by topology.” But disregard it? Only at our peril. In astrophysics generally and cosmology in particular a fantastic

growth has taken place in the years since Weyl’s death, thanks to the existence of red shifts in stellar spectra (which show—he was the first truly to explain—that the universe is expanding) and a marvelous armament of telescopes, of not one kind alone, but four: x ray, optical, infrared, and

radio. Among all developments in astrophysics, surely none would have gripped his imagination more than the black hole, a star that has undergone complete gravitational collapse.

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Already in the earliest days of “gravitation-as-geometry” Weyl taught us a useful new view of a “mass.”!5 Draw a sphere around it. Stretch this

sphere out in time into a fattened world line, a world tube. What happens to a star cluster, a whole collection of masses interacting gravitationally with one another? Viewed in spacetime in Weyl’s way, it becomes a twisting, writhing pattern of world tubes. To predict that pattern, he explained, we don’t have to look inside the tubes.

Weyl’s way of looking at mass has a special relevance for a black hole—itself invisible—that happens to be paired with a visible companion. Weyl would be delighted today to find that the black hole is not simply an object of pencil and paper, that it really exists. We already have striking evidence for two black holes in the range of 10 to 20 times the mass of the sun.!® Each is invisible itself. Each by its powerful pull swings about in a tight, swift orbit a normal star which we can and do see. We see also x rays. They do not come from the black hole itself.

They come from gas spewed out onto the black hole from its normal neighbor. The inward-streaming gas is crunched up to high density, and therefore enormous temperature, by the powerful pull of the completely collapsed object. Hence the x rays. They fluctuate in intensity from millisecond to millisecond because of random variation in the density of the gas falling in, as the smoke coming out of a factory chimney fluctuates in its darkness from second to second. In addition to those two black holes of stellar mass there also exists at the center of the Milky Way, according to ever stronger evidence,!7 a black hole with mass about three-and-a-

half-million times the mass of the sun. Never has curved, empty space come more spectacularly to man’s attention than it does in black hole physics. Never has any branch of

physics been developed more fully and more richly on the basis of purely

geometric reasoning. And never more insistently than in black hole physics have we been driven to the very frontiers between gravitation theory and quantum theory.

From Black Hole and Quantum to “Information Has Mass” Jacob Bekenstein found himself forced in 1973 to conclude that the surface area of the so-called horizon of a black hole not only is analogous to entropy, it is entropy; the surface gravity not only is analogous to temperature, it is temperature.!8 This conclusion seemed so preposterous to Brandon Carter and Stephen Hawking that they set out to disprove it. Along the way Hawking discovered that marvelous process,!? now

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known by his name, through which a black hole—indeed endowed after

all with a Bekenstein temperature—can evaporate particles and radiation

(less than one watt, however, from a black hole with a the mass of the

sun, and less in proportion as the mass is greater). Black hole physics has led to one great discovery that has in it not one

word of black hole physics. I refer to the by now famous formula of Paul Davies and William Unruh.”° It tells us that an accelerated detector, located in cold empty space, will nevertheless, by reason of that very acceleration, experience and register a temperature, a temperature proportional to the product of Planck’s quantum constant and that acceleration. This result generalizes Bekenstein’s conclusion about the temperature at the “surface” of a black hole. The Davies-Unruh formula ties together three great domains of physics. One is relativity. The second is quantum theory. The third, heat physics or thermodynamics or statistical mechanics, is also at bottom a part of information theory. I know no more beautiful discovery in recent years, nor any that connects more instructively three fields of endeavor dear to Weyl’s thinking and writing. A brave new proposal of Bekenstein is now the subject of exploration by more and more investigators:?! that there is no device whatsoever that will store a given number of bits of information which does not have a product of mass and linear dimensions—expressed in appropriate units—

which is at least as great as that number of bits. Information is not dreamlike nothingness. What an incentive to put “information” into the

center of our thinking about physics! And to ask, is information the foundation for all we see and know?

From Genes To DNA and from Evolution to Teleology Information theory, Wey] knew, is central to the gene, the machinery of life, and evolution. “The mighty drama of organic evolution,” as Weyl

called it, was for him no domain of thought to be left to-a few specialists, but a vital topic of concern to every thinking person. He gave it an important place in 1947 when he updated his Philosophy of Mathematics and Natural Science. “The decisive point,” he suggests, “is perhaps this: when one deals with complex molecules consisting of something like a million atoms, the manifold of possible atomic combinations is immensely larger than those actually occurring in nature.” Combina-

tions capable of functioning as genes are extremely rare and can be

“found” only by a selective process that probes many possibilities and

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uses previously conquered positions as bases for further advance, slowly groping its way from simple to more complicated structures. “But this formulation of the problem,” he adds, “does not give more than the

vaguest hint for its solution.”2?

How Weyl] would have delighted in the DNA of Francis Crick and

James Watson. How fascinated he would have been by the “life ma-

chine” of Manfred Eigen and his Gottingen colleagues, showing as it does the stupendous variety of life forms that can develop, and emphasizing the role of what we can only call “accident” in deciding which shall come into being. How eagerly he would have studied those twin discoveries of John J. Hopfield: nature’s method of “proofreading” molecules and DNA, without which life would quickly end in disaster; and insights into how the coupling of neuron to neuron powers memory and memory search.?3

In what way did life begin? Weyl describes the idea of A. I. Oparin

that organic molecules, formed by chance processes and accumulated in favorable spots, in time built up—in the absence of enzymatic breakdown—to the concentration at which self-duplicating molecules could form.?4 He would have been interested in the proposal that droplets were the centers of accumulation and the place of origin of life,?5 and in the theory, more widely studied today, that it was clay which served as the

organizing material.?6

The concept that life fills every ecological niche was not new to Weyl;

but how interested he would have been in the 1978 finding of those stu-

dents of evolutionary history, V. Salvini-Plawen and Ernst Mayr, that the eye—the “window of the mind”—originated over and over again, independently, at least 40 times.2” What would he have said to the thesis of Homer Smith, so vividly expressed in his Pulitzer Prize-winning book,

Kamongo, that man himself may, from the standpoint of the future devel-

opment of the evolutionary tree, mark a blind alley of life? In contrast, Weyl himself, discussing theology, remarks that “the temptation of an in-

terpretation in terms of an overall plan of evolution is almost irre-

sistible.”?8 Could he have known that the distinguished physiologist

Christian Bohr, father of Niels Bohr, while wholeheartedly accepting and

supporting the Darwinian theory of evolution at a time when that position was not popular, nevertheless also felt that evolution, understood

deeply, would prove to be compatible with ultimate purpose? Teleology, come into physics? How? “Is it conceivable,” Weyl asks, “that immaterial factors having the nature of images, ideas, ‘building plans,’ also intervene in the evolution of the living world as a whole?”

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Bohr’s Great Smoky Dragon The question about teleology that Wey] put to himself we have more

temptation than ever to put to ourselves in this day, when the deeper lessons of quantum theory are so widely perceived. The idea is old that the past has no existence except in the records of today. In our time this thought takes new poignancy in the concept of Bohr’s elementary quantum phenomenon and the so-called delayed-

choice experiment.” Ascribe a polarization, a direction of vibration, to the photon that began its journey six billion years ago, before there was any Earth, still less any life? Meaningless! Not until the analyzer has been set to this, that, or the other specific chosen orientation; not until the

elementary quantum phenomenon that began so long ago—and stretches out, unknown and unknowable, like a great smoky dragon through the vast intervening reach of space and time—has been brought to a close by an irreversible act of amplification; not until a record has been produced of either “yes, this direction of polarization” or “no, the contrary direction of polarization”; not until then do we have the right to attribute any polarization to the photon that began its course so long ago. There is an inescapable sense in which we, in the here and now, by a delayed setting of our analyzer of polarization to one or another angle, have an inescapable, an irretrievable, an unavoidable influence on what we have the right to say about what we call the past.

This circumstance is one of the more striking information-theoretic as-

pects of what we call existence. Moreover, the delayed-choice elemen-

tary quantum phenomenon is well established by theory and, within the last few years, by experiment. Any view of existence which does not reckon with quantum theory and the elementary quantum phenomenon is medieval. Quantum theory marks the summit of the exact natural science of our day—that “exact natural science” which, Weyl reminds us, “is the most distinctive feature of our culture.”3!

Intellectual Antecedents The man who ranged so far in his thought had mathematics as the firm backbone of his intellectual life. Distinguished as a physicist, as a philosopher, as a thinker, he was above all a great mathematician, serving

as professor of mathematics from 1913 to 1930 at Zurich, from 1930 to 1933 at Gottingen, and at the Princeton Institute for Advanced Study

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from October 1933 to his retirement. What thinkers and currents of thought guided Weyl

physics?

into his lifework:

mathematics,

philosophy,

“As a schoolboy,” he recalls, “I came to know Kant’s doctrine of the

ideal character of space and time, which at once moved me powerful-

ly.”32 He was still torturing himself, he tells us, with Kant’s Schema-

tismus der reinen Verstandesbegriffe when he arrived as a university stu-

dent at Géttingen. That was one year before special relativity burst on the world. What a time to arrive, just after David Hilbert, world leader of

mathematics, had published his Grundlagen der Geometrie, breaking Kant’s predisposition for Euclidean geometry and taking up, in the great tradition of Karl Friedrich Gauss and Bernhard Riemann, the construc-

tion and properties of non-Euclidean geometries, and—having just pub-

lished an important book on number theory, Zahlbericht—was giving ab-

sorbing lectures on that field of research. Philosophy! Mathematics! Physics! Each was sounding its stirring trumpet blast to an impressionable young man. Mathematics, being represented in Gottingen by its number-one man, won the number-one place in Weyl’s heart. Allow here a pause for a brief song of thanksgiving. Shall we dedicate

it to that Prince of Hanover whom the English-speaking world knows as

George II? Or shall we praise instead the advisers at whose insistence that ruler initiated, within a few years of each other, two now famous communities of learning? Those centers, both precious to Hermann Weyl, are known today as Gottingen (1734) and Princeton (1746). The

advisers, blessed be their names—Christian Wolff, the disciple of Leib-

niz in the German-speaking world, and a group of concerned men of learning in the colony of New Jersey—had for the two schools a common purpose: to testify to the glories of creation by looking at them, investigating them, and teaching about them. The goal transmutes itself into ever new language with the arrival of ever new generations. In our century this powerful Géttingen-Princeton tradition, springing straight out of the age of enlightenment, has nourished deep learning—a happy, intense, livelong-day search by great thinkers for beauty, order, and understanding. What way of work did Weyl adopt? Three ways we know to make advances: the way of the mole, the mutt, and the map. The mole starts at one point in the ground and systematically goes forward. Great science

has been done by people so guided. The mutt sniffs around and is led on from one clue to another. Great physics is done that way. But the third method of advance is marked by the mapmaker, the philosopher who

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conceives the overall picture, has a feeling for how things fits together

and finds his way, by that sense of fitness, to where new truth lies. That

was Weyl. To Kant, to the Gottingen of Gauss and Riemann, and to Weyl the number-one example of mapmaker, of philosopher, of guide in the enterprise of discovery was Leibniz. “Among the heroes of philosophy,” Weyl

tells us, “it was Leibniz above all who possessed a keen eye for the essential.”33 He goes on to remind us that “Leibniz planned to span Europe by a network of academies, centers of research which he expected to become a strong combine for the promotion of enlightenment.”*4 Hermann Weyl

and his longtime Princeton colleague, Kurt Gédel, shared an interest in

Leibniz’s notes on his project of a characteristica universalis. Leibniz hoped for a system for discovering truth in all the great wide world of thought comparable in its power to the method that Newton had brought to physics. Leibniz argued that such a tool of thought, such a method, such a philosopher’s stone, once discovered, would be so powerful that it could be entrusted only to young people of the highest moral character. If philosophy, the map, displayed the goals, mathematics—in the

shape of Hilbert—showed the arriving Gottingen student the way. Weyl tells us the impression made upon him by Hilbert’s irresistible optimism, “his spiritual passion, his unshakable faith in the supreme value of science, and his firm confidence in the power of reason to find simple and clear answers to simple and clear questions.” No one who in his twenties had the privilege to listen to Weyl’s lectures can fail to turn around and apply to Weyl himself those very words. Neither can anyone who reads Weyl, and admires his style, fail to be reminded of Weyl’s own writing by what he says of the lucidity of Hilbert: “It is as if you are on a swift walk through a sunny open landscape; you look freely around, demarcation lines and connecting roads are pointed out to you before you must brace yourself to climb the hill; then the path goes straight up, no am-

bling around, no detours.”3> Electrified by Leibniz and Kant, and under the magnetic influence of Hilbert, Weyl leaped wholeheartedly, as he later put it, into “the deep river of mathematics.” That leap marked the starting point of his lifelong contributions to ever widening spheres of thought. Out of Weyl’s thinking, out of his speaking, out of his writings—and out of work since his day—what guidance can we now discover on our quartet of questions; the mechanism of existence, the origin of the quantum, the problem of the continuum, and the deeper foundations of the

idea of time?

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The Four Mysteries Existence, the preposterous miracle of existence! To whom has the world of opening day never come as an unbelievable sight? And to whom have

the stars overhead and the hand and voice nearby never appeared as unutterably wonderful, totally beyond understanding? I know no great thinker of any land or era who does not regard existence as the mystery of all mysteries. But is the quantum a mystery, too? We know that the way the quantum theory works is no mystery. It is expounded in a hundred texts. But from what deeper principle does its authority and its way of action derive? What central concept undergirds it all? Surely the magic central idea is so compelling that when we see it, we will all say to each other, “Oh how simple, how beautiful! How could it have been otherwise? How could we

have been so stupid so long?” But what is the decisive clue to it all that we of today are missing? The continuum of natural numbers: who could dispense with them who works with matter and motion, particles and fields, space and time?

Indeed as Wey] reminds us, “Classical analysis, the mathematics of real variables as we know it and as it is applied in mathematics and physics, has simply no use for a continuum of numbers of different levels [integers, rational fractions, algebraic numbers, etc.].” Yet, he goes on to say,

“(L.E.J.] Brouwer made it clear, as I think beyond any doubt, that there is

no evidence supporting the belief in the existential characters of the totality of all natural numbers.” More generally, he adds, “belief in this tran-

scendental world of [of mathematical ideals, of propositions of infinite length, and of a continuum of natural numbers] taxes the strength of our faith hardly less than the doctrines of the early Fathers of the Church or of the scholastic philosophers of the Middle Ages.”3® Then how can physics in good conscience go on using in its description of existence a number system that does not even exist? Time? The concept did not descend from heaven, but from the mouth of man, an early thinker, his name long lost. Time today is in trouble. Time ends in a big bang and gravitational collapse. Quantum theory denies all meaning to the concepts of before and after in the world of the very small. Most of all, time has not yet been brought into submission to the rule of physics. It is fed in from outside physics. It has someday to be derived from inside physics—when physics is deep enough to measure up to the task. Four puzzles? Four clues. Shall we look at them one by one?

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Existence: The Anthropic Principle Let us begin on puzzle number one, existence, with what sounds at first

hearing as a far-away note, a solitary and pregnant passage from a 1919 paper of Hermann Wey! on general relativity. There he points out the first of the by now famous large-number coincidences of physics in a single

sentence, which we can be forgiven for taking apart into three: “It is a

fact that pure numbers appear with the electron, the magnitude of which

is totally different from one. For example, the ratio of the electron radius

to the electron’s gravitational radius is of the order of 104°, The ratio of the electron radius to the world radius may be of similar proportions.”37 This coincidence between two enormous numbers of very different

origin was called in a paper 12 years later by Fritz Zwicky “Weyl’s hypothesis.”38 But not everybody reads the literature. Later it and further such relations were called “Eddington’s large number coincidences,”39

then, later, “Dirac’s large numbers,’#° and so they are widely known to-

day. But it all began with Wey].

What feature of nature lies behind these large-number coincidences?

What fixes these and other dimensionless constants of physics? Advocates of the anthropic principle, nowadays investigated by more and more physicists and astrophysicists, propose a perspective-shattering answer: not only is man adapted to the universe, the universe is adapted to man. Imagine a universe in which one or another of the fundamental dimensionless constants of physics differs from this world’s value by a few percent one way or the other. The consequences for the physics of stars so multiply themselves up—according to the analyses of numerous investigators4!—that man could never have come into being in sucha universe. The anthropic principle superficially looks like a tautology: we’re adapted to the universe because we’re adapted to the universe. However, closer study by Brandon Carter* shows that the idea leads to an amazing, concrete, and someday testable prediction: it sets a limit of a few

hundred million years, at most, on the time that the earth will continue to

be an inhabitable planet. This prediction is derived from our knowledge of evolutionary biology and from modern statistical analysis. A simple mathematical expression, called Carter’s inequality, relates the likely du-

ration of life on Earth in the future to the number of improbable evolutionary steps required in the past for the emergence of intelligent life. Is the machinery of the universe so set up, and from the very begin-

ning, that it is guaranteed to produce intelligent life at some long-distant

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point in its history-to-be? And is this proposition testable by the Carter prediction? Perhaps. But how should such a fantastic correlation come about between big and small, between and machinery and life, between future and past? Some who investigate the anthropic principle put forward the notion of an ensemble of universes, distinguished one from another by different values of the dimensionality and the dimensionless constants of physics. In the overwhelming majority of cases, they argue, intelligent life is and always will be impossible. We belong, on this view, to one of the rare exceptions, a universe where awareness can and does develop. We can reject some of these ideas without rejecting everything. We can forgo the notion of an ensemble of universes as outside the legitimate bounds of logical discourse. We can nevertheless examine the anthropic principle itself as an attractive working hypotheses—attractive because it exposes itself, by its predictive power, to destruction in the sense of Karl Popper‘ and because it makes sense out of numbers that would otherwise have no rationale. But without multitudes of universes to experiment on, to bungle and to ruin a la David Hume, with solely this one and

only universe to work with, how can history ever have made things come out right, ever given a world of life, ever thrown up a communicating

community of the kind required for the establishment of meaning? In brief, how can the machinery of the universe ever be imagined to get set up at the very beginning so as to produce man now? Impossible! Or impossible unless somehow—preposterous idea—meaning itself powers creation. But how? Is that what the quantum is all about? To ask this question is to look at the puzzle of existence from a new perspective; to see a thread of connection with puzzle number two, the how-come of the quantum. Machinery, Law, Quantum

Machinery of existence for us means laws of physics under the overarch-

ing governance of the quantum principle; in brief, laws and the quantum. How can the quantum ever be understood as powered by meaning? Or laws of physics, by meaning? Weyl reminds us that “postulation of the external world does not guarantee that such a world will arise . . . from the phenomena . . . through the cognitive work of reason . . . which attempts to create concordance. For this to take place,” Weyl emphasizes—updating Kant’s concept of reality as “that

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which is connected with perception according to laws” —“it is necessary that the world be governed throughout by simple elementary laws.’44 Those laws, so beautiful, so necessary for an understandable, mean-

ingful world, and on first inspection so full of structure, turn out every

one of them on closer look to be built in large measure on tautology,

mathematical identity, the most elementary statement of algebraic geometry: the principle that the boundary of a boundary is zero. Electromagnetism, in the shape of Maxwell’s equations, seen in four-dimensional perspective, falls apart into two divisions, one equivalent to the statement that the one-dimensional boundary of the two-dimensional boundary of a

three-dimensional region is identically zero; the other, that the two-di-

mensional boundary of the three-dimensional boundary of the four-di-

mensional region likewise identically vanishes. The concept of the vanishing of the boundary of a boundary both in its 1-2-3 and in its 2-3-4

forms is used again in gravitation physics and yet again in the Yang-Mills

or chromodynamic or string theory—of one or another degree of sophis-

tication—of elementary particle physics. How strange, we say at first. And then we ask ourselves, how could it have been otherwise? Surely—big bang and gravitational collapse advise us—the laws of physics cannot have existed from everlasting to everlasting. They must have come into being at the one gate of time, must fade away at the other. But at the beginning there were no gears and pinions, no corps of Swiss watchmakers to put things together, not even a preexisting plan. If

this assessment is correct, every law of physics must be at bottom like

the second law of thermodynamics, higgledy-piggledy in character, based on blind chance. Physics must be in the end law without law. Its under-

girding must be a principle of organization which is no organization at

all. In all of mathematics, nothing of this kind more obviously offers it-

self than the principle that the boundary of a boundary is zero. That this

principle should pervade physics, as it does—is that the only way that nature has to signal to us a construction without a plan, a blueprint for physics that is the very epitome of austerity? F No. A second sign directs the seeker for the plan of existence still more clearly to austerity: the quantum. What is the thread that connects mystery number two, the quantum,

with puzzle number one, the machinery of existence?

Does the very concept of existence imply that there must be a world sitting “out there”? That was the view of many a great thinker before the

advent of quantum theory—and of Einstein himself to the end of his days. Nothing made him more unhappy than the thought that the observ-

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er-participator has anything to do with the establishment of what one is accustomed to call reality. In the last talk he ever gave, some months before his death, to my seminar on relativity, he explained how he had come to relativity and what relativity meant to him, but went on to express his discomfort with quantum theory: “If a person, such as a mouse,

looks at the universe, does that change the state of the universe?” And to

the visitor defending quantum theory to him in his study he objected against its probability features in the words, “God does not play dice.”45 Weyl, in contrast, spoke up for the physics community when he stated,

“Quantum theory is incompatible with the idea that a strictly causal theo-

ry of unknown content stands behind it. . from classical to quantum physics are no the relinquishment of absolute space and success, if measured by the empirical facts

rably greater.”4¢

.. The reasons for the passage less compelling than those for time by relativity theory; the made intelligible, is incompa-

No one saw deeper into the central point of quantum theory than Niels

Bohr, lifelong friend of Hermann Wey]; and no one stated its importance

more strongly than he in his last interview, a ed death: “They [certain philosophers] have tant to learn something and that we must be very great importance. . . They did not see

few hours before his unexpectnot that instinct that it is imporprepared to learn something of that it [the complementary de-

scription of nature as it is seen in quantum theory] was an objective descrip-

tion—and that it was the only possible objective description.”47 Only possible? There is not a single sight, not a single sound, not a single sense impression which does not derive in the last analysis from

one or more elementary quantum phenomena.

Objective? Not until the observing sense, or observing device—by its

geometry, its layout, and its adjustment—has chosen the question to be

asked, and by its registration has made a record long enough lived to produce internal or external action, has an elementary quantum phenomenon taken place that contributes to the formation of what we call reality. No other way do we know to build this reality. Existence? How else is it brought into being except through elementary quantum phenomena? Unbelievable! The number of bits of information that anyone can accumulate in a lifetime is incredibly small compared to the richness we know to be there in the great wide world. Even if we include more than a single

observer-participator and count up the contribution of every member of the meaning-establishing community, of every observer-participator past, present, and future, what hope is there for deriving existence out of quantum

acts? Of them there is at most a countable infinity. In contrast, existence

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seems to present us everywhere with continuous infinities: a continuous infinity of locations for particles, a continuous infinity of field strengths, a

continuous infinity of degrees of freedom of dynamic space geometry. Issue number two, the how-come of the quantum, here shows some

thread of connection with issue number three, the continuum. How close

is that connection?

The Continuum The continuum of natural numbers, Wey] taught us, is an illusion. It is an

idealization. It is a dream. With numbers of ever-increasing mathematical

sophistication we can approach that limit ever more closely; but we commit a folly if we think we can ever get there. That, in poor man’s lan-

guage, is the inescapable lesson of Gédel’s theorem and modern mathematical logic.

Do we not have to say that the notion of a physical world with a continuous infinity of degrees of freedom is an equal idealization, an equal folly, and equal trespass beyond strict logic? Do we not do better to recognize that what we call existence consists of countably many iron posts of observation between which we fill in by an elaborate papier-maché construction of imagination and theory? The

artist paints in the faces of five angels, with diminishing size, followed by a row of dots of still further decreasing size, stretching out into a line

that runs to the horizon; but the beholder believes himself to see an in-

finitude of angels. When Bohr tells us that quantum theory gives us the only objective description of nature of which one can possible conceive, is he not also telling us that no description can make sense which is not founded upon the finite? For the advancing army of physics, battling for many a decade with heat and sound, fields and particles, gravitation and spacetime geometry, the cavalry of mathematics, galloping out ahead, provided what it thought to be the rationale for the natural number system. Encounter with the quantum has taught us, however, that we acquire our knowledge in bits; that the continuum is forever beyond our reach. Yet for daily work the concept of the continuum has been and will continue to be as indispensable for physics as it is for mathematics. In either field of endeavor, in any given enterprise, we can adopt the continuum and give up absolute logical rigor, or adopt rigor and give up the continuum, but we can’t pursue both approaches at the same time in the same application.

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Adopt rigor or adopt the continuum? These ways of speaking should not be counted as contradictory, but as complementary. This complementarity between the continuum and logical rigor we accept and operate with today in the realm of mathematics. The hard-won power thus to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Wey] took a leading part.‘ The level of synthesis achieved by now in mathematics is still far beyond our reach today in physics. Happily the courageous outpost-calvary of mathematical logic prepares the way, not only for the main

cavalry that is mathematics, but also for the army that is physics, and nowhere more critically so than in its assault on the problem of existence. Time

Time, among all concepts in the world of physics, puts up the greatest re-

sistance to being dethroned from ideal continuum to the world of the dis-

crete, of information, of bits. Of physics the heart is dynamics, and of dy-

namics the heart is time. That time parameter we treat today, however, as provided for us free of charge from outside, as our forebears regarded elasticity a hundred years ago. In our day we have learned that there is no such thing as elasticity in the space between the electron and the nucleus.

Elasticity, thanks to solid state physics, has been reduced from primordial

and precise to secondary, approximate, and derived. Time today requires a like reduction. Reduce time? The idea of reduction is old. Weyl reminds us that “the

doctrine of the subjectivity of sense qualities has been intimately connect-

ed with the progress of science ever since Democritus laid down the principle, ‘Sweet and bitter, cold and warm, as well as the colors, all these

things exist but in opinion and not in reality; what really exist are unchangeable particles, atoms, which move in empty space.’”4? In accordance with this view of Democritus, we understand green today as a char-

acteristic frequency of 5.7 x 10!4 vibrations per second; freezing, a characteristic energy of 3.7 x 107!4 g cm?/sec?; and a detectable sound, an air pressure amplitude of 10-3 g/cm sec?—motions indeed in empty space. But time: how is time to be reduced to more primitive concepts? Reduced from the continuum to something built on bits? And along with the reduction of time how are we to understand that puzzling conservation of “T’ from decade to decade, so vividly expressed by Wey] in his quotation from Der Rosenkavalier, where the marshal’s wife looks into her mirror

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and asks, “How can it really be that I was little Resi—and that I also one

day will be old woman?” Of all obstacles to a thoroughly penetrating account of existence, none looms up more dismayingly than “time.” Explain time? Not without explaining existence. Explain existence? Not without explaining time. To

uncover the deep and hidden connection between time and existence, to

close on itself our quartet of questions, is a task for the future.

More Problems? More Clues, More Hope A great problem, we know, means great hope, according to that time-hon-

ored doctrine of “no discovery without a paradox.” A still better formula has emerged out of the science of this century: no great advance without a double mystery, a double paradox, a double problem, two clues that can be played off against each other to yield the answer. Fortunate are we to have before us two such mighty mysteries as time and existence—each linked with two other great questions, the quantum and the continuum. Last year was the hundredth birthday not only of Hermann Weyl but also of Niels Bohr. Their double drumbeat summons us to a great under-

taking, tells us that we can and must achieve four victories:

Understand the quantum as based on an utterly simple and—when we see it—completely obvious idea. Explain existence by the same idea that explains the quantum. Through this larger vision of existence and the quantum, recognize

that the continuum of that physical world out there and the bit-by-bit means by which alone we can define that world are not contradictory, but complementary. Reduce time into subjugation to physics. As we face these stirring challenges, a warm memory gives us courage. Hermann WeyI has not died. His great works speak prophesy to us in this century and will continue to speak wisdom in the coming century. If we seek a single word to stand for the life and work of Hermann Weyl, what better word can we find than passion? Passion to understand the secret of

existence was his, passion for that clear, luminous beauty of conception

which we associate with the Greeks, passionate attachment to the commu-

nity of learning, and passionate belief in the unity of knowledge.

From concluding address given at the Hermann Weyl Centenary Congress, University of

Kiel, July 3, 1985.

Hendrik Anthony Kramers

A. Kramers, Professor of Theoretical Physics at the Uni-

versity of Leiden, a man of deep culture and noble charac-

®@ ter, was one of the great apostles of the new age of quantum theory. Kramers

was born in Rotterdam December

17, 1894, the

third of five sons of a physician. Two of the sons became physicians

themselves, one a chemical engineer, and one a professor of Arabic lan-

guages. Hendrik Anthony even as a small child had to wear strong glasses, but this handicap in sports went with a bent for study. Particular delights were Horace and the other Latin poets and Cicero and his friends. Then and later he wrestled with questions of theology, that

product of generations of high intellect and wonder about the great human mysteries. The fascination of this subject never left him, and he kept as a favorite author the Swiss Karl Barth, theologist of theologists.

The family was deeply Calvinistic. At the same time Kramers had a unique capacity for friendship—responsive to friends, dependent on

them, enchanting to them; an awareness of others; a natural gaiety; a

love of music; and a deep pleasure in making music himself on piano or cello. How deeply must he have felt the loss of his mother when he was only 18. How natural that he tried to comfort a friend who was dis-

turbed in the face of death, and who asked where was the God Who Dries the Tears—this at a time when he must have been aware that his own death was only a few days off. To others he could say, “You theologists speak about the miracle when you no longer understand it, but I consider it a miracle when I sometimes understand a little of it.” Fundamental in Kramers’ attitude towards life, physics, music, friends was “wonder, meeting with the miracle.” Mysteries of the more everyday kind also presented their attraction, languages particularly. Kramers by the end of his life read and spoke Danish, Dutch, English, French, German, Italian, and Swedish, knew

well Greek and Latin, and had studied Finnish and Russian. His growth

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and reading never stopped. Shakespeare was a life-long love, and King Lear a treasure to be viewed ever and again from new sides for new riches. Wide and human interests were already awake when he went to the University of Leiden in 1912 for four years of study. Talented in mathematical analysis and in physical insight, Kramers found himself in Leiden irresistibly drawn by the richness and deep problems of theoretical physics. His professor, Paul Ehrenfest, was one of the great consciences of science. No one was more deeply disturbed by paradox, inconsistency, or inadequacy of the foundations. Ehrenfest’s famous writings on the principles of statistical mechanics are a testimonial to his logical rigor and absolute honesty. Never so convinced of his own value to science as those who knew his merit, Ehrenfest was also not one to present his students to the world with a blare of trumpets.

Kramers, at first advised by Ehrenfest to become a high school teacher,

took such a position at Arnhem, where he instructed for two months.

Then came the normal military draft followed by dismissal at the end of

a week on account of eyesight. At this point Kramers took control of his

own career.

Niels Bohr had put forward in 1913 the quantum theory of the atom, So revolutionary that its concepts had to be formulated as first principles, beyond justification by already existing ideas. Success in the first applications of these principles, and the support of Rutherford and others for the new ideas, had still in 1916 left many leaders in physics unconvinced. A great task was ahead to extend the range of application of the quantum theory from hydrogen to other atoms; from atoms to molecules and to condensed forms of matter; from steady state condi-

tions to problems of rate of transition; from matter to electromagnetic

radiation; and above all, to clarify great questions of fundamental principle. Bohr had been called back from Manchester in 1916 to become professor of theoretical physics in Copenhagen. There he set about making opportunities for others to work alongside him. They were destined to be young men, Conant’s “uncommitted minds,” the great. moving power in the advances of science. Great causes make great men, but in all the history of science has there been anywhere but at Copenhagen such a long-continued and brilliantly productive friendly association of a num-

ber of great men in one center as now developed? Of the new apostles

one of the greatest was to be Kramers. Twenty-one years old, he arrived

in Denmark

in 1916, in the middle of the

war via boat from Holland,

and came as Bohr says “without any notice to a place where nobody had

heard of him before.”

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A central issue in the then small Copenhagen circle was to determine,

with as much clarity and definiteness as possible, how far the ideas and

concepts of a proper quantum theory could be expected to resemble, or correspond with, the notions employed by the previous classical theory in treating the same physical problems. Bohr had already employed this notion of correspondence in arriving at his early quantum theory of the energy levels of the hydrogen atom. He and Sommerfeld had also made

some application of the correspondence principle in analyzing the general nature of the radiation to be expected from an atomic system. Kramers now investigated the complicated motion of the electron in a hydrogen atom subjected to an external electric field, and used the correspondence principle to predict the intensities of the many fine lines observed in the spectrum of an atom so disturbed, finding a remarkable correlation with

observation. A similar attempt by Kramers to explain the features of the helium spectrum encountered difficulties. Their origin became clear only

after the wave-mechanical formulation of quantum mechanics had been developed. Both pieces of work concerned systems in which the elec-

trons had insufficient energy to escape, and so moved in bounded orbits.

Kramers now turned to the case of a fast electron projected into an atom-

ic field of force from outside, and analyzed the radiation to be expected

on the basis of the correspondence principle. This important investigation gave a new understanding of the mechanism of generation of x rays by electron bombardment. It also allowed useful predictions to be made about the reverse process of absorption of electromagnetic radiation by an atom with the ejection of an electron. He and Bohr and other members

of the Copenhagen Institute made significant advances in understanding

the shell structure of atoms and the correlation between electronic orbits and chemical valence. The most fruitful of Kramers’

investigations at Copenhagen dealt

with the influence of radiation incident on an atom in causing the scattering from the atom of radiations both of the original wave length, and of modified frequency. He established a general relation between these

scattering processes and the mechanisms of emission and absorption of radiation. This so-called dispersion theory, and its implications, refine-

ments, and generalizations, always had an important place in Kramers’

interests. Later in his career he returned to a derivation of the scattering formula from a deeper point of view, connecting it with a general manifestation of the principle of causality. While still at Copenhagen, he and Heisenberg made further advances in the formulation of the dispersion

theory, making

still more manifest the connection it provided between

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observable quantities which referred to processes of absorption of a photon and those which described scattering of a photon. This work was the foundation of Heisenberg’s new formulation of quantum mechanics. Here reference was made entirely to observable quantities. The description of nature became at last completely free of reference to the classical mechanical description of position and velocity. Kramers was a master of the new methods both of Heisenberg and of Schrodinger and de Broglie, to which he himself made important contributions. However, he was wiser than many of the physicists of the time in continuing to employ the principle of correspondence as a valuable guide to illuminate the significance of quantum theory in new realms of

physics and its ever-present relation to classical ideas.

First assistant at the Copenhagen Institute for Theoretical Physics by 1920, and lecturer there by 1924, Kramers left Denmark in 1926 to become Professor of Theoretical Physics in Utrecht. From there he was called in 1934 to Leiden, where he remained professor until his death on

April 24, 1952. As professor, Kramers not only lectured on the several branches of theoretical physics and guided a seminar, but also had responsibility for advanced students, of whom 27 did their Ph.D. dissertations partly or wholly under his supervision. In his many able students Kramers won new exponents for theoretical physics. In turn, the stimulus of giving systematic lectures and having the collaboration of these young men had its part in calling to Kramers’ attention new domains of application of quantum theory, and important questions of principle. His field of work became wider and showed in ever-growing measure his originality and talent. Early in his Utrecht career Kramers found a mathematical scheme of approximation to the solutions of the wave equation of the new quantum mechanics, of such a form as to bring out in an especially clear way the correspondence with classical theory. Now called the Jeffreys-WentzelKramers-Brillouin method because of its discovery in different forms by other investigators, this technique of analysis was applied by Kramers and his students to problems of atomic and molecular physics. In a later two-volume systematic exposition of quantum theory, he not only made especially good expository use of the JWKB technique, but also illuminated the whole subject by his symmetry, generality, and elegance of treatment. Paramagnetism, ferromagnetism, statistical mechanics, and ra-

diation theory were, besides quantum methodology, the subjects that chiefly claimed the interest of Kramers

for the rest of his life, as evi-

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denced in many papers, alone and with students. However particular the topic in some of these studies, it is the associated question of principle

that furnishes for him the main motivation. This search for generality, the originality of approach, and the appropriateness of the mathematical methods, make the beauty of Kramers’ work.

One cannot refrain from mentioning titles farther afield, either in the

writings of Kramers, or in the dissertations of his students: “What is mat-

ter?’; “Condensation in interstellar space”; “Linear regression analysis of economic time series”; “Vibrations of a gas column.” Fortunate are those

who have heard him give his lecture on the differing character of physics as carried on in the various countries of the world. Fascinated are those who have read his Leiden inaugural lecture, “The Physicist as Stylist.” The war brought heavy concerns, dangerous situations, and also more human ones. Students sought by the enemy were kept in early 1945 “underwater” in the basement of the physics laboratory. Close confinement

of so many had its inevitable effect on tempers and tension. Kramers

therefore changed his place of work to this student refuge. Calm and silence ensued; he worked; they worked too. At another time he went with

a neighboring farmer and horse and cart and brought potatoes to the people of the laboratory. Concerned about the control of atomic weapons, Kramers accepted appointment by the Netherlands in 1946 to the United Nations Atomic Energy Commission in New York. There he was elected chairman and in spite of great difficulties succeeded by his powers of moderation in mak-

ing possible a unanimous report that control is technologically feasible. To political feasibility the path is still long. That Kramers worked so hard for such a far-off goal is a tribute to his strength of principle. If in this

work he was a citizen of the world, so was he also as president of the In-

ternational Union of Physics from 1946 to 1951, a post for which he was uniquely fitted by his sense of responsibility, his knowledge of physics and languages, and his gift for friendship.

Fortunately for friends, colleagues, and students in the United States,

Kramers made many trips to this country. He already had the foreboding

that his last visit would be his sojourn in Princeton in late 1951, and es-

pecially at this time he showed a touching concern to share life with each of the friends he was not to see again.

Reprinted from “Hendrik Anthony Kramers (1894-1952)” in Yearbook of the American Philosophical Society (1953).

Hideki Yukawa as Uniquely Ecumenical

o have visited once again the home of Hideki Yukawa a few weeks after his death, to have seen there his portrait and the inscriptions from many lands and people, to have talked at length

with his wonderful wife and son about times past is unforgettably to have

been reminded of his unique place in the history of science. The idea for which he won the Nobel Prize set a tide going in elementary particle physics which had and has irresistible force. The links that he and his colleagues forged with all the world made and make Japan an imposing influence in physics for good. The institute established under his leader-

ship has nurtured a whole generation of new leadership in science, and

more.

The Yukawa I knew was more than a world figure. He was a very human individual. When my wife took Mrs. Yukawa shopping just after

their arrival in Princeton, he had translated the grocery list into English;

and my wife knew enough to realize that “ordinary sauce” meant “soy

sauce.” The car, the too-small car that he bought from us, he drove ac-

cording to the principle previously made famous by Dirac, until his wife,

with her marvelous sense of rhythm, could intervene, take over the driv-

ing, and save his life and her own. I will never forget the honor and pleasure it was to walk and talk with him and Homi J. Bhabha and Einstein in Marquand Park in Princeton. Neither can I forget the broad-ranging discussion with him of physics, and the history of physics, and the great

men of physics at later times in his office in Kyoto. There I came to

know about Eastern great men and great ways of thinking about science

that I would have never otherwise appreciated. Never did I appreciate more than there the difference between the sharp “this is true, that is not

true” of western thought and the “maybe yes, maybe no” that Yukawa lived and breathed.

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In an address I gave in Japan in 1953, I made comparison between two outlooks on fundamental physics as they showed, and still show today.

One I identified with Saigo Takamori: direct, headstrong attack on na-

ture, using straightforward techniques, and pushing perturbative expansions and accelerator energies to the limit. The otherI identified with

Sugawara no Michizane: searching for the hidden harmonies by listening

to the still, small voice of nature. If Tomonaga represented the latter and Nishina the former, Yukawa had the ecumenical breadth to deal on understanding terms with both. Yukawa’s life and work leave a lasting memorial. How can I forget him? How can the world forget him?” Reprinted from the Journal of the Physics Society of Japan (1982).

FROM HALF-LIFE TO HUMAN LIFE

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Dealing With Risk

hat progress is mankind making in fitting the nuclear power plant risk into all its long history of dealing with risk? Can we learn anything from looking at this new risk in the perspective of old risks, death from lightning or electric power, from crash of train or car, from break of dam or dike? See how we poor mortals, with all our mistakes, make the new our

own? And trace out some of the stages by which the body politic fits the new risk into its reckoning: terror fosters imagination, imagination fos-

ters understanding, understanding fosters openness, and openness fosters control? Nowhere more vividly than in today’s debates about nuclear

power plants does one see going on all at once the several stages of our assimilation of a new technology from terror to understanding and from

openness to control.

No one earlier than I was jerked out of nuclear-physics research into confrontation with these issues of nuclear power plant safety and control. Monday, January 16, 1939, I had gone to New York to meet Niels Bohr arriving for three months of lectures on quantum theory at Princeton. Quickly I got the great news of the fission of uranium that he had brought from Copenhagen, communicated to him just before he left, by

Otto Robert Frish. Bohr and I immediately set to work to understand the mechanism of fission. No consequence of the principles we uncovered

was more important than the identity of the nuclei most susceptible to fission, uranium-235 and plutonium-239.

Plutonium, element 94, does not even exist in nature. It had been made only in the laboratory, and then only in unseeably small amounts. Never has any substance risen so spectacularly from invisibility to center stage as did plutonium in the ensuing three years. The reason is simple. Plutonium lends itself to separation from uranium by chemical means, as ura-

nium-235 never could.

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The Engineering of Alchemistry An observer from afar, looking upon the scene in late 1944, would have

been convinced that he was looking at one alchemist’s dream inside another. It was preposterous enough to think that dead uranium, put into regularly-spaced crannies in tons of dead black graphite, would come

alive. It was still more preposterous to imagine this life, this silent darting back and forth of invisible neutrons, as producing in the course of

time not merely a few atoms of plutonium, but billions upon billions of them, the philosopher’s dream of synthesizing a new element achieved in

kilogram amounts.

i

Fate put me into the center of this second dream, the engineering of

alchemy. Was it because I had started as an engineer before I became a physicist? Was it because my first job, at the age of 16, had been among motors and diesel generators in a silver mine in the mountains of Mexico? Or was it because I, as much as any physicist in the Chicago project, felt that our work so far would be wasted if it did not lead to engineering? At any rate, Arthur Compton had selected me as a carrier of the

physics know-how from the Chicago project to E.I. du Pont de Nemours and Company of Wilmington, Delaware, the firm designated to construct and operate the world’s first plutonium producers. General Leslie R. Groves had prevailed on du Pont to undertake the unprecedented task of engineering alchemistry. This company in synthesizing ammonia and in carrying nylon from idea to product and in other achievements of chemical engineering had shown unsurpassed speed. Moreover, in decades of manufacture of gunpowder and dynamite and other explosives it had established an enduring tradition of making the dangerous safe. It was a great experience to become acquainted with the du Pont people, the way of work that achieved such speed, and the daily concern that secured such safety.

Learning to Think Safety Experiments in physics and experiments in chemistry I knew something

about, but it was new to learn the history of du Pont’s experiments in

ways to get people to work safely. Bring in a safety expert to lecture to a group of workmen? Pleasant it might be to sit for a while, and pleasant

too to joke about the outsider’s strange ideas; but as one walked back to

the job of installing that pipe or erecting that chemical process vessel,

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what was the difference between the lecture and pouring water ona duck’s back? Then a new dispensation began. The new expert that came in had a

new competence. It was not his function to lecture about safety. Teach foremen how to hold a conference—that was his job. Now the responsibility for safety has been passed to the foreman, and he has to spread it over his workmen. He calls them together. “Boys, we have to put up the process vessel today. How are we going to do it so we won’t have an accident?” There is a great silence. With it goes a great temptation for the boss to start telling the men how to do the job. But don’t, he has learned. So the silence continues. Then at last one of the workmen speaks up,

“Chief, last time we did anything like this, 1 was pushing the wheelbar-

row and stumbled over that rubber hose and nearly broke my leg. Can’t we do something about that?” Somebody else suggests a simple walkway cover over the hose.

Internal concern about safety, not external, had long ago become the

heart of du Pont’s safety program. It was one satisfaction of it to see the steady improvement of level of safety record to one of the highest and

best in the world. There was an unexpected side benefit. The thinking ahead that made the job safer also made it swifter.

My first meeting as a Chicago representative with du Pont engineers and chemists took place around the council table at Wilmington on Thanksgiving Day 1942, some days before the December 2 startup of the

first man-made nuclear reactor.

There was not one decision reached that first day nor in all the days and months to come that did not respond to those three slogans of today’s

engineer: safe, swift, sure. If ever anyone had to recognize unprecedent-

ed risks and deal with them, this group did, builders of plutonium production reactors, ancestors of all of today’s nuclear power plants. Two questions more than any others called for attention: How to protect against radiation, and how to guarantee against a runaway reaction. How to protect against radiation is a long story, the thought and work of hundreds of able people. Meticulous housekeeping was measure number-one for dealing with radiation. With enough time and care almost everyone acquires the necessary radiation-safety discipline; and those who don’t are moved to other work. The second measure for deal-

ing with radiation is shielding, 30 centimeters of concrete here, a meter

there, according to the amount of radioactive material undergoing decay

behind the wall. It is no wonder that in construction of a single handful

of nuclear reactors at the Hanford Engineer Works in the middle of the

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state of Washington more concrete was poured than it took to build the Panama Canal. It may some day be in the power of man to predict and even govern the course of a tornado. Today it isn’t. Residents of areas attacked from

time to time by a tornado are accustomed to build under each house a “tornado cellar” in which to hide until the danger is passed. No one can predict when a storm of sleet and snow may trap the alpine climber for days, but he can save himself by waiting it out in a shelter. My extended family of 15, young and old, are together weeks at a time in the summer 13 kilometers from a great nuclear powerplant. I do not worry for their safety. But if I did have reason, I know that shovel and earth, simple ev-

eryday earth, would be the answer. All of the radiation from all of the radioactivity from all the nuclear power reactors all the world together, concentrated in a single mass, radiating directly down on the heads of all my family, but separated from them by a leach-resistant membrane and

four meters of earth, would be utterly harmless. Shielding, we know, is

the handiest of all protections against radiation, and earth is the handiest of all shielding. Distinct from any physical effect of radiation is the psychological fear of radiation. No feature of radiation can do more to create fear than its invisibility. It is one thing to have tens of experts dealing with radiation;

another, hundreds of engineers; and another, thousands and tens of thousands of workmen; and by now hundreds of thousands. It was the first

step in dealing with this problem to make the invisible visible. Everyone was provided with a radiation badge. The level of exposure hardly ever rose above the background level of the usual natural atmospheric radioactivity and the cosmic rays. That provided one reassurance. A second came from the existence at every site of a group of experts exclusively concerned with radiation protection. The third reassurance was primarily psychological, but it was as im-

portant as the other two because it encouraged a positive outlook toward

radiation. The name of the monitoring group and the activity in which it engaged was not “radiation physics,” it was “health physics.” That term was the wise invention of one of du Pont’s wise men, Roger Williams. Health physics it became in 1943, and health physics it remains today, not only in du Pont, but also all over the world. The very name has had

an upbeat consequence for the outlook of the outstanding worldwide corps of professionals who deal with this problem today.

Will the nuclear reaction “run away”? How could the reactor most reliably be kept under control? Enrico Fermi’s control device is widely

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known: a metal rod covered with cadmium. Lowered into a well in the uranium-graphite reactor, it absorbed enough neutrons to stop the reaction. Gradually hoisted to the appropriate point, there it allowed the reaction to proceed at a safe level. That was all very well for an experimental reactor that never produced, and was never intended to produce, heat at

rate of more than 200 watts. But what was to assure control of a plutonium production reactor, putting out heat not in watts or kilowatts or megawatts but hundreds of megawatts? One cadmium or boron rod was not enough. A whole array of rods was required. Only so could one be assured that the reactor could be shut down in case of accident, such as

failure of cooling or earthquake or the unexpected. But suppose something blocked the wells into which these control rods were to fall? Or something went wrong with the release mechanism? Then what? It was enough for du Pont to raise this question for the organization to come up with an answer: a second, quite independent system of rods. And suppose this system also failed? The response was the design and installation of yet a third safety system, small shot containing boron that could be poured into holes in the reactor. A seismometer was used to set off the three safety systems of the first Hanford reactor and shut it down in case of earthquake. At the end of a long thin wire hung a metal weight, centered in a metal cup with a small gap between weight and cup. A tremor of the earth displaces the cup but not the free-hanging weight. The electric contact triggered the release of the control rods. In the very simplicity of this and many other devices lay

one assurance of reliability.

