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Glimpsing Reality: Ideas in Physics and the Link to Biology Edited by Paul Buckley and F. David Peat
Twenty years ago Paul Buckley and F. David Peat asked several physicists, biologists, and chemists who had been involved in some of the most exciting discoveries in modem scientific thought to participate in the interviews that formed the heart of the book A Question of Physics: Conversations in Physics and Biology. Glimpsing Reality is an expanded version of that book.
The conversations - with Bohm, Pattee, Penrose, Rosen, Rosenfeld, Somorjai, Weizsacker, Wheeler, and Nobel prizewinners Heisenberg and Dirac, cofounders of quantum theory, and Prigogine - explore issues which have shaped modern physics and ones which hint at what may form the next scientific revolution. The discussions range over a set of basic problems in physical theory and their possible solutions - the understanding of space, time, and cosmology, the genesis of quantum theory and criticism of the standard interpretations of it, quantum and relativity theories and attempts to unite them and the conceptual links between physics and biology. The approach is nontechnical, with an emphasis on the basic assumptions of modem science and their implications for understanding the world we live in.
All of the original interviews have been preserved. An introduction has been added to expand the thematic content of the mini-introductions preceding each interview. A new conversation (between the editors) has been added, a dialogue that places the fundamental ideas of quantum theory in a broad perspective to include work on chaos theory and superstring theory. Also new to this volume are two original essays that further develop the main thrust of the text - an exploration of the boundaries between physics and biology with the supervening idea being quantum theory and problems of its interpretation.
PAUL BUCKLEY was formerly associate professor of chemistry at l'Universite Laval. He has been science adviser to several government agencies and was, in 1992-3, Visiting Scientist in the Department of Physiology and Biophysics at Dalhousie University.
F. DAVID PEAT is a physicist and author of many books, including Einstein's Moon: Bell's Theorem and the Curious Quest for Quantum Reality; Superstrings and the Search for the Theory of Everything; and Synchronicity, the Bridge between Matter and Mind.

Glimpsing Reality: Ideas in Physics and the Link to Biology
EDITED BY PAUL BUCKLEY AND F. DAVID PEAT
UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

© University of Toronto Press Incorporated 1996 Toronto Buffalo London Printed in Canada
ISBN 0-8020-0575-6 (cloth) ISBN 0-8020-6994-0 (paper)
Revised and expanded edition of A Question of Physics: Conversations in Physics and Biology (University of Toronto Press 1979).
Printed on acid-free paper
Canadian Cataloguing in Publication Data
Main entry under title: Glimpsing reality : ideas in physics and the link
to biology Rev. ed. Previously published under title: A question of physics. ISBN 0-8020-0575-6 (bound) ISBN 0-8020-6994-0 (pbk.) I. Physicists - Interviews. 2. Biologists Interviews. I. Buckley, Paul, 1938- . II. Peat, F. David, 1938- . III. Title: A question of physics. QC15.B83 1995 530 C95-932356-2
University of Toronto Press acknowledges the financial assistance to its publishing program of the Canada Council and the Ontario Arts Council.

TO OUR PARENTS

Contents
Preface to the Revised Edition 1x Preface to the First Edition xi Introduction to the Revised Edition xiii CONVERSATIONS Werner Heisenberg 3 Leon Rosenfeld 17 David Joseph Bohm 34 Carl Friedrich von Weizsacker 61 Paul Adrien Maurice Dirac 70 Roger Penrose 77 John Archibald Wheeler 87 llya Prigogine 98 Robert Rosen, Howard Hunt Pattee, and Raymond L. Somorjai: a symposium in theoretical biology 111 F. David Peat and Paul Buckley: reflections after twenty years 151 ESSAYS Paul Buckley: evolution and quantum consciousness I 6 I Robert Rosen: the Schrodinger question: What is life? fifty years later 168 Appendix: the troubles of quantum theory 191 Glossary 195

Preface to the revised edition
Twenty years ago we asked several physicists, including two of the cofounders of quantum theory, Werner Heisenberg and Paul Dirac, to participate in the interviews which form the heart of this book. The present work is an expanded version of A Question of Physics, which appeared in 1979. All of the original interviews have been preserved without change. An introduction has been added to expand the thematic content of the mini-introductions preceding the conversations. A new conversation has been added, which is intended as a kind of update on developments since the first edition appeared, and two original essay-type contributions have been included to further develop some of the ideas presented in the main text.

Preface to the first edition
This book contains interviews with physicists, biologists, and chemists who have been involved in some of the most exciting discoveries in modern scientific thought. Some time ago we approached the Canadian Broadcasting Corporation with a proposal for a series of radio programs in which the revolutions taking place in physics during the last fifty years could be explored. The series would attempt to re-create the elation and argument, the disappointment and confusion, which physicists experienced during the origins of the quantum theory, along with some of the more exciting developments in quantum and relativity theories. By presenting science through the voices of its practitioners we hoped to convey a vivid, if at times unpolished, first-hand account. The resulting interviews are the origin of the present book, in which we have preserved the tempo and integrity of the original dialogues by indulging in the minimum amount of editing.
The success of the venture depended to a great extent upon the enthusiasm of the scientists we interviewed, and here we feel lucky in having selected physicists who have not only made important contributions to human thought but have also the ability to transmit their ideas clearly and directly.
In selecting topics for discussion we have betrayed our own prejudices. Rather than dwell upon the successes of modern physics we have explored the cracks in its fifty-year-old fa~ade. We have concentrated on areas which, we feel, hint at the next scientific revolution. Perhaps in this context we own an apology to an important group of scientists - those engaged in elementary particle research. Some physicists feel that the search for 'ultimate building-blocks of matter' is one of the most promising modern areas of research. It was our belief, however, that there are

xii Preface
deeper questions to be explored, and that the goal of 'the most fundamental particle' is somewhat of a throwback to the presuppositions of classical physics.
We have also included in this book, which is otherwise concerned with the problems of physics, a round-table discussion on theoretical biology. This young subject has all the intellectual challenge and excitement associated with physics in the twenties. Possibly in reading of the biologist's responses to his present difficulties we may be better able to understand the situation which faced physicists at a time when no atomic theory existed and there was simply an accumulation of spectroscopic data and a new and confusing quantum principle. The discussion also provides an example of the way in which traditional boundaries between the sciences are erased as similar questions are raised and mathematical techniques employed in diverse disciplines.
We hope that this book will serve as a useful overview for the practitioner of science and, at the same time, give the non-scientist some understanding of the revolution which has taken place in our understanding of the world. It was our intention to avoid technical terms and maintain a level of discussion accessible to a broad audience, but at times the scientists we interviewed became involved in questions which have troubled the scientific community for nearly half a century. They are to be excused for occasionally forgetting that 'the collapse of the wave function,' 'nonclassical logic,' and 'the Copenhagen interpretation' are not topics which the average family discusses over morning coffee. We trust that our short appendix will be helpful in providing a background for such questions.
For assistance in the preparation of the manuscript, we extend our deepest thanks to Jane Wykes, who cheerfully undertook the arduous task of verifying the transcripts with the original tapes and typed the first edited version.
PAUL BUCKLEY
F. OA VIO PEAT

Introduction to the revised edition
One of the things which makes physical theory intellectually attractive to many persons is the great amount of discussion which characterized quantum theory during its early stages and which continues enthusiastically, if less intensely, at the present time. Today there is fresh discussion centred on the foundations of quantum mechanics, and it appears that those foundations are not as firm as one had earlier thought. Though quantum mechanics is, in its formalism and in its detailed practice, extremely hard edged and very successful, it does invite alternative interpretations which are competing for attention. It seems to some that the revolution in science, which accompanied the early days of the century that is drawing to a close, is not yet finished despite the outstanding efforts of many great minds. But one really need not ask whether the revolution is finished for there are always the voices of dissent, and good questions keep getting asked even if decades go by before true attention is paid to them. All this just adds to the excitement which currently prevails in physics and which likely influences the work of other disciplines and activities. At the same time, however, one finds a note of seriousness, not to say unease, as a characteristic of the present mood.
Werner Heisenberg and Leon Rosenfeld are this book's spokespersons for the standard interpretation, also known as the Copenhagen interpretation, and they comment extensively upon its characteristics. Heisenberg calls the interpretation abstract, and possibly this has been a stumbling-block for some physicists, though the limitations of using ordinary language in physical descriptions are evident. Heisenberg and Rosenfeld communicate very clearly their sensitivities on the issue of language and the boundaries of classical concepts. They also give us many insights on the conditions of the origin of the quantum theory, thus leaving us with valuable pointers for contemporary studies in the history and philosophy of science. Of course, the interpretation may

xiv Introduction to the revised edition

be formulated more rigorously than can be set out in these two interviews, but

most would admit that it is good to hear the story from those near the centre of

the action in the discussions of the 1920s in Copenhagen, Gottingen, and other

European cities.

There is one alternative interpretation which has been recently pointed to

in the pages of Scientific American (May 1994) and this is David Bohm's

'ontological interpretation.' It is a serious contender among some theoretical

physicists, biding its time until the day arrives and the orthodox interpretation

no longer maintains its general acceptance. In his interview David Bohm

explores meaning in a probing critique of attitudes in physics. Once again the

question of the use of language is brought into the foreground where it

belongs. The feeling that there is something newly positive about quantum

theory is exemplified by Carl Weizsacker, who directs our attention to tense

logic and to the issue of human time. He also discusses historical perspectives

as they might apply to our period and this theory.