A Site Near a City? With the arrival of peace, nuclear reactors had a new task to shoulder with

new risk considerations. It was necessary to turn from reactors for produc-

ing plutonium to reactors for producing power reactors, closer to great centers of population than the Hanford reactors ever were. They were located in a great tract of desert country, sagebrush and sand, dry and scorching hot in the summer, through which runs the great and beautiful

blue Columbia River, carrying ice-cold water direct from the glaciers of

British Columbia. Well do I remember our deliberations that led to that choice of site. Among all the possibilities in North America, the Hanford location offered the number-one combination of pure water for cooling the reactors, large security area, and distance from any big city.

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The power plants of the peacetime world could have none of these luxuries, neither the ideal water nor the huge site nor the hundreds of

kilometers separation. What new provisions would have to be made to deal with the new problems? A Reactor Safeguard Committee was established to help ensure that the new developments would be safe developments. The common law in the Icelandic sagas and in the English-speaking world is a matter of precedents built upon the decisions in special case after special case. So it has been in the nuclear power industry in the United States.

The first important case arose from the request of the General Electric

Company to build a nuclear power plant near Schenectady, New York. Our members assembled to hear and study the proposal, among them Abel Wolman, professor of sanitary engineering at the Johns Hopkins University of Baltimore, Dr. Harry Wexler of the U.S. Weather Bureau, Manson Benedict, professor of nuclear engineering at the Massachusetts

Institute of Technology, and Richard Feynman, Edward Teller, and I, professors of physics at Caltech, Berkeley, and Princeton. For the first time in a peacetime context we found ourselves forced to make a worst-case analysis of a nuclear power plant disaster, such as I had already made for the Hanford plutonium producer. However improbable, suppose that all controls fail and that all cooling—normal and emergency—of the hot uranium stops. Nevertheless, we could assure ourselves, no piling of improbability on improbability whatsoever could lead to any nuclear explosion of the reactor. Moreover, the loss of coolant meant an end to the nuclear chain reaction. Nothing more of a nuclear

character could happen than the normal radioactive decay of the barium

and lanthanum and other products of the uranium fissions that had already taken place. In consequence, the heat output would instantly drop to about five percent of the normal level and thereafter slowly fall in the course of minutes, hours, and days. Might that after-heat not ultimately melt and perhaps even vaporize the uranium? Earthquakes and other accidents being what they are, how then can one exclude the possibility that some substantial fraction of the accumulated radioactivity will esCape to the atmosphere and be carried downwind in the ensuing hours? That, we concluded, is the worst case. And how bad is the worst case?

Does that depend on the vagaries of the wind? In one way, yes; in anoth-

er way, no. Few there are among us who have not watched the smoke es-

caping from a tall factory chimney. It swirls and spreads, and as it spreads undergoes swirls of yet larger scale. The result is simple. Even in

a wind steady in its direction hour after hour there takes place a certain

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minimum amount of dispersion. Seven kilometers downstream the smoke has spread over a band one kilometer wide. Seventy kilometers downwind the spread is ten kilometers; and so on. This simple finding of our friends in the world of meteorology gave us what we needed to figure out the dilution of the radioactivity. Our distinguished colleague, Abel Wolman, had already taught us the number-one equation of sanitary engineering, “pollution plus dilution equals solution.” We took as focus of attention the people of a city, walking around in the open, without any protection, and directly downwind from the utterly implausible accident. We concluded that they are nevertheless safe from any death-dealing exposure to radiation if only the powerplant is separated from the city by 8 kilometers when the power level is 250 megawatts or 16 kilometers when the power level is 1000 megawatts, or more generally the safe distance is proportional to the square root of the power level. This square root principle was used in setting the distance of the General Electric reactor and has been used in one

way or another ever since.

Dome and Disaffection The chance of this worst case ever happening was clearly unbelievably

small, but could it not be made still smaller? Location of the powerplant

underground would provide an excellent supplemental guarantee of safety for more than one reason. However, it was and is expensive—too expensive for us to recommend.

Instead, we advised a dome to catch and

hold the smoke of the burning uranium should ever the reactor itself lose

all cooling and be disrupted. Today those domes, some metal, some con-

crete, have become in the Western world the sign and symbol of the nu-

clear power plant with its overriding concern for safety. In October 1949 the U.S. Reactor Safeguard Committee met with the corresponding British committee at Harwell, near Oxford, to check each

other’s reasoning and to see if any stone had been left unturned in the

search for yet greater safety. It was an encouragement to find that we had independently arrived at the same square root formula with the same constant to govern the distance between powerplant and city. It was a disappointment not to come upon any quick sure way to dispose of the ra-

dioactivity accumulated in the reactor in the case the reactor itself or the

dome around it were torn open by explosive act of sabotage or meteoric impact or some catastrophe equally unexpected. Why not put two or

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three of the familiar-looking oil storage tanks nearby? Why not have automatic provisions to remove the covers and ignite the oil in case the re-

actor and the dome were both disrupted? Would that not be sure to create a gigantic flame? And would not that flame carry the radioactive products of nuclear fission kilometers up into the sky and dilute them so effectively that the risk to anybody would be minimal? It was easy to discard such a proposal. What was designed to save one from the

consequences of one accident was even more likely to have an accident

of its own. Other schemes to deal with an accident we considered too, but none could be found which was at the same time simple, reliable, and

safe—none except an underground site, too expensive, and the dome, which all accepted. The advisory groups of the two nations agreed on safe distance, and ona dome still further to increase safety. But what was the chance of an accident, anyway? It was small, unbelievable small, but how

small? It

fell to me to discuss this issue. There are three independent safety systems to cut off the nuclear reaction, I pointed out. Suppose there is only one chance in a million that the first control rod system fails. Then there is a backup; and suppose there is a chance of only one in a million that it also fails. Even then, there is still the third safety system, with, say, like-

wise only one chance in a million to fail. Treating the problem as a purely mechanical one, therefore, one would conclude that there is only one chance in a million million million for the reactor to escape cutoff. What is the chance, however, that someone

will come in who is so

well trusted and so well-versed in the intricacies of the control system that he knows how to turn off system A, and turn off system B, and turn off system C? That is one of the questions we have to ask, I suggested, if we are to arrive at any realistic estimate of the probability of an accident.

I cited the statistics I had collected on acts of sabotage in the United

States during the two world wars. Although the United States took the

field against Germany in both wars, there was much pro-German senti-

ment during the first war, and there were correspondingly more acts of sabotage then than in the second, when the climate of opinion was entirely different. What would the saboteur look like, I went on as we sat

around the meeting table, who would run the nuclear reactor out of con-

trol and to meltdown—and,

if he could, to vaporization? Trusted, he

could move wherever he would in the reactor building. Technically so competent, he would know the relevant details of the three control systems and know how to turn them all off. He would be a loner. He would

be animated by some twisted ideology. As I spoke, across the table from

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me sat Klaus Fuchs, trusted member of the other group. Neither they nor I had any way to know that, loner as he was, he was also a spy, and had

already given away the secrets of the greatest weapons in human history. One month later he was in prison. Madmen and fanatics the world has always had. Their number and their activity, we know, rises and falls with the cycles of international

peace and international crisis. Terrorists today have telling tools and telling targets. The hijacking of airplanes is a case in point. The threat there is clear; but equally clear is the response of society, sometimes too strong, sometimes too weak, but in the end coming into a commonsense balance with the danger. Paradoxically, no system that is absolutely perfect ever can be perfect because it is too restrictive, too expensive, too counterproductive. What the right balance is against bank robbery, railroad sabotage, and assassination, what combination of alarm system,

security organization, mock raid, and community alertness is generally

discovered by the common

sense of society itself. However, banks are

wise enough not to disclose all the precautions that they take against robbery, and nuclear plant managers are sensible enough not to reveal their provisions against sabotage. Distinct from sabotage, with its delib-

erate intent to create trouble, is operator failure, operator misunderstand-

ing, operator carelessness, and its prime cause, management shortsight-

edness, management carelessness, and management disorganization.

Well run du Pont had moved out of the nuclear reactor field. New organizations had come into it. A primarily technical advisory body such as

ours kind ophy after

did not have the scope to foresee nor the power to set up the right of national nuclear regulatory agency, animated by the right philosto guide management and operator alike. It took several incidents my time to start such restructuring and one widely publicized acci-

dent to update it.

Dams and Dikes Our committee could not deal with the risks of a new technology without

looking at them in the perspective of other times and other technologies. In every great library there is more than one compendium of disaster, from trainwreck to airplane crash and from building collapse to mine ex-

plosion. However, no disaster that we could find—associated with the

work of man—provided a more relevant comparison than dam failure. Here again the life of a city may be at stake. Here again people are inno-

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cently going about their daily work heedless of a potential disaster kilometers upstream or upwind. In both cases the new construction has

beneficent aims. Both have to go through stage after stage of review and check. To be or not to be is decided in the end by the political process. In both the community gain is counted as more than the community risk. For both dam and reactor, the risk of an accident can be made unbeliev-

ably small. In neither can the risk be made altogether zero. There is one great difference. Dams have failed. Cities of thousands have been destroyed in a few minutes. But never in the West has a non-research per-

son ever been killed in a reactor accident.

How safe are dams made? Less money, less safety; more money, more

safety—that much is obvious. But how safe? In my own country dams on

navigable streams are under the jurisdiction of the U.S. Corps of Engineers; other dams under the Bureau of Reclamation of the U.S. Depart-

ment of the Interior. Sometimes there will be little floods and little earthquakes; other times, big floods and big earthquakes. Let an existing dam stand if it is judged safe against the kind of accident that will happen on the average once in 10,000 years. Insist that a new dam shall be strong

enough to withstand and earthquake of the once-in-10,000-years variety. That is working policy. The day after the dam fills, of course, an earthquake may hit such as might be expected only once in a million years, and everyone downstream be swept to destruction; but that is the chance

the community takes. After the first seven years of its life, I resigned from the Reactor Safeguard Committee because its work had become too demanding for one whose primary duty lay in physics itself. However, I kept up a deep interest in the philosophy of risk. In 1956, when I had the great honor to occupy the Lorentz Professorship of Physics at the University of Leiden, I took advantage of the occasion to visit the dike system with which Hendrik Antoon Lorentz had been so deeply concerned. Maps of 60 years ago and older show us the Zuyder Zee, a gulf of 3600 square kilometers reaching from the North Sea deep into the northern Netherlands. Unpredictable storm made it an ever present source of danger to land and life. As early as 1667 the great Simon Stevin, military- and water-engineer, proposed plans to dike the coast and drain the land. Little happened.

About the turn of the present century C. Lely came to sit in the Dutch

parliament. He was a realist but also an enthusiast to get on with the job. As is often the case, however, arguments for led to arguments against. The growing conviction of one group in the Parliament that the proposed

project would be the salvation from new disaster was matched by the

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growing conviction of another group that the dike would be a sure prescription for disaster. In the past, they argued, the fury of the North Sea could wear itself out in the shallows of the Zuyder Zee. However, the dike would so concentrate the power of the storm that when at length it broke, the villagers of the reclaimed land and the old land as well would be overwhelmed by a disaster beyond all previous experience. The Parliamentarians could not agree on the dike but they could agree on the man to ask about the dike, Lorentz. He had no wish to project himself into this new activity. His heart and soul were in his investigations of the great discoveries of the day in quantum physics and relativity. Widely regarded as the father figure of physics of his time, admired by the young Niels Bohr, and also a great admirer of Niels Bohr, he was, like Bohr, more than a scientist; he was first of all a citizen. He took up the heavy new responsibility, making only the condition that he should have an outstanding young engineer to help him in the task. Day after day Johannes Theodoor Thijsse helped Lorentz with his calculations of the effect of tide and river flow, and of wind and storm.

Calculation brought consensus. The Dutch dike system began its great expansion. Peaceful and productive towns came into being on land that once lay at the bottom of the sea. When I visited in 1956, Thijsse had become a leader in the Dutch Dike System and was busy with the planning of the extensions in the neighborhood of Rotterdam. One day I heard him give a lecture at the Dutch Academy, followed by questions. How do you

decide how high to make the dikes? There is no height that will provide an absolute guarantee, Thijsse explained (Figure 1). Build it so high and it will be overcome by a storm once every 200 years. Build it 20 or 25 centimeters higher and it will be overcome by a storm on the average

only once every 400 years. We can make that figure 800 years by adding 20 or 25 centimeters more; and so on, one more factor of two reduction in risk for every 20 or 25 centimeters added to the height. But there is no height that will guarantee absolute safety. Then how does cost come in, Thijsse was asked? In the same way cost

comes into the buying of insurance, he replied. We count up the cost of the house and the factories, the roads and the fields, and balance the total

amount at risk against the cost of more insurance, the cost of another 20 or 25 centimeters added to the dikes. But what do you put in for the value of the people, one member of the academy objected. Thijsse smiled. No matter what number we might put in our calculation for the value of a human being, we would get into infinite trouble, he explained. Nobody is willing to put a value to a human life. Therefore we leave the population

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out altogether from our calculations. But if we were really consistent, he continued, we would put in a negative value for it because here in the Netherlands we pay 600 guilders to anyone who will emigrate.

Has a Life a Money Value? Impossible politically it was and is for the planners of the Dutch dikes to put a figure on a human life. I learned later, however, that there are occasions when the moral force of the community comes down in exactly the opposite way and insists on setting a money value on a human life. Death by failure of an engineering structure is a case in point. The families of those killed sue. Typically the judge awards a cash settlement equal to the would-have-been lifetime earnings of each man. A money value for a human life the judge was forced to make explicit. Many another agency of the community has to make from time to time a similar estimate, generally however without daring to make it public. It will cost a small town three million dollars to take a dangerous S-

curve out of the highway. It will be difficult to justify the expense if that curve costs only one traffic death every ten years, but easy if it costs two deaths a year. In an impoverished third-world country, where a human being’s life-time earnings are lower by a factor of ten or a hundred, the community will decide that a safety improvement so expensive is not worth it. Sad then it is for the visitor from a more fortunate part of the world to see the body of the victim of the accident of half an hour ago lying beside the road, covered with a white sheet until the family can come for it.

Simple Measures Against Everyday Risks Where there are many accidents, there is often room for a simple idea

that will save many lives at a minor cost. Seatbelts for automobile passengers are now required by law, we know, in many countries. Many of

us have visited a testing laboratory or at least have seen motion pictures

of the test in action: the car, the dummy,

the crash against the wall, and

the follow-up damage tally. The difference between the damage with and without seatbelts is so impressive that one hardly needs a reminder of the familiar motto, “Seatbelts saves four lives out of five.” Who will devise a still more clever and effective slogan to save those who still regard it as manly or macho to drive without a seatbelt?

METERS FLOOD OVER AMSTERDAM “N.A.P.”

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cal

2

SOE

1 WALI) |

fui

100

i

hua

it

hut

10 1 FREQUENCY PER YEAR

i

fue

0.1

1

0.01

Ficure 1. The higher the dike, the lower the risk that it will be overwhelmed by storm. With a height of 2.5 meters above “normal Amsterdam level” a dike will be overwhelmed once on the average every 2.5 years, according to records made over the period from 1808 to 1956. Each additional 0.25 meters, more or less, cuts the frequency of overtopping to half. The extrapolated probability for a four-meter height is three times ina thousand years; for a six-meter height, seven times in a million years; and for the 3.85-meter flood of the early morning of February 1, 1953, once in every 200 years. Diagram adapted, and numbers extracted, from J. Kriens, “De hoogte van de Netherlandse dijken; een economisch beslissingsprobleem,” pp. 110-132 in H. J. Lombaers, J. J. Meinardi, and D. Revestijn, eds., Operationele Research in Nederland, Het Spectrum, Utrecht/Antwerp, 1969, itself based on Rapport Deltacommissie, Staatsdrukkerij—en Uitgev-

erij-bedriff, ’s-Gravenhage, 1961.

Keeping one’s car up to a proper safety standard in many communities

is no longer a matter of individual choice but compulsory periodic inspection. There we see community values overriding individual careless-

ness, and see it still more conspicuously in the speed limits imposed on

drivers in so many lands. In my own country the National Highway Traffic safety Administration estimates that the 55-mile-an-hour or 90-kilo-

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meter-an-hour speed limit saved more than 54,600 lives in an eight-year period, and twice that number of crippling accidents. Congressional approval of that national speed limit came in part from safety considerations but even more from the oil crisis. It is interesting to try to cast up a balance sheet of the consequences of this speed limit. My own numbers are afflicted with the uncertainties that beset all estimates. I figure an an-

nual cost of six billion dollars a year in increased work-connected time. Against this cost is a saving in fuel and automobile wear that totals ten billion dollars a year by my reckoning, and a saving in lifetime earnings of those who would otherwise have been killed or crippled of also ten billion dollars a year. By almost any reckoning the 20-billion gain outbalances the six-billion cost, basis enough for that bumper sticker I see so often,‘“We can live with the 55-mile limit.” The life of the doctor is well known, who so often late at night has to

drive on a dark tar or macadam road to reach an ailing patient. It is all too easy to mistake the location of the edge and go into the ditch. If a

yellow line down the middle of the road saves one from the collision

from an oncoming car, why cannot a white line on the edge of the road

save one from going into the ditch? This idea struck the physician as he

drove in the dark. He took it to the New Jersey State Highway Commis-

sion, long a leader in promoting highway safety. Now the idea has spread far from the place of origin, example of the room that remains for individual initiative. If we have all learned something from the New Jersey doctor, perhaps we can also learn from the example of our Soviet and European friends who require in every car a first-aid kit located in plain sight on the ledge behind the back seat. It is an essential idea in

Bohr’s concept of the open world that we should all be free to travel and

learn from one another and bring back experience to help in our common problems.

Community Progress on Safety and Health It is one thing for the community to be concerned about risk, and quite

another for the community to be intelligently concerned about risk. It

was community concern that translated the idea of the doctor into the reality of the white stripe and gave us the seat-belt law, the 90-kilometer speed limit, and the divided highway. In time, community concern, plus safety precautions and safety training in the great du Pont tradition, will bring down our dismaying losses (Figure 2) from all causes outside the

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human body, all trauma, all “injury, wound, shock, or the resulting condition or neurosis”—seventy-three thousand deaths per hundred million of population in the course of a year. What if we never aged? What if ideally we could all survive to age 100? At present accident rates we would not all be around on that happy day to congratulate each other. Out of the 100 million population considered in Figure 2 we would have lost by ac-

cident, by trauma, by one external cause or another seven million of our

number. Out of 100 people, seven would be dead. Progress developed countries are making today in overcoming these external risks, but much faster progress in overcoming the risks internal to the body. Figure 3 comes from a study reported by James F. Fries, M.D., in The New England Journal of Medicine. The seven percent loss by trauma in one hundred years of life sets an upper limit to what good

health by itself can achieve. But how far we have all come since 1900 in

I I TOTAL I i MOTOR VEHICLES i T SUICIDE I I HOMICIDE I I FALLS T BURNS i DROWNING i ELECTRICITY I

AIRPLANES ‘1g80 1979 10 100

I

I

I I

; 1,000

© 10,000

100,000

FiGurE 2. Deaths from trauma—“injury, wound, shock, or the resulting condition or neurosis” —per 100 million of U.S. population in one year; or, equivalently, deaths via trauma per one million living an imagined hundred years. Calculated at U.S.A. 1978/79 rates. Based on data compiled by the National Center for Health Statistics, U.S. Department of Health and Human Services.

FROM

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TRAUMA IDEAL

75

g

PERCENT SURVIVING

100 (=

LIFE

25

Ficure 3. Survival probability in its dependence upon age (U.S. population); reproduced from James F.. Fries, M.D., The New England Journal of Medicine, volume 303, number 3 of July 17, 1980, pages 130-135.

moving toward that healthcare ideal! And how much further we can still hope to go—living on the average to age 85—as we learn the art of

healthy living! My concern with risk began with nuclear reactors. What should I say now, forty years later, about nuclear reactor risks? First, that safety remains as clearly here as in other realms of risk a community matter. Out of the community comes in my own country the Nuclear Regulatory

Commission, outgrowth of the Reactor Safeguard Committee, with

which I began this account. As the highway speed regulator comes under

a different governance than the road builder, as the safety division of the Federal Aviation Agency is independent of the aviation promotion activi-

ties of the Civil Aeronautics Board, so the safety-conscious Nuclear Reg-

ulatory Commission is independent of the energy-conscious Department of Energy. New thinking on how to assess risk is coming out of this regulatory agency and similar regulatory bodies in other advanced countries,

including Denmark. One such approach, developed and described by Norman C, Rasmussen and others, has won the name of “probabilistic risk assessment,” but to describe it here would take us into too much

technical detail. Some there were in the early years who called the Reactor Safeguard Committee

the Reactor Brake Committee.

Perhaps, however, the car

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that has brakes is more likely to complete a long trip than one that doesn’t! In the intervening 37 years, more than a million and a quarter people have died by motor vehicle accidents ina U.S. populati on of roughly 200 million but not one non-research person by a nucl ear reactor accident. Technology requires surveillance for safety, clea rly enough; and surveillance requires a specialized regulatory agency; but the first political principle is equally clear, that the regulator should not be under the regulation of the regulatee!

Perception of Risk Second, over and beyond risk itself, I have come to realize, is perception of risk. Psychological trauma can be as real as physical injury. The African of old did not have to kill his enemy. It was enough for the intended victim to know that a magic spell had been laid upon him by the native witchdoctor at the instance of his opponent. Awareness of the hex led to fear, fear led to paralysis of activity, paralysis led to failure of the vital functions and to death. At 4 4.M. Wednesday, March 28, 1979, several water pumps stopped working in the cooling system of the Unit 2 nuclear reactor located on Three Mile Island on the Susquehanna River about 16 kilometers southeast of Harrisburg, Pennsylvania’s state capital, with a population of

68,000, and directly across the river from the little town of Goldsboro,

with its population of 600. Through a complicated sequence of operator

failures and further equipment failure, a portion of the reactor lost its

cooling water and melted, releasing fission products into the space between the reactor and protective dome. Those in charge misunderstood

the situation. Saturday morning, March 31, they stated that a bubble of

hydrogen might be growing within the reactor, might explode, and in this way might disrupt the dome and release radioactivity to the chances of the winds. By Saturday evening, a Goldsboro councilman reported, 90

percent of the town’s population had left. By Wednesday, April 4, most of the residents had returned, still filled with worry about what might

happen. The fear and upset were contagious. They were not helped by the lavish coverage on television and in print. In the end it was recognized that the very idea of a hydrogen bubble exploding within the reac-

tor was mistaken. It was a mistake in physics and a mistake in engineer-

ing that led to the idea that there could be any hydrogen bubble, and a

mistake in management

that led to the publication of the untruth, so

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catastrophic in its consequences. Psychological in origin though those consequences were, they were nevertheless real—the greatest tragedy of the whole accident. How is one to secure the responsible management of perception? That is a fascinating problem of politics, politics in the highest sense of the word politics. In time of war the art has developed of propaganda and counterpropaganda, of information and disinformation. There at least one is helped by some knowledge of the general effect that the enemy seeks to achieve. Is it not becoming a still more difficult responsibility to manage the perceptions of a peacetime risk, when it is beyond the power of man to predict the irresponsible vagaries of press and television? However, there is a long history to suggest that community common sense will prevail. A steam locomotive? Capable of the unbelievable speed of 40 kilometers an hour? What could be more terrifying? And more clearly dangerous? It is no wonder that many a community ruled that a man must walk or ride ahead of the locomotive and carry a flag or lantern to warn the good citizens of the approach of the monster. It took years to calm fears. It did not take years of one hundred percent accident-free operation, but it took years of reasonably safe operation. September 1982 marked the hundredth anniversary of the world’s first city-wide electric lighting system. When electricity arrived, it brought its own cloud of fear with it. Lightning and locomotive were at least visible, but electricity was the invisible killer.

Moreover, inexperienced workmen sometimes installed unsafe wiring when they put the new electric lights into New York houses. The consequence was more than one fire sensationally reported in the newspapers. For the public to have had the fright of the Three Mile Island accident and to discover in the end that no one had been killed or was even likely to be killed perhaps marks the first step in a changed perception of the nuclear power reactor itself, its assimilation among the more familiar hazards of locomotives and motorcars, electricity and airplanes.

Disposal of the By-Products of Nuclear Power For the radioactive wastes of nuclear power plant operation a comparable acceptance has been slower in coming. Almost 40 years have gone by, it has sometimes been said, and we still haven’t got a good way to store ra-

dioactive waste. However, it is possible to state the situation in slightly different words: Almost 40 years have gone by in which we have been able to

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get along with our present temporary means of storing nuclear waste. It is a

blessing for the problem of disposal that so much of time has been taken because it has provided time to think and learn, to learn and think,

Encase the waste in concrete blocks? Drop those blocks to the floor of the ocean? Whatever attractiveness that idea might at first have presented

did not last long. Risk of a crack in the concrete, risk of the contents dis-

solving and attaching to organic matter decaying on the sea floor, risk of

marine worms feeding on this contaminated food, risk of bottom-feeding

fish eating those worms, risk of codfish eating those bottom-feeding fish, added up to a clear “NO.” In the meantime each selected site could con-

tinue to store spent uranium slugs under water in so-called “cooling ar-

eas” before chemical processing and could put into carefully built and monitored storage tanks the radioactive products of fission after their chemical separation. Some of the fission products lose any detectable ac-

tivity in a few hours; some, in a few days; some, in a few years; and

some only after centuries.

We have monitored nuclear wastes for 40 years; but it is sometimes

asked, do human institutions possess the permanence to monitor nuclear wastes for 40 centuries? That question creates the pressure to find a way

to store wastes that will be superior to any now in use in the sense that it

will require no monitoring and no care. In my own country more than 50

million dollars a year are presently being spent to develop permanent

methods of managing nuclear waste, of which the so-called “high level wastes” represented by fission products are the pace setters. Already by 1978 a factory had been developed which will encase these wastes in glassy substances, tough and unbelievably resistant to erosion and corrosion. Why then isn’t the problem of waste disposal already solved? Be-

cause of two undecided issues, not of physics, but of politics. One has to

do with where, the other do with what. What shall be put away forever? The fission products and the plutonium? Or only the fission products? And where shall it be stored? In my backyard, or yours?

The so-called Tri-City area in the middle of the state of Washington is

near the first and still heavily used reactor site. People there are eager for it to be designated as a national nuclear waste depository. They are familiar with the atom. They know that such an assignment will bring work

and jobs. However, still more favorable in its geology than is one or other highly stable underground salt bed, picked tionwide search. Is a nuclear waste repository acceptable to an unfamiliar be tempting for a political candidate in a local election to

their location out after a na-

public? It can make himself

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known by a rousing declaration, “Why should the nuclear wastes from the rest of the country be allowed to pollute our beautiful state?” A few years ago a clamor arose in southern New Jersey, not about nuclear wastes but about garbage. “Yes, we will let that landfill operator near Burlington build land on New Jersey garbage; but we will pass a law to keep him from increasing his business by bringing in garbage from the neighboring

state of Pennsylvania.” The law was passed. The landfill operator sued.

Eventually the Supreme Court of the United States decided that the law was unconstitutional interference with freedom of commerce between the states. By similar court procedure or action of the United States Congress or both it appears reasonable to believe that one or two or three national repositories will be established. The other political issue that holds up the immediate move of waste from temporary to permanent storage is more difficult. It has to do with that issue which is termed “the proliferation of nuclear weapons.” A third-world country has a nuclear power plant, busy providing electricity for economic development. Plutonium is created as a by-product of the operation of that powerplant. What is to prevent a new dictator, a new Idi Amin, from chemically extracting that plutonium and making bombs to threaten his neighbor? And how can advanced countries expect thirdworld countries to forgo the extraction of the plutonium they produce unless they will themselves give it up? These questions have put the United States in something like the position of Hamlet, Prince of Denmark. To bury the plutonium or not to bury it, that is the question. Is it more blessed to leave the plutonium with the radioactive products of nuclear fission, seal them all up together in a vitreous container, and bury it for-

ever deep underground? Or is it more blessed to save and use that plutonium, use it to manufacture the energy that men on Earth never cease to

need? The factory has been ready for years to start vitrifying nuclear wastes for burial. It was no problem of waste disposal that stopped it from getting on with the job. It was the command of Hamlet, of President

Carter in Washington. Bury the plutonium? Or save and use it? This

question, like other questions of where to bury waste, presents a fascinating mixture of the technical and the political. The statesman-engineer is

the man of the hour here as so often in the work of advancing the world

from yesterday to today and from today to tomorrow.

Visitors to Rome are shown the place where many a bridge was swept away by raging floods of the Tiber River. At length the Romans picked out a first-rate engineer. He guaranteed to build a bridge that would last

for 40 years. It still stands today, 2,000 years later. The engineer of our

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own day, given by the community the responsibility, the support, and the means, has no difficulty to guarantee a storage procedure good for a thousand years or more. But the products of nuclear fission, unencumbered by plutonium and other transuranic elements made in the operation of a reactor, already well before a thousand years are out, fall in radioac-

tivity to less than the original uranium that got destroyed. Mankind ends up diminishing the world’s store of radioactivity, not increasing it. The water that many of us drink passes over rocks containing natural uranium. As a consequence water picks up radioactive radon gas. So does the air around us. The source of the radioactivity in both cases is natural, the “still warm ashes of creation” that are spread all over the sur-

face of the globe. Bit by bit, as we burn uranium and vitrify and bury the products of combustion, we decrease the amount of radioactivity in the world. We lock it up safer from access to ground water than it ever was before. The “nuclear waste problem,” like almost every problem in this world of ours, is the doorway to opportunity. As we make our way into the world of tomorrow,

with its endless

frontiers and its opportunities for a deeper and richer civilization than ever before, we will meet and overcome many a new risk. But we know

that the greatest risk of all is what it always has been—to be born—for then we are sure to die.

The Balance of Benefit and Risk A university-aged granddaughter, who read the first draft of these remarks, commented,

“Your have

said so much

about the risks. Why

don’t you say something about benefits?” So I consulted a manager of

Connecticut Yankee, the nuclear power plant which at that time had produced more kilowatt-hours of electric energy, 60 billion of them, than any other power station in the world. He tells me that the plain simple everyday family that live in the average residence use 6000 kilowatt-hours a year to meet lighting, cooking, heating, and other needs. That energy, coming as it does today from the mixture of nucle-

ar-and oil-fueled power plants, costs them $480, but in the absence of

nuclear energy would cost them $680. The saving that uranium gives,

$200, is no small amount to the small family, especially the family

faced by hard times. It is no wonder that in my own country the Nation-

al Association for the Advancement of Colored People has spoken up in favor of nuclear energy, as has many a labor union. To the well-off

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low cost may be a luxury. To millions of people trying hard to stay afloat low cost means everything.

The Statesman-Engineer The balancing of opportunity against risk, danger against progress, is of course as old as mankind. The challenges transcend engineering in the

narrower sense of that term: They catch up the minds and hearts of the wider community. They fill the pages of the press, they fuel debates between Parliamentarians, they make the meat of the law and the labor of judges. But in our day a new a wider sense attaches to the word “engineer.” He is more than a technical specialist. He knows more than the harmonious matching of pipe to pressure, of engine to load, and of com-

munication-channel capacity to signal input. He understands more. He knows how society works. He is concerned to match technology harmoniously with the larger community. Distinguished members of the Danish Society of Engineers are examples of this new man. Never more than today, and never more than in dealing with risk, do opportunity and responsibility call for the statesman-engineer. Blessings upon all the world’s wise engineers!

Address given under the auspices of Dansk Ingenigrforening at Ingenigrhuset, Copenhagen, Thursday, October 7, 1982, on the occasion of the author’s receipt of the Niels Bohr International Gold Medal.

To Benjamin Franklin

ou who worked for great ends, Remind us that all progress goes in small steps.

You who worked so well with others,

Let us not forget that we could have done nothing Were it not for those with whom we were privileged to work.

You who helped to build on these shores a new society, Tell us that no advance is possible That does not conserve the best out of the past.

You who thrilled France and Europe

With your account of the great new democracy across the

water

And forged the alliance with France, without which we

would have fallen, Help us to remember that politics, in the highest sense of the word,

Always comes first.

You whose great friend Jefferson said in the days of Napoleon,

“Rather marry ourselves to the British fleet and nation Than let all Europe fall under the dominion of one power,”

.

You who twice since then have seen Europe rescued from over-arching tyranny

And most recently saved from economic collapse, Point out to us the granite constants of foreign policy, And remind imperfect us why again and again we must ally ourselves with great if imperfect Friends of

Liberty.

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“Hang together,” you once told us,

“Or hang separately!” You who see us today amid the unfamiliar perils of the nuclear age,

Tell us that openness is the best counter to fear and

phobia And teach us your famous prayer: “God grant that not only the love of liberty But a thorough knowledge of the rights of man May pervade all nations on earth,

So that a philosopher may set his foot anywhere on its surface And say: This is my country.”

From Franklin Day address October 15, 1969 at the Franklin Institute, Philadelphia, Penn.

TO

BENJAMIN

FRANKLIN

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Science and Survival

cience is an intensely human activity. It bears directly on the issue of human survival. It tolls out the eons of time that dwarf human history. It surveys the thousands of millions of light years of emptiness that surround the lonely human scene. It spells out the rolling dice of evolution, that led to the man of this particular era of history, with

today’s face and eyes and height. All this knowledge about man in space and man in time has been forced on us by our entry into the age of science. Before that time one could suppose that the human race forever was, is, and evermore shall

be. Who knew enough intelligently to ask whether our part of the universe would always exist? Or our solar system and our planet? Or, most

of all, our species? Who could have imagined den of planning for the future of man as a found loaded on man’s own shoulders? In an that a benign providence or at least a neutral

that the unbelievable burrace would some day be earlier time one could say fate had the human future

in its keeping. One could wait patiently for the unrolling of the fabric of

history. One could hope that the lines traced out there would be not too unfavorable. One could delude himself into thinking that he could not in any case do much to affect that future for the better. Today we know a little more! If there is any central theme and mes-

sage to be read out of what we have learned, I submit that it is this: Man can and must take control of his own fate. Otherwise, what chance is

there for survival?

Man, the Source of Purpose In a Universe Without Purpose That we alone have the ultimate responsibility is stated nowhere more

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clearly than in the writings of one who is both scientist and philoso-

pher, Michael Polanyi. His books, Personal Knowledge! and The Study of Man* won the 1959 Lecomte du Nouy prize? as outstanding studies of the nature of science, of thought, of man, and of moral commitment.

Polanyi analyzes the purpose of man. He makes the case that by itself

the universe is meaningless. Nowhere in that reach of space can one read any sure direction. Physical forces act, molecules collide, galaxies

separate. Radiation flows outward. Evolution proceeds. In all this blind activity there is no purpose, he argues. Whatever purpose there is, man himself has to supply—this is his leading theme. Polanyi thus paints

the picture of a world in which thoughtful minds commit themselves to purpose, make decisions, and themselves give shape to the future. “By this act,” he writes, “a prime cause emergent in time has directed itself at aims that are timeless.” There are many to whom the idea of a world without any purpose— except what we and our fellow men agree upon— comes at first as a dreadful shock. Later comes the feeling of challenge; and then at last an

inspiration: a feeling that we who felt ourselves so small amidst it all are, in the end, the carriers of the central jewel, the flashing purpose that

lights up the whole dark universe.

Seven Warnings That the Universe is Not Designed for Human Benefit If the concept of a world without a built-in purpose comes as a shock, even so it is not the first warning that the universe is not designed for

our special benefit. Seven other messages have come to us out of philosophy and science to the same effect. Let me discuss them in chronological

order under these heads: (1) Death is unavoidable. (2)

We are always in the minority. (3) We are not at the center of the universe. (4) The shape of the future is governed by the shape of the past. (5) Evolution with all its accidents, not design, brought us to our pre-

sent temporary human state. (6) Our universe is not static but dynamic and evolving.

(7) We have found no way to exclude the existence of

life on other planets. There is not one of these seven conclusions which did not trouble thought when it was first spread upon the record. There is not one which does not pose new issues about the long-term survival of the human race.

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Three Mathematical Models to Analyze Further Where the Future is Fixed and Where It is Subject to Control We can win some further perspective on these issues. We can size up

more fully what the future holds in store, and where we have freedom of

action, and where we are constrained by the laws of nature. For this purpose we can look into three mathematical models. One—the geometrodynamical model for the universe—gives some insight into the dynamics of expansion and recontraction of the cosmos. A second—the statistical model—tells something about the approach of all temperatures, regardless of their initial disparities, to a uniform and deadly equality. The third—the fluctuation model—deals with the opposite type of phenomenon, the development of the particular out of the accidental. All three will unite in suggesting that so far as we can now see, and despite the seven blows that I have mentioned to one’s first naive hopes, man does have a future, provided that he takes the helm away from

blind chance and steers a proper course: a survival course, with science for a compass.

First Warning: Death Puts Life Above Individual Life So much for a brief foreshadowing of the issues. Now for the first of the warnings that the world is not designed for the individual pursuit of happiness! No one knows who was the first man who understood the message of death: that every one of us is doomed to die; that the

life of the individual is nothing; that the life of the race, the group, the

family, the continuing generation after generation, lesson has to be learned anew in every generation. the first half of his life as if he were going to live does not understand in the second half of his life

is what counts. The Who does not live forever? And who how limited is the

time left to do what he can for the unrolling fabric of life that is going to go on and on?

Second Upset: Minority Status The second upset to hopes of a special providence also came so far back in the past that there is no record of the reactions to it: the discovery that to whatever race we belong, to whatever tribe we belong,

to whatever little community

we belong, we are in the minority. As

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we confronted another civilization, another tribe, or another commu-

nity in competition or conflict or combat, we found that we had to work towards a larger unity—or go under. “If you can’t beat them, join them!” We know today that cooperation and competition reinforce each other. / Neither can exist without the other. The interaction of cooperation and competition—and the effect of these interactions in bringing about

hierarchy upon hierarchy of organization—has nowhere been so thoroughly analyzed as in that branch of mathematical economics which we

know

as The Theory of Games

and Economic

Behavior, associated

with the names of Von Neumann and Morgenstern? and their followers.> If to be in a minority in one regard or another happens to us all, is it not also often a salutary experience? When competition is indicated, what motivates one more powerfully than to be in a minority? When cooperation is the right response, what can lead to that response more promptly? And if both cooperation and competition fail, and one goes under, as so many minority groups have gone under in the past, where are better examples to be found of honor and valor under adverse

circumstances?

As William Blake® put it, “To be an Error and to be

Cast out is a part of God’s design.”

Copernicus and the Third Upset to Man’s Privileged Position A third warning that man’s place in the scheme of things is not an automatically privileged one came from Copernicus, so close to modern times that we know the reaction to it. How dreadfully demeaning it seemed to the status of our race to find that we do not stand at the center

of the solar system! Yet this lesson was assimilated and—honor to the truth—the world goes on very much as it always did!

Fourth Concern: A Deterministic Universe Hard on Copernicus followed Galileo and Newton and Newton’s de-

terministic laws of mechanics—and through them a fourth much greater upset to man’s view of his place in nature. According to these

laws it is enough to know the present position of an object, and its present velocity, and the forces to which it is subject, in order to be able to predict its entire future—and its past as well. One who thought him-

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self freely studying the universe suddenly found himself caught up in a world-machine. Not only did the vision open out of being able to predict with ironclad certainty the rise and fall of the tides, the motions of the planets, the evolution of the solar system, and the rotation

of the Milky Way. One also was led with Laplace’ to think of calculating the motion of every molecule and atom everywhere in the universe—and with them all one’s own actions and thoughts for all the years to come. For this purpose one had only to know the initial position and velocity of every particle. Then the Newtonian world-machine took over. In it man served only as a tiny cog whose motions had been laid down from time immemorial.

This completely deterministic view of nature brought dismay to all

who had some hope and belief in the principle of free will. What good is it to think that one has achieved something by an effort of the will when it all was foreordained anyway?

The very Newtonian mechanics that seemed to deny free will nevertheless greatly reinforced the remarkable intellectual movement of rationalism, which in turn paradoxically opened up more doors for the useful exercise of free will than one had ever before dreamed to exist. The argument of rationalism was simple. The movement of the heavenly bodies, previously so mysterious, had been accounted for with astronomical accuracy by something so simple as the inverse square law of force. Therefore one must expect that other mysteries will also yield to intelligence. A rational approach should turn up not only new machines and better methods of manufacture, but also sensible solutions to ancient problems of all kinds, whether social, economic, or politi-

cal. The revolutionary influence of this doctrine both in Europe and in America is a part of history too well known to require recall here. What a contrast between the age of reason,® the American Revolution, and the French Revolution on the one hand—and with them our

own feeling today of freedom to reason and to act—and on the other hand the idea that determinism is supreme and freedom of will is imaginary! Does this contrast mean that even three hundred years after Newton we have not submitted to the lesson of his mechanics? Why do we persist in acting as if we have free will? Because this is the only

practical way to live a full life? Or because Niels Bohr has suggested that free will and determinism are not contradictory, but rather comple-

mentary concepts for describing human experience? Both! We have philosophical as well as practical reason behind us when we exercise free will!

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Complementarity

The principle of complementarity arose out of modern quantum mechanics. It states that “any given application of classical [non-quantum] concepts precludes the simultaneous use of other classical concepts

which in a different connection are equally necessary for the elucidation of the phenomena.” This principle was forced on one from studies at an atomic scale of distances, where the wave character of nature manifests itself. Historically, the position of an electron and the momentum of an electron were the first quantities to be recognized as having a complementary character, in the following sense: The equipment required to determine position, and the equipment required to determine momentum are incompatible with each other. They have such a character, no matter how ingeniously they are constructed, that they cannot both be used in studies on the same particle at the same time. Thus one can know the position at the cost of ignorance about momentum. Or one can know the momentum, with no opportunity to measure position—nor even, under the circumstances, to give any well-defined meaning to position. One

has to be prepared for the possibility that an experimenter may use either type of equipment. Therefore one cannot dispense with either concept—either momentum or position—in the description of nature. However, one cannot use both concepts at the same time. In this sense the

two are complementary.

If it is impossible even in principle to ascribe at the same time posi-

tions and momenta to all the particles in the universe, how can those ini-

tial conditions be known from which Laplace was prepared to calculate the entire past and future of the world? And without these initial value data, how can anyone make even a start at predicting the future? Along this line of reasoning, attempts have sometimes been made to strike

down Newton’s determinism. But the matter is not so simple. The central

equation of quantum mechanics is just as deterministic—when analyzed in mathematical terms!°—as are the equations of classical Newtonian

mechanics. Unclear is only what this mathematical detérminism has to

say about physical and philosophical determinism, particularly in the case of a closed universe.!! For reliable conclusions about the degree of uniqueness and determinism in the dynamics of a closed universe, we wait for the outcome of work now actually in progress on applying the

quantum principle to such a closed system.

Independent of any quantum analysis of a closed universe, Bohr has argued on more general grounds that determinism does not contradict

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free will. He extends the principle of complementarity out of the domain of quantum physics into a general philosophical principle. Position and

momentum, he points out, are not the only concepts complementary to

each other. There are many other pairs of concepts which are used in the description of human experience which are also complementary to each other in a similar sense: The experimental arrangement that allows one to study the one aspect of nature automatically excludes one from using on the same occasion the approach required to study the complementary aspect of the same happening. Free Will Complementary to Determinism

Specifically, let us analyze a man’s behavior in deterministic terms. We

say that actions are determined, not by free will, trations and physical-chemical potentials in the really to be an analysis, however, and not mere open up the brain case and measure these enzyme

but by enzyme concenbrain. If this analysis is talk, we must actually concentrations and po-

tentials. But as soon as we make these determinations, we interfere dras-

tically with the mechanism of life. We strip the organism of every means for exercising free will in the normal sense of the word. Conversely, instead of analyzing life from the deterministic side, observe the free-will aspect. Then it is necessary to leave the organism free to follow its own course. In this way one deprives himself of every possi-

bility for finding the enzyme concentrations and potentials that he must have for a deterministic prediction of the future.

The type of analysis known under the name of determinism, and the mode of description called free will, are thus complementary. The application of the one concept most directly and inescapably prevents any use of the conditions under which the other could ever be applied. This very complementarity in the conditions of use guarantees against any contradiction between the concepts of free will and determinism. This is Bohr’s argument put in its sharpest form. To him it was a

deeply considered but always tentative line of reasoning. Some investiga-

tors have been completely skeptical of analysis so philosophical in char-

acter. They have been unwilling to take seriously any idea in this area un-

til it can be translated into precise mathematical terms. Bohr himself

sought, not for any such mathematical formulation, but for a still deeper conceptual insight into the issue of free will and determinism, not least

through advances in molecular biology. Today, therefore, the discussion

has not ended; it is only beginning!

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The conclusion? What more could man want in the way of free will than what he already feels he has? If he will use this gift to take the control of his future out of the hands of a blind chance, that is his choice.

This freedom is all the more precious now because for a time it appeared

lost. What a recovery we have made from being ranked by Newtonian

dynamics as mere cogs in a deterministic machine! That fourth upset to

man’s preconceived idea of his place in the scheme of things was only temporary. Not so the fifth!

Fifth Upset to a Privileged Position: Man the Product of Blind Evolution Of all the scientific developments that one can name, none has had a more drastic and continuing effect in revising the human outlook than

evolution. It has answered the ancient question, “Where did man come

from?” We have lost our unique status. Our history is one with that of the other animals. We and they were all brought into being together by end-

less tides of mutation, multiplication and selection, mutation, multiplication and selection, repeated over and over for several thousands of mil-

lennia. Evolution!” has such a central place in any assessment of the human future that it is appropriate to comment on it in more detail when we come to our mathematical models, and the third and last collection of them, models for fluctuations.

Sixth Upset: A Universe Destined to Recontract to Destruction? As compared to evolution, the sixth warning that the universe was not designed for man’s special benefit comes more recently and out of the

world of physics. Einstein’s general theory of relativity, applied to the simplest model of the universe, predicts that the cosmos will go on expanding— as it is expanding now—until it reaches a maximum size. Then it will recontract and come once again to a state of enormous concentration of energy. Temperatures will mount so high—if this simplest

of models is applicable to our universe—that all life will be destroyed. Does man then have only a finite future ahead of him? Or is it not an

oversimplified model for analyzing this kind of question to start with an

ideal spherical universe? Is not its very sphericity a prime reason why it

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implodes to an ideal mathematical condensation? To recognize this oversimplification is motive enough for looking more closely at the dynamics of geometry, the first of the three mathematical models soon to

be discussed. This sixth warning against believing in any special place for man in the scheme of the universe thus ends with a question mark. So does the seventh and last.

Seventh Concern: Life on Earth Secondary to Life in the Rest of the Universe? There is no convincing evidence that all life in the universe is confined to this planet. There are roughly 10!! suns in our own galaxy, and there are roughly 10!! galaxies in the estimated volume of the universe.}3 If there

are then 10”? or more stars altogether, how can one rule out the possibility that at least one of them warms a planet still more suited than Earth to support life? Are not the statistical odds overwhelming that life on Earth occupies a secondary position relative to life elsewhere in the universe? If there is life on another planet, why have we not heard from it? As well ask why have they not heard from us! Only a beginning has been made towards trying to detect signals from distant sources, and towards trying

to signal ourselves.!4

What will we do when we discover life on another planet? What reassessment will we then make of man’s place in the universe? Will we not react as we always have in the past, with surprise and interest—and

then with a new age of exploration and adventure? On this point each of

us must draw his own conclusions!

What Conclusion from the Seven Shocks? Anyone who has felt the seven shocks and warnings that we have reviewed can hardly be imagined to believe that he occupies a special place in the planning of the universe!

To discover that no planning has been done for our benefit is one thing. It would be quite another assessment to find that man’s long-term future is foreordained to baleful blackness. Which of these two judgments better summarizes the evidence we have seen about the prospects for human survival?

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Despair Because the Self Has No Future? For some it is already total blackness to find death inescapable. Then think no more! Forget the future! Live for the pleasures of the hour! So have spoken some who are bitter, disillusioned, and angry with fate. The rest of us have a happier view. We know we have been saved for today by generation after generation of care one for another. No one—it is clear—lives to himself alone. Each is inescapably tied into the unrolling fabric of life. His birth is a link to the past; his children, a bond to the future; his character, a commitment to the present. Cen-

turies of evolution—and of struggle of the larger group for survival— have stamped into the inner fiber of everyone who is left undying traits of courage and self sacrifice. Why else would so many in times past have given their lives for the larger cause—a cause often grasped

only in part?

Or Commitment to the Larger Cause?

Of our seven warnings about the unplanned place of man in this lonesome universe, evolution thus transmutes four from messages of dismay to inspiration for commitment to the larger cause: Death? Turned from sorrow over the lost one to celebration that his or her most precious gifts endure in the continuing life. Minority status—and life on another planet, if found? Signals that the world of life for which one can live is not smaller than he thought, but larger.

The accident-filled evolution that brought us into being?!* If so much has been accomplished by accident, how much more can

be achieved by purpose?