Paul Dirac surely represents the many physicists who remain untroubled by

problems of interpretation; in his interview he resolutely refuses to talk about

it. He prefers instead to comment upon certain cosmological issues, but he

does make a few remarks on the then current state of theoretical physics. We

are especially glad to have this interview as it is one of the very few that he

consented to give. The interview with Roger Penrose introduces some of his

imaginative work on twistors and the nature of space-time. John Wheeler

ranges over geometrical ideas of space and time and also opens up some of the

inner feelings possible in science, pointing toward its beauty. Wheeler also

believes that the quantum theory allows us to feel that we are participating

~ith Nature in the unfolding universe.

•

Ilya Prigogine firmly states a belief in participation based upon his results

in the field of irreversible thermodynamics involving dissipative structures.

This work seems to open out toward a biological frame and the more sophis-

ticated notions of order which life sustains. Life itself is the subject of the

mini-symposium involving Howard Pattee, Robert Rosen, Raymond Somor-

jai, and the co-authors. It becomes the locus of a spirited search for coherence

in life's complexity and how best to grasp it. They attempt to demonstrate

how physics and biology might relate in a more fruitful way than is found at

present.

Along with its sharp edges and hard-won understanding, quantum mechan-

ics may stimulate new feelings of participation in Nature. 'Evolution and

Quantum Consciousness' by Paul Buckley is a series of reflections studying

the implications of the coexistence of a theory of evolution and a quantum the-

ory. In his essay, 'The Schrodinger Question: What Is Life? Fifty Years Later,'

Robert Rosen examines some of the consequences for biology of asking this

question today in Schrodinger's own manner. And because Erwin Schrodinger

xv Introduction to the revised edition
is one of the co-founders of the quantum theory this makes another connection for us between the sciences of matter and the sciences of life which are presented in this book.

Conversations

Werner Heisenberg
While a student of Arnold Sommerfeld at Munich in the early 1920s Werner Heisenberg (1901-75) first met the Danish physicist Niels Bohr. He and Bohr went for long hikes in the mountains and discussed the failure of existing theories to account for the new experimental results on the quantum structure of matter. Following these discussions Heisenberg plunged into several months of intensive theoretical research but met with continual frustration. Finally, suffering from a severe attack of hay fever, he retreated to the treeless island of Helgoland. After days spent relaxing and swimming Heisenberg suddenly experienced the giddy sensation of looking down into the heart of nature and conceived the basis of the quantum theory. He took this theory to Bohr at Copenhagen, and for the next few weeks they argued and probed its implications long into the night. The results of these discussions became known as the 'Copenhagen interpretation of quantum theory' and are accepted by most physicists. Aspects of the interpretation include Heisenberg's uncertainty principle and Bohr's principle of complementarity.
Heisenberg made other important discoveries in physics, and became one of the most distinguished physicists of the century. He was awarded the Nobel Prize for Physics in 1932. His scientific attitudes reflect a debt to philosophy and in particular his respect for Plato. Some of his thoughts on science and society are recorded in a readable autobiography entitled Physics and Beyond.
In recent years Heisenberg adopted the unpopular position of criticizing research in elementary particle physics and proposing that symmetries and not elementary particles form the fundamental starting-point for a description of the world. Towards the end of this chapter he touches upon this theory and its reception.

4 Werner Heisenberg
Professor Heisenberg was interviewed one sunny morning in his office at the Max Planck Institute in Munich. We began by asking Heisenberg to recall the early days of quantum theory but it became apparent that great men have no desire to live in the past and he was just as eager to talk about the future of physics.
DP Could you reminisce about the time when you arrived at the idea of quantum mechanics?
At that time, there was general discussion among young physicists about the possible ways to establish a coherent quantum theory, a coherent quantum mechanics. Among the many attempts, the most interesting for me was the attempt of H.A. Kramers to study the dispersion of atoms and, by doing so, to get some information about the amplitudes for the radiation of atoms. In this connection, it occurred to me that in the mathematical scheme these amplitudes behaved like the elements of a mathematical quantity called a matrix. So I tried to apply a mathematical calculus to the experiments of Kramers, and the more general mechanical models of the atom, which later turned out to be matrix mechanics. It so happened at that time I became a bit ill and had to spend a holiday on an island to be free from hay fever. It was there, having good time to think over the questions, that I really came to this scheme of quantum mechanics and tried to develop it in a closed mathematical form.
My first step was to take it to W. Pauli, a good friend of mine, and to discuss it with him, then to Max Born in Gottingen. Actually, Max Born and Pascual Jordan succeeded in giving a much better shape and more elegant form to the mathematical scheme. From the mathematical relations I had written down, they derived the so-called commutation relations. So, through the work of Born and Jordan, and later Paul Dirac, the whole thing developed very quickly into a closed mathematical scheme.
I also went to discuss it with Niels Bohr, but I can't be sure whether this was in July, August, or September of that year [1925).
Half a year later the first papers of E. Schrodinger became known. Schrodinger tried to develop an older idea of Louis de Broglie into a new mathematical scheme, which he called wave mechanics. He was actually able to treat the hydrogen atom on the basis of his wave mechanical scheme and, in the summer of 1926, he was also able to demonstrate that his mathematical scheme and matrix mechanics were actually two equivalent mathematical schemes, that they could be simply translated into each other. After that time, we all felt that this must be the final mathematical form of quantum theory.

5 Werner Heisenberg
DP Had you and Bohr begun the interpretation ofthis work before Schrodinger 's paper came out?
Of course, there was continuous discussion, but only after Schrodinger's paper did we have a new basis for discussion, a new basis for interpreting quantum theory. In the beginning there was strong disagreement between Schrodinger and ourselves, not about the mathematical scheme, but about its interpretation in physical terms. Schrodinger thought that by his work physics could again resume a shape which could well be compared with Maxwell's theory or Newton's mechanics, whereas we felt that this was not possible. Through long discussions between Bohr and Schrodinger in the fall of 1926, it became apparent that Schrodinger's hopes could not be fulfilled, that one needed a new interpretation. Finally, from these discussions, we came to the idea of the uncertainty relations, and the rather abstract interpretation of the theory.
PB Did Schrodinger ever like that interpretation?
He always disliked it. I would even guess that he was not convinced. He probably thought that the interpretation which Bohr and I had found in Copenhagen was correct in so far as it would always give the correct results in experiments; still he didn't like the language we used in connection with the interpretation. Besides Schrodinger, there were also Einstein, M. von Laue, M. Planck, and others who did not like this kind of interpretation. They felt it was too abstract, and too far removed from the older ideas of physics. But, as you know, this interpretation has, at least so far, stood the test of all experiments, whether people like it or not.
PB Einstein never really liked it, even until the day he died, did he?
I saw Einstein in Princeton a few months before his death. We discussed quantum theory through one whole afternoon, but we could not agree on the interpretation. He agreed about the experimental tests of quantum mechanics, but he disliked the interpretation.
DP / felt that at some point there was a slight divergence between your views and Bah,- 's, although together you are credited with the Copenhagen interpretation ofquantum mechanics.
That is quite true, but the divergence concerned more the method by which the interpretation was found than the interpretation itself. My point of view was that, from the mathematical scheme of quantum mechanics, we had at least a partial interpretation, inasmuch as we can say, for instance, that those eigenvalues which we determine are the energy values of the discrete stationary states, or those amplitudes which we determine

6 Werner Heisenberg
are responsible for the intensities of the emitted lines, and so on. I believed it must be possible, by just extending this partial interpretation, to get to a complete interpretation. Following this way of thinking, I came to the uncertainty relations.
Now, Bohr had taken a different starting-point. He had started with the dualism between waves and particles - the waves of Schrodinger and the particles in quantum mechanics - and tried, from this dualism, to introduce the term co111ple111entari(11, which was sufficiently abstract to meet the situation. At first we both felt there was a real discrepancy between the two interpretations, but later we saw that they were identical. For three or four weeks there was a real difference of opinion between Bohr and myself, but that turned out to be irrelevant.
nr Did this ha1•e its origin in your d(!krent plulosophical approaches?
That may be. Bohr's mind was formed by pragmatism to some extent, I would say. He had lived in England for a longer period and discussed things with British physicists, so he had a pragmatic attitude which all the AngloSaxon physicists had. My mind was formed by studying philosophy, Plato and that sort of thing. This gives a different attitude. Bohr was perhaps somewhat surprised that one should finally have a very simple mathematical scheme which could cover the whole field of quantum theory. He would probably have expected that one would never get such a self-consistent mathematical scheme, that one would always be bound to use different concepts for different experiments, and that physics would always remain in that somewhat vague state in which it was at the beginning of the 1920s.
DP In the interpretation you gave at that time, you seemed to imply that there did exist an ideal path and that somehow the act ofmeasuring disturbed the path. This is not quite the same as the inte1pretation that you hold now, is it?
I will say that for us, that is for Bohr and myself, the most important step was to see that our language is not sufficient to describe the situation. A word such as path is quite understandable in the ordinary realm of physics when we are dealing with stones, or grass, etc., but it is not really understandable when it has to do with electrons. In a cloud chamber, for instance, what we see is not the path of an electron, but, if we are quite honest, only a sequence of water droplets in the chamber. Of course we like to interpret this sequence as a path of the electron, but this interpretation is only possible with restricted use of such words as position and velocity. So the decisive step was to see that all those words we used in classical physics - position, velocity, energy, temperawre, etc. - have only a limited range of applicability.