Someone has said that life is like a performance on a violin, in which

one learns to play the instrument as one turns to face the audience. Might it be even more in keeping with the truth to compare life with a

new kind of ball game, played for keeps? At first one only stands and

watches the fascinating spectacle, thinking oneself a privileged onlooker. Then the game swirls about one. One is buffeted four times [items 1,

2, 5, and 7 of the chronological list of shocks!]. One suddenly realizes

he or she longs to has gone mates to

will not be here forever. One is oneself a participant. One besmaller groups, but there are always larger groups. The game on so far without purpose. It is now up to player and teamsupply the objective.

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The one-time onlooker joins in. and joy to discover that birth and for this game as no one was ever player plays still more vigorously

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The participant is filled with surprise past evolution have made him or her made for any other game. The new than did older generations, but with a

new question on the mind. How much giving purpose to the game?

freedom

does evolution allow for

Then comes a fifth upset, the idea of determinism

[item 4 on the his-

torical list!] and the question it brings—despite all talk of complementarity—about a rule of the game: Is not the future fixed by the past? Finally,

there is a sixth and seventh buffet [warnings 3 and 6 above] showing that

one occupies no central position on the playing field and raising the

question, Will there even be left, after several thousand more millennia,

any field on which to play?

Seven Warnings Leading to a New Ideal and Three Questions In brief, seven warnings have been seen against attributing a privileged

position to the individual. They can be transmuted into seven inspirations to accept a new ideal for life: Take control away from blind fate and do the steering ourselves! But out of the seven warnings there re-

mains a residuum of three questions: about the safety of our playing

field; about the degree of determinism imposed on the game; and about the leeway afforded by evolution for choosing direction for the game. These three questions about the universe, about determinism, and

about evolution are beyond our power to treat in any final way today.

However, in all three areas, investigations are now actively under way,

and deeper insights are to be expected in the future.

Three Mathematical Models to Aid the Analysis

Among ways of winning insight into complicated issues none has proved more fruitful in the history of physics than to seize upon and exploit a simple idealized model. Out of the familiar model of an ideal gas, for ex-

ample, one has learned deep lessons about the meaning of pressure, temperature, and entropy. Moreover, the conclusions from these studies

could be taken over to real gases with only minor modifications. Therefore it is appropriate to touch on three simplified mathematical models which give us insight into at least some aspects of the three questions

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that confront us. The first is the geometrodynamical model for the expanding and recontracting universe. The second is the statistical model for deterministic dynamics. The third is the fluctuation model for diver-

gent processes.

Pure Geometrodynamics as a Special Case of General Relativity

Pure geometrodynamics is the study of the geometry of curved empty space—empty of matter and empty of all field except electromag-

netism—and of the change of this geometry with time in accord with

Einstein’s standard 1916 geometrodynamics or “general relativity.”!¢ This geometry provides a model for the dynamics of the universe. We will have to recognize that the model has simplifications compared to the actual situation. Nevertheless, we want to know what the model has to say about conditions of very high density and very high temperature, such as would extinguish life as we know it. To treat adequately situations in which here and there matter comes to conditions of enormous density is beyond our power today. We do not know enough about the structure of matter, when atomic nuclei have

been squeezed into contact and when this superdense matter has been compacted further, to densities higher by powers of ten than standard nuclear density.!7 We do not know whether matter is then crushed out of existence. We are at the unexplored frontier between relativity physics and elementary particle phenomena. To circumvent these obstacles to analyzing the dynamics of a model

universe, we can limit attention to an idealized kind of physics where no so-called “real matter” comes into evidence. This is the simplification of pure geometrodynamics as compared to standard geometrodynamics. In that standard general relativity, space is regarded as curved, but as cause for the curvature one admits “real matter,” such as is made out of

electrons, protons, and neutrons. In contrast, pure geometrodynamics limits attention to those sources of curvature—those masses and fields—which one now knows how to treat as built out of empty curved space itself.

Background for the Concept of Curved Spacetime A few words are appropriate here about curvature, and what can be built out of curved empty space, before a turn back to the dynamics of the expansion and recontraction of the universe and what it has to say about human prospects.

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To the Bernhard Riemann of 1854 we owe a remarkable argument

why space should be curved. The reasoning has two parts. The geometry

of space tells a particle how to move—how else would the object know what is a straight line? But if space thus acts on the particle, then by the principle of action and reaction the particle should likewise have an effect on space. Or as Einstein later put it, Riemann was the first to realize that the geometry of our physical world cannot and does not stand in God-given perfection high above the battles of matter and energy. Instead, it is a participant, responding to the motion of particles, and departing from Euclidean rectilinearity. It is a curved space. Riemann developed the mathematical tools to analyze the curvature of a space of any number of dimensions. However, the physical foundations eluded him. That his judgment and powers of analysis did not win through to today’s general relativity is due more to the fact he did not recognize time on the same footing as space than to any other single cir-

cumstance.!8 For Einstein the step to four-dimensional curvature was

easier. He went from special relativity and the flat spacetime of 1905 to the curved spacetime and general relativity of 1916.

Tests of General Relativity The naturalness of this curved spacetime and the description it gave of “gravitation” was to Einstein the convincing evidence that he was on the right track. His less philosophically oriented audience of 1916 came to the same conclusion in another way, from the consequences of the theory, the three famous tests of general relativity.!9 For the precession of the perihelion of the planet Mercury, Einstein’s general relativity predicts 43.03 seconds of arc per century, as compared to 42.56 + 0.94 observed; for the bending of light which grazes the sun, 1.751 seconds

of arc compared to 2.01 + 0.27 (1947 eclipse) and 1.70 + 0.10 (1952 eclipse); and for the reddening of light which rises 22.5 meters against gravity, a change of frequency of 4.92 parts in 10!5 predicted, com-

pared to 5.13 + 0.51 parts in 10! observed.

Is Everything Made of Curved Empty Space? The checks with observation encouraged Einstein’s contemporaries to try to think of more experiments. Others were encouraged by the natu -

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ralness of a geometric account of gravitation to ask a deeper question, whether all of physics is a branch of geometry. In other words: Is spacetime—as one has considered in the past—only an arena within

which fields and particles move about and interact as “physical” and “foreign” entities? Or is the four-dimensional continuum a kind of

magic dough out of which everything we see is made: (1) one type of curvature in one region of space describes a gravitational field; (2) a rippled geometry with a different type of curvature somewhere else is

all there is to an “electromagnetic”

wave; and (3) a region, where the

curvature is knotted up into a configuration of high stability, moves through space as a unit, and behaves as a particle? Is spacetime an are-

na, or is it everything???

This space theory of matter, as William Clifford called it as early as

1870,?! was then only a dream, remained so during Einstein’s life, and

is still a vision as challenging as ever. It is difficult to name any issue in all of physics more central than this: whether matter is a manifestation of space, or whether the world consists of something more than pure ge-

ometry. Whether we like to think of ourselves as made of emptiness has little to do with the issue! The “solid” world already disappeared long ago, when atomic physics came in, with tiny electrons circulating through practically empty space. It does not change the solidity of the floor on which one stands to stop calling it more than 99.99% vacuum, and to start regarding it as made up altogether of emptiness!

New Features of Spacetime at Small Distances Physics today takes no stand on an issue as deep as the geometrical character of nature—and can’t! This science, like other sciences, has to

proceed on an empirical basis, using the concepts that work. It makes use of the idea of curved spacetime in dealing with gravitational phenomena, the interior of dense stars, and the dynamics of the universe.

In other realms of physics, as concerned, for example, with the solid state, the nucleus, and elementary particles, it has seemed completely reasonable to look apart from the curvature of space. If geometrical phenomena are to have any influence at all at small distances, then the

primary manifestation of the new effects must take place at distances of the order of

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eres quantum 4 "n angular momentum

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ee al of gravitation

"a

(speed of light)*/2 Seeo x0

some

This distance is fantastically small compared to the 10-8 cm of atomic dimensions, the 10~!2 cm of nuclear extensions, and the 107!4 cm of ele-

mentary particle dimensions. Is it prophetic of the importance of geometrical considerations that they direct our attention as well to dimensions which are astronomically small as to those which are astronomically great?

It could be feared that we have no right to talk about physics at 10-33

cm when we do not even understand the elementary particle physics of 10-'4 cm! One might have reasoned similarly in the early years of this century. He could have said that it was out of place to try to understand the atom and what goes on at such a small distance as 10-8 cm when one did not yet even understand the work hardening of metals and the physics of micrometallurgy at 10 and 10-4 cm! As it turned out, work hardening and tempering are caused by dislocations in the lattice arrangement of the atoms of the metal. These effects are unimportant in their influence on the atoms themselves. However, they could hardly have been understood if one had not already beforehand found out a great deal about the atom, and recognized that its structure dominates

over—and controls the form of—structures many powers of ten larger than it in scale. Similarly with all the simple estimates that one can make about the small-scale curvature of spacetime. If we accept general relativity and the quantum principle, we expect a turbulent and characteristic inner activity to be going on in the geometry at distances of the order of 10-33 cm. The effective energy density associated with these fluctuations calculates out as stupendous as compared to anything associated with elementary particles. On this basis, the structure of particles

would seem very secondary indeed compared to finer grained and more

turbulent structure pervading all space.

The Idealization of Geometrodynamics: Advantages and Doubts To the extent that this estimate of the situation is well founded, it would

appear reasonable in a first, rough analysis of the dynamics of the expan-

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sion and recontraction of the universe to disregard elementary particles altogether, and all the unsolved problems that they present today. In making this idealization to a universe built of pure geometry and nothing more—a completely geometrodynamical universe—one runs the danger that in throwing particles out of consideration, he may be throwing out much more than he thinks. Some who have made outstanding contributions to elementary particle physics think of the particles themselves—

not only electrons, protons, and neutrons, but also the various kinds of

mesons and hyperons—as the prime source of all the dynamics of inter-

est. That may be so, and the geometrodynamical model may be very far

from reality. At the same time it appears to be the only well-defined model available that allows us to investigate all the stages of the dynamics of a universe—both at low density, as corresponds to the present state of affairs, and at high density, where we are concerned about the possibility for life to continue. Moreover, we have learned since 1955 that this elementary geometrodynamical model has tantalizing points of corre-

spondence with the real world.?2

Geometrodynamic Models for Mass and Charge “Real” particles, one finds, are not the only allowable source of mass.

Standard general relativity offers a way to build mass out of pure geometry. A sufficiently great concentration of electromagnetic wave energy— or gravitational wave energy—when properly arranged, will hold itself together for some time by its own gravitational attraction in a ball of radiation, a so-called “geon.” This object moves through space as a unit. It undergoes deflection like any other mass when it passes by a center of attraction. Moreover, the geon itself exerts a gravitational attraction of its own. In this respect it behaves like “real” mass. Yet nowhere inside it is

there to be found any “real” mass—only curved empty space!

Other calculations—likewise based on standard general relativity, again without any inventive elements or changes in the theory, but again excluding all “real” matter from the building site—show that electric charge can be manufactured out of curved empty space. One is not con-

fined to “real” particles as the sole carriers of free electric charge! It has to be emphasized that the geon and the type of charge discussed here depend for their construction on the principles of classical geometrodynamics. What modifications come about when allowance is

made for the quantum of action, we do not yet know. Therefore, these

models for mass and charge have absolutely no evident direct connection

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whatsoever with the mass and charge seen on the elementary particles of

the real physical world, with their decisively quantum character. The simple model of physics built on curved empty space, Einstein’s equations, and the quantum principle—or more briefly, “quantum geometrodynamics”—thus gives no account of real particles. At the same time, this model has already suggested that particles are structures very secondary and unimportant energy-wise compared to the quantum fluctuations at a scale of ~10-*3 cm pervading geometry throughout all space. Moreover, out of the equations of geometrodynamics already at the classical level, there showed up, as if by magic, objects that one had no right in the beginning to expect to be there: geometrical mass and geometrical charge. Therefore, one can conceivably win further important new insights by pushing on into the quantum aspects of geometrodynamics— and, provided that one keeps his sense of critical judgment about the results, what can he lose? There is no other model available for discussing

the issue of particular interest to us here: the high-density aspects of the expansion and recontraction of the universe! So with this model we now turn back to the problem for the sake of which we embarked in the first place on this discussion of geometrodynamics.

The Dynamic Universe Why an expanding and recontracting universe? Why not a static cosmos? A static result was what Einstein expected when he and Friedmann first applied general relativity to the dynamics of a universe. For simplicity,

they idealized the matter—of which so much in the actual universe is collected into stars and galaxies—as spread about essentially uniformly, like dust or rocks, in a spherical, and therefore closed, universe. The

equations allowed one to calculate the radius of this spherical universe as a function of time. The result can be described in remarkably simple terms. Chalk a mark on a car’s tire at its point of contact with the ground. As the car advances, it rises to a maximum height and then sinks back. The plot of distance up as a function of distance advanced by the wheel gives the same cycloidal curve, apart from a scale factor, as represents

the radius of the universe as a function of time! The identity of the two curves is not surprising when one recognizes that one deals in both cases

with objects drawn together by their mutual gravitational attraction.

Moreover, the result is not changed when the mutually attracting objects are changed from real rocks, made of real matter, to geons, made of emp-

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ty curved space, as befits an idealized purely geometrodynamical model of the universe. The dynamical character calculated for the universe contradicted not only Einstein’s expectations of a static equilibrium, but also everyone’s idea at that time of what the astronomical evidence showed. This contradiction, coming as it did in the very early period of general relativity, seemed to Einstein an argument that he had made a mistake in the equations of general relativity, for which he had had such sound physical arguments. He reluctantly introduced a new so-called “cosmological term” for which the only warrant was that it would give a static universe! But then came the observations of many astrophysicists and the analysis of Hubble, showing that the universe is not static but expanding. From that time on, Einstein dropped the cosmological term and argued for the equations of relativity in their original form. If it had been possible to keep faith in that original form from the beginning, the predicted expansion of the universe could have been counted as a fourth decisive test of general relativity,

along with the other three well-known experimental tests! By the time Einstein dropped it, the cosmological term had found its way into much literature. Containing an unknown and therefore adjustable constant, it had given rise to a variety of models very confusing to the unwary student who reads the past in hopes of finding out the thinking of today. The multiplicity of models was compounded by another circumstance. To Einstein, general relativity meant not only his equations for the curvature of spacetime, but also a boundary condition on the

geometry—a requirement that space should be closed.?3 Others often disregarded the boundary condition and considered models of the universe with a hyperbolic or other open geometry. However, if one (1) accepts Einstein’s strongly stated arguments for limiting attention to a geometry closed in space, (2) idealizes this geometry in a first simple analysis as

having uniform curvature, (3) treats the case of mass so loosely distribut-

ed that it gives rise to no pressure, and (4) rejects—with Einstein—the cosmological term, then the Friedmann-Einstein solution for the expand-

ing and recontracting universe is the only solution there is! Moreover, if

mass does exert pressure against mass, then this change does not modify the prediction of an expansion and a recontraction. Only the details are

altered. The cycloidal curve for radius as a function of time is modified

to a plot of radius against time closer in form to the entire upper half of a circle. This prediction of an expansion that slows up and turns into a contrac-

tion is thus clear and straightforward. Furthermore, it has a definite con-

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sequence about the comparative sizes of two numbers. One of these numbers is the actual lapse of time from the start of the expansion to the present. The other is extrapolated time back to the start of the expansion: the time one would estimate from the present separation of any two galaxies and the present rate at which that separation is increasing. As the present rate should be s/ower than the rate in the past, so the time estimated from

the present rate of expansion—the extrapolated time— should be longer than the actual time of expansion. According to theory, the extrapolated time back to the start of expansion should exceed the actual time by a factor of 1.5 or more. The present best figures, 13 x 10? years (+50%) extrapolated time versus 7 x 10° to 10 x 10° years actual time, offer no clear contradiction to this prediction. In contrast, the figures of less than a decade ago were grossly incompatible with the expected ratio of 1.5 or more: 2 x 10° years extrapolated time versus 5 x 10° years even for the age of the earth! The reason, we now know, was an error in the calibra-

tion of the scale of distances from galaxy to galaxy. Some took this temporary discrepancy with theory very seriously, gave up Einstein’s theory,

and put forward ideas about the continuous expansion of the universe and the continuous creation of matter. Now that the discrepancy has been

cleared up, the prime motivation for considering such free inventions has disappeared. General relativity has shown its soundness by standing up to still another crisis! So much for the leading evidence”4 that the expansion of the universe is slowing down. So much, too, for the reasoning that any model based on Einstein’s theory and possessing anything like the closure of a sphere will recontract to a condition of unlimited density, fatal to all life.

Deep Issues about the Geometrodynamic Model Universe The straight dynamical analysis of the geometry during the turnabout

from contraction to expansion poses deep issues of principle?> not likely to be solved immediately. These issues cannot be properly described, but can at least be hinted at, by a brief list of topics requiring investigation: 1. Do space-like hypersurfaces always develop infinite curvature near the phase of maximum contraction? 2. At that point can one escape a properly quantum and probabilistic description of the geometry, in which one does not ask what the three-

geometry is, but what is the probability for this, that, or the other threegeometry?

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3. In contrast to other dynamical systems, which can be prepared in one or another of many conceivable quantum states, is the closed geometrodynamical model universe special, in that there is only one possible quantum state in which it can exist? 4. What is the relation between the concept of such a unique quantum state on the one hand, and on the other a classical so-called quasi-ergodic motion, which over and over again in the course of time comes indefi-

nitely close to repeating its past motion?

5. What does quantum mechanics say about the relation between ob-

server and observed in such a closed universe? Evidently we have much to explore! But nothing that we have learned so far from the study of the geometrodynamical model universe gives reason to be dismayed about

the long-term prospects for life in the universe.

Statistical Model for Deterministic Dynamics We turn from our first mathematical model to a second one, from curved

space to statistics, when we explore a second issue, the deterministic character of mechanics. We take up the statistical model of dynamics in order to have a second look at the earlier topic of determinism. For the

present purpose we forego the point of view of complementarity. In other words, we look apart from the actual quantum character of the particles of which we and our surroundings are made. We adopt here the classical point of view, according to which the initial positions and velocities of the particles determine the entire future—provided that these pieces of information are known with sufficient precision. In actuality, of course, we have nowhere near this amount of information about even

so simple a system as a nearly ideal gas. We have to describe the system

in statistical terms —counts of the number of particles with this, that,

and the other velocity—rather than a detailed statement of the position and velocity of every single particle. Along these lines we have been led to a statistical account of temperature, and entropy, and the second law of thermodynamics, with its statement that the degree of disorder in the world always increases. Hold a finger in the flame of a match. The sensation of burning is like nothing else on earth! It seems as far as anything well could be from possessing an explanation in terms of matter and motion, particularly matter and motion at the level of the almost infinitesimally small. Yet we know the workability and good sense of that mechani-

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cal account of temperature—and of the corresponding account of

entropy.

Let heat flow from a gram of water at the boiling point to a gram of water at the freezing point. An exchange of 50 calories brings the two to a common temperature of 50°C. This flow of heat implies a flow of entropy—or, more transparently, a factor of increase in the probability of the final distribution of energy relative to the initial one—which in

proper dimensionless units is not an increase by a factor of 104°° nor by a factor of 104°, but an increase in probability by a factor of 1.0 4:000,000,000,000,000,000,000

No wonder that one has often said that it is overwhelmingly probable that the two grams of water will come to a common temperature! No wonder that one similarly argues that the sun will cool or that the universe will eventually come to a uniform temperature! Yet one came to all of these statistical considerations in the first place because one was

trying to describe a system of whose initial conditions one did not have an adequate knowledge. One argued that almost all conceivable initial conditions, compatible with one’s incomplete evidence about the two grams of water from outside, would lead to the outcome that we have just described. In principle, however, the initial conditions could have been those unexpected molecular positions and velocities such that the already hot gram would go on to boil, and the already cold gram would begin to freeze! Under ordinary conditions one can disregard this rare

chance. However, when one concerns himself with the universe as a whole, he deals with a unique system to which statistical considerations

do not necessarily apply. In other words, purely statistical calculations by themselves do not suffice to assure us whether entropy will increase or decrease during a phase of recontraction of the universe. We do not know, therefore, whether biological time—geared

as it is to the direc-

tion of entropy increase—will then run forward or backwards compared to the direction of dynamical time as presently defined. We come here again to an issue at the frontier of analysis. We are not dismayed at

the prospects for the long-term survival of life, but neither do we have the right to assume a favorable result from the analysis as a foregone

conclusion. One cannot turn away from statistics without asking who would ever

have conceived of temperature and entropy as aspects of motion if the science of mechanics had been left to develop unassisted by the shock of

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events. Who, dealing with the collision of two or three particles, would ever have dreamed that the generalization of his problem to very large numbers of particles would lead to such sophisticated concepts? The evolution of qualitatively new concepts out of previously elementary situations as we go to the limit of very large numbers—here, very large numbers of particles—is the most instructive lesson to be carried over from statistics as we turn to our third and final mathematical model— fluctuations”® as a model for some aspects of evolution,

Fluctuations, Divergent Phenomena, and Life Some years ago, Irving Langmuir made an interesting distinction” between convergent and divergent phenomena. The most elementary con-

vergent phenomena easily mentioned is the flow of heat from a gram of hot water to a gram of cold water, leading to the equalization of the two

temperatures. That type of convergent effect is very far from being typical of all that goes on in the world, Langmuir stresses. Consider the Indian Ocean lying still under the sun, absorbing heat hot summer day af-

ter hot summer day. The heat energy is converted into energy of evaporated moisture. This energy piles up in more and more dangerous amounts in the still air lying overhead—but there is no way to let it loose! The air is still and humid. Through this ocean a ship plows its steady course. Evening approaches. A sailor who has come off watch strolls to the bow, lights a cigarette, and smokes it as he watches the sea

coming toward him. The rising current of warm air starts an updraft. The updraft just suffices to trigger off a greater and greater flow of warm air upward. The mariner is in at the birth of a hurricane. It could just as well have been started three hundred miles away if the sailor had lighted his cigarette there. Here is fate! Whether that island and those people are or are not to be engulfed by a tidal wave depends on the

lighting of a cigarette at one place or another. We have here a divergent phenomenon in the sense of Langmuir—a process where a small effect gets multiplied up into a great outcome. No divergent phenomenon has been studied in more detail than a nuclear chain reaction. Fluctuations in output occur in a small reactor run at conditions close to critical. In Los Alamos days there was an experiment known as twisting the dragon’s tail. The fissile material was assembled for a brief period into a supercritical configuration. An accident in such an assembly cost the life of a fine young man, Louis Slotin. But

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in a normal experiment one measured the total number of neutrons giv-

en out during the period of supercriticality. This number varied substan-

tially from case to case, under otherwise identical conditions. The rea-

son? Random fluctuations in the time when the first few neutrons came

off to initiate the chain reaction. Here was a case where a small initial

variation produced a large difference in the final output.

The concept of a divergent phenomenon comes particularly to the

fore when one considers evolution. Here, too, the outcome depends in a

striking way on minor differences at the beginning. We have here the direct opposite of the uniformizing trend evidenced in statistical mechanics and in the phenomenon of temperature equalization. The number of different combinations of genes which can be conceived mathematically is stupendous. Even if the whole surface of the earth were populated with human beings, all different, still these genetic samples would fall fantastically short of realizing even the tini-

est fraction of the possibilities.28 This circumstance tells us that

which ones amongst the conceivable gene combinations are actually realized is a matter of what in one sense of the word one would call

accident.

A New Concept to be Read Out of Life? Considering this nonstatistical feature of life, Glass stresses”? that biology has aspects which one can never hope to explain by physical law. Would it be out of place to accept this statement in the same spirit that

Niels Bohr uses in speaking of a great truth? A great truth, he says, is a truth whose opposite is also a great truth. To say that biology cannot be described in terms of physical law is to say that biology is not like statistical mechanics or thermodynamics. One cannot write a simple equation for the evolution of a species as one writes an equation for the rate of equalization of temperature between two bodies in contact! Evolution is not convergent, but divergent.

What, then, would one mean by a new concept to describe life if a

statistical concept analogous to entropy or temperature is out of the

question? Surely one is not speaking of anything in principle so elemen-

tary as a microscopic description of biological processes. We do not question that biology, like thermodynamics, can be accounted for in terms of the laws of interaction between individual atoms and

molecules—laws which are symmetric in time, well defined, and free of

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any sort of mysticism. There is nothing in the way of a new concept for which we feel any need at this level! Qualitatively new concepts arise out of previously simple situations—

all our past experience tells us—whenever the number of similar objects

becomes very large. In this connéction one hesitates to mention once again the concepts of temperature and entropy. To put too much emphasis on statistical mechanics is to give the false impression that the limit of large numbers gives rise to qualitatively new concepts only in the case of convergent processes. An example of a contrary kind is furnished by the theory of games—typically divergent in character. In the limiting case where very large numbers of participants take part in a game, it is typical for optimal strategy to force on the players layer after layer of organizational hierarchy.*” The concept of hierarchy is here the feature analogous in its newness to the temperature and entropy that we have already seen

arising out of statistical mechanics—and analogous, we have to assume,

to the concept that we have yet to see arising out of the analysis of the

life process. Temperature and hierarchy are concepts like nothing else. Equally distinct must be the new concept for which we are groping. What can be its character? Does it have to do with “choice,” “freedom of choice,” enor-

mous numbers of options and an unpredictability of the future,

a chance

for some little action that one of us takes to influence the whole course of affairs for generations to come? How can anything of which we have such a foggy notion be expressed in clear language, let alone be given a quantitative formulation? Against trying to be any more specific at the present stage of our knowledge, it is warning enough to pick up an old book on the subject of heat and read the dreadful foolishness that was written on the subject of the “caloric”!

A Story of Determinism and Choice It is better to tell a story having to do with determinism and choice. A dozen of us were seated in a living room after dinner. One would be sent out. In his absence the rest of us agreed on a word. When he returned he had the right to “yes” or “no” answers to twenty questions to help him find the word, if he could. At length unhappily my turn came. When I re-

turned and started asking my twenty questions, I sensed that something had changed about the situation. The further I got with my queries—"Is it an animal”; “Is it white’—the more difficulty did the one questioned

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appear to have in replying. At length the word was pinned down— it was

“cloud”—and I was let in on the secret. When I had gone out, it had been

agreed It was asked, But by

not to select a word, but to act as if a word had been agreed upon. easy for the first man—he could answer as he pleased when I “Is it an animal?” So could the second when I asked, “Is it white?” the time four or five questions had been asked, the possibilities

were so narrowly limited that the next answer could not be at random. It

was nevertheless a rule that everyone in the room had to have in mind at each stage of the game a word consistent with all the answers that had gone before! Hence all the difficulty. The friend (E. T.) who had explained to me the secret of the game went on to philosophize a little. “How similar your expectations when you came into the room to the attitude all of us frequently adopt towards life! We imagine that the final answer has already been laid down—that we have only to wait to the end

until we shall see what it was. We don’t realize that the very questions we ask of life—and the actions we take—condition the answers that we get back!” Evidently we do not have in hand today a mathematical model which allows us clearly to sort out the concept—valid in the appropriate largenumber limit—which is unique to life. Our position on this third issue, like that on statistics and the direction of time, and on geometrodynamic contraction and high densities, ends with a question mark. Nothing that

we now know argues against the long-term continuance of life; but at

least three questions require a much deeper understanding before we have any right to take a final stand on this issue.

Our Choice At this stage in history we have to get on with the business of life without knowing the answers to these questions. Many of us have taken part

in enterprises of great moment where the facts about certain vital issues simply were not available. Most of the important decisions of life, from

marriage to decision on a career, are made without a knowledge of all the

facts—and generally made successfully.

Can we be equally successful in giving direction to life? It is not necessary to have all the facts in hand to try! Here the latitude in choice open to us in regard to the long-term future is fantastic compared to anything we ever had before. The absence of any beneficent providence run-

ning the machinery means that we cannot simply wait and hope for the

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best. Neither can we discover the purpose of man by studying the universe. Purpose, as Polanyi emphasizes, came into being with man. The spark of thoughtfulness on this planet, conceivably with a glow ona planet here or there among the distant stars, lights up the dark purposeless reaches of space. We ourselves can make the purpose of life what we collectively choose. If we do not set the goals, no one will do it for us. We can let this planet hurtle through space to a dreadful fate. We can let rich planetary landscapes elsewhere lie forever untrodden by human beings. We can let evolution take its blind course. We can let humanity degenerate into a single crowded planet of large-scale ants, collectivized and regimented, with all diversity of thought extinguished. Or we can recognize that the fate of man lies in our own hands. Step by step we can struggle to a mastery of that fate. Not only can we raise up the stature of life on this planet. We can plant islands of life and thought and purpose here and there through boundless reaches of space. How fast to go at this enterprise, we are learning to decide every time we vote a budget and priority for molecular biology, for space exploration, and for every other activity that gives us new power over the future. Generation after generation of human talent has gone through life poisoned in outlook and frustrated in purpose, only to be thrown at the end

onto the great wasteheap of spent human life. Now at last we have a new vision. Philosophy passes the judgment. Human idealism raises the flag. Science shows the possibilities. Education spreads the motivation. We, the human species, can and must take control of our own fate. How else can

we survive over the long pull?

Abridged from January 16, 1962 address at the University of Delaware.

The Place of Science in Modern Life

n May of 1895 Formosa had won freedom from continental China. She was not to come under effective Japanese rule until a year later. A new government came into being. A proclamation was issued be-

ginning with these words, “ We, the intellectuals and common people of

Formosa, are determined to resist subjugation.” At first these words sound to us a little old fashioned. The modern world is a democratic world. We will not put any man on a pedestal of ivory and kow-tow to him. We rightfully refuse to regard the scientist or the professor or the businessman as a sacred cow. No one today is an ob-

ject of worship because of his position. The world of today is so complex that everyone is in some sense called upon to be an intellectual. We have given up the idea that some people are surplus. We think of each fellow citizen as a potential national asset. We demand a higher standard of public education and better libraries so that everyone can contribute more from the ability that lies within him. That is a part of the modern outlook that we are determined not to give up. We cannot give it up. Any nation that abandons that ideal will go under. As we turn back to the declaration of 1895 and read again those words, “We, the intellectuals and common

people of Formosa, are determined to resist subjugation,” still more thoughtfully, we nevertheless begin to appreciate more sympathetically

what its authors had in mind. We think of the old days and the traditional scholar-gentry class that then existed. We recall the high tradition of public service that had come down to that class from ancient China. We real-

ize some of the implications of that phrase, “we, the intellectuals . . .”°— not, “We, the privileged intellectuals,” not “We, the high and mighty intellectuals,” but “We, the intellectuals whose deep obligation it is to plan ahead for the welfare and safety of all of us, and we, the everyday people who also think and plan, but not on so large a scale, we stand

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united in the defense of our country and its future—our fates are tied up together.” So we might paraphrase some of the ideals that lay in that

1895 statement. Let us then take the Formosan declaration, not in an unworthy way, but as signifying in this higher sense a special dedication on the part of a special group of people, an extra obligation to serve. How then can we formulate the distinction which it contains in these days when everyone, in every walk of life, is forced in some sense to be an intellectual to meet

the problems of the day? I propose that we distinguish between a light intellectual and a heavy

intellectual. This distinction has nothing to do with the diet, or if it does,

the connection escapes me.

Light Industry and Heavy Industry Our colleagues in economics differentiate between light industry and heavy industry. Powdered metals, they tell us, belong to heavy industry, because materials furnish the wherewithal for other industries to build upon. Houses on the other hand, they remind us, belong to light industry, because they serve the consumer directly. Heavy industry is the founda-

tion, even when it deals with objects as light as grains of metal. Standing

upon that foundation is an industry called light, even when it constructs objects as heavy as houses.

The Light Intellectual and the Heavy Intellectual If we follow the lead of economics about the meaning of light and heavy, what shall we mean by a “light intellectual”? A light intellectual, we will say, is one who keeps the machinery of life going. He doctors the sick, he

renders legal judgments, he gives the accepted instruction, he governs the course of trade. And what is the “heavy intellectual”? The heavy intellectual opens the way to new avenues of existence. He finds a new way to fight disease. He conceives of a new legal invention to pledge the credit of a state so it can build a superhighway where only a poor road was pos-

sible before. He changes the nature of thought and forces a revolution in text books. He conceives of a new industry. If he is a poet or a writer, like Dr. Hu Shih, he may accomplish the greatest miracle of all, and raise up the whole spirit of a country.

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If we accept the distinction between light intellectual and heavy intellectual, between those who keep the world going and those who move

the world ahead, then we can say that the Sino-American Conference on

Intellectual Cooperation is concerned with the obligations and opportunities of the heavy intellectual, especially as they concern Taiwan and the United States. My special subject is then the work of the scientist as one particular kind of heavy intellectual.

Contributing as a Heavy Intellectual to Science I am happy to speak on this subject because today and in the United States there is no better known way for a young man to become a heavy intellectual than to follow one or another of the natural sciences. The number of these degrees awarded in the sciences has increased since 1885 on a curve almost regular except for the periods of the two wars. On the average the rate of production of Ph.D.’s has doubled every ten

years over a period of 75 years. If the rate of increase continues, and if the present rate of population increase also continues, then a few years after the year 2,000, one person out of every 50 will acquire a Ph.D. de-

gree. If this figure sounds fantastic, I can only say in replay that the frontiers of science are limitless. When young man after young man steps

straight out from his Ph.D training into a well-paying job, no one is going to keep other young people from emulating them. They have an increased sense of conviction on this point because they see no other career open to them where they can be more useful to the country. The number of Ph.D.’s in the biological sciences is increasing even

faster than the number in the physical sciences. As Conant puts it, the first

half of this century belongs to the physical sciences, but now we have moved into the half century of the biological sciences. The trends in advanced training lie under the continual observation of the Committee on

Fellowships of the U.S. National Academy of Sciences—National Research Council. Within the past five years, that committee finds, the num-

ber of Ph.D. degrees in the biological sciences has for the first time

crossed and increased above the number of degrees of doctor of medicine.

Hand in hand with this growth in the number of science degrees—de-

grees both in the biological and in the physical sciences—has gone a

growth in scientific activity. Research in government and industrial laboratories has doubled roughly every ten years. When choice is not

enough to being about this increase, the compulsion of competition

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takes hold. Few industries are more competitive or more rapidly changing than drug manufacture. It is not surprising that the expenditure on

research in this industry is unusually high, with figures like 10 percent

not being untypical. In the chemical industry the expenditure of research

runs closer to three percent. How important that expenditure is can be seen from one simple circumstance. Most of the business of our larger chemical companies today lies in products which did not even exist 25

years ago.

If competition forces research, and research forces progress, then one sure way to prevent progress is to set up monopolies ensured against all

competition.

Rate of Expansion Due to Innovations in Science and Technology It is not enough to make minor improvements to stay in the stream of activity today. The carriage maker was making minor improvements in his product in the early years of this century. That did not save him from extinction at the hands of the automobile industry! One of my friends in an industrial organization came up with an idea recently to use the waste steam in a certain large plant to accomplish new and useful things. The change would have cost $50,000, but the return on this expenditure would have been 20 percent each year. He was told that it was outside the policy of his company to spend money on improvements that gave a return so small. It was necessary to have a 30 percent return before it was worthwhile to invest money in a new process. This number is a measure of how rapidly things are changing today! T have an atlas dating from 1906. On that atlas I turned not long ago to the Netherlands, a country not very different from Taiwan in size and population and crowding of population. On that map I saw a tiny dot, the smallest dot that the map maker allows. That dot stood for a community with a population between five and ten thousand, the little town of Eindhoven. Today Eindhoven is one of the great cities of the Netherlands. Its population numbers 134,527. What is the explanation? Was a gold mine

discovered? No, a few “heavy intellectuals” came up with the ideas that built the Phillips Electric Company, a company with makes lamps, electrical appliances, radios, x-ray tubes, and a multitude of more sophisticat-

ed items. One could count on the fingers of one hand the names of the

men whose ideas started off that enterprise. To a place that had almost nothing they gave one of the great industries of the world.

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The possibilities for invention are not limited to the physical sciences, as we know not least from the work of Pasteur. Nor is it neces-

sary to have great industries to benefit from invention, particularly in the area of the biological sciences. It is enough in this connection to recall the great effect of hybrid corn on farm productivity. The contribution of this development to the world’s economy long ago passed the billion dollar mark. Yet this development was brought to pass by the research of a handful of men.

Science, Technology, and Defense ‘ Our possibilities to provide a future for our children and our children’s children depend today not only on our farms and our industry, but also upon our defense posture. There was a time when it was as impolite to speak of national defense in public as to mention sex. Today we are willing to admit that continued

existence is impossible without either. We have also discovered that the defense of the free world depends as

never before on technological advances which may be made by one or two men or by a small group. The other day, reviewing in my mind the programs of the two United States laboratories concerned with nuclear

weapons, I counted up those men who are at work trying to contribute

decisively new ideas for use in case of dire emergency. It was fantastic to discover that only 11 men are concerned actively in this very forward area. What a world, where the liberty of over two billion people can depend on the labors of fewer than a dozen men! However much the safety of a free society depends upon technological

advances, it has come to depend still more upon the good sense and resolution of the average well-informed citizen. He has the good judgment not to believe that nuclear weapons foretell the end of life on earth nor

even—unhappily—the end of all war. He knows that a balance of strate-

gic deterrent power is the best guarantee we have today against the out-

break of war at the all-out level.

However, it is also conceivable—he realizes—to be pushed into a ma-

jor war through what was in the beginning a localized conflict, which

then tion lems fore

grows and spreads out into extends to trouble spots all are less technological than he votes for representatives

an all-out struggle. Therefore his attenover the world. He knows that the probsocial, economic, and political. Therewho will spend his tax money and find

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men—“heavy intellectuals”—to deal as wisely as they can with these larger issues. At the same time our responsible fellow citizen knows that social and economic development cannot come without peace, and peace cannot be maintained in troubled areas without force. He recognizes that the kind of limited war force required for this purpose is completely different from the strategic power required to deter all-out war. Limited war defense makes its own heavy demands for imaginative thinking. At China Lake in the California desert, a few years ago a small group of men conceived of the now famous Sidewinder missile. Only a few months ago a fraction of the Taiwan Air Force, equipped with these small and ingenious devices, turned back the attack of a great and aggressive air armada in a decisive battle. As in this example, so in many free-world countries small groups of dedicated technologists and scientists are working on imaginative new devices and new ways of doing things. These “heavy intellectuals” work to preserve peace today so that other groups of “heavy intellectuals”— such as our honored colleagues in this meeting—can strike the still more

decisive blows for a better tomorrow.

Scientists in Action The contribution of science, whether to defense, or to agriculture and

medicine, or to industry, is marked by nothing so remarkable as this,

that decisively new advances come from small numbers of men and

women. In other words, we have in science a new way to help get on with our human problems. Therefore let us turn from the results of science to a few word pictures of scientists in action. Let us then conclude this discus-

sion with a few concrete proposals that our conference might consider. We look more at scientists in action and less at the subject matter of

science because we are more concerned here today with spirit and human

values than we are with the nature of matter and energy.

Yang, Lee and the Symmetries of Spacetime Let me begin with my friends T. D. Lee and C. N. Yang. They work in the environment of Princeton and Columbia. To them the problems of

the elementary particles, and the decay and transformations of these

mysterious entities, are a day-by-day source of worry and concern and

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delight. Studying over the observational evidence and the past interpretations of that evidence, they found themselves forced to question the then-current assumption that the physical world is symmetric between left-handed and right-handed. In other words, the collisions and spontaneous breakups of elementary particles, when regarded in a mirror, might well really be different in character from the events seen by direct vision. They took this idea seriously and worked out its consequences mathematically. The results led them to suggest new experiments. Their suggestion was taken up by that distinguished, charming, and active experimentalist Miss C. S. Wu (Mrs. L. Yuan). In collaboration with others

at Columbia and at the Bureau of Standards in Washington she carried out decisive tests. Electrons come out of atomic nuclei, the group found, spinning about their own axis preferentially to the left. The world is not symmetric between left and right. Most of you have seen, I am sure, the address Yang delivered at the time when he and Lee received the Nobel Prize for their work. In it he acknowledges his double indebtedness—to the cultural tradition of China and the scientific tradition of the West. Today both continue their work actively in the Western world. There the contacts are richest, there today

the freedom of inquiry is greatest.

Human relations in the profession of theoretical physics, as in many

other branches of science, have interesting and unusual features. Mem-

bers of the profession belong to a kind of island of culture. Physicists in London, New York, Berkeley, Princeton, Paris, Taipei, and Bombay often know each other better than they know their colleagues in other fields of work in the same community. They must if they are to keep up with their work. Some are like bumble bees. They go about from flower to flower picking up pollen in one place and fertilizing blooms in anoth-

er place.

The importance of human give-and-take, of an atmosphere of lively

discussion, shows also in another way. The articles today in physics and

in other fields of science are written far more often by two or three collaborators than by a single author. To cut oneself off from the flow of

ideas is often to decrease one’s effectiveness. As Kettering puts it, “When you lock the laboratory door, you lock out more than you lock in.” Secretiveness is a symptom of sterility. The Geneva Conference of 1955 on peaceful uses of atomic energy

provided for many scientists their first opportunity to exchange ideas

with their Soviet colleagues. For ten years the International Union of

Physics had worked to bring about a substantial East-West meeting. At

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last nuclear energy of all subjects was leading to the rapprochement. The program was full of papers about power plants and the energy needs of the future and the world reserves of uranium ore. But this formal program was given second place by many of the Soviet and Western physicists as soon as they found informal contacts were possible. A group of about 40 went off into a room much smaller than an auditori-

um. There they shared on a blackboard their ideas, their results, their worries, their hopes, their concerns, and their dreams about the struc-

ture of elementary particles and the nature of matter and energy. It would be difficult to name any field of activity where the spirit of giveand-take is more prevalent than in basic science, nor one where political and ideological differences interpose fewer obstacles to genuine human understanding.

The field in which Yang and Lee work is thus one where it is essential to maintain wide contacts; one where a man puts himself at a handicap if he goes to a center too separated from others to allow stimulating weekto-week contacts with workers from other centers. It would be a mistake to conclude, however, that every field of science, or even every field of

physics, demands a large center for its most effective cultivation. There

are many subjects in which a small school can achieve great results. An example is furnished by the work now going on at Brigham Young University in Utah on the physics of high pressures. Two or three good men at modest expense are breaking new ground, and supplying leadership of high quality to their field.

Watson and Crick and Deoxyribonucleic Acid Let me ample: James pher at

turn now from Yang and Lee and physics to my second case exWatson and Crick and what they have done for biochemistry. Watson is a young biochemist at Harvard. Crick is a crystallograCambridge University. Their attention centered on the structure of

a substance known as deoxyribonucleic acid—DNA for short. This sub-

stance has never been synthesized. However it occurs naturally in the nucleus of the living cell. The fundamental problem of life and growth and reproduction leads back always to the still more basic question how a cell divides. When and how the cell divides to form two new cells is governed

by the central nucleus of the cell and by the division of this nucleus into to new nuclei. Before the work of Watson and Crick it was generally agreed that one of the constituents of the nucleus—DNA—has something impor-

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tant to do with the act of division. However, neither the structure of the

DNA molecule nor its relation to the act of division were known.

Watson went from Cambridge, Massachusetts, to join Crick at Cam-

bridge, England, because there the facilities for crystallographic analysis were most suited to their work. Their ingenious analysis led them to the

model of the DNA molecule found in Figure 1. This essential ingredient of all life processes is endowed—they had to conclude—with the amaz-

ing structure of a double spiral. Each of the strands in the spiral is made up of shorter segments—the so-called nucleotide molecules of nucleotides—fitted together one after the other. As a consequence of the work of Watson and Crick, one now has a model to account for the elementary act of duplication in the life process. The spiral of two strands unzippers to make two spirals. It might appear that each new spiral would have only a single strand. Not so! The double spiral begins to

come apart at one end (Figure

1), but not in isolation. It is surrounded

by a nutrient fluid containing many nucleotides. They are potential building blocks to form new strands of spiral structure. This building process goes on at points A and B (Figure 1). It ensures that the two new spirals in process of building will each be double. Moreover, the

ordered pattern of different kinds of nucleotides in the chain—like dif-

ferent kinds of letters in a word—is replicated. The two new double

INN:

Ficure |. Schematic diagram of the beginning of the “unzippering” of a spiral DNA molecule to start the formation of two new DNA molecules.

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spirals, letter for letter, are duplicates of the old one. What a beautiful and simple foundation for the science of life and growth! On the foundation of the work of Watson and Crick, further advances

have already been made in our knowledge of the replication process. It has been feared by many that the unzippering of the spiral molecule, simple as it is in principle, would prove most complicated in actual operation, requiring by way of assistance and support all kinds of enzymes and supplementary reaction. However, recent experiments reveal that little more is necessary for duplication to begin than to put a few DNA molecules into the solution containing the appropriate nucleotides. For DNA molecules to replicate under these conditions turns out to be almost as simple as it is for water to flow down hill. In consequence of this newly discovered simplicity of the process of duplication, the problem of life has completely changed its character in the last three years. Instead of asking how replication takes place, we

now have to ask, what keeps it running away in you and me? How is the

process of duplication kept under control and channeled into orderly growth? What a challenging issue this problem of biological control pos-

es for the future!

The Symbiotic Relation Between Student and Scientist-Teacher What now of the human side of this second case history? The kind of work we have been talking about is done by several professors and several students, working on individual projects, but in day-to-day contact for advice and mutual stimulation. There is a close interaction between teaching and research. There is none of the isolation of a “pure research institute” cut off from all the instruction and all contact with young minds. Kapitza, the great Soviet scientist, wrote to his colleagues in 1944 in a white heat of concern about the state of science in the U.S.S.R. He was worried about the divorce between the institutes and the universities. He was disturbed that the great men were drawn off to monasteries where they had no students. He feared equally that the universities were being left with only third-class professors without power

to fill students with interest in their subjects. He pleaded for the inspir-

ing man working at the frontiers of science to speak to the younger man and to draw him into his subject, to enlist his potential enthusiasm and his sense of dedication.

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The words of Kapitza are as relevant in our own countries as they are in the Soviet Union. We all know the signs of an institute that is drying up. Members creep on along their narrow ruts working in isolation from their fellows. No series of lectures imposes the demands to review one’s field. The member lacks that old and effective impetus to seek out the wider relations of his subject. He has a lesser stimulus to find uncharted areas and to put what is already knownina new and more useful form. In contrast to the great universities and the great institutes, like the Institute for Advanced

Study, the Insti-

tute-in-Isolation has no life-giving stream of bright young men. Young man? Student? No, Conant has a still better word: the man with the uncommitted mind. He is the man who is curious, the man

who is waiting to throw himself into something challenging and important. He is the man who thrives on contact with a leader and adds to his force. If there is no way for the older worker to pass on the seed to the young man with the uncommitted mind, there is little opportunity for the new heavy intellectual to come into being. For this

reason it is inspiring to visit the laboratory of James Watson and of many another leader in present-day science and see the young men at work and in discourse.

John Tukey and The Statistical Generalist Physics and biochemistry are disciplines where the workers make their

own direct contact with nature. Let us turn now to a third example of science in action: statistical analysis. The statistical analyst uses math-

ematics to extract the meaning out of observations which have gener-

ally been made by other workers and which are afflicted by “noise.”

Noise he uses as a general term to indicate disturbances from unpredictable sources. For example, in trying to understand the selling prices of securities, he looks for general trends against a background of day-to-day fluctuations. But the scope of statistics, both in science and in planning policy, is much broader than this example might suggest. Consider by way of illustration the work of Prof. John Tukey.

Most recently he has served a number of months on the joint U.K.-

U.S.A.-U.S.S.R. board looking for a reliable way to distinguish under-

ground weapons tests from explosions. Before that he had much to do with recommending the policy of the United States Pure Food and

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Drug Administration with respect to safe dosages of drugs, taking account of the varied response of one individual as compared to another. Earlier he served on the National Academy of Sciences committee examining the statistical validity of the techniques used to study sexual

behavior. Tukey, though primarily a professor of mathematics at

Princeton, also helps guide a group at the Bell Telephone Laboratories. Make a long distance call by direct dialing. Listen to the musical tones that carry the called number across the continent. Will the automatic

circuits dial the number reliably at the other end? Here there come up important questions of balance. How does the cost of so-called redundant or checkup information compare with the importance of reliability? In scores of questions like these the statistician makes the difference between an unreliable judgment and a first-class outcome. The

imaginative statistician, far from being a narrow specialist, is often the

direct opposite—a generalist: a man who can walk into almost any scientific or commercial operation, find a numerical way to analyze what

is going on, and increase output.

The methods of the statistical generalist can be put to use by al-

most anyone

who has some

basic education

in science and some

imagination. He needs what might be called an emergency kit of sta-

tistical tools, such as Tukey

has made

available to those associated

with him. And he needs a variegated set of case histories set down on paper so that he can see how those tools have been used in practice. May some enterprising young collaborator of Tukey, some Dr.