7 Werner Heisenberg
The point is we are bound up with a language, we are hanging in the language. If we want to do physics, we must describe our experiments and the results to other physicists, so that they can be verified or checked by others. At the same time, we know that the words we use to describe the experiments have only a limited range of applicability. That is a fundamental paradox which we have to confront. We cannot avoid it; we have simply to cope with it, to find what is the best thing we can do about it.
DP Would you go so far as to say that the language has actually set a limit to our domain ofunderstanding in quantum mechanics?
I would say that the concepts of classical physics which we necessarily must use to describe our experiments do not apply to the smallest particles, the electrons or the atoms - at least not accurately. They apply perhaps qualitatively, but we do not know what we mean by these words.
Niels Bohr liked to tell the story about the small boy who comes into a shop with two pennies in his hands and asks the shopkeeper for some mixed sweets for the two pennies. The shopkeeper gives him two sweets and says 'You can do the mixing yourself.' This story, of course, is just meant to explain that the word mixing loses its meaning when we have only two objects. In the same sense, such words as position and velocity and temperature lose their meaning when we get down to the smallest particles.
DP The philosopher Ludwig Wittgenstein originally started offby thinking that words were related to facts in the world, then later reversed his position to conclude that the meaning ofwords lay in their use. Is this reflected in quantum mechanics?
I should first state my own opinion about Wittgenstein's philosophy. I never could do too much with early Wittgenstein and the philosophy of the Tractatus logico-philosophicus, but I like very much the later ideas of Wittgenstein and his philosophy about language. In the Tractatus, which I thought too narrow, he always thought that words have a well-defined meaning, but I think that is an illusion. Words have no well-defined meaning. We can sometimes by axioms give a precise meaning to words, but still we never know how these precise words correspond to reality, whether they fit reality or not. We cannot help the fundamental situation - that words are meant as a connection between reality and ourselves - but we can never know how well these words or concepts fit reality. This can be seen in Wittgenstein's later work. I always found it strange, when discussing such matters with Bertrand Russell, that he held the opposite view; he liked the early work of Wittgenstein and could do

8 Werner Heisenberg
nothing whatsoever with the late work. On these matters we always disagreed, Russell and I.
I would say that Wittgenstein, in view of his later works, would have realized that when we use such words as position or velocity, for atoms, for example, we cannot know how far these terms take us, to what extent they are applicable. By using these words, we learn their limitations.
DP Would it be true to say that quantum mechanics has modified language, and, in turn, language will re-modify the interpretation ofquantum mechanics?
There I would not quite agree. In the case of relativity theory, I would agree that physicists have simply modified their language; for instance, they would use the word simultaneous now with respect to certain coordinate systems. In this way they can adapt their language to the mathematical scheme. But in quantum theory this has not happened. Physicists have never really tried to adapt their language, though there have been some theoretical attempts. But it was found that if we wanted to adapt the language to the quantum theoretical mathematical scheme, we would have to change even our Aristotelian logic. That is so disagreeable that nobody wants to do it; it is better to use the words in their limited senses, and when we must go into the details, we just withdraw into the mathematical scheme.
I would hope that philosophers and all scientists will learn from this change which has occurred in quantum theory. We have learned that language is a dangerous instrument to use, and this fact will certainly have its repercussions in other fields, but this is a very long process which will last through many decades I should say.
Even in the old times philosophers realized that language is limited; they have always been sceptical about the unlimited use of language. However, these doubts or difficulties have, perhaps, been enhanced through the present developments in physics. I might mention that most biologists today still use the language and the way of thinking of classical mechanics; that is, they describe their molecules as if the parts of the molecules were just stones or something like that. They have not taken notice of the changes which have occurred in quantum theory. So far as they get along with it, there is nothing to say against it, but I feel that sooner or later, also in biology, one will come to realize that this simple use of pictures, models, and so on will not be quite correct.
PB At what point does the transition occur from the non-path to the path in a biological system? Is a DNA molecule already a classical object, or is a cell a classical object?