Watson, someday provide us with such an account! I for one would

like to have stories of the emergency tool kit in action on problems ranging as widely as individual differences in susceptibility to drugs, the twinkle of starlight and its correlation with atmospheric disturbances, the quality control of manufactured products, and the consequences of all-or-none representation compared to proportional representation. Each story in “Case Histories of a Generalist” would begin at the moment when a phone call or letter reaches the Sherlock Holmes of the statistical world. It would touch on the human aspects

of the problem. Of course it would also describe the mathematical

analysis—how the statistical tools are put to use. It would include

not only the conclusions but also how they were “sold” to those who had to put them into action. It would end with some account of the

payoff. The gains to the economy and productivity of a country—any

country, at any level of industrialization—from such mathematized use of intelligence are so great compared to the cost involved that a

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sound and imaginative statistical generalist ranks high among heavy intellectuals.

Copenhagen and Niels Bohr My fourth and final example of science in action is the Institute at Copenhagen. Many regard it as the intellectual center of physics. It is the place where many a physics pilgrim goes to talk and dream and debate about the present problems and future prospects of his subject.

Niels Bohr is the Confucius, the Plato, the Lao-Tze of Copenhagen.

Many legends and many true and wonderful stories are told about Bohr.

He divides the week in effect into even-numbered and odd numbered days. On a day of an even number every glimmer of an idea that might help with the problem at hand is seized upon, is built up, is expanded. What is useful in an idea is the focus of attention, not what might be wrong about it! The construction of ingenuity and hope that stands waiting the next morning receives all that day an often devastating series of tests and criticisms and checks. If by night anything is left, it serves as foundation for more building on the next even-numbered day! Niels Bohr is also the man who says there is no hope of making any progress in one’s subject unless one is confronted with a paradox or difficulty. Even so one’s hopes are small until at last he finds a second diffi-

culty. Then at last one can play off one difficulty against the other and

begin to move ahead! One comes to understand at Copenhagen what is the place of theory

in the description of nature. The word “theory” in physics as in most of

science is not at all synonymous with the word “hypothesis.” Instead it stands for an orderly pattern in which to arrange one’s knowledge about a certain field. It consists of concepts and methods of measurements and finally of what many workers call “laws” but what Bohr often more descriptively calls “regularities.” In the past it has often been said that

each new field of human knowledge must begin by defining its con-

cepts. “Define your terms!” How oversimplified and even false it is to begin in this way, one learns in physics. One has come to realize that the

concept which one uses is itself defined by the theory in which it enters.

One would be unable even to define the concept properly—for example momentum—f one had no theory—such as the law of conservation of

momentum—in

which the concept entered. Measurement, too, would be

completely impossible without theory, just as theory would be impossi-

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ble without measurement. One has therefore come to realize that the three organizers of knowledge—concept, method of measurement, and theory—do not come into being in stately hierarchical order but in one single tumultuous creative act. At Copenhagen one thus sees that those who themselves take part in adding actively to human knowledge are perhaps more easily than others able to help us understand both the nature of knowledge and bounds of the knowable. And out of Copenhagen comes Bohr’s definition of science as that human activity which is concerned with extending the range of our experience and reducing this experience to order. Many lessons can be read from the talks and works at Copenhagen, among them not least this, that the highest form of productivity flourishes in an atmosphere of warm human regard one for another. But enough

of word pictures of science in action, from Yang and Lee and the symmetries of spacetime, through Watson and Crick and the nature of life,

and the work of Tukey and the statistical generalists, to Bohr and Copenhagen and the nature of knowledge.

No Static Well-Accepted Outlook Today Let us instead try to assess—from these examples and from what we see going on about us—the nature of the new culture we live in today. How different it is from the past! Agriculture each year constitutes a smaller

and smaller fraction of our civilization. In the United States in the single

year 1957 over 10 percent of the people living on farms left to go to

larger communities and different work. In other parts of the world, for

example in Taiwan, the change has proceeded at a different rate but in the same direction. Human values are not exclusively set by any static society of those who own land. We do not see any more the son going out from the Virginia plantation only to read Thucydides and Tacticus and the great examples of Plutarch’s “Lives.” Nor do we find the young man coming out of a scholar-gentry class only to study the Chinese classics and take an essay type of examination upon them, wonderful though the training was in human values which was secured in this way. Our able young people today train in much smaller numbers for a land-owning and agricultural life, and that in new ways. Mostly they prepare themselves for occupations which did not even exist a few generations

ago. Often they realize that they may well be working a few years from

now in professions which even today have not yet come into being. Be-

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tween one man and another there is not the common perspective of older days. About the significance of human life this is no universally accepted outlook. The theory of evolution has brought new insights into this question. They are far from having yet been fully absorbed into our culture. Compared to evolution, there is hardly any development out of science to which different groups of people react more divergently. Today each country is less and less aptly described in terms of one cul-

ture—Confucian, Muslim, Greco-Roman or Judeo-Christian—and more

and more appropriately viewed as a collection of cultures built around different professions and different fields.of subject-matter specialization.

In the past with its single culture the teacher was often a man of char-

acter and intelligence who did his duty when he discussed with his students the greatest men of all times and of all countries.

The New Training in the Art of Finding Out In the specialized world of today no university fulfills its responsibility to society which concerns itself only with what is already known. It must be occupied even more heavily with the art of finding out. Young people moving up one or another of the many streams of culture that we have to-

day, working in one or another foundation field of human

knowledge,

must find in our universities the doorways that lead on to new advan ces.

Not merely to receive from their professors, but to work alongside them, is the new dispensation. In the university of today that member is behin d who is not contributing actively to the subject he professes, not only through his own efforts, but also through the students he trains. How can young men possibly be trained for the changing modern world unless the older men who train them are themselves leade rs in the transformation of thought? It is difficult to name anything more important for creativity than the feeling that one belongs to an outst anding

group which is ahead in its chosen field of work. As Conan t puts it, one

cannot build up a first-class university by naming to it very good people. One must have the best! Or to put it in other terms, it is not being very useful to society to be the second investigator to find out a new truth!

Great Opportunity also for Smaller Institutions There is nothing about this demand for leadership which the smaller uni-

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versity cannot meet. On the contrary, it would be easy to name in physics alone at least 20 fields of investigation well suited to the budgets of smaller institutions. Every one of the 20 has its own special advantages for the training of much needed young people. Every one is important to science and society. And in every one the world today is sadly behind. Let us hope that the smaller institutions of our two countries will begin to make the kind of contribution, not only in physics but all across the board, that the world’s more research-minded universities have already

shown to be possible and needed. Then we shall have intellectual cooperation between East and West in its highest form—a collaborative effort to

push back the boundaries of human knowledge.

Lecture given on Monday, July 11, 1960, at the Sino-American Conference on Inteilectual Cooperation, held at the University of Washington.

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Beyond the Black Hole

The Sibyline Strangenesses of the Landscape Arthur Wellesley, Duke of Wellington, in the long years of activity in England that followed Waterloo, from time to time for relaxation would

take a companion along for a carriage ride of hours through a distant

countryside unfamiliar to them both. The Iron Duke was accustomed to

draw his companion into his favorite game. From the look of the terrain up to this moment, predict what new panorama will be seen as the car-

riage tops the next long hill. Wellington generally produced the winning

forecast of the lay of the land. Einstein travelled through a different countryside. His ability to sense

ahead of time the upcoming landscape of physics is well known.

Today we find ourselves traversing a new realm. It contains such strange features as the black hole, the gauge or phase field, and complementarity. What lies beyond, over the hill? If all strangenesses of Wellington’s present landscape made for him the best indicators of the new terrain, the same was true, we know, for

Einstein and the same surely holds for physics now. There is no hope of progress, we often say, until we are in possession of a central paradox, a

difficulty, a contradiction. However, in our hearts we know it takes more.

We need two paradoxes. Only then can we play off one egainst the other to locate the new point. Two strangenesses stand out with special prominence in the landscape of

the physics of our day. One is the bounds of time; the other, the quantum. Of the bounds of time the black hole! is the one most immediately ac-

cessible; then, beyond, the big bang” and—if the universe, as Einstein ar-

gued,3 is closed and therefore collapses‘ in time to come—the big crunch.> The bounds of time tell us that physics comes to an end. Yet physics has always meant that which goes on its eternal way despite all surface changes in the appearance of things. Physics goes on, but physics

Pps

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HOLE

stops; physics stops, but physics goes on. That is paradox number one, strange feature number one in the landscape we survey. Paradox number two the quantum principle® thrusts upon us. In every elementary quantum process the act of observation or the act of registration” or the act of observer-participancy® or whatever we choose to call it, plays an essential part in giving “tangible reality” to that which we say is happening. Paradox number two is this: The universe exists “out there” independent of acts of registration but the universe does not exist out

there independent of acts of registration.

If these are no small paradoxes, they suggest no small questions about what lies over the hill. How can one possibly believe that the laws of physics were chiseled on a rock for all eternity if the universe itself does not endure from everlasting to everlasting? If law, field, and substance come into being at the big bang and fade out of existence in the final stage of collapse,’ how can a change so all-encompassing take place except through a process, the elementary mechanism of which has already made itself known? In what other way does an elementary quantum phenomenon become a phenomenon except through an elementary act of observer-participancy? To what other foundation then can the universe itself owe its existence except billions upon billions of such acts of registration?! What other explanation is there than this for the central place of the quantum principle in the scheme of things, that it supplies the machinery by which the world comes into being?!

Laws Derived from Symmetry Considerations

But They Hide the Machinery Underlying Law!2 Before we inspect more closely the two sibyline strangenesses of the

landscape, let us look at the laws of physics themselves to recognize how little guidance they give us in forecasting what lies over the hill. Nothing in all the great achievements of science is more beautiful than Maxwell’s electromagnetism, Einstein’s geometric theory of gravitation,!4 and the Yang-Mills theory!5 of the quark-binding field. Each expressible in a single line, these three theories are the yield of decades of research, hun-

dreds of investigators, and thousands of experiments. However, the more we learn, the more we learn how little we have learned.!6

Are not these three great theories of our time about to suffer the reappraisal already undergone by the great theory of elasticity of an earlier

century?!7 Look at one of the good old textbooks on that subject. The

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first chapter or two deduce the laws of elasticity from elementary symmetry considerations. To say that the energy of deformation of a homogeneous isotropic material goes as the square of the deformation is to be

confronted with two alternatives. Either one must take the trace of the

tensor of deformation and square it, or square the tensor of deformation and take its trace. More generally one makes a linear combination of these two expressions with two disposable constants of proportionality to construct the general expression for the energy of elastic strain. From this reasoning—that there are two constants of elasticity and no more—one goes on to build up all the rest of the great treatise on elasticity of a hundred years ago, complete with theorems, methods of analysis, applications, and all kinds of beautiful problems for the student to solve at the end of each chapter. Likewise in our own time we have textbooks on electromagnetism,!® gravitation,!9 and the Yang-Mills quark-binding field?° or, more generally, on “gauge” fields, or “phase” fields as Professor Yang suggests we call them, again complete with symmetry-argument foundations, theorems, applications, and problems for the student. When we look back to elasticity, however, we recall that the most important fact about the subject—where the forces come from, molecular

interactions between dozens of different atoms and molecules, multiplied

by appropriate direction cosines—was not revealed one bit by these laws of elasticity. A hundred years of the study of elasticity would not have re-

vealed atomic and molecular forces.?! Neither would a hundred years of the study of atomic and molecular forces have revealed that these forces went back for their foundations to Schrédinger’s equation and the motions of individual electrons and nothing more. We had to learn that we should explain, not electronic motions in terms of elasticity, but elasticity in terms of electronic motions. The very considerations of symmetry that had allowed one to master elasticity so early, taken by themselves, would have hidden from view forever the mechanism of elasticity. The considerations of symmetry that reveal law hide the mechanism

that underlies law. This lesson out of elasticity we today see afresh in electromagnetism, gravitation, and the dynamics of the Yang-Mills field, thanks to considerations of Hojman,

Kuchar, and Teitelboim.2? They

consider a spacelike hypersurface 6, slicing through spacetime (Figure 1). They think of the field in question as given on all points of that hypersurface, along with the initial time rate of change of that field or, equivalently, the “field momentum.” They ask, how does one go about predicting what the field will have for values at the points on a later spacelike hypersurface G,. The general marching his troops forward from one river

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SWIL FiGurE 1. The two alternative ways (one dotted, the other dashed) to calculate physics forward step by Hamiltonian step from the spacelike hypersurface 0, to the spacelike hypersurface 0, have to give the same result, the central point of the Hojman-Kuchar-Teitelboim “imbeddability requirement.” This simple demand leads straight to Maxwell electrodynamics, Einstein geometrodynamics, and the Yang-Mills theory of the quarkbinding field.

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to another may move the front ahead faster first on the right and later on

the left, or alternatively order the line to advance more rapidly first on

the left and then on the right, ending up however in the same stance on the same river. So the analyst of the field with his computer calculations

can calculate ahead from instant to instant the successive configurations

of the field either on the dashed or upon the dotted sequence of intermediate spacelike hypersurfaces in the diagram. He, unlike the general, or-

dinarily will arrive at different results for the field on 6, by the two ma-

neuvers, the two alternative slicings of spacetime, the two foliations: two incompatible predictions for one future. The fault, when there is one, is

wrong choice of the particular Hamiltonian law assumed to govern the evolution of the field from instant to instant. When the field in question is a vector field and we restrict attention to

Hamiltonians of the second order, there is only one option that is compat-

ible with consistency. It is Maxwell electrodynamics. When the field is a

tensor field—the metric measuring the distance from point to point on

the spacelike hypersurface—the requirement of consistency leads

uniquely to Einstein’s general relativity theory of gravitation. Any other

Hamiltonian conflicts with the requirement that different ways of figuring ahead should fit into, be imbeddable in, one and the same spacetime

manifold. Finally, when we impose this Hojman—Kuchar—Teitelboim demand of “imbeddability” on a vector field that has an internal spin degree

of freedom, we get the Yang—Mills theory of the quark-binding field.?3

All three great theories of physics fall straight out of the utterly elementary demand for imbeddability, as epitomized in Figure 1. One does not have to recall Einstein’s now abandoned dream of a geometrical unification of the forces of nature.?4 One does not have to have followed the

exciting rebirth of this dream within the framework of that new and

wider concept of geometry which is forced on us by the discovery in nature?5—and in mathematics?°—of “gauge” or “phase” fields, fields pos-

sessing at each point of space an “internal spin” degree of freedom. It is

enough for the theoretical physicist to demand imbeddability to deduce in a few hours what it took great men years of work to establish. Again, the more we learn the more we learn how little we have learned.

Fields in the end remind us more than ever of elasticity: modes of “vibration” of something; modes of a structure quite different from anything that shows on the surface; modes of a substrate, call it pregeometry or call it what one will, that is not and will not be revealed by reasoning

from the top down, only from the bottom up;27 not from the obvious but from the strange. Where better can we turn now for a hint of the new

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than to the two greatest strangenesses of the present landscape, the bounds of time and the quantum?

The Bounds of Time In Figure 2 the sequence of circles starting at the lower left symbolizes a closed universe beginning small and in the course of time becoming larger. Philosophical considerations had guided Einstein to his 1915 geomet-

ric and still-standard theory of gravitation in the first place.?8 Considera-

tions of the same kind, spelled out in his book The Meaning of Relativity,” led him to conclude that the universe must be closed. No one in subsequent years has found any boundary condition comparable in its reasonableness to the requirement of closure.?? Is it necessary to worry about alternatives? Mass-energy so far located falls short of what is re-

quired to curve space up into closure, and the factor of shortfall looks

big, but not big in order of magnitude as compared to the uncertainties of, and discrepancies between, estimates of mass-energy based on (1) the

mass-luminosity relation,3! (2) primordial deuterium,>? and (3) clustering of galaxies.33 A closed model universe with the topology of

a three-dimensional

sphere comes to a maximum volume, begins to contract, and finally collapses, as indicated in Figure 2. Therefore it might seem that all the parti-

cles gather together in a common place at the start of time. However, the

phrase “common place” we know to be a bad phrase and we know how to see that it is bad. We “unroll the space”; or in our symbolic model for

the space, we unroll the circle from north pole to south pole. Then the

separation between two particles measures itself not in miles but in degrees. The spacetime history of the particles then allows itself to be dis-

played—though it is not displayed—in the rectangular diagram of Figure 2 as two vertical lines. It can take hundreds of millions of years after the

big bang before one particle communicates its presence to another parti-

cle that began its life in the same microscopic fireball. The dashed lines in Figure 2 symbolize the outer boundaries of a cloud of dust that gradually shrinks and eventually collapses to a black hole. The singularity at the center of the black hole is seen to be, not a new and distinct bound of time, but part and parcel of the big crunch.34 In a very wide class of models of closed universes compatible with Einstein’s field equations—Marsden and Tipler have recently proved35— the four-dimensional geometry admits a foliation in one way and in one

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way only into slices of constant mean extrinsic curvature. One value of

the mean curvature gives us one spacelike slice. Another value, zero mean curvature, gives us that instant, that unique spacelike slice, that phase of the history of the universe, for which the volume is the largest. Later slices depict the geometry of the universe, whatever its lumps, bumps, and ripples, with successively smaller and smaller volume. How does this circumstance bear on black holes that, once formed, ultimately coalesce into

the final big crunch? The successive hypersurfaces of the foliation en-

glove the singularity of each black hole more and more closely, according

to recent calculations by A. Qadir and me,*® as illustrated schematically in

Figure 3. The “last hypersurface,” the one of infinite mean extrinsic curvature, “establishes contact” simultaneously all along its front with the black hole singularity and the big crunch singularity. No better way could one desire to see that those are not two singularities but one. The generic way of approach to the final singularity, if Belinsky, Kha-

latnikov, and Lifshitz are right,>” proceeds through so-called mixmaster

oscillations in the geometry, with the amplitude, phase, and direction of

the principle axes of the space deformation varying from point to point of the spacelike hypersurface. Therefore also for the approach to the singu-

larity of the physical black hole, as distinguished from the ideal

Schwarzschild “dead’”38’—or Reissner-Nordstrgm charged”? or Kerr rotating*° or Kerr-Newman charged and rotating*!—black hole, it is not un-

reasonable to expect a mixmaster character.

More than a hundred papers’? of recent years, many of them beautiful in method and in results, deal with the physics outside the “horizon” of a black hole but almost none with conditions inside. Thanks to this work we have learned in what sense “a black hole has no hair.”43 A “hair,” a departure from ideality, a perturbation in the geometry outside the horizon associated with irregularities and turbulence when the black hole

formed, washed out by a factor of I/e = 1/2.718. . . in each “characteristic time,” a time of the order of magnitude of 10-4 seconds for a black hole of ten solar masses. Thus such a black hole, one second after matter has

stopped falling in, has attained a fantastic perfection outside.“ Inside the

horizon, however, it is natural to expect the direct opposite: small initial

departures from ideal symmetry as matter falls in across the horizon leading to enormous mixmaster curvature fluctuations from point to

point as one approaches the singularity.‘

How far away is that singularity? My watch, the baryons of which

came into being at the big bang, has ten more years of life. When it stops, can we spare its baryons the ignominy of further use? Instead of burying

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wait ~10° to ~10° years before a signal from the one gets to the other. The

simple 45° algorithm is modified when there are inhomogeneities, such as the black hole “spike hanging from the roof” or the symbolically represented “mixmaster oscillations” of the geometry in the final stages of gravitational collapse.

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the watch or melting it down can we obliterate it? Can we make those ten

years stretch to the end of time, to the singularity after which there is no after? Yes. Can we even choose whether the place of obliteration shall be a black hole or the big crunch? Yes, if there is a big crunch and if it lies at the estimated time*® in the future. For either purpose we must put the watch aboard a powerful rocket, one that will make the factor of time dilatation of the order of 10!! yr/10 yr if in ten years of life we would have it reach the big crunch; or of the order of 104 yr/10 yr, a black hole located in this galaxy. Black Hole as Bound of Time How near the end of time is we are reminded by each new piece of evidence for a black hole, the object of about ten solar masses in the con-

stellation Cygnus remaining the best studied of presumptive black

holes.47 Bursts of x rays suggest a black hole of a hundred to a thousand solar masses at the center of each of five clusters of stars in our own galaxy.48 Charles Townes and his colleagues,4? Jan Oort,5 and

others*! give considerations arguing for a black hole of about 4 x 10° solar masses at the center of the Milky Way. The Lick Observatory

group and others find evidence>? pointing to the possible existence of a black hole of about 5 x 10° solar masses at the center of the violently active galaxy M87. Is it clear that the center of a black hole offers obliteration only, not

the chance to emerge somewhere else in space? In favor of such a possi-

bility for space travel there exists not the slightest evidence. On the contrary, if at any time there ever were a wormhole or tunnel of appreciable

diameter (as distinguished from the dimensions of quantum fluctua-

tions®4), it would collapse with the speed of light.54 The matter that falls

in does not reappear somewhere else. All its details fade away, but its

gravitational attraction remains. Any planet once in circeumambient orbit Stays in orbit. Mass-energy, an exterior property, remains; matter, an interior property, is obliterated. All details of whatever is dropped in are washed away. Provided that

nature has no other long-range charge-conserving field than electromag-

netism, we have to conclude that the resulting black hole is fully characterized by its mass, charge, and angular momentum, and nothing more. Of course mass implies energy, and therefore also the possibility of another

property for a black hole, momentum.*> However we think of this mo-

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FiGurE 3. Black hole and big crunch seen as part and parcel of the final singularity. The closed model universe is uniquely foliated by a sequence of spacelike hypersurfaces distinguished one from another by the value— constant over any one hypersurface—of “the mean extrinsic curvature”; that is, “the trace of the tensor of extrinsic curvature” or “the fractional rate of decrease of volume per second.”

mentum, not as an independent feature of the black hole, but as a consequence of our choice of reference frame. There is another feature of the

black hole, Claudio Teitelboim tells us,>° its spinor spin, that—like mo-

mentum—can be given one value or another depending on our choice of

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reference frame—except that now the frame of reference that comes into consideration is not the Lorentz frame but the spinor reference frame. It does not matter for this reasoning whether we use the theory of supergravity as originally developed by Freedman, van Nieuwenhuizen, and Fer-

rara,>7 and by Deser and Zumino, or whether we follow Teitelboim’s beautiful procedure of taking “the Dirac square root” of Einstein’s general relativity,>? for by these two very different routes we come to the same theory with the same “internal spin—4” or “phase” degree of freedom. Of baryon number, lepton number, and strangeness not a trace is left, if present physics is safe as guide.® Not the slightest possibility is evident, even in principle, to distinguish between three black holes of the same mass, charge, and angular momentum, the first made from baryons and leptons, the second made from antibaryons and antileptons, and the third made primarily from pure radiation.®! This circumstance deprives us of all possibility to count, or even define, baryon and lepton number at the end and compare them with the starting counts.® In this sense the laws of conservation of baryon and lepton number are not violated; they are transcended.

Up the Staircase of Law and Law Transcended to Mutability Picture the development of physics as a staircase. Each step symbolizes a new law or discovery. Each riser marks the attainment of conditions so

extreme as to overcome the usefulness of that law, or transcend it.

Archimedes, discovering how to measure density, could regard it as a constant of nature. However later ages achieved pressures great enough to bring about measurable alterations in density.® The concept of valence® brought into order the major facts of chemistry, but today we know we have only to go to very high temperatures to outrun traditional valence considerations.® Later came the discovery that every atomic nucleus admits rigid classification by its charge number and its mass number;® but the advent of nuclear transmutations®™ destroyed that rigidity.

The laws of conservation of baryon number and lepton number are indis-

pensible in accounting for the wealth of experience in elementary particle physics,” but they have no application in black hole physics.7! There they are not violated, but transcended.

In the end can we not at least say that the black hole has mass and therefore mass-energy? And does not the law of conservation of energy stand up against arbitrarily extreme conditions? In an asymptotically flat

space, yes; in a closed universe, no. There total energy is not even de-

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fined.7? Thus the local law of conservation allows energy in a bounded region as an integral over the tier of that region. The larger the region subsumed ergy, the larger at first is the boundary. However,

one to express the total two-dimensional fronin counting up the enas more and more vol-

ume is swept for energy, the boundary pushes on over the great bulge of the universe and begins to shrink. As we complete the sweep through “the other half of space,” we push this surface down to extinction. The law of conservation of energy degenerates to the identity 0 = 0. This lesson of the mathematics physics puts into other words. To measure the mass-energy of a moon, a planet, a star, or larger system it says, put a satellite in orbit

about it. Measure the period of revolution, apply Kepler’s “1-2-3 law” of motion,”> and obtain the mass. In the case of the closed universe, howev-

er, there is no “outside,” no circumferential highway, in which to orbit a

satellite. The idea of “total mass-energy”—and with it the law of conservation of energy—lose all meaning and application.

At the head of the stairs there is a last footstep of law and a final riser

of law transcended. There is no law of physics that does not require “space” and “time” for its statement. Obliterated in gravitational collapse, however, is not only matter, but the space and time that envelop that matter.’4 With that collapse the very framework falls down for anything one ever called a law of physics. Einstein’s general relativity gives not the slightest evidence whatsoever for a before before the big bang or an after after collapse.’> For law no other possibility is evident but that it must fade out of existence at the one bound of time and come into being at the other.’ Law cannot stand engraved on a tablet of stone for all eternity. Of this strangeness of science we have for symbol the staircase; and for central lesson, “All is mutable.”77

If the lesson comes in two parts, “spacetime ends” and “laws are not eternal,” each can be pursued further.

Spacetime as Idealization A crystal reveals nowhere more clearly than at a crack”® that the concept

of “ideal elastic medium” is a fiction. Cloth shows nowhere more conspicuously than at a selvedge that it is not a continuous medium, but wo-

ven out of thread. Spacetime—with or without “phase” or “internal spin” degrees of freedom—often considered to be the ultimate continuum of physics, evidences nowhere more strikingly than at big bang and collapse

that it cannot be a continuum.7?

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There is an additional indication that space cannot be a continuum. Quantum fluctuations of geometry and quantum jumps of topology are estimated® and calculated! to pervade all space at the Planck scale of distances and to give it a foam-like structure. “Space is a continuum.” So bygone decades supposed from the start when they asked,®? “Why does space have three dimensions?” We, today, ask instead, “How does the world manage to give the impression it has three dimensions?” How can there be any such thing as a spacetime continuum—except in books? How else can we look at “space” and “dimensionality” except as approximate words for an underpinning, a substrate, a “pregeometry,”5 that has no such property as dimension?

Law Without Law “Physical spacetime is not mathematical spacetime” is the one lesson of mutability; the other, “physical law is not ideal mathematical law.” Law that comes into being at the beginning of time and fades away at the end of time cannot be forever 100 percent accurate. Moreover, it must have

come into being without anything to guide it into being. It is not new for a regularity to develop unguided. Thermodynamics, we know, rests upon the random motions of billions upon billions of molecules.*4 Ask any molecule what it thinks about the second law of thermodynamics and it will laugh at the question. All the same the molecules, collectively, uphold the second law. The genera and species of the kingdom of life go back for their foundation to billions upon billions

of accidents of mutation. The fantastically elaborate organization of

plants and animals is of nothing but higgledy-piggledy origin. The laws

of physics themselves, coming into being and fading out of existence: in what else can they have their root but billions upon billions of acts of chance? What way is there to build law without law, field without field, substance without substance except “Individual events. Events beyond law. Events so numerous and so uncoordinated that, flaunting their free-

dom from formula, they yet fabricate firm form’’?85

Strangeness Number Two: Quantum and Chance We have been led to consider chance events, astronomical in number, as the statistical foundation of all the regularities of physics, and this in de-

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fault of any other way to come to terms with mutability and the bounds of time, strangeness number one of the landscape. What kind of chance

event? For a clue it is not clear where else to look except at strangeness number two, the quantum, “God plays dice.”

“T cannot believe that God plays dice.” Who that has known or read Einstein does not remember him arguing against chance in nature?®* Yet this is the same Einstein who in 1905, before anyone, explained that the

energy of light is carried from place to place as quanta of energy,87 accidental in time and space in their arrival; and in 1916, again before any-

one, gave us in his A’s and B’s, his emission and absorption coefficients, the still standard mathematical description of quantum jumps as chance events.88 How could the later Einstein speak against this early Einstein, against the evidence and against the views of his greatest colleagues?

How can our own day be anything but troubled to have to say “nay” to

one teaching, “yea” to others of the great Einstein, the man who gave us in his geometric account of gravitation®? a model, still unsurpassed, for how a physical theory should be founded and what it should do?

Was Einstein’s Thinking Constrained by His Philosophical Antecedents? We are less troubled, more understanding, when we recall the philosophi-

cal antecedents of Einstein’s thinking. They derived from a cast of char-

acters who seemed to live within his cranium and counsel with him as he spoke: Leibniz and Newton, Hume

and Kant, Faraday and Helmholtz,

Hertz and Maxwell, Kirchhoff and Mach, Boltzmann and Planck; but above them all Benedictus de Spinoza, hero and role-creator to Einstein

in youth as well as later life. In earlier centuries no one expressed more

strongly than Spinoza a belief in the harmony, the beauty, and—most of all—the ultimate comprehensibility of nature; in our own century, no one

more than his admirer, Einstein. Guide Einstein to high goals Spinoza

certainly did; but did he not—Hans Kiing suggests?!—on two occasions misguide? Why was 24-year-old Spinoza excommunicated in 1656 from the Am-

sterdam synagogue? Because he denied the bible story of an original cre-

ation.” What was the difficulty with the teaching? In all the nothingness

before creation where could any clock sit that should tell the universe when to come into being! Therefore, Spinoza reasoned, the universe

must endure—from everlasting to everlasting. In contrast, and to Ein-

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stein’s surprise, general relativity already in its first two years predicted that a static three-sphere universe is an impossibility. Of necessity it is dynamic. Consequently Einstein reluctantly changed the theory and introduced? a so-called cosmological term with the sole point and purpose to hold the universe static, to rule out what Alexander Friedmann later

showed®4 was a big-bang-to-big-crunch cosmology. A decade later, when

Edwin Hubble established the expansion of the universe,?> Einstein’s

chagrin about the cosmological term is well known, “the biggest blunder

of my life.”?© Today, looking back, we can forgive him his Spinoza-inspired blunder and give him credit for the theory of gravitation that predicted the expansion. Of all the great predictions that science has ever made over the centuries was there ever one greater than this, to predict, and predict correctly and predict against all expectation a phenomenon so fantastic as the expansion of the universe? When did nature ever grant humanity greater encouragement to believe we will someday understand the mystery of existence? Spinoza’s influence on his thinking about cosmology Einstein could

shake off—but not Spinoza’s deterministic outlook. Proposition XXIX in The Ethics of Spinoza states, “Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of divine nature.”?7 Einstein accepted determinism in his mind, his heart, his very bones. What other explanation is there for his later-life position against quantum indeterminacy than this “set” he had received from Spinoza?

No Elementary Phenomenon is a Phenomenon Until it is a Registered Phenomenon From Einstein’s discomfort we turn to today’s assessment of the central

lesson of the quantum. In Figure 4 the left-hand view symbolizes the concept of the universe of the old physics. Galaxies, stars, planets, and

everything that takes place can be looked at, as it were, from behind the

safety of a one-foot-thick slab of plate-glass without ourselves getting involved. The right-hand view reminds us that the truth is quite different. Even when we want to observe, not a galaxy, not a star, but some-

thing so miniscule as an electron, we have in effect to smash the glass so as to reach in and install measuring equipment. We can install a de-

vice to measure the position, x, of the electron, or one to measure its

momentum, p, but we can’t fit both registering devices into the same

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place at the same time. Moreover the act of measurement has an in-

escapable effect on the future of the electron. The observer finds himself willy-nilly a participator. In some strange sense this is a participa-

tory universe.°8

A story®? may symbolize what it means for the observer to find himself a participator. We had been playing the familiar game of twenty

questions. Then my turn came, fourth to be sent from the room, so that

Lothar Nordheim’s other 15 after-dinner guests could consult in secret

and agree on a difficult word. I was locked out unbelievably long. On fi-

nally being admitted, I found a smile on everyone’s face, the sign of a

joke or a plot. I nevertheless started my attempt to find the word. “Is it animal?” “No.” “Is it mineral?” “Yes.” “Is it green?” “No.” “Is it white?” “Yes.” These answers came quickly. Then questions began to take longer in the answering. It was strange. All I wanted from my friends was a simple yes or no. Yet the one queried would think and think, yes or no, no or yes, before responding. Finally I felt I was getting hot on the trail, that the word might be “cloud.” I knew I was allowed only one chance at the final word. I ventured it: “Is it cloud?” “Yes,” came the reply, and everyone burst out laughing. They explained to me there had been no word in the room. They had agreed not to agree on a word. Each one questioned could answer as he pleased—with the one requirement that he should have a word in mind compatible with his own response and all that had gone before. Otherwise if I challenged he lost. The surprise version of the game of twenty questions was therefore as difficult for my colleagues as it was for me.

What is the symbolism of the story? The world, we once believed, exists “out there” independent of any act of observation. The electron in the atom we once considered to have at each moment a definite position and a definite momentum. I, entering, thought the room contained a definite word. In actuality the word was developed step by step through the ques-

tions I raised, as the information about the electron is brought into being

by the experiment that the observer chooses to make; that is, by the kind of registering equipment that he puts into place. Had I asked different questions or the same questions in a different order I would have ended up with a different word as the experimenter would have ended up with a different story for the doings of the electron. However, the power I had in bringing the particular word “cloud” into being was partial only. A major part of the selection lay in the “yes” and “no” replies of the colleagues around the room. Similarly the experimenter has some substantial influence on what will happen to the electron by the choice of experiments he

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will do on it, “questions he will put to nature”; but he knows there is a certain unpredictability about what any given one of his measurements will disclose, about what “answers nature will give,” about what will

happen when “God plays dice.” This comparison between the world of

quantum questions word is a questions

observations and the surprise version of the game of twenty misses much but it makes the central point. In the game no word until that word is promoted to reality by the choice of asked and answers given. In the real world of quantum physics,

no elementary phenomenon is a phenomenon until it is a recorded phe-

nomenon.10°

Delayed-Choice Experiments!®! Figure 5 recalls the double-slit experiment that did so much to clarify

the issues in the great 30-year dialogue between Bohr and Einstein.!02

All features to the right of the photographic plate—and that plate itselfto convert it into the slats of a venetian new and to be postponed a moment. A photon enters from recorded on the photographic plate by the blackening of a

the slicing of blind!03—are the left and is grain of silver

bromide emulsion. No matter how great the spacing in time between one

photon and the next, the record of arrivals shows! the standard two-slit interference pattern, basis for deducing that each photon has “gone through both slits.” One can also tell “through which slit” each quantum

goes, Einstein argued,!°5 by measuring the vertical component of the

kick that the photon imparts to the photographic plate. If it comes from

the upper hole it kicks the plate down; from the lower hole, up. But for quantum theory to say in one breath “through which slit” and in another “through both” is logically inconsistent, Einstein objected, and shows that the theory itself is inconsistent. Bohr’s response is well known. We have to do with two experiments, not one. We can fasten the photographic plate to the apparatus so it will not move up and down. Then we can register the interference fringes. Or we can free it to slide up and down in a slot, not shown. Then we can measure the vertical kick. But we can’t do both at the same time. The experiments are not contradicto-

ry. They are complementary.106 Now we come to the new feature—delayed choice.!°7 We don’t have

to decide in advance which feature of the photon to record, “through both slits” that pierce the metal screen, or “through which slit.” Let us wait until the quantum has already gone through the screen before we—at our

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Ficure 5. The double-slit experiment both in the familiar version and in the “delayed-choice” version. The familiar layout includes the source of photons at the left, the entering slit, the first lens, the doubly-slit metal screen that covers it, and the photographic plate that registers interference fringes. We secure delayed choice by supplements to this classic ar-

289

rangement. We replace the continuous source of illumination on the left by

a source that gives off one photon per timed flash. We slice the photographic plate to make it into a Venetian blind. We make a last-minute choice, after the photon has already traversed the doubly-slit screen, whether to open this blind or close it. Closed, as shown, it registers ona blackened grain of silver halide emulsion the arrival of that photon “through both slits.” Opened, it allows the light to be focused by the second, or L. F. Bartell, lens on the two photon counters. There being only one photon, only one counter goes off. It tells “through which slit the photon came.” In this sense we decide, after the photon has passed through the screen, whether it shall have passed through only one slit or both.

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free choice—decide whether it shall have gone “through both slits” or “through one.”

We use a carefully timed source. We know when the photon has defi-

nitely passed through the metal screen and is on the last lap of its journey

toward the photographic plate. At this moment we make our choice: open the venetian blind and record through which slit the photon came; or close the blind, use it as a photographic plate, and add to the interfer-

ence-pattern record that testifies to photons all going through both slits.

In the delayed choice experiment we, by a decision in the here and

now, have an irretrievable influence qn what we will want to say about

the past—strange inversion of the normal order of time. This strangeness reminds us more explicitly than ever that “the past has no existence except as it is recorded in the present’!®8; or more generally, in the words of Torny Segerstedt, “Reality is theory.”!0° What we call “reality,” that vision of the universe that is so vivid in our minds, we plaster in between a few iron posts of observation by an elaborate labor of imagination and theory. We have no more right to say “what the photon is doing”—until it is registered—than we do to say “what word is in the room”—until the game of question and response is terminated.

The Central Lesson of the Quantum “No elementary phenomenon is a phenomenon until it is a registered phenomenon.”#! This summary of the central lesson of the quantum takes its two key words from Bohr. “Registered” as Bohr uses it means

“brought to a close by an irreversible act of amplification”! and “com-

municable in plain language.” !!? This adjective, equivalent in most re-

spects to “observed,” has a special feature as compared to that more frequently seen word. It explicitly denies the view that quantum theory rests

in any way whatsoever on “consciousness.”!3 The critical word, “phe-

nomenon,” Bohr found himself forced!4 to introduce in his discussions

with Einstein to stress how different “reality” is from Einstein’s “any rea-

sonable conception of reality.”!5

The Building of “Reality”: This Participatory Universe What lies over the hill? What are we to project ahead out of the present landscape’s two greatest strangenesses? Of these one, the “bounds of

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time,” argues for mutability, law without law, law built on the statistics

of multitudinous chance events, events which—undergirding space and

time—must themselves transcend the categories of space and time. What these primordial chance events are, however, it does not answer;

it asks. Unasked and unwelcomed, the other strangeness, the quantum,

gives us chance. In “elementary quantum phenomenon” nature makes an unpredictable reply to the sharp question put by apparatus. Is the “chance” seen in this reply primordial? As close to being primordial as anything we know. Does this chance reach across space and time?

Nowhere more clearly than in the delayed-choice experiment. Does it have building power? Each query of equipment plus reply of chance inescapably do build a new bit of what we call “reality.” Then for the building of all of law, “reality” and substance—if we are not to indulge in free invention, if we are to accept what lies before us—what choice

do we have but to say that in some way—yet to be discovered—they all must be built upon the statistics of billions upon billions of such acts of observer-participancy? In brief, beyond the black hole, past the two great strangenesses of the landscape and over the hill, what other kind

of universe can we expect to see than one built as “phenomenon” is built, upon query of observation and reply of chance, a participatory

universe?

If the concept of a participatory universe seems to make the world a never-never land, we can recall Samuel Johnson’s remark on kicking the stone. Whatever the theory of reality, the pain in the toe made the stone real enough to him. In recent decades we have judged solid matter no less solid for being made up of electrons, nuclei, and mostly emptiness. It will make the stone no less real to regard it as entirely emptiness.

The Example of Mathematics Mathematics also is emptiness without emptiness. A familiar theorem

tells us that the sum of the three interior angles of a plane triangle is 180°. However, when we review all the definitions, postulates, and ax-

ioms that go into proving that theorem, we find that the statement re-

duces in the end to an identity, equivalent to “0 = 0.” No identity? Then no theorem! It may take 300 pages of computer paper to spell out all of the foundation pieces of a theorem, customary journal proof of which only requires two pages.!!6 But packaged as all the parts of the theorem are, and useful as the theorem is, it is still in the end packaged identity.

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Like the structure of rope with a trick knot, it has only to be pulled on to fall apart into nothingness.

Participatory Universe as Self-Excited Circuit Looking at an empty courtyard, we know that the game will not begin until a line has been drawn across the court to separate the two sides. Where, is not very important; but whether, is essential. “Elementary phenomena” are impossible without the distinction between observing

equipment and observed system;!!” but the line of distinction can run like a maze, so convoluted that what appears from one standpoint to be on one side and to be identified as observing apparatus, from another point of view has to be looked at as observed system.

From “nothingness ruled out as meaningless,” !!8 to the line of distinction that rules it out; from this dividing line to “phenomenon”; from one phenomenon to many; from the statistics of many to regularity and structure: these considerations lead us at the end to ask if the universe is not

best conceived as a self-excited circuit!!? (Figure 6): Beginning with the

big bang, the universe expands and cools. After eons of dynamic development it gives rise to observership. Acts of observer-participancy—via the mechanism of the delayed-choice experiment—in turn give tangible “reality” to the universe not only now but back to the beginning. To

speak of the universe as a self-excited circuit is to imply once more a

participatory universe.

If the views that we are exploring here are correct, one principle, observer-participancy, suffices to build everything. The picture of the participatory universe will flounder, and have to be rejected, if it cannot ac-

count for the building of law; and spacetime as part of law; and out of

law substance. It has no other than a higgledy-piggledy way to build law: out of the statistics of billions upon billions of acts of observer-participancy each of which by itself partakes of utter randomness.

Two Tests

No test of these views looks more like being someday doable, nor more interesting and more instructive, than a derivation of the structure of quantum theory from the requirement that everything have a way to

come into being!°as the word “cloud” was brought into being in the

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6. The universe viewed as a self-excited circuit. Starting small at upper right), it grows (loop of U) and in time gives rise (upper observer-participancy—which in turn imparts “tangible reality” delayed-choice experiment of Figure 5) to even the earliest days of

the universe.

surprise version of the game of twenty questions. No prediction lends it-

self to a more critical test than this, that every law of physics, pushed to the extreme, will be found to be statistical and approximate, not mathematically perfect and precise.

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The Challenge of “Law Without Law” We can ask ourselves if it is not absolutely preposterous to put into a formula anything at first sight so vague as law without law and substance without substance. How can we hope to move forward with no solid ground at all under our feet? Then we remember that Einstein had to perform the same miracle. He had to re-express all of physics in a new language. His curved space seemed to take all definite structure away from anything we can call solidity. In the end physics, after being moved bodily over onto the new underpinnings, shows itself as clear and useful as ever. We have to demand no less here. We have to move the imposing structure of science over onto the foundation of elementary acts of observer-participancy.!?1 No one who has lived through the revolutions made in our time by relativity and quantum mechanics—not least through the work of Einstein himself—can doubt the power of theoretical physics to grapple with this still greater challenge. Paper presented on Wednesday, March 7, 1979, for the Einstein Centennial Celebration, at the Institute for Advanced Study, Princeton.

It from Bit

Quantum Physics Requires a New View of Reality Revolution in outlook though Kepler, Newton, and Einstein brought us,! and still more startling the story of life? that evolution forced upon an unwilling world, the ultimate shock to preconceived ideas lies ahead, be

it a decade hence, a century, or a millennium. The overarching principle

of 20th-century physics, the quantum?—and the principle of complementarity? that is central idea of the quantum—leaves us no escape, Niels Bohr tells us,> from “a radical revision of our attitude as regards

physical reality” and a “fundamental modification of all ideas regarding

the absolute character of physical phenomena.” Transcending Einstein’s

summons? of 1908, “This quantum business is so incredibly important

and difficult that everyone should busy himself with it,” Bohr’s modest words direct us to the supreme goal: deduce the quantum from an under-

standing of existence.

How make headway toward a goal so great against difficulties so large? The search for understanding presents to us three questions, four

“no’”s, and five clues:

Three questions:

How come existence?

How come the quantum? How come “one world” out of many observer-participants? Four “no”s:

No tower of turtles No laws

No continuum No space, no time.

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Five clues: The boundary of a boundary is zero. No question? No answer! The super-Copernican principle. “Consciousness” More is different.

“It from Bit” as Guide in Search for Link Connecting Physics, Quantum, and Information

In default of a tentative idea or working hypothesis, these questions, “no”s and clues—yet to be discussed—do not move us ahead. Nor will any abundance of clues assist a detective who is unwilling to theorize how the crime was committed! A wrong theory? The policy of the engine inventor, John Kris, reassures us, “Start her up and see why she don’t go!” In this spirit” I, like other searchers,8 attempt formulation after formulation of the central issues, and here present a wider overview,

taking for working hypothesis the most effective one that has survived this winnowing: /t from bit. Otherwise put, every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely— even if in some con-

texts indirectly—from the apparatus-elicited answers to yes or no questions, binary choices,? bits.

It from bit symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most instances—an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this is a participatory universe.

Three examples may illustrate the theme of it from bit. First, the photon. With polarizer over the distant source and analyzer of polarization over the photodetector under watch, we ask the yes or no question, Did the counter register a click during the specified second. If yes, we often say, “A photon did it.” We know perfectly well that the photon existed neither before the emission nor after the detection. However, we also have to recognize that any talk of the photon “existing” during the intermediate period is only a blown-up version of the raw fact, a count.

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The yes or no that is recorded constitutes an unsplitable bit of infor-

mation. A photon, Wootters and Zurek demonstrate,!® cannot be cloned. As second example of it from bit, we recall the Aharonov-Bohm

scheme!! to measure a magnetic flux. Electron counters stationed off to

the right of a doubly-slit screen give yes-or-no indications of the arrival

of an electron from the source located off to the left of the screen, both

before the flux is turned on and afterward. That flux of magnetic lines of force finds itself embraced between—but untouched by—the two electron beams that fan out from the two slits. The beams interfere. The shift

in interference fringes between field off and field on reveals the magnitude of the flux, (phase change around perimeter of the included area)=2n x (shift of interference pattern, measured in number of fringes) = (electron charge) x (magnetic flux embraced)/fic.

Here f = 1.0546 x 10-°” g cm/sec is the quantum in conventional units,

or in geometric units!2—-where both time and mass are measured in the

units of length—f = fic = 2.612 x 10-°° cm? = the square of the Planck length, 1.616 x 10-33 = what we hereafter term the Planck area.

Not only in electrodynamics but also in geometrodynamics and in every other gauge-field theory, as Anandan, Aharonov, and others point out,!3 the difference around a circuit in the phase of an appropriately chosen quantum-mechanical probability amplitude provides a measure of the field. Here again the concept of it from bit applies.!4 Field strength or spacetime curvature reveals itself through shift of interference fringes, fringes that stand for nothing but a statistical pattern of yes-or-no registrations. When a magnetometer reads that it which we call a magnetic field, no reference at all to a bit seems to show itself. Therefore we look closer.

The idea behind the operation of the instrument is simple. A wire of

length / carries a current i through a magnetic field B that runs perpendicular to it. In consequence the piece of copper receives in the time t a transfer of momentum p in a direction z perpendicular to the directions of the wire and of the field,

p = Blit = (flux per unit z) x (charge, e, of the elementary carrier of current) x (number, N, of carriers that pass in the time #).

This impulse is the source of the force that displaces the indicator needle of the magnetometer and gives us an instrument reading. We deal with bits wholesale rather than bits retail when we run the fiducial cur-

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rent through the magnetometer coil, but the definition of field founds it-

self no less decisively on bits.

As third and final example of it from bit we recall the wonderful

quantum finding of Bekenstein,!°—totally unexpected denouement of earlier classical work of Penrose,!® Christodoulou,!” and Ruffini!8—re-

fined by Hawking,! that the surface area of the horizon of a black hole, rotating or not, measures the entropy of the black hole. Thus this surface

area, partitioned in imagination (see figure on page 299) into domains

each of size 4h log, 2, that is, 2.77 . . . times the Planck area, yields the Bekenstein number, N; and the Bekenstein number, so Thorne and Zurek explain,2° tells us the number of binary digits, the number of bits, that

would be required to specify in all detail the configuration of the con-

stituents out of which the black hole was put together. Entropy is a mea-

sure of lost information. To no community of newborn outside observers

can the black hole be made to reveal out of which particular one of 2" configurations it was put together. Its size, an it, is fixed by the number, N, of bits of information hidden within it. The quantum, f, in whatever correct physics formula it appears, thus serves as lamp. It lets us see horizon area as information lost, understand wave number of light as photon momentum, and think of field flux as

bit-registered fringe shift. Giving us its as bits, the quantum presents us with physics as informa-

tion.

How come a value for the quantum so small as f = 2.612 x 10-©cm2?

As well as ask why the speed of light is so great as c =3 x 10! cm/sec!

No such constant as the speed of light ever makes an appearance in a truly fundamental account of special relativity or Einstein geometrodynamics, and for a simple reason: Time and space are both tools to measure interval. We only then properly conceive them when we measure them in the same units (see footnote 12). The numerical value of the ratio be-

tween the second and the centimeter totally lacks teaching power. It is an

historical accident. Its occurrence in equations obscured for decades one of nature’s great simplicities. Likewise with f/ Every equation that contains an fi floats a banner, “It from bit.” The formula displays a piece of physics that we have learned to translate into information-theoretic

terms. Tomorrow we will have learned to understand and express all of

physics in the language of information. At that point we will revalue fh =

2.612 x 10-®cm2—as we downgrade c = 3 x 10!9 em/sec today—from constant of nature to artifact of history, and from foundation of truth to enemy of understanding.