9 Werner Heisenberg
There is, of course, not a very well defined boundary; it is a continuous change. When we get to these very small dimensions we must be prepared for limitations. I could not suggest any well-defined point where I have to give up the use of a word. It's like the word mixing in the story; you cannot say 'when I have two things, then I can mix them.' But what if you have five or ten? Can you mix then?
PB It seems to me that there is something very important here about language. We are living beingsjormedfrom coherent stmctures like DNA and we apparently have classical paths and our existence is understandable within this language. But then we can analyse by reducing these complex, coherent wholes to smaller and smaller parts, and is it not perhaps this process ofreduction that is at the root ofthe paradox?
I would say that the root of the difficulty is the fact that our language is formed from our continuous exchange with the outer world. We are a part of this world, and that we have a language is a primary fact of our life. This language is made so that in daily life we get along with the world; it cannot be made so that, in such extreme situations as atomic physics, or distant stars, it is equally suited. This would be asking too much.
PB Is there a fundamental level ofreality?
That is just the point; I do not know what the words jimdamental reality mean. They are taken from our daily life situation where they have a good meaning, but when we use such terms we are usually extrapolating from our daily lives into an area very remote from it, where we cannot expect the words to have a meaning. This is perhaps one of the fundamental difficulties of philosophy: that our thinking hangs in the language. Anyway, we are forced to use the words so far as we can; we try to extend their use to the utmost, and then we get into situations in which they have no meaning.
DP In discussing the 'collapse ofthe wave function' you introduced the notion ofpotentiality. Would you elaborate on this idea?
The question is: 'What does a wave function actually describe?' In old physics, the mathematical scheme described a system as it was, there in space and time. One could call this an objective description of the system. But in quantum theory the wave function cannot be called a description of an objective system, but rather a description of observational situations. When we have a wave function, we cannot yet know what will happen in an experiment; we must also know the experimental arrangement. When we have the wave function and the experimental arrangement for the special case considered, only then can we make predictions. So, in that

IO Werner Heisenberg
sense, I like to call the wave function a description of the potentialities of the system.
oP Then ihe interaction with the apparatus would be a potentiality coming into actuality?
Yes.
DP May I ask you about the Kantian notion ofthe 'a priori,' an idea which you introduced, in a modified sense, into your discussions a/quantum theory.
As I understand the idea of 'a priori,' it stresses the point that our knowledge is not simply empirical, that is, derived from information obtained from the outer world through the senses and changed into data in the content of our brain. Rather, 'a priori' means that experience is only possible when we already have some concepts which are the precondition of experience. Without these concepts (for instance, the concepts of space and time in Kant's philosophy), we would not even be able to speak about experience.
Kant made the point that our experience has two sources: one source is the outer world (that is, the information received by the senses), and the other is the existence of concepts by which we can talk about these experiences. This idea is also borne out in quantum theory.
PB But these concepts are part of the world also.
Whether they belong to the world, that is hard to say; we can say that they belong to our way of dealing with the world.
PB But we belong to the world, so, in a sense, these activities of ours also belong to the world.
In that sense, yes.
DP You modified the 'a priori' by introducing it as a limited concept, is that true?
Of course, Kant would have taken the 'a priori' as something more absolute than we would do in quantum theory. For instance, Kant would perhaps have said that Euclidean geometry would be a necessary basis for describing the world, while we, after relativity, would say that we need not necessarily use Euclidean geometry; we can use Riemannian geometry, etc. In the same way, causality was taken by Kant as a condition for science. He says that if we cannot conclude from some fact that something must have been before this fact, then we do not know anything, and we cannot make observations, because every observation supposes that there is a causal chain connecting that which we immediately experience to that

11 Werner Heisenberg
which has happened. If this causal chain does not exist, then we do not know what we have observed, says Kant. Quantum theory does not agree with this idea, and in fact proves that we can even work in cases where this causal chain does not exist.
DP In a recent theory ofyours, is not causality retained, perhaps in a new form?
We have causality in that sense - that in order to influence something, there must be an action from one point to the next point; no action can happen if there is not this connection. But at this point one gets into rather complicated details.
DP But, even so, you do have causality predicated on the idea ofseparation and action, so this again comes back to a philosophical level: what you mean by separation, and by interaction.
We must speak about 'interaction' and 'separation,' that is quite true, and we use the terms as we did in classical theory. But, again, we see limitation. Complete separation of two events may be possible in classical theory; it is not possible in quantum theory. So we use the terms together with the fact of their limitation.
DP What exactly are the criteria for something to be classical?
I would say the criteria are simply that we can get along with these concepts (e.g. 'position,' 'velocity,' 'temperature,' 'energy'}, and so long as we get along with them, then we are in the classical domain. But when the concepts are not sufficient, then we must say that we have gone beyond this classical domain.
Every system in physics (forget for the moment about biological systems) is always quantum theoretical, in the sense that we believe that quantum theory gives the correct answers for its behaviour. When we say that it is classical, we mean that we do get the correct or the necessary answers by using classical concepts (at least in that approximation in which we can describe the system by classical concepts). So a system is classical only within certain limits and these limits can be defined.
DP How would you include things like irreversibility?
Thermodynamics is a field which goes beyond Newtonian mechanics, inasmuch as it introduces the idea of thermodynamic equilibrium, or canonical distribution as W. Gibbs has put it. Thermodynamics leaves classical physics and goes into the region of quantum theory, for it speaks about situations of observation; it does not speak about the system as it is, but about the system in a certain state of being observed, namely in the