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Four No’s To the question, “How come the quantum?” we thus answer, “Because what we call existence is an information-theoretic entity.” But how come

existence? Its as bits, yes; and physics as information, yes; but whose in-

formation? How does the vision of one world arise out of the informa-

tion-gathering activities of many observer-participants? In the considera-

tion of these issues we adopt for guidelines four “no’’s.

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First no: “No tower of turtles,” advised William James. Existence is

not a globe supported by an elephant, supported by a turtle, supported by yet another turtle, and so on. In other words, no infinite regress. No structure, no plan of organization, no framework of ideas underlaid by another structure or level of ideas, underlaid by yet another level, by yet another, ad infinitum, down to a bottomless night. To endlessness no alternative is evident but loop,! such a loop as this: Physics gives rise to observer-participancy; observer-participancy gives rise to information; and information gives rise to physics. Existence thus built?” on “insubstantial nothingness”? Rutherford and Bohr made a table no less solid when they told us it was 99.9. . . percent emptiness. Thomas Mann may exaggerate when he suggests? that “. . .

we are actually bringing about what seems to be happening to us,” but

Leibniz”4 reassures us, “Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough if, using reason well, we were never deceived by it.” Second no: No laws. “So far as we can see today, the laws of physics cannot have existed from everlasting to everlasting. They must have come into being at the big bang. There were no gears and pinions, no Swiss watchmakers to put things together, not even a pre-existing plan. . . . Only a principle of organization which is no organization at all would

seem to offer itself. In all of mathematics, nothing of this kind more ob-

viously offers itself than the principle that ‘the boundary of boundary is

zero.’ Moreover, all three great field theories of physics use this principle twice over. .

. This circumstance would seem to give us some reassur-

ance that we are talking sense when we think of . . . physics being”?5as

foundation-free as a logic loop, the closed circuit of ideas in a self-refer-

ential deductive axiomatic system.?6 Universe as machine? This universe one among a great ensemble of

machine universes, each differing from the others in the values of the

dimensionless constants of physics? Our own selected from this ensemble by an anthropic principle of one or another form?27 We reject

here the concept of universe as machine not least because it “has to postulate explicitly or implicitly, a supermachine, a scheme, a device, a miracle, which will turn out universes in infinite variety and infinite

number.”28

Directly opposite to the concept of universe as machine built on law is the vision of a world self-synthesized. On this view, the notes struck out

on a piano by the observer-participants of all places and all times, bits

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though they are, in and by themselves constitute the great wide world of

space and time and things. Third no: No continuum. No continuum in mathematics and therefore

no continuum in physics. A half-century of development in the sphere of mathematical logic”? has made it Clear that there is no evidence support-

ing the belief in the existential character of the number continuum. “Belief in this transcendental world,” Hermann Wey] tells us, “taxes the strength of our faith hardly less than the doctrines of the early Fathers of the Church or of the scholastic philosophers of the Middle Ages.”*° This lesson out of mathematics applies with equal strength to physics. “Just as the introduction of the irrational numbers . . . is a convenient myth [which] simplifies the laws of arithmetic . . . so physical objects,” Willard Van Orman Quine tells us,3! “are postulated entities which round

out and simplify our account of the flux of existence... . The conceptual

scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.” Nothing so much distinguishes physics as conceived today from math-

ematics as the difference between the continuum character of the one and

the discrete character of the other. Nothing does so much to extinguish

this gap as the elementary quantum phenomenon “brought to a close,” as Bohr puts it,>? by “an irreversible act of amplification,” such as the click

of a photodetector or the blackening of a grain of photographic emulsion.

Irreversible? More than one idealized experiment*® illustrates how hard it is, even today, to give an all-inclusive definition of the term irreversible.

Those difficulties supply pressure, however, not to retreat to old ground,

but to advance to new insight. In brief, continuum-based physics, no; information-based physics, yes. Fourth and last no: No space, no time. Heaven did not hand down the word “time.” Man invented it, perhaps positing hopefully as he did that “Time is nature’s way to keep everything from happening all at once.”34 If there are problems with the concept of time, they are of our own creation! As Leibniz tells us.>> “. . . time and space are not things, but orders of things . . .”; or as Einstein put it,5® “Time and space are modes by which we think, and not conditions in which we live.”

What are we to say about that weld of space and time into spacetime which Einstein gave us in his 1915 and still standard classical geometrodynamics? On this geometry quantum theory, we know, imposes fluctuations.37 Moreover, the predicted fluctuations grow so great at distances of the order of the Planck length that in that domain they put into question

the connectivity of space and deprive the very concepts of “before” and

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“after” of all meaning.*8 This circumstance reminds us anew that no count of existence can ever hope to rate as fundamental which does translate all of continuum physics into the language of bits. We will not feed time into any deep-reaching account of existence. must derive time—and time only in the continuum idealization—out it. Likewise with space.

acnot We of

Five Clues First clue: The boundary of a boundary is zero. This central principle of algebraic topology,*? identity, triviality, tautology, though it is, is also the unifying theme of Maxwell electrodynamics, Einstein geometrodynamics, and almost every version of modern field theory.4° That one can get so much from so little, almost everything from almost nothing, inspires hope that we will someday complete the mathematization of physics and derive everything from nothing, all law from no law. Second clue: No question, no answer. Better put, no bit-level question, no bit-level answer. So it is in the game of twenty questions in its sur-

prise version.4! (Admitted to the company of others, elicit the word which they supposedly have selected—but haven’t—by their yes-or-no answers to questions like “Does it belong to the animal kingdom?” or “Is it a person?” Eventually—twentieth inquiry or sooner—must come to the decisive yes-no question, “Is the word. . .?” Is the response “No”? Then lose the game. Or “Yes”? Win! Or win if challenge to any reply proves the respondent himself unable to supply a word compatible with all the previous answers. Risk everyone must take to participate—because the word did not exist before the question came.) And 0 it is for the electron

circulating within the atom or a field within a space. To neither field nor particle can we attribute a coordinate or momentum until a device operates to measure the one or the other. Moreover any apparatus that accurately* measures the one quantity inescapably rules out then and there the operation of equipment to measure the other.43 In brief, the choice of question asked, and choice of when it’s asked, play a part—not the whole

part, but a part—in deciding what we have the right to say,44

Bit-registration of a chosen property of the electron, a bit-registration

of the arrival of a photon, Aharonov-Bohm bit-based determination of the magnitude of a field flux, bulk-based count of bits bound in a black hole: all are examples of physics expressed in the language of information. However, into a bit count that one might have thought to be a private

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matter the rest of the nearby world irresistibly thrusts itself. Thus the atom-to-atom distance in a ruler—basis for a bit count of distance— evidently has no invariant status, depending as it does on the temperature and pressure of the environment. Likewise the shift of fringes in the Aharonov-Bohm experiment depends not only upon the magnetic flux it-

self, but also on the charge of the electron. But this electron charge— when we take the quantum itself to be nature’s fundamental measuring unit—is governed by the square root of the quantity e?/fic= 1/137.036..., a “constant” which—for extreme conditions—is as dependent on the local environment*® as is a dielectric “constant” or the atom-to-atom spac-

ing in the ruler. The contribution of the environment becomes overwhelmingly evident when we turn from length of bar or flux of field to the motion of alpha particle through cloud chamber, dust particle through 3°K background radiation or Moon through space. This we know from the analyses of Bohr and Mott,*#® Zeh,4”7 Joos and Zeh,48 Zurek,4? and Unruh and Zurek.*° It from bit, yes; but the rest of the world also makes a contribution, a contribution that suitable experimental design can minimize but not eliminate. Unimportant nuisance? No. Evidence the whole show is wired up together? Yes. Objection to the concept of every it from bits? No.

Build physics, with its false face of continuity, on bits of information! What this enterprise is we perhaps see more clearly when we examine for a moment a thoughtful, careful, wide-reaching exposition®! of the directly opposite thesis, that physics at bottom is continuous; that the bit of information is not the basic entity. Rate as false the claim that the bit of information is the basic entity. Instead, attempt to build everything on the foundation of some “grand unified field theory” such as string theory5*— or, in default of that, on Einstein’s 1915 and still standard geometrodynamics. Hope to derive that theory by way of one or another plausible line of reasoning. But don’t try to derive quantum theory. Treat it as supplied free of charge from on high. Treat quantum theory as a magic sausage grinder which takes in as raw meat this theory, that theory or the other theory and turns out a “wave equation,” one solution of which is “the” wave function for the universe.*? From start to finish accept continuity as right and natural: continuity in the manifold, continuity in the wave equation, continuity in its solution, continuity in the features that it predicts. Among conceivable solutions of this wave equation select as reasonable one which “maximally decoheres,” one which exhibits “maximal classicity’—maximal classicity by reason, not of “something exter-

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nal to the framework of wave function and Schrédinger equation,” but

something in “the initial conditions of the universe specified within quantum theory itself.” How compare the opposite outlooks of decoherence and it-from-bit? Remove the casing that surrounds the workings of a giant computer. Examine the bundles of wires that run here and there. What is the status of an individual wire? Mathematical limit of bundle? Or building block of

bundle? The one outlook regards the wave equation and wave function to be primordial and precise and built on continuity, and the bit to be ideal-

ization. The other outlook regards the: bit to be the primordial entity, and

wave equation and wave function to be secondary and approximate—and derived from bits via information theory.

Derived, yes; but how? No one has done more than William Wootters

towards opening up a pathway*4 from information to quantum theory. He puts into connection two findings, long known, but little known. Already before the advent of wave mechanics, he notes, the analyst of pop-

ulation statistics R. A. Fisher proved®® that the proper tool to distinguish

one population from another is not the probability of this gene, that

gene, and the third gene (for example), but the square roots of these

probabilities; that is to say, the two probability amplitudes, each probability amplitude being a vector with three components. More precisely, Wootters proves, the distinguishability between the two populations is measured by the angle in Hilbert space between the two state vectors,

both real. Fisher, however, was dealing with information that sits “out there.” In microphysics, however, the information does not sit out there. Instead, nature in the small confronts us with a revolutionary pistol, “No

question, no answer.” Complementarity rules. And complementarity as E.C.G. Stueckelberg proved*® as long ago as 1952, and as Saxon made more readily understandable*” in 1964, demands that the probability amplitudes of quantum physics must be complex. Thus Wootters derives

familiar Hilbert space with its familiar complex probability amplitudes from the twin demands of complementarity and measure of distinguishability. Try to go on from Wootters’s finding to deduce the full-blown machinery of quantum field theory? Exactly not to try to do so—except as idealization—is the demand laid on us by the concept of it from bit. How come? Probabilities exist “out there” no more than do space or time or the position of the atomic electron. Probability, like time, is a concept invented

by humans, and humans have to bear the responsibility for the obscurities

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that attend it. Obscurities there are whether we consider probability de-

fined as frequency*® or defined a la Bayes.*? Probability in the sense of frequency has no meaning as applied to the spontaneous fission of the particular plutonium nucleus that triggered the November 1, 1952, H-bomb blast. What about probabilities of a Bayesian cast, probabilities “interpreted not as frequencies observable through experiments, but as degrees of plausibility one assigns to each hypothesis based on the data and on one’s assessment of the plausibility of the hypotheses prior to seeing the

data”? Belief-dependent probabilities, different probabilities assigned to the same proposition by different people?®! Probabilities associated®” with the view that “objective reality is simply an interpretation of data agreed to by large numbers of people’’? Heisenberg directs us to the experiences® of the early nuclear-reaction-rate theorist Fritz Houtermans, imprisoned in Kharkov during the

time of the Stalin terror: “. . . the whole cell would get together to produce an adequate confession

. . . [and] helped them [the prisoners] to

compose their ‘legends’ and phrase them properly, implicating as few others as possible.” Existence as confession? Myopic but in some ways illuminating formulation of the demand for intercommunication implicit in the theme of it from bit! So much for “No question, no answer.” Third clue: the super-Copernican principle.® This principle rejects now-centeredness in any account of existence as firmly as Copernicus repudiated here-centeredness. It repudiates most of all any tacit adoption of here-centeredness in assessing observer-participants and their number. What is an observer-participant? One who operates an observing device and participates in the making of meaning, meaning in the sense of

Fellesdal,® “Meaning is the joint product of all the evidence that is

available to those who communicate.” Evidence that is available? The investigator slices a rock and photographs the evidence for the heavy nucleus that arrived in the cosmic radiation of a billion years ago. Before

he can communicate his findings, however, an asteroid atomizes his laboratory, his records, his rocks, and him. No contribution to meaning! Or at

least no contribution then. A forensic investigation of sufficient detail

and wit to reconstruct the evidence of the arrival of that nucleus is diffi-

cult to imagine. What about the famous tree that fell in the forest with no

one around?® It leaves a fallout of physical evidence so near at hand and so rich that a team of up-to-date investigators can establish what hap-

306

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HOLE

pened beyond all doubt. Their findings contribute to the establishment of meaning. “Measurements and observations,” it has been said,®8 “cannot be fun-

damental notions in a theory which seeks to discuss the early universe when neither existed.” On this view the past has a status beyond all ques-

tions of observer-participancy. It from bit offers us a different vision: “re-

ality is theory’;® “the past has no evidence except as it is recorded in the present.”79 The photon that we are going to register tonight from that four-billion-year-old quasar cannot be said to have had an existence “out there” three billion years ago, or two (when it passed an intervening gravitational lens) or one, or even a day ago. Not until we have fixed arrangements at our telescope do we register tonight’s quantum as having passed to the left (or right) of the lens or by both routes (as in a double slit experiment). This registration like every delayed-choice experiment?! reminds us that no elementary quantum phenomenon is a phenomenon until, in Bohr’s words,”? “It has been brought to a close” by “an irreversible act of amplification.” What we call the past is built on bits. Enough bits to structure a universe so rich in features as we know this world to be? Preposterous! Mice and men and all on Earth who may ever come to rank as intercommunicating meaning-establishing observer-participants will never mount a bit count sufficient to bear so great a burden. The count of bits needed, huge though it may be, nevertheless, so far

as we can judge, does not reach infinity. In default of a better estimate, we follow familiar reasoning”? and translate into the language of bits the

entropy of the primordial cosmic fireball as deduced from the entropy of

the present 2.735 °K (uncertainty < 0.05 °K) microwave relict radiation74

totaled over a three-sphere of radius 13.2 x 10° light years (uncertainty >

35%)"5 or 1.25 x 1078 cm and of volume 2n? radius’,

(number of bits) = (log, e) x (number of nats) = (log, e) x (en-

tropy/Boltzmann’s constant, k) = 1.44... x [(8n4/45)(radius

kT/hc)?| = 8 x 1088.

It would be totally out of place to compare this overpowering number

with the number of bits of information elicited up-to-date by observerparticipancy. So warns the super-Copernican principle. We today, to be sure, through our registering devices, give a tangible meaning to the history of the photon that started on its way from a distant quasar long before there was any observer-participancy anywhere. However, the far

more numerous establishers of meaning of time to come have a like in-

escapable part—by device-elicited question and registration of answer—

IT FROM

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307

in generating the “reality” of today. For this purpose, moreover, there are

billions of years yet to come, billions on billions of sites of observer-participancy yet to be occupied. How far foot and ferry have carried meaning-making communication in fifty thousand years gives faint feel for

how far interstellar propagation is destined”® to carry it in fifty billion

years.

Do bits needed balance bits achievable? They must, declares the concept of “world as system self-synthesized by quantum networking.”77 By

no prediction does this concept more clearly expose itself to destruction, in the sense of Popper.”8

Fourth clue: “consciousness.” We have traveled what may seem a dizzying path. First, elementary quantum phenomenon brought to a close by an irreversible act of amplification. Second, the resulting information expressed in the form of bits. Third, this information used by observerparticipants—via communication—to establish meaning. Fourth, from the past through the billeniums to come, so many observer-participants, so many bits, so much exchange of information, as to build what we call

existence. Doesn’t this it-from-bit view of existence seek to elucidate the physi-

cal world, about which we know something, in terms of an entity about which we know almost nothing, consciousness?”? And doesn’t Marie

Sklodowska Curie tell us, “Physics deals with things, not people’? Using such and such equipment, making such and such a measurement, I get such and such a number. Who I am has nothing to do with this finding. Or does it? Am I sleepwalking?®° Or am I one of those poor souls without the critical power to save himself from pathological science?®! Under

such circumstances any claim to have “measured” something falls flat

until it can be checked out with one’s fellows. Checked how? Morton

White reminds us8? how the community applies its tests of credibility, and in this connection quotes analyses by Chauncey Wright, Josiah Royce, and Charles Saunders

Peirce.83 Parmenides of Elea®4 (~515

B.c.—450* B.c.) may tell us that “What is . . . is identical, with the thought

that recognizes it.” We, however, steer clear of the issues connected with

“consciousness.” The line between the unconscious and the conscious

begins to fade®> in our day as computers evolve and develop—as mathe-

matics has—level upon level upon level of logical structure. We may someday have to enlarge the scope of what we mean by a “who.” This

granted, we continue to accept—as essential part of the concept of it from bit—Follesdal’s guideline,®® “Meaning is the joint product of all the

evidence that is available to those who communicate.” What shall we say

308

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HOLE

of a view of existence” that appears, if not anthropomorphic in its use of the word “who,” still overly centered on life and consciousness? It would seem more reasonable to dismiss for the present the semantic overtones

of “who” and explore and exploit the insights to be won from the phras-

es, “communication” and “communication employed to establish meaning.” Fgllesdal’s statement supplies, not an answer, but the doorway to new questions. For example, man has not yet learned how to communicate with ant. When he does, will the questions put to the world around by the ant and the answers that he elicits contribute their share, too, to the estab-

lishment of meaning? As another issue associated with communication,

we have yet to learn how to draw the line between a communication net-

work that is closed, or parochial, and one that is open. And how to use

that difference to distinguish between reality and poker—or another game®8_so intense as to appear more real than reality. No term in F¢llesdal’s statement posses greater challenge to reflection than “communication,” descriptor of a domain of investigation® that enlarges in sophistication with each passing year. Fifth and final clue: More is different.?° Not by plan but by inner necessity a sufficiently large number of H,0 molecules collected in a box will manifest solid, liquid, and gas phases. Phase changes, superfluidity, and superconductivity all bear witness to Anderson’s pithy point, more is different. We do not have to turn to objects so material as electrons, atoms, and

molecules to see big numbers generating new features. The evolution

from small to large has already in a few decades forced on the computer

a structure?! reminiscent of biology by reason of its segregation of different activities into distinct organs. Distinct organs, too, the giant telecom-

munications system of today finds itself inescapably evolving.®? Will we

someday understand time and space and all the other features that distinguish physics—and existence itself—as the similarly self-generated or-

gans of a self-synthesized information system?93

Conclusion

The spacetime continuum? Even continuum existence itself? Except as idealization neither the one entity nor the other can make any claim to be a primordial category in the description of nature. It is wrong, moreover, to regard this or that physical quantity as sitting “out there” with this or

IT FROM

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309

that numerical value in default of question asked and answer obtained by

way of appropriate observing device. The information thus solicited makes physics and comes in bits. The count of bits drowned in the dark night of a black hole displays itself as horizon area, expressed in the language of Bekenstein number. The bit count of the cosmos, however it is figured, is ten raised to a very large power. So also is the number of elementary acts of observer-participancy over any time of the order of fifty billion years. And, except via those time-leaping quantum phenomena that we rate as elementary acts of observer-participancy, no way has ever offered itself to construct what we call “reality.” That’s why we take seriously the theme of it from bit.

Agenda Intimidating though the problem of existence continues to be, the theme

of it from bit breaks it down into six issues that invite exploration:

One: Go beyond Wootters and determine what, if anything, has to be added to distinguishability and complementarity to obtain all of standard quantum theory. Two: Translate the quantum versions of string theory and of Einstein’s geometrodynamics from the language of continuum to the language of bits. Three: Sharpen the concept of bit. Determine whether “an elementary

quantum phenomenon brought to a close by an irreversible act of ampli-

fication” has at bottom (1) the 0-or-1 sharpness of definition of bit number nineteen in a string of binary digits, or (2) the accordion property of a mathematical theorem, the length of which, that is, the number of supplementary lemmas contained in which, the analyst can stretch or shrink ac-

cording to his convenience. Four: Survey one by one with an imaginative eye the powerful tools that mathematics—including mathematical logic— has won and now offers to deal with theorems on a wholesale rather than a retail level, and

for each such technique work out the transcription into the world of bits. Give special attention to one and another deductive axiomatic system

which is able to refer to itself,?4 one and another self-referential deduc-

tive system. Five: From the wheels-upon-wheels-upon wheels evolution of computer programming dig out, systematize, and display every feature that illuminates the level-upon-level-upon level structure of physics.

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HOLE

Six: Capitalize on the findings and outlooks of information theory,9>

algorithmic entropy,®® evolution of organisms,®” and pattern recognition.°8 Search out every link each has with physics at the quantum level.

Consider, for instance, the string of bits 1111111. . . and its representa-

tion as the sum of the two strings 1001110... and 0110001...

. Explore

and exploit the connection between this information-theoretic statement and the findings of theory and experiment on the correlation between the polarizations of the two photons emitted in the annihilation of singlet positronium” and in like Einstein-Podolsky-Rosen experiments. ! Seek out, moreover, every realization in the realm of physics of the information-theoretic triangle inequality recently discovered by Zurek.11 Finally: Deplore? No, celebrate the absence of a clean clear definition

of the term “bit” as elementary unit in the establishment of meaning. We

reject “that view of science which used to say, ‘Define your terms before you proceed.’ The truly creative nature of any forward step in human

knowledge,” we know, “is such that theory, concept, law, and method of

measurement—forever

inseparable—are

born into the world in

union.”!°? If and when we learn how to combine bits in fantastically

large numbers to obtain what we call existence, we will know better what we mean both by bit and by existence. A single question animates this report: Can we ever expect to under-

stand existence? Clues we have, and work to do, to make headway on

that issue. Surely someday, we can believe, we will grasp the central idea

of it all as so simple, so beautiful, so compelling that we will all say to each other, “Oh, how could it have been otherwise! How could we all have been so blind so long!”

Acknowledgments For discussion, advice, or judgment on one or another issue taken up in this review, I am indebted to Nandar Balazs, John D. Barrow, Charles H. Bennett, David Deutsch, Robert H. Dicke, Freeman Dyson, and the late

Richard P. Feynman as well as David Gross, James B. Hartle, John J.

Hopfield, Paul C. Jeffries, Bernulf Kanitscheider, Arkady Kheyfets, and Rolf W. Landauer; and to Warner A. Miller, John R. Pierce, Willard Van

Orman Quine, Benjamin Schumacher, Abner Shimony, and Frank J. Tipler as well as William G. Unruh, Steven Weinberg, Morton White, Eugene P. Wigner, William K. Wootters, Hans Dieter Zeh, and Wojciech

H. Zurek. For assistance in preparation of this report I thank E. L.

IT FROM

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31

Bennett and NSF grant PHY245-6243 to Princeton University. I give special thanks to the sponsors of the August 28-31, 1989 conference ISQM-Tokyo ‘89 at which the then-current version of the present analy-

sis was reported.

N. G. van Kampen: Did you mean to say that the observer influences the

observed object?

J. A. Wheeler: The observer does not influence the past. Instead, by his

choice of question, he decides about what feature of the object he shall have the right to make a clear statement.

J.-P. Vigier: Two problems. I. The first is that the QSO raise lots of unsolved problems, i.e.—strange quantized N,/log(1+z) relation— correlation with galaxies (Arp)—angu-

lar correlation with brightest nearby galaxies (Burbidge et al.)

Il. The second is that the idea (Einstein et al.) of the reality of fields has

led (assuming that “particles” are field) singularities to the only known justification of the geodesic law. To contest it is to make the meaning of

dynamical behavior purely observer-dependent, i.e., to kill the reality of the physical world.

J. A. Wheeler: 1. The book by Thorne and colleagues, “Black Holes: The Membrane Paradigm,” describes how a supermassive black hole, endowed via accretion with great angular momentum inside and an accretion disk outside, produces counter-directed jets and radiation of great power. I know no other mechanism able to produce quasars. II. No one has discovered a way to get a particle of wave length 2 from point A through empty flat space to a point B at a great distance L

without its undergoing on the way a transverse spread of the order JL. This spread imposes an inescapable limitation on the classical concept of

“worldline.”

Report evolved from presentations at Santa Fe Institute Conferences, May 29 — June 2

and June 4-8, 1989, and at the Third International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, August 28-31, 1989, under the title “Information, Physics, Quantum:

The Search for Links”; and headed

“Can We Ever Expect to Understand Existence?” as the Penrose Lecture at the April 20-22, 1989, annual meeting of Benjamin Franklin’s “American Philosophical Society,

Held at Philadelphia for Promoting Useful Knowledge,” and the Accademia Nazionale

dei Lincei Conference on La Verita nella Scienza, Rome, October 13, 1989.

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REFERENCES

References

NOTE: These references reflect the dates of the essays when they were first

published.

A Septet of Sibyls: Aids in the Search for Truth . Adolf Griinbaum,

“Causality and the Science

Scientist, 40, p. 665 (1952).

. R. R. Bush and F. Mosteller, Stochastic

John Wiley, 1955).

of Human Behavior,” in American

Models for Learning (New York, N.Y.:

. H. Poincaré, La Valeur de la Science (Paris: Flammarion, 1904), pp. 195 and 235,

. N. Bohr and L. Rosenfeld: “Zur Frage der Messbarkeit der elektromagnetischen Feldgrossen,” Mat.—Fys. Medd. Dan. Vidensk. Selsk. 12 no. 8 (1933); English

translationby A. Petersen, 1979. Reprinted in J.

A. Wheeler and W. H. Zurek,

Quantum Theory and Measurement, (Princeton: Princeton University Press,

1983), pp. 479-534.

. N. Bohr, Atomic Theory and the Description of Nature (Cambridge: Cambridge

University Press, 1933), p. 28. See also the chapter by Bohr in P. A. Schilpp’s Albert Einstein: Philosopher Scientist (Evanston, Illinois: Library of Living Philosophers, 1949).

. R. B. Braithwaite, Theory of Games as a Tool for the Moral Philosopher (Cambridge: Cambridge University Press, 1955).

s

Genesis and Observership 1. C. Darwin, 1863, March 29 letter from Down to Joseph Dalton Hooker; in F. Darwin, ed., The Life and Letters of Charles Darwin, Including an Autobiographical Chapter

(New York, N. Y., and London: Appleton, 1919), p. 203. Warm appreciation is expressed to Frederick Burckhardt for locating this source of the cited passage.

REFERENCES

316

2. A.I. Oparin, The Origin of Life, with annotations by Sergius Morgulis (New York, N. Y.: Macmillan,

1938), 1991update; C. B. Thaxton, R. Olsen, and W. Bradley,

The Mystery of Life Origins: Reassessing Current Theories (New York, N.Y.: for a Cell: The Nature and Philosphical Library, 1984), and C. De Duve, Blueprint

Origin of Life (Burlington, N. C.: Patterson, 1991).

3. W. James, Some Problems of Philosophy. A Beginning of an Introduction to Philosophy (New York, N.Y.: Longmans Green, 1911), pp. 38-40. I owe this quotation to Gary Miller. 4. J. A. Wheeler, “Transcending the law of conservation of leptons,” Atti del Convegno Internazionale sul Tema: The Astrophysical Aspects of the Weak Interactions

(Roma, Accademia Nazionale dei Lincei, 1971), pp. 133-164; C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: Freeman, 5.

1973).

L. J. Henderson, The Fitness of the Environment (New York, N. Y.: Macmillan,

1913); 1958 reprint, with an introduction by George Wald, Beacon Press, Boston.

6. R.H. Dicke, “Dirac’s cosmology and Mach’s principle,” Nature 192, pp. 440-441

(1961).

7. B. Carter, “Large number coincidences and the anthropic principle in cosmology,”

in M. S. Longair, ed., Confrontation of Cosmological Theories with Observational Data, 1.A.U. (Dordrecht: Reidel, 1974), pp. 291-298.

8. C. B. Collins and S. W. Hawking, “Why is the universe isotropic,” Astrophys. J.

180, pp.

9.

317-334 (1973).

D. Hume, Dialogues Concerning Natural Religion (London: Robinson, 1779); 1947 reprint by Thomas Nelson, London; U.S. edition thereof [Indianapolis, Indiana (1970 and 1980), and New York, N. Y. (1948): Bobbs-Merrill], p. 148 in latter edi-

tion. I thank Wesley Salmon for this reference.

10. C. F. von Weizsacker, “The Copenhagen interpretation,” in T. Bastin, ed., Quantum

Theory and Beyond (Cambridge: Cambridge University Press, 1971), pp. 25-31.

(See p. 26 for cited quotation.)

11. J. A. Wheeler, “Conference summary: more results than ever in gravitation physics and relativity,” pp. 299-344 in G. Shaviv and J. Rosen, eds., General Relativity and Gravitation; Proceedings of the Seventh International Conference (GR7), Tel-Aviv

University, June 23-28, 1974 (New York, N. Y.: John Wiley, 1974).

12. J. H. Oort, “Distribution of galaxies and the density of the universe,” in Onz-

iéme Conseil de Physique Solvay: La Structure et l’évolution de l’univers (Brussel: Editions Stoops, 1958), pp. 163-183; J. R. Gott, III, J. E. Gunn, D. N.

Schramm, and B. M. Tinsley, “An unbound universe?” Astrophys. J. 194, pp.

543-553 (1974).

13. J. P. Ostriker, P. J. E. Peebles, and A. Yahil, “The size and mass of galaxies and the mass of the universe,” Astrophys. J. Lett. 193, L1-4 (1974); J. P. Ostriker and P. J. E. Peebles, “A numerical study of the stability of flattened galaxies; or, can cold galaxies survive?” Astrophys. J. 186, pp. 467-480 (1973).

14. G.F.R. Ellis and A. R. King, “Was the big bang a whimper?” Comm. Math. Phys. 38, pp. 119-156 (1974); T. B. Criss, R. A. Matzner, M. P. Ryan, Jr., and L. C. Shepley, “Modern theoretical and observational cosmology,” in Shaviv and Rosen, note 11.

REFERENCES

319

15. C. W. Misner and A. H. Taub, “A singularity-free empty universe,” Zh. Eksp. &

Teor. Fiz. 55, p. 233 (1968), English original in Sov. Phys.-JETP 28, p. 122 (1969). 16. S. W. Hawking and R. Penrose, “The singularities of gravitational collapse and cosmology,” Proc. Roy. Soc. London A314, pp. 529-548 (1970).

17. V. A. Belinsky, E. M. Lifshitz, and 1, M. Khalatnikov, “Oscillatory mode of ap-

proach to a singularity in homogeneous cosmological models with rotating axes,” Zh. Eksp. & Teor. Fiz. 60, pp. 1969-1979 (1971); English trans. in Sov.

Phys.—JETP 33, pp. 1061-1066 (1971).

18. R. Penrose, “Singularities in cosmology,” in Longair, note 7, pp. 263-272. 19. J. A. Wheeler, “From relativity to mutability,” pp. 202-247, in J. Mehra, ed., The Physicist's Conception of Nature (Dordrecht: Reidel, 1973).

20. Wheeler, note 4; J. B. Hartle, “Long-range neutrino forces exerted by Kerr black

holes,” Phys. Rev. D3, pp. 2938-2940 (1971); J. B. Hartle, “Can a Schwarzschild black hole exert long-range neutrino forces?” in J. Klauder, ed., Magic without

Magic: John Archibald Wheeler (San Francisco: W. H. Freeman,

1972); J. Beken-

stein, “Nonexistence of baryon number for static black holes,” Phys. Rev. DS, pp.

1239-1246 (1972); J. Bekenstein, “Nonexistence of baryon number for static black

holes, IT”, Phys. Rev. D5, pp. 2403-2412 (1972); C. Teitelboim, “Nonmeasurability

of the baryon number of a black hole,” Let. al Nuovo Cimento 3, pp. 326-328 (1972); C Teitelboim, “Nonmeasurability of the lepton number of a black hole,”

Let. al Nuovo Cimento 3, pp. 397-400 (1972); C. Teitelboim, “Nonmeasurability of

the quantum numbers of a black hole,” Phys. Rev. DS, pp. 2941-2954 (1972).

21, L. Landau and E. Lifshitz, The Classical Theory of Fields, translated by M. Hamermesh (Reading, Mass.: Addison-Wesley, 1951), pp. 335-336; J. Weber and J. A. Wheeler, “Reality of the cylindrical gravitational waves of Einstein and Rosen,”

Rey. Mod Phys. 29, pp. 509-515 (1957).

22. S. A. Hojman, K. Kuchar, and C. Teitelboim, “New approach to general relativity,” Nature Physical Science 245, pp. 97-98 (1973); C. Teitelboim, “How commutators of constraints reflect the spacetime structure,” Ann. Phys. 79, pp. 542-557 (1973); C. Teitelboim, “The Hamiltonian structure of spacetime,” Ph.D. thesis, Princeton

University (1973) available from University Microfilms, Inc., Ann Arbor, Michigan 48106; K. Kuchar, “Canonical quantization of gravity,” in W. Israel, ed. Relativity,

Astrophysics, and Cosmology (Dordrecht: Reidel, 1973); K. Kuchar, “Geometrodynamics regained: a Lagrangian approach,” J. Math. Phys. 15, pp. 708-715 (1974).

23. C. M. Patton and J. A. Wheeler, “Is physics legislated by cosmology?” pp.

538-605 in C. J. Isham, R. Penrose, and D. W. Sciama, eds. Quantum Gravity; an Oxford Symposium (Oxford: Clarendon Press, 1975). This paper lays out for study the idea that the universe is a “self-excited circuit” in which the universe gives rise to the observer and the observer—in development of the ideas of quan-

tum mechanics—gives a meaningful existence to the universe. It recalls the concept of Parmenides of Elia that “what is . . . is identical with the thought that recognizes it” and the concept of George Berkeley “To be is to be perceived.” However, through the kindness of Prof. B. Kanitscheider and Prof. Baumgartner

of the University of Giessen, I have since learned that already in the writings of

the philosopher F. W. J. von Schelling (1775-1854) there is an earlier statement,

318

REFERENCES

in older language, of the present thesis—as Prof Kanitscheider puts it—“dass das Universum von vornherein ein ihm immanentes Ziel, eine teleologische Struktur, besitzt und in allen seinen Produkten auf evolutionare Stadien ausgerichtet ist, die schliesslich die Hervorbringung von Selbstbewusstsein einschliessen, welches dann aber wiederum den Entstehungsprozess reflektiert und diese Reflexion ist die notwendige Bedingung fiir die Konstitution der Gegenstinde des Bewusstseins.” For details he cites M. Schréter (ed.), 1958-59, Schellings Werke, nach

der Originalausgabe in neuer Anordnung herausgegeben, Miinchen, Beck, in 6

vols. See especially, in Vol. 5, his “Darstellung des Naturprozesses” (fragment of a series of lectures on the principles of philosophy given at Berlin the winter of 1843-1844, from the handwritten literary remains), particularly these words from

pp. 428-430: “. . . liessen wir die Idee adseinander treten in ihre Momente, damit sie durch Wiederkehr in die Einheit sich verwirkliche. Das Auseinandergehen

und successiv Wiedereinswerden dieser Momente ist die Natur. Die Wiederherstellung der Einheit ist ihr Ende und der Zweck der Natur. Die Wiederherstellung der Einheit ist die Verwirklichung der Idee. Die verwirklichte Idee ist der Mensch, und er ist die Intention nach nur diese . . . der Mensch hat keinen Zweck, denn er ist selbst Zweck, er ist nur, um Bewusstsein zu sein, und das Bewuss tsein ist der Zweck; der Mensch ist also nichts als Bewusstsein, und nicht noch etwas

anderes . . . Zu dem Menschen hat das gesammte Weltall mitgewirkt . . . Weil er

das Existierende ist, Momente bestimmt, Mensch ist . . . nicht Prozesses—nicht die

so waren alle Potenzen des Universums, alle diese getrennten in ihm als in der letzten Einheit zusammenzugehen . . . der speziell ein Produkt der Erde—er ist ein Produkt des ganzen Erde allein, das ganze Weltall ist bei ihm beteiligt, und

wenn aus der Erde, so ist er . . . doch nicht ausschliesslich fiir sie, er ist fiir alle

Sterne, denn er ist fiir das Weltall, als Endzweck des Ganzen, erschaf fen. Wenn er als lokales Wesen erscheint, so ist er diess nicht ursprtinglich, er ist lokalisiert worden: wie? diess muss durch die Folge sich zeigen. Er ist, wie gesagt, das universale Wesen, und sollte daher nicht an einem bestimmten Punkt, er sollte im Ganzen wohnen . . .”; these ideas epitomized [1993 addition by J.A.W.] by the

theme of Martin Heidegger, “Without the word, no thing may be,” in his On the

Way to Language, ed. and trans. by P. D. Hertz and J. Stamba ugh (New York, 1971); D. Finkelstein, G. Frye, and L. Susskind, “Spacetime code V,” Phys. Rev. D 9, pp. 2231-2236 (1974); D. Finkelstein and G. McCallum, “Unified quantum theory,” pp. 15-54 in L. Castell, M. Drieschner, and C. F. von Weizsiicker, eds.,

Qunatum Theory and the Structure of Time and Space (Munich: Hanser, 1975).

Dicke, note 6.

. H. Alfvén and G. Arrhenius, The Structure and Evolutionary History of the Solar System (Dordrecht: Reidel, 1975).

. C. W. Allen, Astrophysical Quantities (London: The Athlone Press, University of London, second edition 1964).

27. T. Regge, “S-matrix theory of elementary particles,” pp. 395-402 in M, Verde, Atti del

Convegno Mendeleeviano; “Periodicita e Simmetri e nella Struttura Elementare

della Materia” (Torino: Accademia delle Scie nze di Torino,

the cited proposal.

1971). See p. 398 for

REFERENCES

319

28. Henderson, note 5. 29. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete,” Phys, Rev. 47, pp. 777-780 (1935).

30. M. Jammer, The Philosophy of Quantum Mechanics (New York, N. Y.: John Wiley, 1974); N. Bohr, 1949, “Discussion with Einstein on epistemological problems in

atomic physics,” pp. 201-241 in P. A. Schilpp, ed., Albert Einstein: Philosopher-Sci-

entist (Evanston, Illinois: Library of Living Philosophers, 1949) and subsequent paperback reprints elsewhere (1949); reprinted in Bohr’s Atomic Physics and Human Knowledge (New York, N. Y.: John Wiley, 1958), pp. 32-66.

61

S. J. Freedman and R. A. Holt, “Test of local hidden-variable theories in atomic

physics,” Comments Atom. Mol. Phys. 5, pp. 55-62 (1975).

32. E. P. Wigner, “Epistemological perspective on quantum theory,” pp. 369-385 in C. A. Hooker, ed., Contemporary Research in the Foundations and Philosophy of

Quantum Theory (Dordrecht: Reidel, 1973).

33. Ibid. 34, D. Fogllesdal, “Meaning and experience,” pp. 25-44, in S. Guttenplan, ed., Mind and Language (Oxford: Clarendon Press, 1975).

35. R. Knox, undated, limerick quoted in Bertrand Russell, A History of Western Philosophy (New York, N. Y.: Simon and Schuster, 1972), p. 648.

36. J. Roger, Les Sciences de la Vie dans la Pensée Francaise (Paris: Armand Colin, 1963). See p. 101 for the reference to Jean-Baptiste von Helmont, 1648, Ortus

medicine and the story of the mouse. I owe this reference to the kindness of

Thomas Hankins.

Se

M. Eigen and R. Winkler, Das Spiel; Naturgesetze steuern den Zufall (Miinchen: Piper, 1975).

Figure Notes: 1 Misner, Thorne, and Wheeler, note 4. He S. W. Hawking, 1975, “Particle creation by black holes,” Commun. Math. Phys. 43, p. 199.

Til. J. A. Wheeler, “The black hole,” pp. 279-316 in R. Debever, ed., Astrophysics and Gravitation; Proceedings of the Sixteenth Solvay Conference on Physics (Brussels: Editions de I’ Université de Bruxelles, 1974).

Iv.

Wheeler, note 11.

NE N. Bohr, Essays 1958-1962 on Atomic Physics and Human Knowledge (New York, N. Y.: Wiley-Interscience, 1963).

VI.

Bohr, note 30.

320

REFERENCES

Niels Bohr and Nuclear Physics 1. N. Bohr, Roy. Soc. (London) Phil. Trans. A209, p. 281 (1909). 2. N. Bohr, Roy. Soc. (London) Proc. A84, p. 395 (1910). 3.

N. Bohr and F. Kalckar, Kgl. Danske Videnskabernes Selskab Math.-Fys. Meddelser 14, No. 10 (1937).

4. N. Bohr, Phys. Rev. 55, p. 418 (1939); N. Bohr and J. A. Wheeler, Phys. Rev. 56, p.

426 (1939).

N. Bohr, Phil, Mag. 25, p. 10 (1913). SAB

Ibid.

SS

Felix Bloch, Physics Today, p. 32, October 1963.

C. F. von Weizsacker, Z. Physik 88, p. 612 (1934); E. J. Williams, Kgl. Danske Vi-

N. Bohr, Phys. Soc. (London) Proc. 78, p. 1083 (1961).

denskabernes Selskab, Mat.-Fys. Meddelelser 13, p. 4 (1935). 10.

Reprinted in N. Bohr, Nature

137, p. 344 (1936).

11. Report of a correspondent in Nature 137, p. 351 (1936). 12. G. Breit and E. P. Wigner, Phys. Rev. 49, p. 519 (1936). 13. See note 11. 14.

Bohr, note 10.

15. Ibid. 16. Ibid. 17. Bohr and Kalckar, note 3. 18.

N. Bohr, R. Peierls, and G. Placzek; Nature

19.

For an account of this conversation see the article by L. Rosenfeld in Fysisk

144, p. 200 (1939).

Tidsskrift 60, p. 65 (1963).

20. For more on Bohr’s position on nuclear energy and his stand for an open world, see for example J. A. Wheeler, Physics Today, January 1963, p. 30. 21, J. Rainwater, Phys. Rev. 79, p. 432 (1950), submitted for publication April 17,

1950.

22. Wheeler, note 20. 23.

D.L. Hill and J. A. Wheeler, Phys. Rev. 89, p. 1102 (1953).

Delayed-Choice Experiments and the Bohr-Einstein Dialogue 1, M. Planck, “Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum,”

Verhandlungen der Deutschen Physikalischen Gesellschaft 2, pp. 237-245 (1900). 2. E. Rutherford, “Induced radioactivity,” Philosophical Magazine 49, pp.161-192

REFERENCES

321

(1900); E. Rutherford and F. Soddy, “The radioactivity of thorium compounds: I. Investigation of the radioactive emanation,” pp. 321-350, “II. The cause and nature of radioactivity,” pp. 837-860, Journal of the Chemical Society (London) 81,

(1902).

A. Einstein, letter of May 2, 1920, after meeting Bohr. P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Evanston, Illinois: Library of Living Philosophers, 1949). . N. Bohr, “Discussion with Einstein on epistemological problems in atomic physics,” pp. 201-241 in Schilpp, ed., note 4. See for example the relevant two chapters in M. Jammer, The Philosophy of Quantum Mechanics (New York, N. Y.: John Wiley,

1974); and A. Pais, “Einstein and

the quantum theory,” Reviews of Modern Physics 51, pp. 863-914 (1979).

- A preliminary account of the stages in Bohr’s evolution of this term will be found

in A. Petersen, Quantum Mechanics and the Philosophical Tradition (Cambridge,

Mass.: M. I. T. Press, 1968).

Wording of the author in “Beyond the black hole,” pp. 341-375 in H. Woolf, ed.,

Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the

Achievements of Albert Einstein (Reading, Mass.: Addison-Westley, 1980). Planck, note 1.

. A. Einstein, “Uber einen die Erzeugung and Verwandlung des Lichtes betreffenden heuristischen Gesichtpunkt,” Annalen der Physik 17, pp. 132-148 (1905). Rutherford; Rutherford and Soddy, note 2. . N. Bohr, “Constitution of atoms and molecules,” Philosophical Magazine 26, pp.

1-15 (1913).

. A. Einstein, “Strahlungs-emission und-absorption nach der Quantentheorie,” Ver-

handlungen der Deutschen Physikalischen Gesellschaft 18, pp. 318-323 (1916);

“Quantentheorie der Strahlung.” Mitteilungen der Physikalischen Gesellschaft,

Ziirich 16, pp. 47-62 (1916).

14. L. de Broglie, “Les ondes et les quanta,” pp. 507-501, “Les quanta de lumiére, la diffraction, et l'interference,” pp. 548-550, “Les quanta, la théorie cinetique des gases, et le principe de Fermat,” pp. 630-632, Académie des Sciences Paris, Comptes Rend.

177 (1923).

15. W. Heisenberg, “Uber quantentheoretische Umdeutung kinematischer und mechafiir Physik 33, pp. 879-892 (1925). nischer Bezichungen,” Zeitschrift

16. E. Schrédinger, “Quantisierung als Eigenwertproblem,” Ann. der Physik 79, pp. 361-376 (1926). Li, W. Heisenberg, “Uber den anschaulichen Inhalt der Quantentheoretichen Kinematik und Mechanik,” Zeitschrift fiir Physik 43, pp. 172-198 (1927).

18. N. Bohr, “The quantum postulate and the recent development of atomic theory,”

address at the Volta centennial, Como, September 16, 1927, as revised for publication, Nature (London) 121, pp. 580-590 (1928); reprinted in N. Bohr, Atomic Theory and the Description of Nature (Cambridge, U.K.: Cambridge University Press,

1934), pp. 52-91.

S22

REFERENCES

19. The wording here is adapted from that given by N. Bohr in Atomic Theory and the Description of Nature, p. 35, note 18. 20. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 47, pp. 777-780 (1935).

21. N. Bohr, “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 48, pp. 696-702 (1935).

22. The center of discussion in the Bohr-Einstein dialogue was more often the so-called double-slit experiment than the beam splitter depicted in Figure 4. The latter is made the focus of attention here because it presents the central point without getting into the physics of interference patterns.

23. J. A. Wheeler, “The ‘past’ and the ‘delayed-choice’ double-slit experiment,” in A. R. Marlow, ed., Mathematical Foundations of Quantum Theory (New York, N. Y.:

Academic Press, 1978), pp. 9-48. K. F. Weizsicker, Ortbestimmung eines Elektrons durch ein Mikroskop, Zeits. f; Physik 70, pp. 114-130 (1931).

24, Petersen, note 7. 25. Woolf, ed., note 8. 26. “Closed by irreversible amplification,” p. 73; “irreversible amplification,” p. 88: N.

Bohr, Atomic Physics and Human Knowledge (New York, N. Y.: John Wiley, 1958).

27. A homely illustration of this idea is provided by the old parlor game of Twenty

Questions in the “surprise version” described by the author in several places, most recently in “Beyond the black hole,” a chapter in H. Woolf, ed., note 8.

28. See for example B. d’Espagnat, ed., Foundations of Quantum Mechanics (New

York, N. Y.: Academic Press, 1971); E. P. Wigner. “Interpretation of quantum mechanics,” 93 pages of mimeographed notes of lectures delivered at Princeton University in 1976 on deposit in Fine Library, Princeton University, Princeton, N. J.;

M. M. Yanase, M. Namiki, and S. Machida, eds., Theory of Measurement in Quantum Mechanics (Tokyo: Physical Society of Japan, 1980); J. A. Wheeler, “Frontiers

of time,” in N. Toraldo di Francia, ed., Problems in the Foundations of Physics, Rendiconti della Scuola Internazionale de Fisica “Enrico Fermi,” LXXII Corso (Amsterdam: North-Holland, 1979), pp. 395-497.

29. G. Berkeley (1685-1783) in M. W. Calkins, ed., Berkeley: Essays, Principles, Dialogues with Selections from Other Writings (New York, N. Y.: Scribner, 1929), as

reprinted in 1957, pp. 125-126.

30. Why not change “has a decisive consequence for . . .” to “makes all the difference

in the elementary quantum phenomenon”? The word “difference” is not allowable.

We can do the one experiment or the other experiment but the two experiments

simply will not fit into one place at one time. We are dealing with one phenomenon, one “act of creation.” The very individuality of the quantum phenomenon leaves no place for comparing what is with what might have been. 31. For a review of relevant experiments, see especially F. M. Pipkin, “Atomic physics tests of the basic concepts in quantum mechanics,” pp. 281-340 in Advances in Atomic and Molecular Physics (New York, N. Y.: Academic Press, 1978).