l 2 Werner Heisenberg
state of temperature equilibrium. If this equilibrium is not obeyed, then we cannot use thermodynamics. So the whole concept of irreversibility is bound up with the concept of thermodynamic equilibrium.
DP And is this ultimatelv connected with the idea ofa classical limit to something? I am thinking ofthe measurement problem that always seems to be associated with an irreversible process: that we have a de.finite result.for a quantum mechanical system where the quantum mechanics itse{fdoesn 't seem to predict a definite result. That is, the idea ofa quantum mechanical measurement seems to be tied up with the idea ofan irreversible trend.
Yes, to some extent, because on the side of the observer we do use classical concepts. The idea that we do observe something already indicates something irreversible. If we draw a pencil line on a paper, for instance, we have established something which cannot be undone, so to speak. Every observation is irreversible, because we have gained information that cannot be forgotten.
DP To what extent is this related to the symmetry-breaking ofthe quantum mechanical system where one gets classical observables?
I would not like to connect it with symmetry-breaking; that is going a bit far. We try to describe the observational situation by writing down a wave function for the object and the equipment which is in interaction with this wave function. Just by using classical words for the equipment, we have already made the assumption of irreversibility. Or we make the assumption of statistical behaviour, because the mere use of classical words for this observation on the side of the system makes it impossible to know the total wave function of object and equipment. But we cannot use quantum theory for the equipment in a strict sense, because if we wrote down the wave function for the object and the equipment, we could not use classical words for the equipment, so we would not observe anything. We do observe only when we use classical concepts, and just at this point this hypothesis of disorder, of statistical behaviour, comes in.
DP With regard to something like ferromagnetism, the quantum mechanical system has given rise to a macroscopic ordering. Is it true to say that a quantum mechanical system has actually broken its own symmetry and given rise to a classical variable, without any talk about a measuring apparatus, or anything exterior to the system?
Let us consider a ferromagnet as isolated from the rest of the world for some time, and then ask what the lowest state of the system is. We find, from the quantum mechanical calculations, that the lowest state is one in which the whole system has a very large component of magnetic momen-

13 Werner Heisenberg
tum. If we then ask 'what do we observe when we consider this system?' we see that it is convenient to ascribe the classical variable 'magnetic momentum' to the system. So we can use classical terms to describe this quantum mechanical behaviour. But this is not really a problem of observation, only a problem of how the lowest state of the system is defined.
PB How does quantum mechanics deal with time flow or does it in fact say anything at all about it?
I would have to repeat what C. von Weizsacker said in his papers: that time is the precondition of quantum mechanics, because we want to go from one experiment to another, that is from one time to another. But this is too complicated to go into in detail. I would simply say that the concept of time is really a precondition of quantum theory.
PB In the domain where quantum mechanics operates, all ofthe equations are reversible with respect to time, except for one experiment I believe. So time has more to do with macroscopic classical systems than microscopic quantum systems.
I would say that irreversibility of time has to do with this other system, with those problems which I. Prigogine describes in his papers, and is certainly extremely important for the macroscopic application of quantum theory, and also for biology, of course.
DP Can we talk about a new theory ofyours, the non-linear theory of elementary particles? Are you ultimately going to introduce things like gravitation into this theory, and go over to a picture in which space and time emerge?
Again, we have a similar situation as in ferromagnetism. We try to solve the quantum mechanical, or quantum theoretical equation, but we can see that the system acquires properties which then can be described by classical language (e.g. like speaking of a magnetic momentum, etc.). We are hoping that such phenomena as electromagnetic radiation and gravitation also can come out of the theory of elementary particles, and we have reasons to believe that this is so.
DP The idea ofsymmetry is a very important part ofyour theory.
Let's begin more simply by speaking about quantum mechanics, disregarding now the difficulties of elementary particle physics. In quantum mechanics we see that macroscopic bodies have very complicated properties, complicated shapes and chemical behaviour and so on. Coming down to smaller and smaller particles, we finally come to objects which are really very much simpler, for example the stationary states of a hydrogen atom. We describe its properties by saying that these states are a represen-