32. N. Bohr as quoted by J. Bronowski, The Ascent of Man (Boston/Toronto: Little, Brown and Co., 1973), p. 122.

REFERENCES

323

33. For a discussion of this point I am indebted to Professor Andrew Gleason. 34, D. Walsh, R. F. Carswell, and R. J. Weymann, “0957 + 561A,B: twin quasistellar

objects or gravitational lens?” Nature 279, pp. 381-384 (1979); R. J. Weymann, F. H. Chaffee, Jr., M. Davis, N. P. Carleton, D. Walsh, and R. F. Carswell, “Multiple-

mirror observations of the twin QSO 0957 + 516A,B,” Astrophysical Journal 233, L43-L46 (1979); P. J. Young, W. L. W. Sargent, J. A. Kristian, and J. A. Westphal,

“CCD photometry of the nuclei of three supergiant elliptical galaxies: evidence for

a supermassive object in the center of the radiogalaxy NGC6251,” Astrophysical Journal 234, pp 76-85 (1979); D, H. Roberts, P. E. Greenfield, and B. F. Burke.

“The double quasar 0957 + 561: a radio study at 6 centimeters wavelength,” Sci-

ence 205, pp 894-896 (1979); G. G. Pooley. I. Browne, F. J. Daintree, P. K. Moore, R. G. Noble, and D. Walsh, “Radio studies of the double QSO 0957 + 561A,B,”

Nature 280, pp. 461-464 (1979); P. E. Greenfield, D. H. Roberts, and B. F. Burke, “The double quasar 0957 + 561: examination of the gravitational lens hypothesis using the very large array,” Science 208, pp. 495-497 (1980); P. J. Young, J. E.

Gunn, J. A. Kristian, J. B. Oke, and J. A. Westphal, “Double Quasar QSO #0957 + 561A,B: II: Detailed models,” Astrophysical Journal 244, pp. 736-755 (1981); B.

Wills and D. Wills,“Spectrophotometry of the double QSO 0957 + 561,” Astrophys-

ical Journal 238, pp. 1-9 (1980); B. T. Soifer,

G. Neugebauer, K. Matthews, E. E.

Becklin, C. G. Wynn-Williams, and R. Capps, “IR observation of the double quasar

0957 + S61A,B and the intervening galaxy,” Nature 285, pp. 91-93 (1980).

35. C. C. Dyer and R. C. Roeder, “Possible multiple imaging by spherical galaxies,”

Astrophysical Journal 238, L67-L70 (1980), C. C. Dyer and R. C. Roeder, “A range of time delays for the double quasar 0957 + 561A,B,” Astrophysical Journal 238, L133-L136 (1980).

36.

R. J. Weymann, D. Latham, J. R. P. Angel, R. F. Green, J. W. Liebert, D. A. Turn-

shek, D. E. Turnshek, and J. A. Tyson, “The triple QSO PGIIIS + 08: another probable gravitational lens,” Nature 205, pp. 641-643 (1980).

37. In this connection see especially E. H. Gombrich, Art and Illusion: A study in the Psychology of Pictorial Representation (Princeton, N. J.: Princeton University

Press, 1961, 2nd edition, revised), pp. 273, 329, and 394.

38. F. J. Belinfante, Measurements and Time Reversal in Objective Quantum Theory (Oxford: Oxford University Press, 1975); terminology “indelible,” p. 39.

9:

D. Fellesdal, “Meaning and experience,” in S. Guttenplan, ed., Mind and Language

(Oxford: Clarendon Press, 1975), pp. 254. Fgllesdal’s article, the other articles in this book, and the references they make to the still larger literature of meaning, a

central topic of philosophy in Britain and America in recent decades, will indicate the representative character of this statement.

40. Thanks are expressed here to Professors Lawrence P. Horwitz, Zvi Kurzweil, Yuval Ne’eman, Asher Peres, Shmuel Sambursky, Lawrence Schulman, and Elie Wiesel,

each for his part in leading the author to this legend and documenting it as follows: (i) H. Freeman and M. Simon, translators and eds., Midrash Rabbah, Genesis I

(London: Soncino Press, 1939), p. 238, commentary on “Noah walked with God”: “The God before whom my fathers Abraham and Isaac did walk, etc. (Genesis 48:15). R. Berekian in R. Johanan’s name and Resh Lakis gave two illustrations of

324

REFERENCES

this. R. Johanan said: It was as if a shepherd stood and watched his flocks. Resh Lakis said: It was as if a prince walked along while the elders preceded him [Footnote: As an escort, to make known his coming. Similarly, Abraham and Isaac walked before God, spreading his knowledge]. On R. Johanan’s view: We need His proximity. On the view of Resh Lakis: He needs us to glorify Him [Footnote: By

propagating the knowledge of His greatness].” (ii) p. 357, commentary on, “And he blessed him, and said: blessed be Abraham of the God most high, who has acquired [Koneh = maker of] heaven and earth” (Genesis 14:19): “From whom then did He

acquire them?— Said R. Abba: [Acquired is attributive,] as one says, So-and-so has [Koneh =

in possession of] beautiful eyes and hair. R. Isaac said: Abraham used to

entertain wayfarers, and after they had eaten he would say to them, ‘Say a blessing,’ ‘What shall we say?’ they asked. ‘Blessed be the God of the Universe of Whose bounty we have eaten,’ replied he. Then the Holy One, blessed be He, said to him: ‘My name was not known among My creatures, and thou has made it

known among them: I will regard thee as though thou wast associated with Me in the creation of the world’. . . .” (iii) Deuteronomy 32:10: “He found him (Jacob) in

a desert land, and in the waste howling wilderness: he led him about, he instructed him, he kept him as the apple of his eye,” as commented on in Sifrei [analogous to

the Midrash of (i) and (ii) but contains in addition to the Aggadic or legend of the Midrash the Halakhic or law; ed. in the Holy Land before the end of the 4th century

A.D.] §313, “he led him about”: “This is related to Genesis 12:1, ‘Get thee out of

the country’. . . ; ‘he instructed him’: . . . before our father Abraham came into this world it seemed as if the Lord, Blessed Be He, reigned only in Heaven, since it is said, ‘The Lord, God of Heaven, which took me from my father’s house’ (Genesis

24:7). But once Abraham had come into the world [= was born], he Abraham

[thereby] enthroned Him over Heaven and Earth”

(translation from the Hebrew by

'Y. Ne’eman). (iv) Isaiah 43:10: “Ye are my witnesses, saith the Lord, and my ser-

vant whom I have chosen; that ye may know and believe me, and understand that I am he: before me there was no God formed, neither shall there be after me.”

41. R. M. Frye, “Ways of seeing, or epistemology in the arts: Unities and disunities in Shakespearean drama and Elizabethan painting,” in The American Philosophical Society and the Royal Society, Papers Read at a Meeting June 5, 1980 (Philadel-

phia: American Philosophical Society, 1981), pp. 43-73.

42. For new insight into Franklin’s scope and sense see E. Wright, “Benjamin Franklin, the British statesman: a reappraisal,” ibidem, pp. 75-88.

43. A. Einstein, On the Method of Theoretical Physics (New York, N. Y.: Oxford University Press, 1933), reprinted in Philos. Sci. 1, p. 162 (1934).

Einstein and Other Seekers of the Wider View . Hendrik Bode, Frederick Mosteller, John Tukey, and Charles Winsor, “The education of a scientific generalist,” Science 109, pp. 553-558 (1949).

2. Bode et al., note 1. 3. Some further details may be found in Time, May 5, 1967, pp. 48-49.

REFERENCES

325

Hermann Weyl and the Unity of Knowledge 1. H. Weyl, Address on the unity of knowledge delivered at the [1954] Bicentennial Conference of Columbia University. Item no. 165 in K. Chandrasekaran, ed., Hermann Weyl: Gesammelte Abhandlungen, 4 vols. (Berlin: Springer, 1968). (An alter-

native to this four-volume collection is the single-volume Hermann Weyl Selecta, [Cambridge, Mass.: Birkhauser, 1955].)

2. H. Weyl, Gruppentheorie und Quantenmechanik (Leipzig: S. Hirzel, 1928). (H. P. Robertson, trans., Theory of Groups and Quantum Mechanics [New York, N. Y.: Dover, 1950].)

3. H. Weyl, Symmetry (Princeton, N. J.: Princeton University Press, 1952). 4. H. Weyl, Raum Zeit Materie (Berlin: Springer, 1918). (H. L. Brose, trans., Space Time Matter [New York, N.Y.: Methuen, 1922; repr. Mineola, N. Y.: Dover Publications, Inc., 1950].)

5. H. Weyl, Philosophy of Mathematics and Natural Science, revised and augmented

English edition (Princeton, N. J.: Princeton University Press, 1949).

6. Weyl, note 1.

7. Weyl, “Elementary proof of a minimax theorem due to von Neumann,” note 1, vol. 4, item 151. 8. H. Weyl, 1955. Commentary in note

1 (Hermann Weyl Selecta) on his original

1918 idea—for which see note 4, and especially Sitzber. Preussische Akad. Wiss.

[Berlin] Physik-math. Kl, 1918, p. 465, in note 1, Vol. 2, item 31—a commentary

implicit in the relevant section of ref. 2; see also note 1, vol. 3, items 83, 84, and 85. 9.

Weyl, “SO Jahre Relativitatstheorie” (1950), in note 1, vol. 4, item 149.

10. H. Weyl, Was ist Materie (Berlin: Springer, 1924), “One cannot say, here is charge, but only that this closed surface cutting through the field includes charge” (pp. 57ff.). 11.

R. W. Fuller and J. A. Wheeler, Phys. Rey. 128, pp. 919-29 (1962).

12. J. A. Wheeler, Ann. Phys. 2, pp. 604-614 (1957); J. A. Wheeler, 1968, “Superspace and the nature of the quantum geometrodynamics,” in C. M. DeWitt and J. A. Wheeler, eds., Battelle Rencontres:

1967 Lectures in Mathematics and Physics,

(New York, N.Y.: W. A. Benjamin Inc., 1968); C. W. Misner, K. S. Thorne, and J. A. Wheeler,

1973, Gravitation, chaps. 43 and 44 (San Francisco: W. H. Freeman &

Co., 1973); G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, pp. 2752-2756

(1977).

13. U. Gerlach, Phys. Rev. 172, pp. 1325-1330 (1968). 14.

J. Hartle and S. W. Hawking, Phys. Rev. D 28, pp. 2960-2975 (1983).

15.

Weyl, note 4.

16.

R. Giacconi, P. Gorenstein, H. Gursky, and J. R. Walter, Astrophys. J. Lett. 148, L119-127 (1967); A. P. Cowley, D. Crampton, J. B. Hutchings, R. Remillard, and

J.E. Panfield, Astrophys. J. 272 pp. 118-122 (1983).

17. J. H. Oort, Astron. and Astrophys. 15, pp. 295-362, esp. pp. 341-353 (1977). The continuing work of C. H. Townes and his collaborators is providing ever stronger evidence.

326

REFERENCES

18. J. D. Bekenstein, Phys. Rev. D 7, pp. 2333-2346 (1973). 19,

S. W. Hawking, Commun. Math. Phys. 43, p. 199 (1975); S. W. Hawking, Phys. Rev. D 13, p. 191 (1976).

20. W. G. Unruh, Phys. Rev. D 14, p. 870 (1976). See also W. G. Unruh and R. M. Wald, Phys. Rev. D 25, p. 942 (1982).

21. J. D. Bekenstein, Phys. Today 33, no. 1, p. 24 (1980). See also his article in Y.

Ne’eman, ed., 1979, To Fulfill a Vision: Jerusalem Einstein Centennial Sympo-

sium (Reading, Mass.: Addison-Wesley, 1979). For the continuing investigation see, for example, W. H. Zurek and K. S. Thorne, Phys. Rev. Lett. 54, pp. 2171-2175 (1985).

22. Weyl, note 5, p. 296. 23.

J. J. Hopfield, PNAS 77, pp. 5248-5252 (1980); J. J. Hopfield, PNAS 79, pp. 2554— 2258 (1982); J. J. Hopfield, Engin. and Science (Caltech) 46, no. 1, pp. 2-7 (1982).

24, Weyl, note 5, pp. 299-300. 25. Early proposal of L. Onsager. See related discussion in C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes (New York, N. Y.: John Wiley, 1980). See also the article by S. W. Fox in W. H. Heidcamp, ed., The Nature of Life: 13th Nobel Conference (Baltimore, M.D.: University Park Press, 1977).

26. For a review see G. Millot, Sci. Am. 240, no. 4, 108ff (1979). See also A. G. CairnsSmith, Genetic Takeover and the Mineral Origins of Life (Cambridge, Mass.: Cam-

bridge University Press, 1982); A. G. Cairns-Smith, Sci. Am. 252, no. 6, pp. 90-100 (1985).

27. V. Salvini-Plawen and E. Mayr, Evol. Biol. 10, pp. 207-263 (1978). 28. Weyl, note 5, p. 300. 29. See the chapter by J. A. Wheeler in A. R. Marlow, ed., 1978, Mathematical Foundations of Quantum Theory, pp. 9-78, Academic Press; see also the chapter by W.

Miller and J. A. Wheeler in S. Kamefuchi et al., eds., Proceedings of International Symposium of Foundations of Quantum Mechanics, pp. 140-52 (Tokyo: Physical Society of Japan, 1984).

30. A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, pp. 1804-1807 (1982);

C. Alley, O. Jakubowicz, C. A. Steggerda, and W. C. Wickes, in note 29, Kamefuchi et al., pp. 158-164 (1984); T. Hellmuth, H. Walther, and A. G. Zajonc, “Realization of a Mach-Zehnder ‘delayed-choice’ interferometer,” report presented at

the June 1985 Finnish symposium, Foundations of Modern Physics: 50 Years after EPR (1985).

31. Weyl, note 5, p. 216. 32. H. Weyl, Lausanne lecture reprinted in note 1, vol. 4, item 166 (1954). The quotation comes from p. 631.

33. Weyl, note 5, p. 2. 34. H. Weyl, Two lectures given at Princeton University and reprinted in note 1, vol. 4, item 157; see p. 631 (1945).

REFERENCES

327

35. C. Reid, Hilbert (New York, N. Y.: Springer-Verlag, 1970). 36. H. Weyl, Mathematics and logic, preface to a review of “The Philosophy of Bertrand Russell,” Am. Math. Mon. 53, pp. 2-13 (1946).

S75 H. Weyl, Ann. der Physik 59, p. 129 (1919); much amplified in Naturwiss. 22, p145 (1934).

. F. Zwicky, Phys. Rev. 55, p. 726 (1939). . A. S. Eddington, The Mathematical Theory of Relativity, p.167 (Cambridge, Mass.: Cambridge University Press, 1923). P. A. M. Dirac, Nature

A165, p. 199 (1938).

139, p. 23 (1937); P. A. M. Dirac, Proc. Roy. Soc. (London)

41. See J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford: Oxford University Press, 1986).

42. B. Carter, Phil. Trans. Roy. Soc. (London) A370, p. 347 (1983). K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge,

Routledge and Kegan Paul (New York, N. Y.: Basic Books, 1963).

Wey], note 5, p. 125. 45. J. A. Wheeler, “Mercer Street and other memories,” in P. C. Aichelburg and R.

Sexl, eds., Albert Einstein: His influence on Physics, Philosophy and Politics, pp. 201-211 (Braunschweig: Vieweg, 1979).

Weyl, note 5, p. 125.

47, Quoted in E. M. MacKinnon, Scientific Explanation and Atomic

Physics, p. 375

(Chicago, IIl.: University of Chicago Press, 1982).

48. H. Weylet al, 1918, Das Kontinuum (Leipzig, Veit, Repr. New York, N. Y.: Chelsea Press, 1962).

49, Weyl, note 5, p.110. See also p. 112 for ideas of Leibniz like those of Democritus. 50. Ibid, pp. 237-238.

Science and Survival Michael Polanyi, Personal Knowledge (Chicago: University of Chicago Press, 1958). Michael Polanyi, The Study of Man (Chicago: University of Chicago Press, 1958).

3 The Lecomte du Nouy prize is awarded in alternate years in France and America to the author of an outstanding essay, biography, or other work which is of particular

interest “for the spiritual life of our epoch and for the defense of human dignity.”

John von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior, 3rd ed. (Princeton, N. J.: Princeton University Press, 1953).

Annals of Mathematics Study No. 40, Contributions to the Theory of Games, Vol.

4, edited by A. W. Tucker and R. D. Luce (Princeton, N. J.: Princeton University Press, 1959).

328

REFERENCES

6. William Blake as quoted in J. Bronowski, Science and Human N. Y.: Julian Messner,

1956).

Values (New York,

7. Pierre Simon, Marquis de Laplace, as quoted in Hermann Weyl, Philosophy of

Mathematics and Natural Science, revised and augmented English edition based on a translation by Olaf Helmer (Princeton, N. J.: Princeton University Press, 1949),

p. 209: “Une intelligence qui pour un instant donné, connaitrait toutes les forces

dont la nature est animée, et la situation respective des étres qui la composent, si

dailleurs elle était assez vaste pour soumettre ces données a l’analyse, embrasserait

dans la méme formule, les mouvements des plus grands corps de l’universe et ceux

du plus leger atome: rien ne serait incertain pour elle, et l'avenir comme le passé, serait présent 4 ses yeux. L’esprit humain offre dans la perfection qu’il a su donner 4 l’astronomie, une faible esquisse de cette intelligence.” [“Essai philosophique sur

les probabilités,” 2nd ed., 1814, pp. 3-4].

8. Carl L. Becker, The Heavenly City of the Eighteenth-Century Philosophers (New Haven, Conn.: Yale University Press, 1932); paperback, 1959. 9. Niels Bohr, Atomic Theory and the Description of Nature (London and New York:

Cambridge University Press, 1934), p. 10. For the paper, “Light and Life,” in which Bohr uses the point of view of complementarity to discuss free will and

determinism, see his Atomic Physics and Human

John Wiley, 1958).

Knowledge (New York, N. Y.:

10. John von Neumann, The Mathematical Foundations of Quantum Mecha nics, trans-

lated from the German edition by R. T. Beyer (Princeton, N. J.: Princeton Universi-

ty Press, 1955).

11. Quantum mechanics in a closed universe: Hugh Everett III, Revie ws of Modern

Physics, 29, p. 454 (1957); John A. Wheeler, ibid., 29, p. 463 (1957); John A.

Wheeler, “The Universe in the Light of General Relativity,” The Monis t (Box 268,

Wilmette, Illinois), 47, p. 40 (1962).

12. There are many excellent accounts of evolution and its implications. In addition to

Charles Darwin, The Origin of Species (1859) and The Descent of Man (1871), now

both available in unabridged form (The Origin of Species and The Descent of Man, Modern Library, edited by B. A. Cerf and D. S. Klopfer, Random House , New

York [no date]), see for example Loren Eiseley, The Immense Journey (New York, N. Y.: Random House, 1957); Darwin's Century (New York. N. Y.: Doubleday,

1958)—and Eiseley’s Lecomte du Nouy prize-winning book, The Firmament of

Time (New York, N. Y.: Atheneum,

1960)—as well as P. B. Medawar, The Future

of Man (The BBC Reith Lectures, 1959) (New York, N. Y.: Basic Books, 1960),

and Theodosius Dobzhansky, Mankind Evolving: The Evolution of the Human

Species (Silliman Memorial Lectures) (New Haven and London: Yale University Press, 1962).

13.

IAU Symposium No.

15, Problems of Extra-Galactic Research (Berkeley, Calif. ,

1961) edited by G. C. McVittie (New York, N. Y.: Macm illan, 1962). 14. G. Cocconi and P. Morrison, “Searching for Interstell ar Communication,” Nature,

184, 844 (1959). See also Brian Mason, “Organic Matter from Space,” in Scientific

American (March

15.

1963) p. 43.

For response to arguments sometimes made that evolutio n has a built-in machinery

REFERENCES

329

to produce an ever higher and higher form of life, see the Pulitzer Prize-winning account of the evolution of the South African lung fish by a great physiologist, Homer W. Smith: Kamongo (New York, N. Y.: Viking Paperbacks, 1956).

16. The discussion of gravity in the original article has been abbreviated here. An accessible account of gravity is available in J. A. Wheeler, A Journey into Gravity and Spacetime (New York, N. Y.: Scientific American Library, 1990).

17. For a survey of the problems of superdense matter and of the critical mass of a star built of such matter, see, for example, J. A. Wheeler, in H. Y. Chiu and W. F. Hoffman, eds., Gravitation and Relativity (New York, N. Y.: William Benjamin,

Inc., 1963).

18. In the inaugural lecture that he gave in 1854, at the age of 28, Riemann empha-

sized that the properties of space were to be discovered, not by reading Euclid’s axioms, but by experiment. Colleagues were inspired by his lecture to set up tele-

scopes on three mountain peaks near Géttingen and measure how much the sum

of the three angles departed from 180 degrees. If they had desired to measure the curvature of the earth, they could have connected three points by tape lines stretched over the sphere of the earth. However, they were concerned as a conse-

quence of Riemann’s lecture with the larger issue of the curvature of space. Therefore they connected the three points, not by tape lines, but by light rays.

They found no observable deviation from the 180 degrees expected for a triangle

in flat space. K. Schwarzchild made another determination of a related kind over an astronomical reach of space but again without finding any anomaly. Today from general relativity one can calculate in both cases the curvature and the resulting departure from 180 degrees and see that the available sensitivity was not enough to detect the effect.

19. References to the literature of the experimental tests may be found, for example, in J. A. Wheeler, Geometrodynamics (New York, N. Y.: Academic Press, 1962), p. 46.

For a discussion of what the three famous tests of general relativity prove, see L.

Schiff, in Proceedings of the 1962 International Conference on Relativistic Theories

of Gravitation, Warsaw-Jablonna, 1963. For test of the equal rate of fall of objects

of different constitution, see R. H. Dicke, “The Eétvés Experiment,” Scientific

American (December

1961), p. 84.

20. For a fuller assessment of this issue in the light of the present evidence, see

C. W. Misner and J. A. Wheeler, “Classical physics as geometry. Gravition, electromagnetism, unquantized charge, and mass as properties of curved empty space,” Annals of Physics, 2, pp. 525-603 (1957); Wheeler, Geometrodynamics, note 19, and a section by Wheeler in E. Nagel, P. Suppes, and A. Tarski, eds., Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress (Stanford, Ca.: Stanford University Press, 1962), pp. 361-374.

21. W. K. Clifford, paper given before the Cambridge Philosophical Society in 1870, published in the Proceedings of that society, 2, p. 157 (1876).

22, Wheeler, note 19. 23. A. Einstein, The Meaning of Relativity, 3rd ed. (Princeton, N. J.: Princeton University Press, 1950), p. 107. 24, Other observational evidence of a slowing of the expansion is affected by sources

330

REFERENCES of error sufficiently uncertain to make it inappropriate to cite this evidence at all in

the present connection. 25. For further discussion of some of these issues, see, for example, Wheeler, “The Universe in the Light of General Relativity,” note 11. 26.

The term “fluctuations” as used here is not meant to refer to the fascinating mathematical analysis carried out by Volterra, Lotka, and others. They treated the compe-

tition for existence between organisms, one of which preys on another which in turn derives its own sustenance from plants or from a nutrient fluid. The calculated fluctuations in numbers of the two or more species in such mathematical models have been considered to give some insight into the well known variations in the countryside from year to year in the numbers of hares and foxes. Interesting though this work is, it does not have the aspect particularly sought after in the text: qualitatively new concepts arising out of previously simple situations in the limit where a certain number becomes very large.

27. Irving Langmuir, Science 87, p. 119 (1938). 28. Bentley Glass, “The Relation of the Physical Sciences to Biology—Indeterminism and Causality,” in B. Baumrin, ed., Philosophy of Science: The Delaware Seminar, Vol. I (New York, N.Y.: Wiley-Interscience, 1963), pp.223 ff.; P. B. Medawar, The Future of Man (New York, N. Y.: Basic Books,

1960), p. 37.

29. Glass, ibid. 30.

Von Neumann and Morgenstern, note 4; Tucker and Luce, note 5.

Beyond the Black Hole These references provide, not completeness, but some points of access to the literature on

topics in the text and, in some instances close to the central theme, some documentation of the evolution of outlooks. For much help on these references the author thanks Adrienne Harding.

1. Prehistory of black hole: J. Michell, “On the means of discovering the distance, magnitude, & c. of the fixed stars, in consequence of the diminution in the velocity of their light, in case such a diminution should be found in any of them, and such data should be procured from observations, as would be further necessary for that purpose,” Philos. Trans. R. S. London 74, pp. 35-37 (1784) (read Nov. 27, 1783); cited and discussed in S. Schaffer, “John Michell and black

holes,” J. for Hist. Astron. 10, pp. 42-43 (1979); P. S. Laplace, Exposition du systéme du monde, Cercle-Social, Paris, vol. 2, 1795, p. 305, “Un astre lumineux de méme densité que la terre, et dont le diamétre serait deux cents cinquante fois plus grand que celui du soleil, ne laisserait en vertu de son attraction, parvenir aucun de ses rayons jusqu’a nous; il est donc possible que les plus grands corps lumineux de l’univers, soient par cela méme, invisibles.” Laplace gives the calculations underlying this statement in F. X. von Zach, ed., Allgemeine Geographische Ephemeriden, Einer Gesellschaft Gelehrten, Weimar, IV, Band I

3

et)

REFERENCES

St., 1799 (May 1798, p. 603); translated, “Proof of the theorem, that the attractive force of a heavenly body could be so large, that light could not flow out of it,” in S. W. Hawking and G. F. R. Ellis, The Large-scale Structure of Spacetime (Cambridge, U.K.: Cambridge University Press, 1973), pp. 365-368; First treatment of collapse within the framework of general relativity: J. R. Oppen-

heimer and H. Snyder, “On continued gravitational attraction,” Phys. Rev. 56, pp. 455-459 (1939): “The total time of collapse for an observer comoving with the stellar matter is finite . . .; an external observer sees the star asymptotically shrinking to its gravitational radius.”; Coming to terms with gravitational collapse: B. K. Harrison, M. Wakano, and J. A. Wheeler, “Matter-energy at high density; end-point of thermonuclear evolution,” pp. 124-146 in Onzieme Conseil de Physique Solvay, La structure et l'évolution de l'univers (Brussels:

Stoops, 1958), pp. 136-137, white dwarfs and neutron stars shown for the first time to be two sectors of one continuous family giving “the absolutely lowest state possible for an A-nucleon system under the dual action of nuclear and grav-

itational forces,” the equilibrium state of “cold matter ideally catalyzed to the end-point of thermonuclear evolution,” p. 138, “What is the final state of an Anucleon system under gravitational forces when A is large? Perhaps there is no equilibrium state when A is large: this is the proposal of Oppenheimer and Sny-

der,” pp. 139-140. “If we are to reject as physically unreasonable the concept of

an indefinitely large number of nucleons in equilibrium in a finite volume of space, it seems necessary to conclude that the nucleons above a critical number convert themselves to a form of energy that can escape from the system: radia-

tion. . . [C]onditions of superdensity would seem to be particularly favorable for altering the number of nucleons in the universe” (a proposed 1958 rejection of complete gravitational collapse in favor of an as-then undiscovered mechanism of radiation); Ya. B. Zel’dovich, Zh. eksp. teor. Fiz. 42, p. 641 (1962); English

translation in Soviet Physics JETP 15, p. 446 (1962), “The collapse of a small mass in the general theory of relativity,” notes, “By prescribing a sufficiently

large density we can obtain for any given number N of particles a configuration

with mass as close to zero as we please, and clearly less than the mass of the static solution. Such a solution obviously cannot go over into the state of equilibrium (into the static solution), and consequently can only contract without

limit.” J. A. Wheeler, “Geometrodynamics and the issue of the final state,” pp. 315-520 in C. DeWitt and B. DeWitt, eds., Relativity, Groups, and Topology

(New York, N. Y.: Gordon

and Breach,

1964), p. 321. “Thus there exists a sec-

ond crushing point, the ‘Landau-Oppenheimer-Volkoff crushing point,’ with

central density ~10!® g/cm, and mass ~0.7 Mg. One cannot add matter to the

system without initiating collapse . . .. Cannot one save the day by assuming that matter becomes incompressible at a sufficiently high density? No!” The relativistic equation of hydrostatic equilibrium “has the remarkable feature that it provides a mechanism for multiplying pressure. . . (‘divergent chain reaction’)”, p. 325, “No matter how small the number of nucleons that one starts with, in principle they can be pressed from outside with enough pressure to initiate collapse,” pp. 445-449, gravitational collapse of a toroidal bundle of magnetic lines of force; pp. 500-501, Schwarzschild and geon geometry as unstable with respect to gravitational collapse; and a collapsing “cloud of matter may be of dust

332

REFERENCES

and so dilute that its density is 10° g/cm? or less at the moment when its radius

decreases to the order of the Schwarzschild value. Therefore no details of any

equation of state can save it from gravitational collapse,” pp. 502-503. “It is difficult to escape the conclusion that the creation or destruction of matter goes on in regime IV [where quantum effects dominate]. At issue here is not the familiar

process of a positive electron annihilating a negative electron, or an antiproton disappearing by union with a proton. Instead, one is concerned about a process in which ordinary matter—composed of protons, neutrons, and electrons—is

crushed out of existence, or brought into being, by a mechanism intimately connected with gravitation and with the curvature of space. . . . [P]rocesses of bary-

on creation or destruction would seem unavoidable,” pp. 513-516, discussion of relation between the quasistellar objects ‘discovered in 1963 and gravitational

collapse. B. K. Harrison, K. S. Thorne, M. Wakano, and J. A. Wheeler, Gravitation Theory and Gravitational Collapse (Chicago, Illinois: University of Chica-

go Press, 1965), p.vii. “[No] escape is now known. . . from a new physical process. In this process baryons disappear, p. viii, [G]ravitational collapse must occur for a subcritical mass as well as for a supercritical mass [via] a quantum

mechanical tunneling process. . . . [A]Il matter must manifest, however weakly, a new form of radioactivity, in which baryon number changes.” Name “black hole,” J. A. Wheeler, “Our universe: the known and the unknown,” address before the American Association for the Advancement of Science, New York, Dec. 29, 1967, in American Scholar 37, pp. 248-274 (1968) and American Scientist 56, pp. 1-20 (Spring 1968), and in R. Ruffini and J. A. Wheeler, “Introducing the black hole,” Physics Today 24, pp. 30-36 (1971) and in “The black hole,” pp. 279-316 in Astrophysics and Gravitation: Proceedings ofthe Sixteenth Con-

ference on Physics at the University of Brussels, September 1973 (1040 Brux-

elles, Belgium: Editions de I’ Université de Bruxelles, 1974). In black hole physics the laws of conservation of particle number are transcended, J. A. Wheeler, “Transcending the law of conservation of leptons,” in Atti del Conveg-

no Internazionale sul Tema: The Astrophysical Aspects of the Weak Interactions Quaderno N.157 Accademia Nazionale dei Lincei, Roma, pp. 133-164 (1971).

Gravitational collapse implies that “there is no law except the law that there is no law,” J. A. Wheeler, “From relativity to mutability,” in

J Mehra, ed., The

Physicist’s Conception of Nature (Dordrecht: Reidel, 1973), pp. 202-247. Proof

that gravitational collapse is inescapable under assumptions more and more elementary: A. Avez, “Propriétés globales des espace-temps périodiques clos,”

Acad. des Sci., Paris, Comptes Rend. 250, pp. 3583-35R7 (1960); R. Penrose,

“Gravitational collapse and spacetime singularities,” Phys. Rev. Lett. 14, pp. 57-59 (1965); S. W. Hawking, “The occurrence of singularities in cosmology,” Proc. Roy Soc. London A294, pp. 511-521

(1966); R. P. Geroch, “What is a sin-

gularity in general relativity?”, Ann. Phys. (U.S.A.) 48, pp. 526-540 (1960); S.

W. Hawking and G. F. R. Ellis, The Large-scale Structure of Space-time (Cam-

bridge, U.K.: Cambridge University Press, 1973); J. E. Marsden and F. J. Tipler, “Maximal hypersurfaces and foliations of constant mean curvature in general relativity,” preprint, Mathematics Department, University of California at Berkeley, 1979; Theorems on the uniqueness of the geometry around a black hole: B. Carter, “An axisymmetric black hole has only two degrees of freedom,” Phys,

REFERENCES

333,

Rey, Lett. 26, pp. 331-336 (1970); Carter and others in C. DeWitt and B. S. De-

Witt, eds., Black Holes. Proceedings of 1972 session of Ecole d’été de physique

théorique (New York, N. Y.: Gordon and Breach, 1973); Quantum aspects of the black hole: “wormholes” continually being produced and annihilated at the Planck scale of distances, giving rise to a “foam-like structure” of space, J. A. Wheeler, “On the nature of quantum geometrodynamics,” Ann. of Phys. 2, pp. 604-614 (1957); calculation of same by the method of sum over histories, G. W. Gibbons

and S. W. Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D15, pp. 2752-2757 (1977); surface area and surface gravity of black

hole not merely analogous to, but identical with, entropy and temperature, J. Bekenstein, “Black holes and entropy,” Phvs. Rev. D7, pp. 2333-2346 (1973); thermal radiation associated with this effect calculated by S. W. Hawking, “Particle creation by black holes,” Comm. Math. Phys. 43, pp. 199-220 (1975).

. A. Friedmann, “Uber die Krummung des Raumes,” Zeits f. Physik 10, pp. 377-386 (1922); E. P. Hubble, “A relation between distance and radial velocity among ex-

tragalactic nebulae,” Proc. Nat. Acad. Sci. U.S. 15, pp. 169-173 (1929); R. A. Alpher, H. A. Bethe, and G. Gamow, “The origin of chemical elements,” Phys.

Rey. L 73, pp. 803-804 (1948); R. H. Dicke, P. J. E. Peebles, P. G. Rol, and D. T. Wilkinson, “Cosmic-black-body radiation,” Astrophys. J. 142, pp. 414-419 (1965); A. A. Penzias and R. W. Wilson, “A measurement of excess antenna tem-

perature at 4080 Mc/s,” Astrophys. J. 142, pp. 419-421 (1965).

. A. Einstein, The Meaning of Relativity, 3rd ed. (Princeton, N. J.: Princeton University Press, 1950), pp. 107-108, “Thus we may present the following arguments against the conception ofa space-infinite and for the conception of a spacebounded universe [(1) simplicity (2) Machian]; A. Einstein, Essays in Science

(New York, N. Y.: Philosophical Library, 1934), translated from Mein Weltbilde

(Amsterdam: Querido, 1933), “In my opinion the general theory of relativity can

only solve this problem [of inertia] satisfactorily if it regards the world as spatially self-enclosed”’; J. A. Wheeler, “Conference summary:

more results than ever in

gravitation physics and relativity,” pp. 299-344 in G. Shariv and J. Rosen, eds., General Relativity and Gravitation (New York, N. Y.: John Wiley,

1975), pp.

320-324, status of the “mystery of the missing mass,” lens effect and its difficulties as a way to check on closure, difficulties with alternatives to closure.

. A. Avez, note 1, work from which one concludes there aren’t any periodic closed model universes—an indirect argument that a closed universe necessarily collapses; S. W. Hawking and R. Penrose, “The singularities of gravitational collapse and cosmology,” Proc. Roy. Soc. London A314, pp. 529-548 (1969); J. E. Marsden

and F. J. Tipler, note 1, where all “W model universes” are closed and have an upper limit to the time from big bang to big crunch. . JR. Gott, Hl, J. E. Gunn, D. N. Schramm, and B. M. Tinsley, “Will the universe

expand forever?” Sci. American 234, pp. 62-79 (March 1976); p. 69, term “big crunch”; see also note 32; C. M. Patton and J. A. Wheeler, “Is physics legislated by cosmology?” pp. 538-605 in C. J. Isham, R. Penrose, and D. W. Sciama, Quantum Gravity: An Oxford Symposium (Oxford: Clarendon, 1975): principle that the universe must have a way to come into being and to fade out of existence proposed, not as a deduction from cosmology, but as a requirement for cosmology.

334

REFERENCES

N. Bohr, Atomic Theory and the Description of Nature (Cambridge, U.K.: Cambridge University Press, 1934); N. Bohr, Atomic Physics and Human Knowledge (New York, N. Y.: John Wiley, 1958); N. Bohr, Essays 1958-1962 on Atomic Physics and Human Knowledge (New York, N. Y.: John Wiley, 1963).

N. Bohr, “Discussion with Einstein on epistemological problems in atomic physics,” pp. 201-241 in P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Evanston, Illinois: Library of Living Philosophers, 1949), p. 238, “registration”;

Bohr, Atomic Physics and Human

Knowledge,

note 6, p. 88, “irreversible amplifica-

tion” and p. 73, “closed by irreversible amplification.”

J. A. Wheeler, “Genesis and observership,” pp. 3-33 in R. E. Butts and K. J.

Hintikka, eds., Foundational Problems in. the Special Sciences (Dordrecht: Reidel, 1977); p. 26, “direct involvement of observership in genesis”; J. A. Wheeler,

Frontiers of Time (Amsterdam: North-Holland [for the Societa Italiana di Fisica,

Bologna], 1979); also appears from the same two houses with a displacement of 394 in page numbering as pp. 395-497 in G. Toraldo di Francia, ed., Problems

in the Foundations of Physics (Amsterdam: North-Holland Publishing Co., 1979),

pp. 5 ff., “billions upon billions of acts of observer-participancy.””

“Come into being, fade out of existence”: Patton and Wheeler, note 5, and Wheeler, note 8; J. A. Wheeler, “From relativity to mutability,” pp. 202-247 in J. Mehra, ed.,

The Physicist’s Conception of Nature (Dordrecht: Reidel, 1973); in gravitational

collapse the framework falls down for everything one ever called a law; to be contrasted with “Beyond the end of time,” chap. 44, pp. 1196-1217 in C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: Freeman,

1973),

where gravitational collapse was envisaged as precipitating a reprocessing of the universe, except for a penultimate paragraph foreshadowing the concept of genesis through observer-participancy. 10. Ibid. 1.

Challenge to derive quantum principle from the requirements that the universe should have a way to come into being: Patton and Wheeler, note 5, p. 564; Wheeler, “Genesis and observership,” note 8, p. 29; Wheeler, Frontiers of Time, note 8, p. 8.

12. Derivation from symmetry principle hides the machinery underlying physical law: Wheeler, “Genesis and observership,” note 8, pp. 15-16; Wheeler, Frontiers of Time, note 8, section 4.

13. J.C. Maxwell, “A dynamical theory of the electromagnetic field,” Trans. Roy. Soc. London 155, p. 459 ff. (1865); A Treatise on Electricity and Magnetism, ed. (Oxford: Clarendon, 1892).

1873; 3rd

14. A. Einstein, “Die Feldgleichungen der Gravitation,” Preuss. Akad. Wiss. Berlin,

Sitzber, pp. 844-847 (1915).

1S. C.N. Yang and R. L. Mills, “Conservation of isotopic spin and isotopic gauge invariance,” Phys. Rev. 96, pp. 191-195 (1954).

16. To be distinguished from the “I believe that it would be worth trying to learn

something about the world even if in trying to do so we should merely learn that

REFERENCES

335

we do not know much,” of K. Popper, Conjectures and Refutations, The Growth of

Scientific Knowledge, 2nd ed. (London: Routledge and Kegan Paul, 1972), p. 29.

17. A. E. H. Love, The Mathematical Theory of Elasticity (Cambridge: U.K., Cambridge University Press, 1892); 4th ed. (New York, N. Y.: Dover, 1944).

18. J. D. Jackson, Classical Electrodynamics, 2nd ed, (New York, N. Y.: John Wiley, 1975); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Oxford: Pergamon,

1960).

19. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York, N. Y.: John Wiley, 1972); C, W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: Freeman,

1973).

20. L. D. Faddeev, book on the theory of the Yang-Mills field, scheduled for 1979 publication.

21, The discussion here comes from Wheeler, “Genesis and observership,” note 8, p. 16 and Misner, Thorne, and Wheeler, note 19, pp. 1206-1208.

22. S. Hojman, K. Kuchar, and C. Teitelboim, “New approach to general relativity,” Nature Phys. Sci. 248, pp. 97-98 (1973); C. Teitelboim, “How commutators of

constraints reflect spacetime structure,” Ann. of Phys. 79, pp. 542-557 (1973); and

C. Teitelboim, “The Hamiltonian structure of spacetime,” doctoral dissertation,

unpublished, Princeton University, 1973; available from University Microfilms, Inc., Ann Arbor, Michigan 48106; K. Kuchar, “Canonical quantization of gravity,”

pp. 238-288 in W. Israel, ed., Relativity, Astrophysics, and Cosmology (Dordrecht:

Reidel, 1973); and K. Kuchar, “Geometrodynamics regained: a Lagrangian ap-

proach,” J. Math. Phys. 15, pp. 708-715 (1974); C. Teitelboim, “Surface deforma-

tions, spacetime structure, and gauge invariance” in C. Aragone, ed., Relativity, Fields, Strings and Gravity: Proceedings of the Second Latin American Symposium

on Relativity and Gravitation SILARG II held in Caracas, December 1975 (Caracas: Universidad Simén Bolivar, 1976); S. A. Hojman, K. Kuchar, and C. Teitel-

boim, “Geometrodynamics regained,” Ann. of Phys. 76, pp. 88-135 (1976).

23. Ibid., Hojman, Kuchar, and Teitelboim, ““Geometrodynamics regained.” 24, A. Einstein, “Autobiographical notes,” pp. 2-95 in P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Evanston, Illinois: Library of Living Philoso-

phers, 1949); in pp. 89-95 Einstein discusses his attempts to find a unified field theory; M. A. Tonnelat, La Théorie du Champ Unifié d’Einstein et Quelques-uns de ses Développements (Paris: Gauthier-Villars,

1955), and M. A. Tonnelat, Les

Théories Unitaires de |’Electromagnétisme et de la Gravitation (Paris: Gauthier-

Villars, 1965).

25. R. Utiyama, “Invariant theoretical interpretation of interaction,” Phys. Rev. 101,

pp. 1597-1607 (1956), gravitation recognized for the first time as a gauge theory; Gauge theory of gravitation step by step recognized as equivalent to the metricplus-torsion theory of gravitation originally urged by Elie Cartan on geometrical grounds: “Sur une généralisation de la notion de courbure de Riemann et les es-

paces a torsion,” Acad. Sci., Paris, Compt. Rend.

174, pp. 593-595 (1922), for

more on the development of which see R. Debever, ed., Elie Cartan — Albert Einstein Letters on Absolute Parallelism 1929-1932 (Princeton, N. J.: Princeton Uni-

336

REFERENCES

versity Press, 1979). The history and bibliography of this growth in understanding to what is today known as the Einstein-Cartan-Sciama-Kibble (or U,) theory of

gravitation, derivable in its spin-torsion parts from a Lorentz gauge, is recounted by A. Trautman, “On the Einstein-Cartan equations,” Bull. Acad. Polon. Sci., Ser.

Sci. Mat. Ast. et Phys. 20, pp. 185-190 and in “Theory of Gravitation,” pp.

179-198 in J. Mehra, ed., The Physicist’s Conception of Nature (Dordrecht: Rei-

del, 1973); by F. W. Hehl, P. v. d. Heyde, G. D. Kerlick and J. M. Nester, “General relativity with spin and torsion: foundations and prospects,” Rev. Mod. Phys.

48, pp. 393-416 (1976), who clarify the gauge associated with translations; and in

a still more recent perspective by Y. Ne’eman, “Gravity is the gauge theory of the parallel-transport modification of the Poincaré group,” pp. 189-215 in K. Bleuler, H.R. Petry, and A. Reetz, eds., Differential Geometrical Methods in Mathematical Physics II (New York, N. Y.: Springer, 1978); Electromagnetic field as gauge field, H. Weyl, “Gravitation und Elektrizitat,” Preuss. Akad.

Wiss., Berlin,

Sitz’ber. pp. 465-480 (1918); brief summary of subsequent developments, including (1) recognition that the right concept is not gauge, but phase, (2) the BohmAharonov experiment, and (3) “f,,, underdescribes electromagnetism, . . +6 Aydx# overdescribes electromagnetism, . . . [and the] phase factor exp (ie/ fc) 6 Aydx# is just right to describe electromagnetism” in T. T. Wu, “Introduction to gauge theory,” pp. 161-169 in K. Bleuler, H. R. Petry, and A. Reetz, eds., Differential

Geometrical Methods in Mathematical Physics Il (New York, N. Y.: Springer,

1978); Introduction of non-Abelian phase field by Yang and Mills, note 15; Phys-

ical evidence for gauge theory. Reviewed in L. O’ Raiffeartaigh, “Hidden gauge

symmetry,” Rep. Prog. Phys. 42, pp. 159-223 (1979), also—for example—in R.

E. Taylor, “Introduction, 6, /o7,” pp. 285-286 and in H. Fritzsch, “Flavordynamics,” pp. 593-603 in S. Homma, M. Kawaguchi, and H. Miyazawa, eds., Proc. of

the 19th Int. Conf. High Energy Physics, Tokyo, August 1978, Phys. Soc. of Japan, 1979; also in Y. Ne’eman, Symétries jauges et variétés de groupe, Les Presses de

P'Université de Montréal, 1979: p. 33, phenomenological findings of the quark model and scaling; pp. 34-35, Yang-Mills field meets four out of five requirements of the observational evidence (more on pp. 44-46) and perhaps the fifth, confinement of quarks (more on pp. 46 ff.). Proof that matrix elements go down at high energy as required by observation rather than continuing to go up as predicted by Fermi theory of the weak interaction, D. Gross and F. Wilczek, “Ultraviolet behavior of non-abelian gauge theories,” Phys. Rev. Lett. 30, pp.

1343-1346 (1973) and H. D. Politzer, “Reliable perturbative results for strong interactions?”, Phys. Rev. Lett. 30, pp. 1346-1349 (1973). Discovery of neutral curtents as predicted by the Weinberg-Salam model, six experiments in 1973 reviewed in Proc. Int. Conf. on High Energy Physics 1974 (Didcot, U.K.:

Rutherford Laboratory, 1975). D. J. Sherlen and 19 others, “Observation of parity violation in polarized electron scattering,” pp. 267-290 in Proc. of Summer Insti-

tute on Particle Physics July 10-21, 1978: Weak Interactions—Present and Future, Report 215 (Stanford: Stanford Linear Accelerator Center,

1978). Observa-

tion of parity violation in conformity with the Weinberg-Salam model. SLAC experiment on electron-deuteron scattering and polarization fits the predictions, including the predicted angle of symmetry breaking, of the Weinberg-Salam theo-

ry. It is not clear whether the theory will give correctly the observed confinement

REFERENCES

337

of quarks. Renormalizability of the theory has been proved (literature in O’Raiffeartaigh, above, p. 194). 26. For a survey of the mathematics of non-Abelian gauge fields today, see for example M. E. Mayer, “Gauge fields as quantized connection forms,” a chapter in K. Bleuler and A. Reetz, Differential Geometrical Methods in Mathematical Physics I (New York, N. Y.: Springer, 1977), and M. E. Mayer, “Characteristic classes and solutions of gauge theories,” pp. 81-104 in K. Bleuler, H. R. Petry, and A. Reetz, eds., Differential Geometrical Methods in Mathematical Physics II (New

York, N. Y.: Springer, 1978), as well as other papers in the latter volume. In his second paper, p. 98, Mayer notes the intensive interaction now taking place in this subject between mathematics and physics, between “the classification of algebraic vector bundles of rank 2 over P,” and Yang-Miils theory. Central to this subject is the Atiyah-Singer index theorem: M. F. Atiyah and I. M. Singer, “The index of elliptic operators, I, III,” Ann. of Math. 87, pp. 484-530 and pp. 546-604 (1968); R. S. Palais, Seminar on the Atiyah-Singer Index Theorem (Princeton, N. J.: Princeton University Press, 1965); M. F. Atiyah, R. Bott, and V. K. Patodi,

“On the heat equation and the index theorem,” Inventiones Math. (1973); errata, 28, pp. 277-280 (1975). 27.

19, pp. 279-330

Misner, Thorne, and Wheeler, note 19, p. 1207, Fig. 44.2.

28. “Last Lecture of Albert Einstein,” as recorded by J. A. Wheeler, pp. 207-211

in P.

C. Aichelburg and R. U. Sexl, eds., Albert Einstein: His Influence on Physics, Phi-

losophy and Politics (Braunschweig/Wiesbaden: Vieweg, 1979); Einstein, note 24; A. Einstein, “Uber das Relativitatsprinzip und die aus demselben gezogenen Folgerungen,” Jahrb. Radioakt. 4, pp. 411-462 (1908); A. Einstein, letter to Ernst Mach dated June 26, 1913, reproduced in Misner, Thorne, and Wheeler, note 19,

pp. 544-545, Fig. 21.5. For this and other correspondence between Einstein and Mach in the original German, see “Die Beziehungen zwischen Einstein und Mach,

dokumentarisch dargestellt,” pp. 109-115 in F. Herneck, Einstein und sein Weltbild (Berlin: Der Morgen,

29.

1979).

Einstein, The Meaning of Relativity, note 3.

30. “Mach’s principle” interpreted as the requirement that the universe be closed, thus to provide a boundary condition to separate allowable solutions of Einstein’s equation from physically inadmissible solutions, J. A. Wheeler in Onziéme Conseil de Physique Solvay, La structure et l’évolution de l'univers (Brussels: Stoops, 1958), pp. 49-51; H. Hénl in E. Bruche, ed., Physikertagung Wien (Mosbach/Baden:

Physik Verlag,

1962); J. A.

Wheeler, “Geometrodynam-

ics and the issue of the final state,” note 21, pp. 363-399 and pp. 411-425, esp. p. 425, “every so-called ‘asymptotically flat’ geometry taken up hereafter will be considered to be a part of a closed universe”; J. A. Wheeler, “Mach’s principle as boundary condition for Einstein’s equations,” pp. 303-349 in H. Y. Chiu and W. F. Hoffmann,

Gravitation and Relativity (New

York, N. Y.: W. A. Ben-

jamin, 1964); “Mach’s principle and the origin of inertia,” section 21.12, pp. 543-549 in Misner, Thoren, and Wheeler, note 19. J. Isenberg and J. A. Wheeler, “Inertia here is fixed by mass-energy there in every W model universe,” a chapter in the Einstein memorial volume edited by F. de Finis, appearing in

338

REFERENCES

Italian through Barbieri, Florence, and in English through Johnson Reprint, New York, 1979.

31. J. H. Oort, “Distribution of galaxies and the density of the universe,” pp. 163-181 in Onziéme Conseil de Physique Solvay: La structure et l’évolution de l’univers (Brussels: Stoops,

32.

1958).

Density of matter in the universe as estimated from abundance of primordial deuterium and other methods, J. R. Gott, TI, J. E. Gunn, D. N. Schramm, and B. M. Tinsley, “An unbound universe?” Astrophys. J. 194, pp. 543-553 (1974); see also note 5.

33: M. Davis, E. J. Groth, and P. J. E. Peebles, “Study of galaxy correlations: evidence for the gravitational instability picture in a dense universe,” Astrophys. J. 212, L 107-L

111 (1977): “with Q = 1 [density equal to that required for closure] we end

up with a power law yw (8) [for correlations of galactic density as a function of apparent angular separation] terminated by a sharp break, in agreement with the observations . . . [and in] conflict with a low density cosmological model.”; E. J.

Groth and P. J. E. Peebles, “Statistical analysis of catalogs of extragalactic objects VII. Two- and three-point correlation functions for the high resolution ShaneWirtanen catalog of galaxies,” Astrophys. J. 217, pp. 385-405 (1977).

R. Penrose; “Singularities in cosmology,” pp. 263-271 in M. S. Longair, ed., Con-

frontation of Cosmological Theories with Observational Data (Dordrecht: Reidel,

1974); Fig. 7, p. 270, “. . . from the point of view of the topological or causal struc-

ture, all the ‘stalactites’ which represent black hole singularities could be straight-

ened out.”; A. Qadir and J. A. Wheeler, “Black hole singularity as part of big

crunch singularity,” submitted May 24, 1979, for J. Geheniau Festschrift, being

edited by R. Debever and M. Demeur, Université Libre de Bruxelles.

a5. J. E. Marsden and F. J.. Tipler, note 1. 36. Qadir and Wheeler, note 34. 2h

V. A. Belinsky and I. M. Khalatnikov, “On the nature of the singularities in the general solution of the gravitational equations,” Zh. Eksp. Teor. Fiz. 56, pp. 1700-1712 (1969); English translation in Sov. Phys. JETP 29, pp. 911-917. V. A. Belinsky and I. M. Khalatnikov, “General solution of the gravitational equations with a physical singularity,” Zh. Eksp. Teor. Fiz. 57, pp. 2163-2175 (1969); English translation in Sov. Phys. JETP 30, pp. 1174-1180 (1970); I. M. Khalatnikov and E. M. Lifshitz, “General cosmological solutions of the gravitational equations with a singularity in time,” Phys. Rev. Lett. 24, pp. 76-79 (1970); E. M. Lifshitz and I. M. Khalatnikov, “Oscillatory approach to singular point in the open cosmological model,” Zh. Eksp. Teor. Fiz. Pis’ma 11, pp. 200-203 (1970); English translation in Sov. Phys. JETP Lett. 11, pp. 23-125 (1971); V. A. Belin-

sky, 1. M. Khalatnikov, and E . M. Lifshitz, “Oscillatory approach to a singular point in the relativistic cosmology,” Usp. Fiz. Nauk

102, pp. 463-500 (1970); En-

glish translation in Advances in Physics 19, pp. 525-573 (1970); V. A. Belinsky, E. M. Lifshitz, and I. M. Khalatnikov, “Oscillatory mode of approach to a singularity in homogeneous cosmological models with rotating axes,” Zh. Eksp. Teor.

Fiz. 60, pp. 1969-1979 (1971); English translation in Sov. Phys. JETP 33, pp.

1061-1066 (1971); J. D. Barrow and F. J. Tipler, “Analysis of the singularity

REFERENCES

339

studies by Belinski, Khalatnikov, and Lifshitz,” submitted to Ann. of Physics,

1979"

38. K. Schwarzschild, “Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie,” Preuss. Akad. Wiss. Berlin, Sitzungsb., K1. Math. -Phys. -

Tech., pp. 189-196 (1916) .

39. H. Reissner, “Uber die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie,” Ann. der Physik 50, pp. 106-120 (1916); G. Nordstrom, “On the

energy of the gravitational field in Einstein’s theorem” Proc. Kon. Ned. Akad. Wet.

20, pp. 1238-1245 (1918).

40. R. P. Kerr, “Gravitation field of a spinning mass as an example of algebraically

special metrics,” Phys. Rev. Lett. 11, pp. 237-238 (1963); B. Carter, “Global struc-

ture of the Kerr family of gravitational fields,” Phys. Rev. 174, pp. 1559-1571

(1968).

41. E. T. Newman, T. E. Couch, K. Chinnapared, A. Exton, A. Prakash, and R. Torrance, “Metric of a rotating, charged mass,” J. Math. Phys. 6, pp. 918-919 (1965).

42. For the literature on black holes see for example the bibliographies in H. L. Shipman, Black Holes, Quasars and the Universe (Boston: Houghton Mifflin, 1976); C.

DeWitt and B. DeWitt, eds., Black Holes, Les Houches 1972, Lectures Delivered at the Summer School of Theoretical Physics of the University of Grenoble (New York, N. Y.: Gordon and Breach, 1973); H. Gursky and R. Ruffini, Neutron Stars, Black lloles and Binary X-ray Sources (Dordrecht: Reidel, 1975); R. Giacconi and

R. Ruffini, Physics and Astrophysics of Neutron Stars and Black Holes (Amsterdam: North-Holland,

1978).

43. “A black hole has no hair or particularities,” J. A. Wheeler, “From Mendeleev’s atom to the collapsing star,” pp. 189-233 in M. Verde, ed., Atti del Convegno Mendeleeviano, Accad. delle Sci. di Torino, 1971, esp. pp. 191-192; “Hair” of most extreme character—the “spike” of density formed by a particle falling into a

black hole—fades away exponentially: R. Ruffini and J. A. Wheeler, “Relativistic

cosmology and space platforms,” pp. 45-174 in Proceedings of the Conference on

Space Physics (Paris: European Space Research Organization, 1971); adaptation of curve of fall appears as Fig. 25.5 on p. 667 of Gravitation, note 9; B. Carter, “An axisymmetric black hole has only two degrees of freedom,” note 1; Carter, “Black hole equilibrium states,” in C. DeWitt and B. S. DeWitt, Black Holes, note 1, Section 12, “The pure vacuum no hair theorem,” pp. 205-209; No hair in the sense of a weak-interaction force caused by leptons which have fallen into the black hole: J. B. Hartle, “Long-range neutrino forces exerted by Kerr black holes,” Phys. Rev. D3, pp. 2938-2940 (1971); J. B. Hartle, “Can a Schwarzschild black hole exert

long-range neutrino forces?”, pp. 259-275 in J. Klauder, ed., Magic Without Magic: John Archibald Wheeler (San Francisco: Freeman,

1972), esp. pp. 271-274; C.

Teitelboim, “Nonmeasurability of the lepton number of a black hole,” Nuovo Cimento II, no. 3, pp. 397-400 (1972); “Nonmeasurability of the quantum numbers of a black hole,” Phys. Rev. DS, pp. 2941-2954 (1972); No hair left from baryons that have gone down the black hole: J. Bekenstein, “Nonexistence of baryon number for static black holes,” I, Phys. Rev. D5, pp. 1239-1246 (1972); II, Phys. Rev.

DS, pp. 2403-2412 (1972); C. Teitelboim, “Nonmeasurability of the baryon num-

340

REFERENCES

ber of a black hole,” Nuovo Cimento Lett., Il, no. 3, pp. 326-328 (1972); see however M. J. Perry, “Black holes are coloured,” Phys. Lett. 71B, pp. 234-236 (1977)

who gives reasons to believe that a black hole may act as the source of a Yang-

Mills field.

Rate of attainment of perfection outside black hole: W. H. Press, “Long wave trains of gravitational waves from a vibrating black hole,” Astrophys. J. Lett. 170, pp105-108 (1971); M. Davis, R. Ruffini, W. H. Press, and R. H. Price, “Gravitational

radiation from a particle falling radially into a Schwarzschild black hole,” Phys. Rev. Lett. 27, pp. 1466-1469 (1971); S. W. Hawking and J. B. Hartle, “Energy and angular

momentum flow into a black hole,” Commun. Math. Phys. 27, pp. 283-290 (1970).

45. N. Zamorano, Interior Reissner-Nordstrom Black Holes, doctoral dissertation, The

University of Texas at Austin, August 1979, available from University Microfilms, Inc., Ann Arbor, Michigan 48106; J. Pfautsch, unpublished results extending those of Zamorano.

46. Misner, Thorne, and Wheeler, note 19, p. 738, Box 27.4. 47. V. M. Lyutyi, R. A. Sunyaev, and A. M. Cherepashchuk, “Nature of the optical

variability of Hz Herculis (Her X-I) and BD + 34° 3.815 (Cyg X-l),” Sov. A.st. AJ

17, pp. -6 (1973); U. Avni and J. N. Bahcall, “Ellipsoidal light variations and masses of X-ray binaries,” Astrophy. J. 197, pp. 675-688 (1975). Possibility of Cyg X-I secondary being either a black hole or a normal early-type star discussed; C. R.

Canizares and M. Oda, “Observations of rapid X-ray flaring from Cygnus X-l,” Astrophy. J. 214, L119-L122 (1977); J. N. Bahcall, “Masses of neutro n stars and

black holes in X-ray binaries,” Ann. Rev. Astron. and Astrophys. 16, pp. 241-264

(1978); pp. 261-263 discuss the data on Cyg X-l, and give references; D. M. Eardley, A. D. Lightman, N. I. Shakura, S. L. Shapiro, and R. A. Sunyaev, “A status re-

port on Cygnus X-l,” Comments Astrophys., Comments Mod. Phys. Part C7, pp. 151-160 (1978). A review article with 61 references.

48. J. E. Grindlay, “Two more globular cluster X-ray sources?” Astrophy J. Lett. 224, L107-L111

(1977).

49, E. R. Wollman, “Ne II 12.8 11 emission from the galactic cente r and compact H II regions,” doctoral thesis, University of California, Berkeley, 1976; available from

University Microfilms, Ann Arbor, Michigan 48106; E. R. Wollman, T. R. Geballe,

J. H. Lacy, and C. H. Townes, “Spectral and spatial resolution of the 12 . 8 micron

Ne I I emission from the galactic center,” Astrophy. J. Lett. 205, LS-L9 (1976); E.

R. Wollman and C. H. Townes, “Ne II micron emission from the galactic center.

II,” Astrophy. J. 218, L103-L107 (1977); J. H. Lacy, F. Baas, C. H. Townes, and T.

R. Geballe, “Observations of the motion and the distribution of the ionized gas in the central parsec of the galaxy,” Astrophy. J. 227, L17-L20 (1979). 50. J. H. Oort, “The galactic center,” Astron. and Astrophys. 15, pp. 295-362 (1977); See esp. pp. 341, 343, 347, 349, 352; and on p. 353, “It is there fore possible that Practically the whole of the 4 — 6 x 10° Mg deduced from the Ne II observations would be concentrated in the ultracompact radio source; it migh t be the mass of a black hole in the center.” ol

K. I. Kellermann, D. B. Shaffer, B. G. Clark, and B. J. Geldzahler, “The small radio

REFERENCES

341

source at the galactic center,” Astrophy. J. 214, L61-L62 (1977); L. F. Rodriguez

and E. J. Chaisson, “The temperature and dynamics of the ionized gas in the nucleus of our galaxy,” Astrophy. J. 228, pp. 734-739 (1979).

52. P. J. Young, J. A. Westphal, J. Kristian, and C. P. Wilson, “Evidence for a super-

massive object in the nucleus of the/galaxy M87 from SIT and CCD area photome-

try,” Astrophy. J. 221, pp. 721-730 (1978); W. L. W. Sargent and P. J. Young, “Dynamical evidence for a central mass concentration in the galaxy M87,” Astrophy. J. 221, pp. 731-744 (1978); J. Stauffer and H. Spinrad, “Spectroscopic observations of the core of M87,” Astrophy. J. Lett.

231,

L51-L56

(1979).

BEE Wheeler, “On the nature of quantum geometrodynamics,” Gibbons and Hawking, “Action integrals and partition functions in quantum gravity,” Bekenstein, “Black holes and entropy,” and Hawking, “Particle creation by black holes,” note 1; J. A.

Wheeler, “Superspace and the nature of quantum geometrodynamics,” pp. 242-307 in C. DeWitt and J. A. Wheeler, eds., Battelle Rencontres:

1967 Lectures in Mathe-

matics and Physics (New York, N. Y.: Benjamin, 1968), pp. 263-268 and pp. 286-290, including Figure 5 on p. 265 and Figure 8 on p. 289; or, in German, J. A. Wheeler, Einstein's Vision (Berlin: Springer, 1968), esp. pp. 39-46 (including Figure 8) and pp. 68-78 (especially Figure 10).

54, R. W. Fuller and J. A. Wheeler, “Causality and multiply connected spacetime,” Phys. Rey. 128, pp. 919-929 (1962). 5:

D. Christodoulou, “Reversible and irreversible transformations in black-hole physics,” Phys. Rev. Lett. 25, pp. 1596-1597 (1970); D. Christodoulou and R. Ruffini, “Re-

versible transformations of a charged black hole,” Phys. Rev. D4, pp. 3552-3555 (1971). The resulting formula for the energy, E, of the black hole in terms of its momentum, p, charge Q, intrinsic angular momentum S, and irreducible mass Mjy = {(surface area of horizon/167) 2], all being measured in geometric units, is

E? =p? + (Mix + Q?/ 4Miy)? + S?/ 4M;

56. P. Cordero and C. Teitelboim, “Remarks on supersymmetric black holes,” Phys.

Lett. 78B, pp. 80-83 (1978): the most general black hole with supercharge is equivalent, under supersymmetry transformation, to a black hole without supercharge— as a black hole with momentum is equivalent under Lorentz transformation to a black hole without momentum.

ave D. L. Freedman, P. van Nieuwenhuizen, and S. Ferrara, “Progress toward a theory of supergravity,” Phys. Rev. D13, pp. 3214-3213 (1976).

58. S. Deser and B. Zumino, “Consistent supergravity,” Phys. Lett. 62B, pp. 335-337 (1976).

-

59. C. Teitelboim, “Supergravity and square roots of constraints,” Phys. Rev. Lett. 38,

pp. 1106-1110 (1977); R. Tabensky and C. Teitelboim, “The square root of general

relativity,” Phys. Lett. 69B, pp.453—-456 (1977).

60. Note 43. 61. Lepton number of black hole not measurable, Hartle, “Long-range neutrino forces

exerted by Kerr black holes,” Hartle, “Can a Schwarzschild black hole exert longrange neutrino forces?”, and Teitelboim, “Nonmeasurability of the lepton number of a black hole,” and “Nonmeasurability of the quantum numbers of a black hole,”

REFERENCES

note 43; see also Carter, “An axisymmetric black hole has only two degrees of freedom,” and C. DeWitt and B. S. DeWitt, eds., Black Holes, note 1; Baryon number of

black hole not measurable, Bekenstein, “Nonexistence of baryon number for static

black holes,” Teitelboim, “Nonmeasurability of the baryon number of a black hole,” and Perry, “Black holes are coloured,” note 43; see also Carter, “An axisymmetric black hole has only two degrees of freedom,” and C. DeWitt and B. S. DeWitt, eds., Black Holes, note 1.

62. J. A. Wheeler, “Transcending the law of conservation of leptons,” note 1; Wheeler, “From relativity to mutability,” note 9, p. 202, “Baryon number and lepton number are well defined quantities for a normal star; but when this star collapses to a black hole, the well established laws of conservation of particle number lose

all applicability. “

.

63. Staircase described, Wheeler, “From relativity to mutability,” note 9, p. 241. 64, Archimedes of Syracuse (287-212 B.C.), Peri ochoumenon (On Floating Bodies);

method of determining density by weighing the object, first in air, then under water; reputed to have been found in answer (“Eureka”—I have found it) to the question of Hieron, king of Syracuse, whether his “gold” crown did not contain an admixture

of silver.

65. Fixity of density transcended: J. A. Morgan, “The equation of state of platinum to

680 GPa,” High Temperature-High Pressure 6, pp. 195-201 (1974), density approximately doubled via use of gun; H. K. Mao, P. M. Bell, J. W. Shaner, and D. J. Steinberg, “Specific measurements of Cu, Mo, Pd, and Ag and calibration of Ruby R, fluorescence pressure gauge from 0.06 to | Mbar,” J. Appl. Phys. 49, pp. 3276-3283 (1978), use of nuclear explosion to go to extreme density; C . E . Ragan It, M. G. Silbert, and B. C. Diven, “Shock compression of molybdenum to 2.0 TPa

by means of a nuclear explosion,” J. Appl. Phys. 48, pp. 2860-2870 (1977),

achievement of pressures in the 30 megabar range, and determination of increase of density by a measured factor of about 3; L. V. Al’tshuler, N. N. Kalitkin, L. V. Kuz’mina, and B. S. Chekin, “Shock adiabats for ultrahigh pressures,” Soviet Phys. JETP 45, pp. 167-171 (1977), the extreme of published pressures, 50 megabars, where any measurements have been made. Thanks are expressed here to William Deal for guidance to this literature.

66. J. Dalton, Sept. 6, 1803, first table of atomic weights, Sept. 6, 1803, idea that

chemical combination takes place between atoms of different weights, law of com-

bination in multiple proportions, and atomic theory, included in outline form by

his consent in the third ed. of T. Thomson, System of Chemistry, 1807, and in the first volume of Dalton’s own New System Or Chemical Philosophy (Manchester:

S. Russell, 1808). A. Avogadro, “Essai d’une maniére de déterminer les masses relatives des molécules élémentaires des corps, et des proportions selon lesquelles elles entrent dans les combinaisions,” Jour. de Phys. (1811); under identical physical conditions equal volumes of gas contain the same number of molecules. C. F. Gerhardt, Introduction a l’étude de la chimie par le systéme unitaire,

1848, sim-

plest molecular formulas for organic compounds and systematic use of “rational”

chemical formulas. $. Cannizzaro, Sunto di un corso di filosofia chimica,

1858,

distinction between molecular and atomic weights and deduction of atomic

REFERENCES

343

weights from vapor density or specific heat; E. Frankland, “On the dependence of

the chemical properties of compounds upon the electrical characters of their constituents,” Roy. Inst. Proc. 1, pp. 451-454 (1852), atom of each elementary substance can combine only with a certain limited number of the atoms of other ele-

ments, foundation of theory of valency. F. A. Kekulé, “Uber die constitution und die Metamorphosen der chemischen Verbindungen und iiber die Natur der Kohlenstoffs,” Liebig, Annal.

106, pp. 129-159 (1858): carbon tetravalence with some of

the affinities of the generic carbon atom bound by atoms of other kinds, some bound by other carbon atoms, a result also obtained independently and reported by A. S. Cooper, Acad. des Sci., Paris, Comptes Rend.,

1858.

67. Carbon found to have valence three in the first free radical discovered, triphenyl

methyl: M. Gomberg, “An instance of trivalent carbon,” Jour. Amer. Chem. Soc. 22, pp. 757-771 (1900); opened way to the realization that valence can be transcended in a few cases at room temperature and for every atom at a sufficiently high temperature.

68. Mass number; isotopes: F. Soddy, “Radio elements and the periodic law,” Chem.

News 107, pp. 97-99 (1913), elucidates the chemical identity discovered by B. B. Boltwood in 1906 and by H. N. McCoy and W. H. Ross in 1907 between radioactively distinct ionium, radiothorium, and thorium, and discovered in other cases by Soddy himself and other workers in the subject; Charge number: H. G. J. Moseley, “High-frequency spectra of the elements,” Phil. Mag. 26, pp. 1024-1034 (1913); same title, II, Phil. Mag. 27, pp. 703-713 (1914): determination of number of elementary charges on the nucleus, and the place of the corresponding element in the

periodic table, by measuring the wave lengths of the strongest lines in the x-ray spectrum of the atom and applying Bohr’s theory of the atom.

69. H. A. Becquerel, “Sur les radiations émises par phosphorescence,” Acad. Sci., Paris, Compt. Rend.

122, pp. 420-421

(1896), discovery of natural-radioactivity; E.

Rutherford, “Collision of o particles with light atoms. IV. An anomalous effect in nitrogen,” Phil. Mag. 37, pp. 581-587 (1919), first artificial transmutation; J. D. Cockroft and E. T. S. Walton, “Experiments with high-velocity positive ions. Part I. Disintegration of elements by high-velocity protons,” Proc. Roy. Soc. London

137, pp. 229-242 (1932) and M. A. Tuve and L. R. Hafstad, “The emission of dis-

integration-particles from targets bombarded by protons and by deuterium ions at 1200 kilovolts,” [Letter] Phys. Rev. 45, pp. 651-653 (1934).

70. Baryon conservation: F. Reines, C. L. Cowan, Jr,. and M. Goldhaber, “Conserva-

tion of the number of nucleons,” Phys. Rev. 96, pp. 1157-1158 (1954); F. Reines,

C. L. Cowan, Jr., and H. W. Kruse, “Conservation of the number of nucleons,”

Phys. Rev. 109, pp. 609-610 (1957); G. N. Flerov, D. S. Klochov, V. S. Skobkin

and V. V. Terent’ev, “Spontaneous fission of Th??? and the stability of nucleons,”

Sov. Physics Doklady 3, pp. 79-80 (1958); G. Feinberg and M. Goldhaber, “Mi-

croscopic tests of symmetry principles,” U.S. Nat. Acad. Sci., Proc. 45, pp. 1301-1312 (1959); G. Feinberg and M. Goldhaber, “Experimental tests of symmetry principles,” Science 129, p. 1285 (1959); H. S. Gurr, W. R. Kropp, F. Reines, and B. Meyer, “Experimental test of baryon conservation,” Phys. Rev. 158, pp.

1321-1330 (1967). J. Learned, F. Reines, and A. Soni, “Limits on nonconservation

344

REFERENCES

of baryon number,” Phys. Rev. Lett. 43, pp. 907-909 (1979); nucleon lifetime greater than about 10°0 yr at 90% confidence level; Baryon conservation seriously questioned: S. Weinberg, “Cosmological production of baryons,” Phys. Rev. Lett. 42, pp. 850-853 (1979); Lepton conservation: M. Goldhaber, “Weak interactions:

leptonic modes—experiment,” pp. 233-250 in Proceedings of the 1958 Annual International Conference on High Energy Physics at CERN; V. R. Lazarenko, “Dou-

ble beta decay and the properties of the neutrino,” Usp. Fiz. Nauk 90, pp. 601-622 (1961), English translation in Sov. Phys. Uspekhi 9, pp. 860-873 (1967); B. Pontecorvo, “Neutrino experiments and the problem of conservation of leptons,” Sov. Phys. JETP 26, pp. 984-988 (1968); K. Boher, et al., “Untersuchung iiber die Er-

holtung der -Leptonenzahl,” Helv. Phys. Acta 43, 111-132 (1970); R. I. Steinberg, K. Kwiatkowski, W. Maenhaut, arid N. S. Wall, “Experimental test of charge conservation and stability of the electron,” Phys. Rev. D12, pp. 2582-2586 (1975); mean life of electron against decay into nonionizing particles greater than 5.3 x 102! yr.

71.

Wheeler, note 62.

72. Energy not defined in a closed universe: J. Weber and J. A. Wheeler, “Reality of the cylindrical gravitational waves of Einstein and Rosen,” Rev. Mod. Phys. 29, pp. 509-515 (1957); p. 512, “There is no such quantity as total energy, for example, in a closed universe; there the integrated conservation laws reduce to the trivial identi-

ty, zero equals zero”; J. A. Wheeler, “Geometrodynamics and the issue of the final

state,” ref. 3, pp. 434-435, “The key point for defining mass is the existence of a region where the geometry goes over asymptotically to the Schwarzschild character.

When there is no such region, then it is not known how to give an unambiguous meaning to the term “mass,” This is particularly the case for a closed universe.

There is no asymptotically flat region in which to measure the pull of the system by the bending of light or by the periods of planetary orbits and their precession. If there is no experimental way to measure mass for a closed universe, and no theoretical way to define mass, this is happily compatible with the circumstance that no one knows any use for the concept of the mass of a closed universe. Therefore it would appear appropriate to reject this phrase as being physically meaningless as well as being subject to misunderstanding”; Misner, Thorne, and Wheeler, note 19,

pp. 457-458.

73. Misner, Thorne, and Wheeler, note 19, p. 450: (mass of center of attraction)! = (2n/orbital period)? (semi-major axis of ellipse)?.

74, J. A. Wheeler, “Superspace and the nature of quantum geometrodynamics,” pp. 242-307 in C. M. DeWitt and J. A. Wheeler, eds., Battelle Rencontres, 1967 Lec-

tures in Mathematics and Physics (New York, N. Y.: Benjamin, 1968); p. 254, “.. . the dimensions of the collapsing system in a finite proper time are driven down to

indefinitely small values. The phenomenon is not limited to the space occupied by matter. It occurs also in the space surrounding the matter.”

Ta No before, no after: /bid., p. 254, at small distances and in the final phase of col-

lapse “‘spacetime’ is nonexistent, ‘events’ and the ‘time ordering of events’ are without meaning, and the question ‘what happens after the final phase of gravitational collapse’ is a mistaken way of speaking.” In “From relativity to mutability,”

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Wheeler, note 1, p. 227, “.. . there is no such thing as spacetime in the real world of quantum physics . . complementarity forbids. [S]uperspace leaves us space but

not spacetime and therefore not time. With time gone the very ideas of ‘before’ and ‘after’ also lose their meaning.” J. A. Wheeler, Frontiers of Time, note 8: p. 6, “Nowhere more clearly than in the ending of spacetime are we warned that time is not an ultimate category in the description of nature.” p. 20, “‘Before’ and ‘after’ don’t rule everywhere, as witness quantum fluctuations in the geometry of space at the scale of the Planck distance. Therefore ‘before’ and ‘after’ cannot legalistically rule anywhere. Even at the classical level, Einstein’s standard closed-space cosmology denies all meaning to ‘before the big bang’ and ‘after the big crunch.’ Time cannot be an ultimate category in the description of nature. We cannot expect to understand genesis until we rise to an outlook that transcends time.” p. 75, “Not the slightest warrant does Einstein’s equation give for thinking there can be

any such thing as a ‘before’ before the big bang or an ‘after’ after the big crunch or after the collapse of a star to a black hole. These three processes mark three ‘gates of time.” p. 85, “Little escape is evident from these words: there is no ‘before’ before the big bang and no ‘after’ after the big crunch. Time ends with spacetime. The universe does not endure from everlasting to everlasting. Everything came

from ‘nothing’ “

76. J. A. Wheeler, Frontiers of Time, note 8: “There never was a law of physics that did not require space and time for its statement. With collapse the framework falls. down for everything one ever called a law The laws of physics were not installed in advance by a Swiss watchmaker, nor can they endure from everlasting to everlasting. They must have come into being. They could not always have been accurate.

They are derivative and superficial, not primary and revelatory.” This position, based on the conclusion that the category of “time” is itself not primordial, but secondary, derivative, and approximate, differs in that respect from Peirce, who tacitly accepts the primordiality of time: The philosophy of [Charles S.] Peirce: Selected Writings, ed. by J. Buchler (London: Routledge and Kegan Paul, 1940); paperback

reprint under the title Philosophical Writings of Peirce (New York, N. Y.: Dover, 1955), p. 358, “May they [these forces of nature] not have naturally grown up?”

See further on that page, also pp. 335-337 and p. 353 (quoted on pp. 593-595 of Quantum Gravity: An Oxford Symposium, note 5).

77. Mutability: Wheeler, “From relativity to mutability,” note 9. 78. Crack in crystal: A. Joffe, “On the cause of the low value of strength,” pp. 72-76,

and “On the mechanism of brittle rupture,” pp. 77-80 in International Conference on Physics. London 1934. A Joint Conference Organized by the International Union of Pure and Applied Physics and the Physical Society. Papers and Discus-

sions in Two Volumes. Vol. 2. The Solid State of Matter (Cambridge: Cambridge University Press and The Physical Society, 1935).

UES Collapse inevitable: Avez, “Propriétés globales des espace-temps périodiques clos,” Penrose, “Gravitational collapse and spacetime singularities,” Hawking, “The occurrence of singularities in cosmology,” Geroch, “What is a singularity in general relativity?” Hawking and Ellis, The Large-scale Structure of Space-time, and Marsden and Tipler, “Maximal hypersurfaces and foliations of constant mean curvature in general relativity,” note 1. Theorem on inescapability of singularity: Hawking

346

REFERENCES

and Penrose, note 4. Consideration of details of approach to singularity in the generic case: note 37. 80. Quantum fluctuations in topology and geometry predicted and estimated at the Planck scale of distances: Wheeler, “On the nature of quantum geometrodynamics,” note 1; Wheeler, “Superspace and the nature of quantum geometrodynamics,” note 53; and pp. 1190-1194 in Gravitation, note 19. 81. These fluctuations calculated: Gibbons and Hawking, “Action integrals and partition functions in quantum gravity,” note 1; further calculations, M. J. Perry, S. W. Hawking, and G. W. Gibbons, “Path integrals and the indefiniteness of the gravitational action,” Nucl. Phys. B 138, pp. 141-150 (1978). 82. I. Kant, Kritik der reinen Vernunft, 1781, enlarged ed. 1787, English translation by F. M. Miiller, Critique of Pure Reason (Garden City, N. Y.: Anchor, 1966); p. 24,

three dimensions of space (as other laws of nature) as a “precondition for the possibility of phenomena”; see however chapter 11 in A. Grunbaum, Philosophical Problems of Space and Time (New York, N. Y.: Knopf, 1963); H. Poincaré,

Derniéres Pensées, 1913; English translation by J. W. Bolduc, Mathematics and

Science: Last Essays (New York, N. Y.: Dover, 1963). Chapter 3, pp. 27-28: space as analyzed, not metrically, but via analysis situs (topology in the large) shows it-

self to be three-dimensions”; P. A. Ehrenfest, “In what way does it become mani-

fest in the fundamental laws of physics that space has three dimensions?”, Proc. Amsterdam Acad. 20, pp. 200-209 (1917): only in three-dimensional space is sense

made by the laws of gravitation and planetary motion, the duality of (1) translation

and rotation, of (2) force and pair of forces, and of (3) electric field and magnetic

field; H. Weyl, Philosophy of Mathematics and Natural Science (Princeton, N. J.: Princeton University Press, 1949), paperback reprint (New York, N. Y.: Atheneum, 1963); p. 36, only in a space with an odd number of dimensions “will darkness fol-

low the extinction of a candle”; gauge invariance holds only for three dimensions; other considerations and reference to others who have asked, “why three dimensions?” A. Staruszkiewicz, “Gravitation theory in three-dimensional space,” Acta

Phys. Polonica 24, pp. 735-740 (1963): in three-dimensions Einstein’s field equa-

tion requires space to be flat, thereby making geodesics be straight lines; but gravitation nevertheless shows itself in the global equivalent of curvature produced by cone-like singularities.

83. Pregeometry: J. A. Wheeler, ““Geometrodynamics and the issue of the final state,” pp. 315-520 in C. DeWitt and B. DeWitt, eds., Relativity, Groups, and Topology

(New York, N. Y.: Gordon and Breach, 1964): pp. 495-499, “. . . [T]he number of

dimensions should not be assumed in advance; it should be derived to be four.” “... [A]ny derivation of the four-dimensionality of of spacetime can hardly start with the idea of dimensionality.” “. . . [O}ne can imagine probability amplitudes

for the points in a Borel set to be assembled into manifolds with this, that, and the other dimensionality.” “. . . [DJefine an action principle over a collection of points

of undefined dimensionality. One might also wish to accept to begin with the idea of a distance, or edge length, associated with a pair of these points, even though this idea is a very great leap, and one that one can conceive of later supplying with a foundation of its own. . . . [T]here must be a connection in the appropriate action principle between every point and every other point. . . . Try therefore a propagator

REFERENCES

347

of the form doe exp tS ciagram Here the sum goes over all conceivable ways of connecting the given number of vertices up into nearest neighbors, whatever the dimensionality or lack of dimensionality of these “wiring diagrams. How this phase depends upon the topology of the diagram is to be deduced—in whole or in part—from natural combinatorial principles.” C. W. Misner, K. S. Thorne. and J. A. Wheeler, Gravitation (San Francisco: Freeman, 1973), pp. 1203-1212, including discussion of “pregeometry as the calculus of propositions.” C. M. Patton and J. A. Wheeler, “Is physics legislated by cosmogony?”, pp. 538-605 in C. J. Isham, R. Penrose, and D. W. Sciama, Quantum Gravity: An Oxford Symposium (Oxford: Clarendon, 1975); p. 573, “[The] concept of ‘ideal mathematical geometry’ is too

finalistic to be final and must give way to a deeper concept of structure [. . . ]

‘pregeometry’,” pp. 589-591, Appendix B, Report on the search for pregeometry,

February—March—April 1974: “[W]e have to give up the idea that pregeometry is the calculus of propositions, or the statistics of propositions, or the mathematical machinery of any formal axiomatic system”; J. A. Wheeler, “Pregeometry: moti-

vations and prospects,” in A. R. Marlow, ed., Quantum Theory and Gravitation:

Proceedings of the May, 1979 Conference, Loyola University (New York, N. Y.: Academic, 1980), pp. 1-12. Pregeometry viewed as the statistics of billions upon

billions of acts of observer-participancy.

84, “Thermodynamics rests upon the random motions of billions upon billions of

molecules”: for key selections from the original literature see S. G. Brush, Kinetic Theory. Vol. 1. The Nature of Gases and of Heat and Vol. 2. Irreversible Process-

es (Oxford: Pergamon, 1965-1966); C. Darwin, Origin of Species by Means of

Natural Selection (London: J. Murray, 1859); T. Dobzhansky, Genetics and the

Origin of Species (New York, N. Y.: Columbia Univserity Press, 1937); M. Eigen, “The origin of biological information,” pp. 594-632 in J. Mehra, ed., The Physicists’ Conception of Nature (Dordrecht: Reidel, 1973); M. Eigen and R. Winkler, Das Spiel: Naturgesetze steuern den Zufall (Munich: Piper, 1975).

85. Frontiers of Time, note 8, p. 6. 86. A. Einstein, note 24, p. 87, “The statistical character of the present theory would

then have to be a necessary consequence of the incompleteness of the description of the systems in quantum mechanics, and there would no longer exist any ground for the supposition that a future basis of physics must be based upon physics.” Einstein’s last lecture, Wheeler, note 28, “. . . it [quantum mechanics] seems to make

the world quite nebulous unless somebody, like a mouse, is looking at it.”

87. A. Einstein, “Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. der Phys.

17, pp. 132-148 (1905).

88. A. Einstein, “Strahlungs-emission und -absorption nach der Quantentheorie,” Deutsche physikalische Gesellschaft, Verhandlungen,

18, pp. 318-323 (1916);

“Quantentheorie der Strahlung,” Physikalische Gesellschaft, Ziirich, Mitteilungen

16, pp. 47-62 (1916).

89. Einstein, note 14. 90. A. Einstein, letter to Maurice Solovine, January 1,1951, “Ich habe keinen besseren Ausdruck als den Ausdruck [religiés] fiir dieses Vertrauen [von Spinoza] in die

348

REFERENCES

verniinftige und der menschlichen Vernunft wenigstens einigermassen zuganlgliche Beschaffenheit der Realitat.” Letter to Max von Laue, May 1933, regarding the capitulation of intellectuals to the advent of gangsterism, “Wo stiinden wir wenn Leute wie Giordano Bruno, Spinoza, Voltaire und Humboldt so gedacht und

so gehandelt hatte?” (these two letters reproduced in F. Herneck, Einstein und sein

Weltbild (Berlin: Der Morgen, 1979], p. 35 and p. 87). Letter to The Reporter,

published May 5, 1955, a few days after his death, “. . . ignoramuses who use their

public positions of power to tyrannize over professional intellectuals must not be accepted by intellectuals without a struggle. Spinoza followed this rule when he

turned down a professorship at Heidelberg and (unlike Hegel) decided to earn his living in a way that would not force him to mortgage his freedom.” Statement in Forum 83, pp. 373-437 (1930), “Just in this appears the moral side of our nature—

that internal striving towards the attainment of truth, which under the name amor intellectualis was so often emphasized by Spinoza.” oi

Appreciation is expressed here to Professor Hans Kiing for emphasizing in June 1978 at Tiibingen the influence of Spinoza on Einstein’s outlook.

92. “But Spinoza rejected the idea of an external Creator suddenly, and apparently capriciously, creating the world at one particular time rather than another, and creating it out of nothing,” article “Spinoza,” pp. 231-239, vol. 21, Encyclopaedia Brittanica, 1959 edition, Chicago, Illinois, p. 235.

93. A. Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativitiitstheorie,” Preuss. Akad. Wiss., Berlin, Sitzber, pp. 142-152 (1917).

94, A. Friedmann, note 2. 95. E.P.

Hubble, note 2.

96. A. Einstein as quoted by G. Gamow, My World Line (New York, N.Y.: Viking, 1970).

o

B. de Spinoza, Ethics, finished at The Hague 1675 and circulated privately; English translation by H. White and A. H. Stirling, 1899.

98. “Participatory,” note 8. 99. Story of twenty questions: in Frontiers of Time, note 8. 100. “Phenomenon”: Introduced by N. Bohr to meet and overcome the objections of Einstein, note 7, p. 230. Preliminary account of stages in Bohr’s evolution of this term, A. Petersen, Quantum Mechanics and the Philosophical Tradition (Cam-

bridge, Mass.: M. I. T. Press, 1968). “No phenomenon is . . . until itis. . . ,” used by

J. A. Wheeler in Varenna lectures of 1977; revised in printed version, Frontiers of Time, note 8, to read “No elementary phenomenon. . .” to exclude macroscopic phenomena. The ending used there, “. . . until it is an observed phenomenon,” is revised here to “. . . until it is a registered phenomenon” to exclude any suggestion that quantum mechanics has anything whatsoever directly to do with “conscious-

ness” and to recall Bohr’s point that an irreversible act of amplification is required to bring an elementary phenomenon to a close.

101. J. A. Wheeler, “The ‘past’ and the ‘delayed-choice’ doubleslit experiment,” in A.

R. Marlow, ed., Mathematical Foundations of Quantum Theory (New York, N. Y.: Academic, 1978).

REFERENCES

349

102. N. Bohr, note 7; Chapters on the Bohr-Einstein dialog in M. Jammer, The Philosophy of Quantum Mechanics (New York, N. Y.: John Wiley, 1974).

103. This “Venetian blind” and other experimental arrangements, alternative to that depicted in note 101, have been devised and generously communicated to the author by Professor L. F. Bartell of the University of Michigan at Ann Arbor.

104.

A. R. Wilson, J. Lowe, and D. K. Butt, “Measurement of the relative planes of polarization of annihilation quanta as a function of separation distance,” J. Phys. G:

Nuc. Phys. 2, pp. 613-624 (1976). “No significant change in the correlation was observed over separations of up to 2.5 m.”

105. Bohr, note 7. 106. Ibid.; Complementarity defined, N. Bohr, Atomic Theory and the Description of Nature (Cambridge, U. K.: Cambridge University Press, 1934), p. 35.

107. Wheeler, note 101. 108. “Past” exists only in the present, Frontiers of Time, note 8, p. 21. 109. T. Segerstedt as quoted in note 8, p. 21. 110. Bohr, note 100. 111. N. Bohr, Atomic Physics and Human Knowledge, note 6, p. 73 and p. 88, closed by irreversible amplification.

112. N. Bohr, Essays 1958-1962 on Atomic Physics and Human Knowledge, note 6, p. 3 and pp. 5, 6, unambiguously communicable in plain language.

113. . E. P. Wigner, “Are we machines?” Proc. Am. Philos. Soc. 113, pp. 95-101 (1969), p. 97; E. P. Wigner, “The philosophical problem,” pp. 1-3 in B. d’Espagnat, ed., Foundations of Quantum Mechanics (New York, N. Y.: Academic, 197i), p. 3.

114. }. Bohr, note 100. 115. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?”, Phys. Rev. 47, pp.

777-780 (1935).

116. See for example D. Gorenstein, “The classification of finite simple groups. I. Sim-

ple groups and local analysis,” Bull. Am. Math. Soc. 1, pp. 43-199 (1979), especially Chap. 1, section 3, “Why the extreme length?”: “There exists an often expressed feeling in the general mathematical community that the present approach to the classification of simple groups must be the wrong one—no single theorem can possibly require a 5000-page proof!”; also the discussion on pp. 50-52 of problems and progress in completing the classification.

117.

For a study of this distinction between and interaction of observed system and observing equipment see especially M. M. Yanase, “Optimal measuring apparatus,” Phys. Rev. 123, pp. 666-668 (1961); E. P. Wigner, “The problem of measurement,” Am. J. of Phys. 31, pp. 6-15 (1963); E. P. Wigner, “Interpretation of quantum mechanics,” 93 pages of mimeographed notes of lectures delivered at Princeton University in 1976, on deposit in Fine Library, Princeton University, Princeton, New Jersey; A. Peres, “Can we undo quantum measurements?”, 1979 preprint, Center for Theoretical Physics, The University of Texas at Austin.

118. “Nothingness” ruled out as meaningless: Parmenides of Elia, poem (~502 B.C.) Nature, part 2 “Truth,” as summarized in article “Parmenides,” pp. 327-328 in Vol .

REFERENCES

350

17 of Encyclopaedia Brittanica, 1959 edition, Chicago, p. 327: “There are three ways of research, and three ways only. Of these, one asserts ‘It is not, and there must be not-being.’ This is utterly forbidden: what is not cannot even be thought of. A second way [is] that of mortals without wisdom, who say of what is that ‘it is and is not,’ ‘is the same and not the same.’ In contrast to them the way of truth starts from the proposition ‘/t is, and not-being is impossible.’” 119.

Universe as a self-excited circuit: in “Is physics legislated by cosmogony,” note 83, p. 565 and in Frontiers of Time, note 8, p. 11.

120. C. Patton and J. A. Wheeler, “Is physics legislated by cosmogony,” pp. 538-605 in C. J. Isham, R. Penrose, and D. W. Sciama, Quantum Gravity: An Oxford Sympo-

sium (Oxford: Clarendon, 1975), p. 575, “Towards the finding of this ‘pregeometry’ no guiding principle would seem more powerful than the requirement that it should provide the universe with a way to come into being. It is difficult to believe that we can uncover this pregeometry except as we come to understand at the same time the necessity of the quantum principle, with its ‘observer-participator, ‘in the

construction of the world.” Frontiers of Time, note 8, “No test of these views looks more like being someday doable, nor more interesting and more instructive, than a

derivation of the structure of quantum theory from the requirement that everything

have a way to come into being out of nothing.” J. A. Wheeler, ““Pregeometry: moti-

vations and prospects,” and W. K. Wootters, “Information is maximized in photon polarization measurements,” to appear in A. R. Marlow, ed., Quantum Theory and Gravitation: Proceedings of the May, 1979 Conference, Loyola University (New York, N. Y.: Academic,

1980), pp. 13-26.

121. Move over onto the new “foundation of elementary acts of observer-participancy.” For three steps towards this development see (a) R. M. F . Houtappel, H. Van Dam, and E. P. Wigner, “The conceptual basis and use of the geometric invariance principles,” Rev. Mod. Phys. 37, pp. 595-632 (1965), especially §§4.1-4.5 on pp. 610-616; (b) W. Wootters, “Information is maximized in photon polarization mea-

surements,” to appear in A. R. Marlow, ed., note 83; and (3) A. Peres, “Can we undo quantum measurements?,” The University of Texas Center for Theoretical Physics preprint, September 1979.

It from Bit 1. J. Kepler (1571-1630), Harmonices Mundi, five books (1619). The appendix to Kepler’s Book 5 contains one side, the publications of the English physician and thinker Robert Fludd (1574-1637) the other side, of a great debate, analyzed by

Wolfgang Pauli [W. Pauli: “Der Einfluss archetypischer Vorstellungen auf die Bildung naturwissenschaftlicher Theorien bei Kepler” in Naturerkldrung und Psyche (Zurich: Rascher, 1952) p. 109-194; reprinted in Wolfgang Pauli: Collected Scientific Papers, eds. R. Kronig and V. F. Weisskopf (New York, N. Y.: John Wiley,

1964) Vol. 1, p. 1023]. Totally in contrast to Fludd’s concept of intervention from on high [Utriusque Cosmo Maioris scilicet et Minoris Metaphysica, Phvsica atque

technica Historia, Ist ed. (Oppenheim,

1621)] was Kepler’s guiding principle, Ubi

REFERENCES

351

materia, ibi geometria—where there is matter, there there is geometry. It was not directly from Kepler’s writings, however, that Newton learned of Kepler’s three great geometry-driven findings about the motions of the planets in space and in time, but from the distillation of Kepler offered by Thomas Streete (1622-1689),

Astronomia Carolina: A New Theorie of the Celestial Motions (London,

1661); I.

Newton: Philosophiae naturalis principia mathematica, \st ed. (London, 1687); A Einstein: “Zur allgemeinen Relativitatstheorie” Preuss. Akad. Wiss. Berlin, Sitzber

(1915) pp. 7998-01; also (1915) pp. 832-839, 844-847; (1916) pp. 688-696 and

(1917) pp. 142-152; J. A. Wheeler, Journey into Gravity and Spacetime (New York, N. Y.: Scientific American Library, Freeman, 1990), offers a brief and ac-

cesssible summary of Einstein’s 1915 and still standard geometrodynamics which

capitalizes on Elie Cartan’s appreciation of the central idea of the theory: the boundary of a boundary is zero.

2. J. G. Mendel, “Versuche iiber Pflanzenhybriden” Verhandlungen des Naturforschenden Vereins in Briinn 4 (1866); C. R. Darwin (1809-1882), On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in

the Struggle for Life (London, 1859); J. D. Watson and F. H. C. Crick, “Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid” Nature 171

(1953) pp. 737-738.

3. M. Planck, “Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum” Verhand. Deutschen Phys. Cesell. 2 (1900) pp. 237-245. 4. N. Bohr, “The quantum postulate and the recent development of atomic theory” Nature 121(1928) pp. 580-590. Reprinted in J. A. Wheeler and W. H. Zurek, eds., Quantum Theory and Measurement (Princeton, N. J.: Princeton University Press,

1983) pp. 87-126. The mathematics of complementarity cover stated anywhere more sharply, more generally, and Gruppentheorie und Quantenmechanik (Leipzig: Hirzel, that the totality of operators for all the physical quantities form an irreducible set.

I have not been able to disearlier than in H. Weyl, 1928), in the statement of the system in question

5. N. Bohr, “Can quantum-mechanical description of physical reality be considered complete?” Phys Rev. 48 (1935) pp. 696-702; reprinted in Wheeler and Zurek, note

4, pp. 145-151.

6. A. Einstein to J. J. Laub, 1908, undated, Einstein Archives; scheduled for publication in The Collected Papers of Albert Einstein, group of volumes on the Swiss years 1902-1914, Volume S: Correspondence, 1902-1914 (erinesion University Press, Princeton, New Jersey).

7. J. A. Wheeler, “Assessment of Everett's ‘relative state’ formulation of quantum theory” Rev. Mod. Phys. 29 (1957) pp. 463-65; J. A. Wheeler, “On the nature of quantum geometrodynamics,” Ann. of Phys. 2 (1957) pp. 604-614;

J. A. Wheeler: “Superspace and the nature of quantum geometrodynamics,” in Battelle Rencontres: 1967 Lectures in Mathematics and Physics, eds. C. M. DeWitt

and J. A. Wheeler (New York, N. Y.: Benjamin, 1968) pp. 242-307; reprinted as “Le superespace et la nature de la géométrodynamique quantique,” in Fluides et

REFERENCES

Champ Gravitationnel en Relativité Générale, No. 170, Colloques Internationaux (Editions du Centre National de la recherche Scientifique, Paris, 1969) pp. 257-322;

J. A. Wheeler, “Transcending the law of conservation of leptons,” in Atti del Convegno Internazionale sul Tema: The Astrophysical Aspects of the Weak Interactions (Cortona “11 Palazzone,” 10-12 Giugno 1970), Accademia Nationale die Lincei, Quaderno N. 157 (1971) pp. 133-64; C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco, Calif.:

Freeman, 1973) p. 1217; paragraph on participatory concept of the universe;

J. A. Wheeler: “The universe as home for man,” in The Nature of Scientific Discov-

ery, ed. O. Gingerich (Washington, D. C.: Smithsonian Institution Press, 1975) pp. 26 1-296; preprinted in part in American Scientist, 62 (1974) pp. 683-691; reprinted in part as T. P. Snow, The Dynamic Universe (St. Paul, Minn.: West, 1983) pp.

108-109;

C. M. Patton and J. A. Wheeler, “Is physics legislated by cosmogony?,” in Quantum Gravity, eds. C. Isham, R. Penrose, and D. Sciama (Oxford: Clarendon,

1975)

pp. 538-605; reprinted in part in Encyclopaedia of Ignorance, eds. R. Duncan and M. Weston-Smith (Oxford: Pergamon, 1977) pp. 19-35; J. A. Wheeler, “Include the observer in the wave function?” Fundamenta Scientiae: Seminaire sur les fondements des sciences (Strasbourg) 25 (1976) 9-35; reprinted

in Quantum Mechanics A Half Century Later, eds. J. Leite Lopes and M. Paty (Dordrecht: Reidel,

1977) pp. 1-18;

J, A. Wheeler, “Genesis and observership,” in Foundational Problems in the Special Sciences, eds. R. Butts and J. Hintikka (Dordrecht: Reidel, 1977) pp. 1-33; J. A. Wheeler, “The ‘past’ and the ‘delayed choice’ double-slit experiment,” in Mathematical Foundations oJ Quantum Theory, ed. A. R. Marlow (New York,

N. Y.: Academic, 1978) pp. 9-48; reprinted in part in Wheeler and Zurek, note 4, pp. 182-200;

J. A. Wheeler, “Frontiers of time,” in Problems in the Foundations of Physics, Proceedings of the International School of Physics “Enrico Fermi” (Course 72), ed.

N. Toraldo di Francia (Amsterdam: North Holland, 1979) pp. 395-497; reprinted in part in Wheeler and Zurek, note 4, pp. 200-208;

J. A. Wheeler, “The quantum and the universe,” in Relativity, Quanta, and Cosmology in the Development of the Scientific Thought of Albert Einstein, Vol. 11., eds.

M. Pantaleo and F. deFinis (New York, N. Y.: Johnson Reprint Corp., 1979) pp.

807-825;

J. A. Wheeler, “Beyond the black hole,” in Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, ed. H.

Woolf (Reading, Mass.: Addison-Wesley, 1980) pp. 341-375; reprinted in part in Wheeler and Zurek, note 4, pp. 208-210; J. A. Wheeler, “Pregeometry: motivations and prospects,” in Quantum Theory and

Gravitation, proceedings of a symposium held at Loyola University, New Orleans, May 23-26, 1979, ed. A. R. Marlow (New York, N. Y.: Academic, 1980) pp. 1-11;

REFERENCES

353

J. A. Wheeler, “Law without law,” in Structure in Science and Art, eds. P. Medawar and J. Shelley (New York, N. Y.: Elsevier North-Holland, 1980 and Amsterdam: Excerpta Medica, 1980) pp. 132-54; J. A. Wheeler, “Delayed-choice experiments and the Bohr-Einstein dialogue,” in

American Philosophical Society and the Royal Society: Papers read at a meeting, June 5, 1980 (Philadelphia: American Philosophical Society, 1980) pp. 9-40;

reprinted in slightly abbreviated form and translated into German as “Die Experimente der verz6gerten Entscheidung und der Dialog zwischen Bohr and Einstein,”

in Moderne Naturphilosophie ed. B. Kanitscheider (Wiirzburg: Konigshausen and Neumann, 1984) pp. 203-222; reprinted in Niels Bohr; A Profile, eds. A. N. Mitra,

L. S. Kothari, V. Singh, and S. K. Trehan (New Delhi: Indian National Science Academy, 1985) pp. 139-168;

J. A. Wheeler, “Not consciousness but the distinction between the probe and the probed as central to the elemental quantum act of observation,” in The Role of Consciousness in the Physical World, ed. R. G. Jahn (Boulder: Westview,

pp. 87-111;

1981)

J. A. Wheeler, “The elementary quantum act as higgledy-piggledy building mechanism,” in Quantum Theory and the Structures of Time and Space, Papers presented

at a Conference held in Tutzing, July 1980, eds. L. Castell and C. F. von Weizsacker (Munich: Carl Hanser, 1981) pp. 27-304;

J. A. Wheeler, “The computer and the universe,” Int’! J. Theo. Phys. 21 (1982) pp.

557-571;

J. A. Wheeler, “Bohr, Einstein, and the strange lesson of the quantum,” in Mind in

Nature, Nobel Conference XVII, Gustavus Adolphus College, St. Peter, Minnesota, ed. Richard Q. Elvee (New York, N. Y.: Harper and Row, 1982) pp. 1-30 (also pp.

88, 112, 113, 130-131, 148-40);

J. A. Wheeler, Physics and Austerity (in Chinese) (Anhui, China: Anhui Science and Technology Publications, 1982); reprinted in part (Lecture 11), in Krisis, Vol.

1, No. 2, ed. 1. Marculescu (Paris: Klinckscieck, 1983) pp. 671-75;

J. A. Wheeler, “Particles and geometry,” in Unified Theories of Elementary Particles, eds. P. Breitenlohner and H. P. Durr (Berlin: Springer, 1982) pp. 189-217; J. A. Wheeler, “Black holes and new physics,” in Discovery: Research and Schol-

arship at the University of Texas at Austin, 7, No. 2 (Winter 1982) pp. 4-7;

J. A. Wheeler, “On recognizing law without law,” American J. Phys. 51 (1983) pp.

398-404;

i

J. A. Wheeler, “Jenseits aller Zeitlichkeit,” in Die Zeit, Schrifter der Carl Friedrich von Seiemens-Stiftung, Vol. 6, eds. A. Peis! and A. Mohler (Munich: Oldenbourg,

1983) pp. 17-34;

J. A. Wheeler, “Elementary quantum phenomenon as building unit,” in Quantum

Optics, Experimental Gravitation, and Measurement Theory, eds. P. Meystre and

M. Scully (New York and London: Plenum,

1983) pp. 141-143;

J. A. Wheeler, “Bits, quanta, meaning,” in Problems in Theoretical Physics, eds. A. Giovannini, F. Mancini, and M. Marinaro (Salerno: University of Salerno Press,

354

REFERENCES

1984) pp. 121-141; also in Theoretical Physics Meeting: Atti del Convegno, Amalf, 6-7 maggio 1983 (Naples: Edizioni Scientifiche Italiane, 1984) pp. 121-134; also in Festschrift in Honour of Eduardo R. Caianiello, eds., A. Giovannini, F. Mancini,

M. Marinaro, and A. Rimini (Singapore: World Scientific, 1989) pp. 133-154;

J. A. Wheeler, “Quantum gravity: the question of measurement,” in Quantum Theory of Gravity, ed. S. M. Christensen (Bristo: Hilger, 1984) pp. 224-233;

W. A. Miller and J. A. Wheeler, “Delayed-choice experiments and Bohr’s elementary quantum phenomenon,” in Proceedings of International Symposium of Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, eds. S. Kamefuchi et al. (Tokyo: The Physical Society of Japan, 1984) pp. 140-151; J. A. Wheeler, “Bohr’s ‘phenomenon’ and ‘law without law,” in Chaotic Behavior in Quantum Systems, ed. G. Casati (New York, N. Y.: Plenum,

1985) pp. 363-378;

A. Kheyfets and J. A. Wheeler, “Boundary of a boundary principle and geometric structure of field theories,” Int’l J. Theo. Phys. 25 (1986) pp. 573-580; J. A. Wheeler, “Physics as meaning circuit: three problems,” in Frontiers of NonEqulilibrium Statistical Physics, eds. G. T. Moore and M. O. Scully (New

N. Y.: Plenum,

1986) pp. 25-32;

York,

J. A. Wheeler, “Interview on the role of the observer in quantum mechanics,” in eds. P. C. W. Davies and J. R. Brown (Cambridge, U.K.: Cambridge University Press, 1986) pp. 58-69;

J. A. Wheeler, “How come the quantum,” in New Techniques and Ideas in Quantum Measurement Theory, D. M. Greenberger, ed., Ann. New York Acad. Sci. 480

(1987) pp. 304-316;

J. A. Wheeler, “Hermann Wey] and the unity of knowledge,” in Exact Sciences and

their Philosophical Foundations, eds. W. Deppert et al. (Frankfurt am Main: Lang, 1988) pp. 469-503; appeared in abbreviated form in American Scientist 74 (1986) pp. 366-375;

J. A. Wheeler, “World as system self-synthesized by quantum networking,” IBM J. of Res. and Dev. 32 (1988) pp. 4-15; reprinted, in Probability in the Sciences, ed.

E. Agazzi (Amsterdam: Kluwer, 1988) pp. 103-129;

J. A. Wheeler, “How come the quantum,” in New Techniques and Ideas in Quan-

tum Measurement Theory, D. M. Greenberger, ed., Ann. New York Acad. Sci. 480 (1987) pp. 304-316.

. B. d’Espagnat, Reality and the Physicist: Knowledge, Duration, and the Quantum World (Cambridge, U.K.: Cambridge University Press, 1989); P. Mittelstaedt and E. W. Stachow, eds.: Recent Developments in Quantum Logic (Zurich: Bibliographisches Institut, 1985);

J.S. Bell, Collected Papers in Quantum Mechanics (Cambridge U.K.: Cambridge University Press, 1987).

J. W. Tukey, “Sequential conversion of continuous data to digital data,” Bell Laboratories memorandum of September 1, 1947, marks the introduction of the term “bit”; reprinted in Origin of the Term Bit, ed. H. S. Tropp Annals Hist. Computing,

6 pp. 152-155 (1984).

REFERENCES

355

10. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature

279 (1982) pp. 802-803; W. K. Wootters and W. H. Zurek, “On replicating photons,” Nature 304 (1983) pp. 188-189.

11. Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the

quantum theory,” Phys. Rev. 115 (1959) pp. 485-491; J. D. Bekenstein: Baryon

Number, Entropy, and Black Hole Physics, Ph.D. thesis, Princeton University

(1972); photocopy available from University Microfilms, Ann Arbor, Michigan.

12. Wheeler, Journey into Gravity and Spacetime, note 1; Misner, Thorne, and Wheeler, Gravitation, note 37.

i3. J. Anandan, “Comment on geometric phase for classical field theories,” Phys. Rev. Lett. 60 (1988) p. 2555; J. Anandan and Y, Aharonov: “Geometric quantum phase and angles,” Phys. Rev. D 38 (1988) pp. 1863-1870; includes references to the literature of the subject.

14. Wheeler, “Bits, quanta, meaning,” note 7. a: J. D. Bekenstein, “Black holes and the second law,” Nuovo Cimento Lett. 4 (1972) pp. 737-740; J. D. Bekenstein: “Generalized second law of thermodynamics in black hole physics,” Phys. Rev. D. 9 (1973) pp. 3292-3300; J. D. Bekenstein: “Black hole thermodynamics,” Physics Today 33 (1980) pp. 24-31.

16. R. Penrose, “Gravitational collapse: the role of general relativity,” Riv. Nuovo Cimento I (1969) pp. 252-276.

17. D. Christodoulou, “Reversible and irreversible transformations in black hole physics,” Phys. Rev. Lett., 25 (1970) pp. 1596-1597.

18. D. Christodoulou and R. Ruffini, “Reversible transformations of a charged black hole,” Phys. Rev. D 4 (1971) pp. 3552-3555.

19. S. W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43

(1975) pp. 199-220; S. W. Hawking: “Black holes and thermodynamics,” Phys.

Rey. 13 (1976) pp. 191-197.

20. W. H. Zurek and K. S. Thorne, “Statistical mechanical origin of the entropy of a rotating, charged black hole,” Phys. Rev. Lett. 20 (1985) pp. 2171-2175. 21. Wheeler, “World as a system self-synthesized by quantum networking,” note 7; Misner, Thorne, and Wheeler, Gravitation, note 7, p. 1217.

22. W. Shakespeare, The Tempest, Act IV, Scene |, lines 148 ff. 23. T. Mann, Freud, Goethe, Wagner (New York, N. Y.: Knopf, 1937) p. 20; trans. by H. T. Lowe-Porter from Freud und die Zukunft.

24, G. W. Leibniz as cited in J. R. Newman, The World of Mathematics (New York, N.Y.: Simon and Schuster, 1956).

25. Wheeler, Physics and Austerity, note 7. 26. N.E. Steenrod, Cohomology Operations (Princeton, N. J.: Princeton University Press, 1962); C. Ehresmann, Catégories et Structures (Paris: Dunod,

1965); D.

Lohmer, Phédinomenologie der Mathematik: Elemente einer Phiinomenologischen Aufkldrung der Mathematischen Erkenntnis nach Husserl (Norwell, Mass.: Kluwer,

356

REFERENCES

1989); A. Weil, “De la métaphysique aux mathématiques,” Sciences, pp. 52-56; reprinted in A. Weil, Ouevres Scientifiques: Collected Works, Vol. 2, 1951-64 (New York, N. Y.: Springer, 1979) pp. 408-412.

27. J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (New York, N. Y.: Oxford University Press, 1986) and literature therein cited.

28. Wheeler, Physics and Austerity, note 7. 29. See for example the survey by F. Feferman, “Turing in the land of O(z),” and related papers on mathematical logic, in R. Herken, The Universal Turing Machine: A Half-Century Survey (Hamburg: Kammerer & Unverzagt, 1988; and Oxford: Oxford University Press, 1988) pp. 113-147.

30. H. Weyl, “Mathematics and logic.” A brief survey serving as a preface to a review of The Philosophy of Bertrand Russell, Amer. Math. Monthly 53 (1946) pp. 2-13.

31. W. V. O. Quine, p. 18 in the essay “On what there is,” in From a Logical Point of View, 2nd ed. (Cambridge, M:

Harvard University Press, 1980) pp. 1-19.

32. Bohr, note 5 33.

Wheeler, “Bits, quanta, meaning,” note 7.

34, Discovered among graffiti in the men’s room of the Pecan Street Cafe, Austin, Texas. 35. G. W. Leibniz, Animadversiones ad Joh. George Wachteri librum de recondita Hebraeorum philosophia, c. 1708, unpublished; English translation in P. P. Wiener, Leibniz Selections (New York, N. Y.: Scribners,

1951 ) p. 488.

36. A. Einstein as quoted by A. Forsee in Albert Einstein Theoretical Physicist (New York, N. Y.: Macmillan,

1963) p. 81.

37: Wheeler, “On the nature of quantum geometrodynamics,” Ann. of Phys. 2 (1957)

pp. 604-614; J. A. Wheeler, “Superspace and the nature of quantum geometrodynamics,” in Baitelle Rencontres: 1967 Lectures in Mathematics and Physics, eds. C. M. DeWitt and J. A. Wheeler (New York, N.Y.: Benjamin, 1968) pp. 242-307; reprinted as “Le superespace et la nature de la géométrodynamique quantique,” in Fluides et Champ Gravitationnel en Relativité Générale, No. 170, Colloques Internationaux (Editions du Centre National de la Recherche Scientifique, Paris, 1969)

pp. 257-322; C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (San Francisco, Calif: Freeman,

1973), §43.4 and p. 1217.

38. Wheeler, “Frontiers of time,” in Problems in the Foundations of Physics, Proceedings of the International School of Physics “Enrico Fermi” (Course 72), ed. N. Toraldo di Francia (Amsterdam: North Holland, 1979) pp. 395-497; reprinted

in part in Wheeler and Zurek, note 4, pp. 200-208.

39, E. H. Spanier, Algebraic Topology (New York, N. Y.: McGraw-Hill, 1966). 40. A. Kheyfets and Wheeler, “Boundary of a boundary principle and geometric struc-

ture of field theories,” Int’l J Theor. Phys. 25 (1986) pp. 573-580; E. Cartan, La Géométrie des Espaces de Riemann, Mémorial des Sciences Mathématiques (Paris:

Gauthier-Villars, 1925); B. Cartan, Lécons sur la Géométrie des Espaces de Riemann (Paris: Gauthier-Villars, 1925); C. W. Misner, K. S. Thorne, and Wheeler,

Gravitation (San Francisco, Calif.: Freeman,

1973), Chap. 15; M. Atiyah, Collected

Papers. Vol 5: Gauge Theories) (Oxford: Clarendon, 1988).

REFERENCES

357

41. Wheeler, “The ‘past’ and the ‘delayed choice’ double-slit experiment,” in Mathematical Foundations of Quantum Theory, ed. A. R. Marlow, (New York, N.Y.:

Academic, 1978) pp. 9-48; reprinted in part in Wheeler and Zurek, note 4, pp. 200-208. Wheeler, “Frontiers of time,” in Problems in the Foundations of Physics, Proceedings of the International School of. Physics “Enrico Fermi” (Course 72, ed. N. Toraldo di Francia (Amsterdam: North Holland, 1979)

pp. 395-497; reprinted in part in Wheeler and Zurek, note 4, pp. 200-208.

42. W. K. Wootters and W. H. Zurek, “Complementarity in the double-slit experiment: quantum nonseparability and a quantitative statement of Bohr’s principle,” Phys.

Rey. D19 (1979) pp. 473-484.

43. Bohr, note 4; W. Heisenberg, “Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Zeits. f, Physik 43 (1927) pp. 172-198. English translation in J. A. Wheeler and W. H. Zurek, note 4, pp. 62-84; N. Bohr and L. Rosenfeld, “Zur Frage der Messbarkeit der elektromagnetischen Feldgréssen,”

Mat.-fys. Medd. Dan. Vid. Selsk. 12, no. 8 (1933); English translation by Aage Petersen, 1979, reprinted in Wheeler and Zurek, note 4, pp. 479-534.

Wheeler, “Bits, quanta, meaning,” note 33; Wheeler, “Physics as meaning circuit:

note 7. three problems,”

45. D. J. Gross, “On the calculation of the fine-structure constant,” Phys. Today 42,

No. 12 (1989).

N. F. Mott, “The wave mechanics of o-ray tracks,” Proc. Roy. Soc. London A126

(1929) 7484; reprinted in Wheeler and Zurek, note 4, pp. 129-134.

47. H. D. Zeh, “On the interpretation of measurement in quantum theory,” Found. Phys. | (1970) pp. 69-76; H. D. Zeh, The Physical Basis of the Direction of Time (Berlin: Springer, 1989).

E. Joos and H. D. Zeh, “The emergence of classical properties through interaction with the environment,” Zeits.f, Physik B59 (1985) pp. 223-243.

49, W. H. Zurek, “Pointer basis of quantum apparatus: Into what mixture does the

wavepacket collapse?” Phys. Rev. D24 (1981) pp. 1516-1525; W. H. Zurek, “Environment-induced superselection rules,” Phys. Rev. D26 (1982) pp. 1862-1880; W. H. Zurek, “Information transfer in quantum measurements: irreversibility and

amplification,” in Quantum Optics, Experimental Gravitation, and Measurement

Theory, eds. P. Meystre and M. O. Scully (New York, N. Y.: Plenum, 1983) pp. 87-116.

50. W. G. Unruh and W. H. Zurek, “Reduction of a wave packet in quantum Brownian motion,” Phys. Rev. D40 (1989) pp. 1071-1094. 51. J. B. Hartle, “Progress in quantum cosmology,” published in Proceedings of 12th International Conference on General Relativity and Gravitation, eds. N. Ashby, D. Bartlett, and W. Wyss (Cambridge, U.K.: Cambridge University Press, 1990).

52. M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge, U.K.:

Cambridge University Press, 1987); L. Brink and M. Henneaux, Principles of String Theory: Studies of the Centro de Estudios Cientificos de Santiago (New York, N. Y.:

Plenum,

1988).

358

REFERENCES

53. Wheeler, “Superspace and the nature of quantum geometrodynamics,” note 37; Hartle, note 51; S. W. Hawking, “The Boundary Conditions of the Universe,” in Astrophysical Cosmology, eds. H. A. Bruck, G. V. Coyne, and M. S. Longair (Vatican City: Pontificia Academic Scientiarum, 1982) pp. 563-594; A. Vilenkin, “Creation

of universes from nothing,” Phys. Lett. B117 (1982) pp. 25-28; J. B. Hartle and S. W. Hawking, “Wave function of the universe,” Phys. Rev. D28 (1983) pp.

2960-2975.

54, W. K. Wootters, “The acquisition of information from quantum measurements,” Ph.D. dissertation, University of Texas at Austin (1980); W. K. Wootters, “Statisti-

cal distribution and Hilbert space,” Phys. Rev. 23 (1981) pp. 357-362.

55, R. A. Fisher, “On the dominance ratio,” Proc. Roy. Soc. Edin. 42 (1922) pp.

321-341; R. A. Fisher, Statistical Methods and Statistical Inference (New York,

N. Y.: Hafner, 1956) pp. 8-17.

56. E. C. G. Stueckelberg, “Théoréme Het unitarité de S,” Helv. Phys. Acta 25 (1952) pp. 577-580; E. C. G. Stueckelberg, “Quantum theory in real Hilbert space,” Helv.

Phys. Acta 33 (1960) pp. 727-752.

57. D. S. Saxon, Elementary Quantum Mechanics (San Francisco: Holden, 1964). 58. H. J., Larson, Introduction to Probability Theory and Statistical Inference, 2nd ed. (New York, N. Y.: John Wiley,

1974).

59. E. Schrédinger, “The Foundation of the Theory of Probability,” Proc. Roy. Irish Acad. 51A (1947) pp. 51-66 and pp. 141-146; E. T. Jaynes, “Bayesian methods:

General background,” in Maximum Entropy and Bayesian Methods in Applied Statistics, ed. J. H. Justice (Cambridge, U.K.: Cambridge University Press, 1986) pp. 1-25; R. Viertl, ed., Probability and Bayesian Statistics (Singapore: World Scientific, 1987); R. D. Rosenkrantz, ed., E. T. Jaynes: Papers on Probability, Statis-

tics, and Statistical Physics (Hingham, Mass.: Reidel-Kluwer, 1989).

. P. J. Denning, “Bayesian learning,” American Sci. 77 (1989) pp. 216-218.

. J.O. Berger and D. A. Berry, “Statistical analysis and the illusion of objectivity,” American Sci. 76 (1988) pp. 159-165. . J. Burke, The Day the Universe Changed (Boston: Little, Brown,

1985).

. _F. Beck [pseudonym of the early nuclear-reaction rate theorist Fritz Houtermans]

and W. Godin: translated from the German original by E. Mosbacher and D. Porter,

Russian Purge and The Extraction of Confessions (London: Hurst and Blackett, 1951).

Wheeler, “World as system self-synthesized by quantum networking,” note 7. . D. Fellesdal, “Meaning and experience,” in Mind and Language, ed. S. Guttenplan

(Oxford: Clarendon, 1975) pp. 25-44.

. Wheeler, “Bits, quanta, meaning,” note 7.

+ G. Berkeley, Treatise Concerning the Principles of Understanding, Dublin (1710; 2nd ed. 1734); re his reasoning that “No object exists apart from mind,” cf. article

Berkeley by R. Adamson, Encyclopaedia Brittanica, Chicago 3 (1959) 438. 68. Hartle, note 51.

69. . T. Segerstedt, as quoted in Wheeler, “Frontiers of time,” note 7, p. 415.

REFERENCES

359

70. Wheeler, “The ‘past’ and the ‘delayed choice’ double-slit experiment,” note 7, p. 41. 71. Wheeler, “The ‘past’ and the ‘delayed choice’ double-slit experiment,” note 7; Miller and Wheeler, “Delayed-choice experiments and Bohr’s elementary quantum

phenomenon,” note 7.

72. Bohr, note 5.

B. Ya. B. Zel’dovich and I. D. Novikov, Relativistic Astrophysics, Vol. 1: Stars and Relativity (Chicago: University of Chicago Press, 1971).

74. G. F. Smoot et al., Structure in the COBE Differential Microwave Radiometer First-Year Maps, Astrophys. J. Lett. 396 (1992) pp. L1-L5. 75. Misner, Thorne, and Wheeler, note 7, p. 738, Box 27.4; or J. A. Wheeler, Journey into Gravity and Spacetime, note 1, Chap. 13, p. 242.

76. G. K. O'Neill, The High Frontier, 4th ed. (Princeton, N. J.: Space Studies Institute, 1989); R. Jastrow, Journey to the Stars: Space Exploration—Tomorrow and Beyond (New York, N. Y.: Bantam, 1989).

77. Wheeler, “World as system self-synthesized by quantum networking,” note 7. 78. K. Popper, Conjectures and Refutations: the Growth of Scientific Knowledge (New York, N. Y.: Basic Books, 1962).

79. R. W. Fuller and P. Putnam, “On the origin of order in behavior,” General Systems (Ann Arbor, Michigan) 12 (1966) pp. 111-121; R. W. Fuller, “Causal and Moral Law: Their Relationship as Examined in Terms of a Model of the Brain,” Monday Evening Papers (Middletown, Conn.: Wesleyan University Press, 1967); G. M. Edelman, Neural Darwinism (New York, N. Y.: Basic Books, 1987); W. H. Calvin,

The Cerebral Symphony (New York, N. Y.: Bantam, 1990).

80. W. W. Collins, The Moonstone (London, 1968); J. Allan Hobson, Sleep (New York, N. Y.: Scientific American Library, Freeman,

1989) pp. 86, 89, 175, 185, 186.

81. I. Langmuir, “Pathological Science,” 1953 colloquium, transcribed and edited, Phys. Today, 42, No. 12 (1989) pp. 36-48; N. S. Hetherington, Science and Objec-

tivity: Episodes in the History of Astronomy (Ames, Iowa: Iowa State University

Press, 1988); W. Sheehan, Planets and Perception: Telescopic Views and Interpretations (Tucson, Ariz.: University of Arizona Press, 1988).

82. M. White, Science and Sentiment in America: Philosophical Thought from Jonathan Edwards to John Dewey (New York, N. Y.: Oxford University Press, 1972).

83. C. S. Peirce, The Philosophy of Peirce: Selected Writings, ed. J. Buchler (London: Routledge and Kegan Paul, 1940), passages from pp. 335, 336, 337, 353, and 358; reprinted in Encyclopedia of Ignorance, ref. 7, pp. 593-595. Peirce’s position on

the forces of nature, “May they not have naturally grown up,” foreshadow though it

does the concept of world as self-synthesized system, differs from it in one decisive

point, in that it tacitly takes time as primordial category supplied free of charge from outside.

Parmenides of Elea [c. 515 B.C.450 B.C.], poem Nature, part Truth, as summa-

rized by A. C. Lloyd in article Parmenides, Encyclopaedia Brittanica, Chicago 17

(1959) 327,

360

REFERENCES

85.

G. E. Pugh, On the Origin of Human

Values (New York,

1976); “Human

Values,

86.

Follesdal, note 65.

87.

F. W. J. von Schelling [1775-1854], in Schellings Werke, nach der Originalaus-

Free Will, and the Conscious Mind,” preprinted in Zygon 11 (1976) pp. 2-24.

gabe in neuer Anordnung herausgegeben, 6 vols., ed. M. Schréter (Munich: Beck, 1958-1959), esp. Vol. 5, pp. 428-430, as kindly summarized for me by B. Kanitscheider: “dass das Universum von vornherein ein ihm immanentes Ziel, eine teleologische Struktur, besitzt und in allen seinen Produkten auf evolutionare Stadien

ausgerichtet ist, die schliesslich die Hervorbringung von Selbstbewusstsein einschliessen, welches dann aber wiederum den Entstehungsprozess reflektiert und

diese Reflexion ist die notwendige Bedingung fur die Konstitution der Gegenstinde

des Bewusstseins.”

"

88. J. von Neumann and 0. Morgenstern, Theory of Games and Economic Behavior (Princeton, N.J.: Princeton University Press, 1944); J. Wang, Theory of Games (New York, N. Y.: Oxford University Press, 1988).

89. J.R. Pierce, Symbols, Signals, and Noise: The Nature and Process of Communication (New York, N. Y.: Harper and Brothers, 1961); M. Schwartz, Telecommunica-

tion Networks: Protocols, Modeling and Analysis (Reading, Mass.: Addison-Wes-

ley, 1987); M. S. Roden, Digital Communication Systems Design (Englewood

Cliffs, N. J.: Prentice Hall, 1988).

90. P. W. Anderson, “More is different,” Science 177 (1972) pp. 393-396. 91. C. Mead and L. Conway, Introduction to VLSI [very large-scale integrated-circuit design] Systems (Reading, Mass.: Addison-Wesley, 1980); P. B. Schneck, Super-

computer Architecture (Norwell, Mass.: Kluwer, 1987).

92. Schwartz, note 89; Roden, note 89. 93. F.E. Yates, ed , Self-Organizing Systems: The Emergence of Order (New York, N. Y.: Plenum,

1987); H. Haken, Information and Self-Organization: A Macro-

scopic Approach to Complex Systems (Berlin: Springer, 1988); T. Kohonen, SelfOrganization and Associative Memory, 3rd ed. (New York, N. Y.: Springer, 1989).

94, C. Smorynski, Self-reference and Model Logic (Berlin: Springer, 1985). 95. G. J. Chaitin, Algorithmic Information Theory, rev. 1987 ed., (Cambridge, U.K.:

Cambridge University, 1988), J. P. Delahaye, “Chaitin’s equation; an extension of

Gédel’s theorem,” Notices Amer. Math. Soc. 36 (1989) pp. 984-987; J. F. Traub,

G. W. Wasilkowski, and H. Woznaikowski, Information-Based Complexity (San Diego: Academic, 1988); P. Young, The Nature of Information (Westport, Conn.:

Praeger-Greenwood,

1987).

96. W. H. Zurek, “Algorithmic randomness and physical entropy,” Phys. Rev. A40 (1989) pp. 4731-4751 . 97. M. Eigen and R. Winkler, Das Spiel: Naturgesetze steuern den Zufall (Munich:

Piper, 1975); W. M. Elsasser, Reflections on a Theory of Organisms (Frelighsburg,

Quebec: Orbis, 1987); G. Nicols and I. Prigogine, Exploring Complexity: An Introduction (New York, N. Y.: Freeman, 1989). 98.

S. Watanabe, ed., Methodologies of Pattern Recognition (New York, N. Y.: Aca-

REFERENCES

361

demic, 1967); J. Tou and R. C. Gonzalez, Pattern Recognition Principles (Read-

ing, Mass.: Addison-Wesley, 1974); H. Haken, ed., Pattern Formation by Dynamic Systems and Pattern Recognition (Berlin: Springer, 1979); H. Small and E. Garfield, “The geography of science: disciplinary and national mappings,” J. of Info. Sci. 11 (1985) pp. 147-159; M. Agu, “Field theory of pattern recognition,” Phys. Rev. A37 (1988) pp. 4415-4418; M. Minsky and S. Papert, Perceptions:

An Introduction to Computational Geometry, 2nd ed. (Cambridge, Mass.:

Massachusetts Institute of Technology Press, 1988); L. A. Steen, “The science of patterns,” Science 240 (1988) pp. 611-616; B. M. Bennett, D. D. Hoffman and C. Prakash, Observer Mechanics: A Formal Theory of Perception (San Diego:

Academic,

1989).

J. A. Wheeler, “Polyelectrons,” Ann. New York Acad. Sci. 46 (1946) pp. 219-238.

. D. Bohm, “The paradox of Einstein, Rosen, and Podolsky,” originally published as section 15-19, Chapter 22 of D. Bohm, Quantum Theory (Englewood Cliffs, N.J.: Prentice-Hall, 1950), reprinted in Wheeler and Zurek, note 4, pp. 356-368.

- W. H. Zurek, “Thermodynamic cost of computation: Algorithmic complexity and the information metric,” Nature 34 (1989) pp. 119-124.

102. E. F. Taylor and J. A. Wheeler, Spacetime Physics (San Francisco: Freeman, 1963) p. 102.

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Acknowledgments

A SEPTET OF SIBYLS: AIDS IN THE SEARCH FOR TRUTH was originally published in American Scientist 44, pp. 360-377 (1956). Copyrighted © 1956 by the Society of the Sigma Xi and reprinted by permission of the copyright owner. GENESIS AND OBSERVERSHIP copyrighted © 1977 by Dordrecht Holland, D. Reidel Publishing Company, Boston, Mass. All rights reserved. OUR UNIVERSE: THE KNOWN AND THE UNKNOWN reprinted from The American Scholar, volume 37, number 2, Spring 1968. Copyright © 1968 by the United Chapters of Phi Beta Kappa. THE MORALE OF RESEARCH PEOPLE was originally published in Discovery: Research and Scholarship at the University of Texas at Austin, volume 1, num-

ber 3, March, 1977, pp. 2-3.

BE THE BEST TO GIVE THE MOST unpublished, typescript dated February, 1983, address at 100th anniversary celebration of the University of Texas at Austin. TO NICOLAUS COPERNICUS this Copernicus dedication is abbreviated from a longer version which appears at the end of J. A. Wheeler, “The Universe as Home for Man,” O. Gingerich, ed., The Nature of Scientific Discovery (Wash-

ington, D.C.: Smithsonian Institute Press, 1975), pp. 292-293.

TO JOSEPH HENRY this dedication was previously unpublished. Photograph by Joseph Henry Laborstories, Princeton, University, of engraving by L. S. Punderson, based on a painting by F. Mooney. Engraved for the Annual of Scientific American, 1852. THE QUALITY OF COLLEAGUESHIP AT PRINCETON reprinted from Princeton Alumni

Weekly, volume 66, 1966, pp. 8-9.

NIELS BOHR AND NUCLEAR PHYSICS reprinted from Physics Today, volume 16, 1963, pp. 36-45 as reprinted in Niels Bohr Centennial Special Issue of Physics Today, volume 38, 1985, pp. 66-72. Articled adapted from the original address.

DELAYED-CHOICE EXPERIMENTS AND THE BOHR-EINSTEIN DIALOGUE updated for

publication in The American Philosophical Society and the Royal Society, Pa-

pers read at a Meeting June 5, 1980 (Philadelphia: The American Philisophical Society, 1981) pp. 11-40.

364

ACKNOWLEDGMENTS

THE OUTSIDER reprinted from condensation in Newsweek of March 12, 1979, 14, 1879—April

page 79. Original paper, titled “Albert Einstein, March 1955,” was published

ed. (Washington,

in C. K. McEuen,

18,

D. C.: National

Academy of Sciences, 1980), pp. 97-117. TO ALBERT EINSTEIN reprinted from the National Academy of Sciences Letters to

Members 9, number 3, June 1979, pages 1-3. This portrait by Frank Mahood

for frontpiece of Albert Einstein, The Human Side: New Glimpses from His

Archives,

selected and edited by Helen Dukas and Banesh

Hoffman

(Princeton,

N. J.: Princeton University Press, 1979).

NO FUGITIVE AND CLOISTERED VIRTUE reprinted from Physics Today, volume number 1, January 1963, pages 30-32.

16,

EINSTEIN AND OTHER SEEKERS OF THE WIDER VIEW reprinted from the Indianapolis Journal of Mathematics and Physics, volume 1-2, 1982-83, pages 1-25. MARIA SKLODOWSKA CURIE AND THE WORLD OF THE SMALL revised for publication in abbreviated form from Maria Sklodowska—Curie:

Proceedingds of a Symposium, 160, pages 1197-1200,

Warsaw,

Centenary Lectures;

17-20, 1967 and in Science, volume

1968.

HERMANN WEYL AND THE UNITY OF KNOWLEDGE Originally published in W. Deppert, ed., Proceedings of the Internationaler Hermann-Weyl-Kongress: Exakte Wissenschaften and thre philosphische Grundlegung, 1986.

HENDRIK ANTHONY KRAMERS reprinted from “Hendrik Anthony Kramers

(1894-1952), Yearbook of the American Philosophical Society, pages 355-360, 1953. HIDEKI YUKAWA

AS UNIQUELY

ECUMENICAL

reprinted from the Journal of the

Physical Society of Japan, volume 37, pages 324-325, 1982. DEALING WITH RISK originally published by the committee for the Niels Bohr International Gold Medal, 1982, for private distribution.

TO BENJAMIN FRANKLIN reprinted from The Franklin Institute News, Winter—Spring 1970, pages 6-7. Black-and-white photograph of the 1772 color portrait of Franklin by Charles Wilson Peale, based on the 1767 portrait by David Martin, Hall of the American Philosophical Society, Independence

Square, Philadelphia.

SCIENCE AND SURVIVAL reprinted from “Science and Survival,” in B. Baumrin,

ed., Philosophy of Science: The Delaware Symposium, (New York, N. Y.: Wiley-Interscience, 1963).

Volume 2, 1962-1963

THE PLACE OF SCIENCE IN MODERN LIFE reprinted from Sino-American Confernece on Intellectual Cooperation, Report and Proceedings (Seattle, Washington: Iniversity of Washington Department of Publication and Printing, 1960), pages 47-67.

ACKNOWLEDGMENTS

365

BEYOND THE BLACK HOLE reprinted from “Beyond the Black Hole,” in Harry Wolff, ed., Some Strangeness in the Proportion (Reading, Mass.: AddisonWesley, 1980), pages 341-375.

IT FROM BIT reprinted from “Information, Physics, Quantum: The Search for Links,” in Kobayashi et al., eds., Foundations of Quantum Mechanics in Light of New Technology, Komiyama Printing, Tokyo, 1990, pages 354-368. Almost identical version printed in W. Zurek, ed., Complexity, Entropy and the Physics of Information, Addison-Wesley, Redwood City, California, 1990, pages 3-28. Abbreviated version in Scienza & Tecnica, Annuario della EST, 90/91, pages 355-364,

1991.

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Index

Aharonov-Bohm effect, 297, 302-303 Analogy, as stimulus to creativity,

13,

16

“Anthropic principle” of Dicke and Carter, 36-38, 185

Baryons, 31, 281 Bekenstein, Jacob,

Causality, 114

185

Chicago project, 202 Christodoulou, D., 298

Clifford, William, 239 Collins, C.B., 24 117, 138,231

178

Bekenstein temperature,

179

Belinsky. V.A., 277

Compton, Arthur, 202 Conservation laws momentum, Convergent

Correspondence,

angular momentum, 279-281 singularity, 30, 277

Bohr, Aage, 110

Bohr, Niels, 5, 11, 18, 25, 40, 93-131, 138-143, 181, 193, 201, 231-232, 264

Bush, R.R., 9

Carlson, Chester, 148

14, 247

principle of, 17, 139,

177 Cosmic radiation, 95

Cosmological term, 54, 243

Crab Nebula, 47-49 Crick, Francis, 180, 259-261 Curie, Maria Sklodowska,

307

161-170,

112-131, 288

atom, 16 liquid-drop model, 93, 99, 106 W., 95 G., 97-98

Bremsstrahlung, 97

processes,

Copernicus, N., 83

Bethe H.A., 95 Big bang, 24, 28-31, 187 Black hole, 56, 178, 271

Bohr-Einstein dialogue,

10

particle number, 31, 281

120

Beta decay, 167

Bohr’s Bohr’s Bothe, Breit,

178,

Complementarity, principle of, 18-20,

Bekenstein number, 298

Berkeley, George,

Carter, Brandon, 24, 36-38,

Dams,

209-212

Darwin, Charles, 21, 23, 144 Davies—Unruh formula, 179 de Broglie, Louis, 115, 165 Defence, and technological advances,

256

Delayed-choice experiment,

288

118, 181,

368

INDEX

at cosmological scale,

124-127

Delbriick effect, 96

Deoxyribonucleic acid. See DNA Determinism,

232, 249

Dicke, R.H., 24, 36-38, 68 Dirac, P., 65-66, 113 Dirac’s large numbers,

185

Gauge field theory, 176, 273 Gauss, Karl Friedrich, General relativity, 24,

182 185, 233, 237

quantization, 60 tests of, 238

Genes, 179, 248 Geometrodynamics,

59, 228, 237, 240

Dispersion theory, 194

Geons, 241-242

DNA, 67, 179-180, 259-261

Grand unified field theory, 176 Gravitation, geometrical theory of, 28

Divergent processes,

14, 247

Dutch Dike System, 211-213

Gerlach, Ulrich,

177

. Gravitational collapse, 27-32, 50-53, 187

Eddington’s large-number coincidences, 185

Gravitational lensing, 124

Ehrenfest, Paul, Eigen, M., 45

193

Griinbaum,

Eigen, Manfred,

180

Einstein, Albert, 28, 53, 68, 112-131, 136, 157, 237-238, 243, 276, 284-285

Gravitational radiation, 58 A., 4

Hahn, O., 102

Handler, P., 79 Hartle, James,

Einstein—Podolsky—Rosen experiment,

Hawking,

Einstein’s field equations, 35, 276

Heisenberg,

39-44

Einstein’s theory of gravitation, 28

Elasticity, 32-33, 273

Electric charge, geometrodynamic models for, 241 Electromagnetism,

162,

187

Elementary particles, 65-66 Fermi, Enrico, 7, 204 Ferrara, S., 281

Feynman,

Richard, 206

Fisher, R.A., 304

Follesdal, D., 42, 305, 307-308 Franklin, Benjamin,

130, 223

Freedman, S.J., 40, 281 Friedmann, Alexander, 28-29, 242, 285 Friedmann model universe, 29

Friedmann-Einstein solution, 243 Galactic distances, 28 Gamma rays absorption, 101

anomalous scattering, 96

Gamow,

G., 102

Gamow penetration integral, 106

298

177

Stephen, 24, 59,

194-195

Werner,

115,

177-178, 117,

165,

Heitler, W., 165 Henderson, 1.j., 24, 38 Henry, J., 84

Hilbert, David, 182 Hill, D., 110 Hojman-K uchaf-—Teitelboim “imbeddability requirement,” 273-275 Hojman, S.A., 35 Holt, R.A., 40 Hopfield, John,

180

Hubble, Edwin, 285 Hubble time, 29, 54-55 Hume, David, 24, 186

Hydrogen bomb, 6, 73 Hypersurface,

274

Indeterminacy,

117

Indeterminism,

139

Intuition, 150 James,

W., 23

Jeffreys-Wentzel-Kramers-Brillouin method,

195

INDEX

369

Joos, E., 303

Natural numbers, continuum of, 189

Kalckar, F., 101

Neutron star, 51-53

Neutrino, 167

Kaluza, T.F.E., 176 Kant, Immanuel,

Neutrons, resonance capture of, 97 Newman, E.T., 277

182, 186

Kapitsa, P.L., 78, 261 Kelvin, Lord, 10, 168

Newtonian mechanics, 231

Kerr, R.P., 277

Nuclear constitution, models of,

Nordstrom, G., 277 Nuclear chemistry, 165

Kepler’s law, 32

Khalatnikov, I.M., 277 Kramers, Hendrik Anthony,

Kris, John, 296

99-109

191-196

Nuclear fission, 102-108, 201 Nuclear masses,

103

Kuchaf, K., 35

Nuclear physics, and Niels Bohr,

Langmuir, I., 14, 34

Nuclear quadruple moments,

93-111

Lawrence Livermore Laboratory, 73

Lee, T.D., 257-259 Leibniz, G.W., 183 Leptons,

Lewis, Gilbert N., 115 Lick Observatory group, 279 Life, 38, 247-249 on another planet, 234

Lifshitz, E.M., 59, 277

Light, bending by the sun, 53 Liquids, instability in, 14

Lorentz, Hendrick Antoon, 210

Los Alamos Scientific Laboratory, 73 Magnetic flux, 297, 302-303

Marsden, J.I., 276

Mass, geometrodynamic models for,

241 Matter, the origin of, 23 Maxwell, James Clerk, 145, 161

Maxwell’s theory, 162

Measurements, theory and principles of, 11

Missing matter, 57

145

Momentum, conservation of, 10 Morgenstern, Oskar, 175, 229

Mosteller, F., 9

Mott, N.F., 303

Three Mile Island accident, 217

Nuclear transformations,

110

Nuclear weapons control, Bohr’s memorandum,

141

Nucleotides, 260 Observer-participancy,

295-302, 305 Ockham, W., 70

36-44,

120,

Oort, Jan, 279 Oparin, A.I.,

180

Oppenheimer, R., 87

Ostriker, J.P., 28

Peebles, P.J.E., 28 Peierls, R., 101

Penrose, R., 298 Photon,

180

Meitner, L., 96, 102 Mendeleev, D.I., 145 Minkowski, Hermann,

radioactive wastes, 218-221 risk assessment, 206-212, 216

safety, 203

31, 281

Mayr, Ernst,

Nuclear reactors

108

115, 296

Physical laws, mutability of, 27-32 Placzek, G., 101, 105 Planck length, 64-66,

Plank, Max, 112, 115 Plutonium-239, 201 Podolsky,

169, 301

B., 39

Poincaré, H., 10

Polanyi, Michael, 227 Popper, Karl, 186, 307 Princeton University, 86-89, 172-174

Probabilistic risk assessment, 216

370

INDEX

Proton-electron mass ratio,

105

Spinoza,

Benedictus,

157, 284

Purcell, E., 78

Statistical analysis, 262-264 Statistical models, 245

Qadir, A., 277 Quantum, 59, 112-115, 164, 283, 290, 295-302

Stellar astrophysics, instability in, 14 Stockton, Alan, 125 String theory, 187

Quark-binding field, 273

Symmetry, 24, 32, 257-259

Quantum

Teitelboim, Claudio,

Quantum geometrodynamics, 60, 177, 242 Quasars, 48, 124-125

fluctuations,

170, 283

Supernova, 47-50 Superspace, 60-64

35, 280

Radiation protection, 204

Teller, Edward, 206 Thermonuclear combustion, 36

Rayleigh, Lord,

Thermonuclear explosions, 5

Rainwater, J., 108

103

Rayleigh-Taylor instability, 14 Reactor Safeguard Committee,

206-207, 216 Red shift, 53, 125

Thermonuclear defence, Thomson, J.J., 164

Thomson, William, 153 Thorne, K.S., 298 Time, 190

Regge, T., 38 Reissner, H., 277 Relict radiation, 27, 306

Tipler, F.J., 276 Townes, Charles, 279

Trial and error, 8

Riemann, Bernhard,

182, 238

Tukey, John Wilder,

Roosevelt, Franklin,

141-142

Universe, 47-70

Roger, J., 44 Rosen,

N., 39

Rosenfeld, L., 11

154, 262-264

closed model, 31-32, 276-279

deterministic, 229

Rossi B., 95

dynamic, 242-244

Salvini-Plawen, V., 180 Schrodinger, Erwin, 115, 117 Schrodinger state function, 40

Friedmann model, 29

Ruffini, R., 298 Rutherford, E., 94, 112

Schrédinger’s equation, 35, 68 Schwarzschild, K., 277

Science

in modern life, 252-267

and survival, 226-251 Singularity, models of, 28 Smith, Homer, 180

Solvay Congress, 1913, 165, 169

Sommerfeld, 194

Spacetime, 61-62,

curved, 237

110

176

as idealization, 282 at small distances, 239

symmetries of, 257

and elementary quantum phenomena, 128 expansion, 53-56 genesis of, 23-46 Hubble age, 29

participatory, 290-293, 296

Universe fine-structure constant, 37

Unruh, W.G.,

303

Uranium-235, 102, 105, 202

Uranium-238, 102, 105

Valence, 34, 281 van Nieuwenhuizen, P., 281 von Helmholtz, Hermann, 152-153 von Neumann, John, 175, 229 von Weizsacker, C.F., 95, 102

Watson, James, 180, 259-261 Wexler, Harry, 206

INDEX Weyl, Hermann, 171-191 Wheeler, John Archibald, 24, 28, 31, 35, 105,

107-110,

177, 272-273,

371 Yang, C.N., 257-259 Yang-Mills theory, 187, 272-274 Yukawa,

Heideki,

276-277, 279 Wigner, EP., 40, 42, 97-98

Zeh, H.D., 303

Winter, Norbert, 151

Se

Nt ska TE Winkler, R., 45 Wolman,

Abel, 206

197-198

Zel'dovich, Ya.B., 58-59 oe

Zwicky, Fritz, 185

Wootters, William, 297, 304

Xerography, 148

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