14 Werner Heisenberg
tation of the fundamental symmetries, such as rotation in space. So when we describe a system by writing down a few quantum numbers (in hydrogen atoms, we have the principal quantum number and the angular momentum number) this means that we know nothing except to say that this object is a representation of symmetries. The quantum numbers tell us which kind of symmetries we mean; the numbers themselves say that this object has these special properties. Thus, when we come to the smallest objects in the world, we characterize them in quantum mechanics just by their symmetry, or as representations of symmetries, and not by specifying properties such as shape or size.
DP There are symmetries that are not related to operations in the world, e.g. the internal symmetries such as isospin. What meaning do they have? Do you think they are related ultimately to the properties ofspace and time?
I suspect that isospin is a symmetry similar to space and time. I cannot say that it is related to them. I would say that there are a number of fundamental symmetries in this world which may in future be reduced to something still simpler, but so far we must take them as given, as a result of our experiments. One of the most fundamental symmetries is the symmetry of the Lorentz group, that is space and time, and then isospin groups, scale groups, and so on. So there are a number of groups which are fundamental in the sense that in describing the smallest particles we refer to their behaviour and transformations.
The idea is that one can distinguish between a natural law, a fundamental law, which determines for instance a spectrum of elementary particles, and the general behaviour of the cosmos, which is perhaps something not at once given through this law. I might remind you, for instance, of Einstein' s equations of gravitation. Einstein wrote down his field equations and thought that gravitational fields are always determined by them. But the cosmos is not unambiguously determined by these field equations, although there are several models of the cosmos which are compatible with them. In the same sense, I would say that there is an underlying natural law which determines the spectrum of elementary particles, but the shape of the cosmos is not unambiguously determined by this law. Logically, it would be possible to have various types of cosmos which are in agreement with it. However, if a certain cosmological model has been 'chosen,' then this model, of course, has some consequences for the spectrum of elementary particles.
DP Are you saying that there exist laws which are independent or outside the universe, outside the world, which reality breaks, or that it breaks the symmetry represented by the laws?

15 Werner Heisenberg
'Laws' just means that some fundamental symmetries are inherent either in nature or in our observation of nature. You may know about the attempts of Weizsacker, who tried to derive the laws simply from logic. We have to use language to arrive at conclusions, to study alternatives, and he questions whether from the alternatives alone we can arrive at these symmetries. I don't know whether his attempts are successful or not. In physics, we can only work with the assumption that we have natural laws. If we have no natural laws, then anything can happen, and we can only describe what we see, and that's all.
DP Anotherjeature ofyour theo,y which seems to go against the current trend- partons and quarks, etc. - is that youjeel that no particle is any more elementa,y than any other.
Even if quarks should be found (and I do not believe that they will be), they will not be more elementary than other particles, since a quark could be considered as consisting of two quarks and one anti-quark, and so on. I think we have learned from experiments that by getting to smaller and smaller units, we do not come to fundamental units, or indivisible units, but we do come to a point where division has no meaning. This is a result of the experiments of the last twenty years, and I am afraid that some physicists simply ignore this experimental fact.
DP So it would seem that elementary particles are just representations of symmetries. Would you say that they are notfundamental things in themselves, or 'building-blocks ofthe universe,' to use the old-fashioned language?
Again, the difficulty is in the meaning of the words. Words like buildingblocks or really existing are too indefinite in their meaning, so I would hesitate to answer your questions, since an answer would depend on the definitions of the words.
DP To be more precise, ultimately could one have a description ofnature which needed only elementary particles or, alternatively, a description in which the elementary particles would be defined in terms ofthe rest ofthe universe? Or is there no starting-point, as it were, no single axiom on which one can build the whole ofphysics?
No. Even if, for instance, that formula which Pauli and I wrote down fifty years ago turned out to be the correct formulation for the spectrum of elementary particles, it is certainly not the basis for all of physics. Physics can never be closed, or brought to an end, so that we must turn to biology or such things. What we can hope for, I think, is that we may get an explanation of the spectrum of elementary particles, and with it also an

16 Werner Heisenberg
explanation of electromagnetism and gravitation, in the same sense as we get an explanation of the spectrum of a big molecule from the Schrodinger equation.
This does not mean that thereby physics has come to an end. It means that, for instance, at the boundary between physics and biology, there may be new features coming in which are not thought of in physics and chemistry. Something entirely new must happen when I try to use quantum theory within the realm of biology. Therefore I criticize those formulations which imply an end to physics.
DP Is it ever possible to reduce physics or any element ofphysics purely to logic and axioms?
I would say that certain parts of physics can always be reduced to logical mathematics or mathematical schemes. This has been possible for Newtonian physics, for quantum mechanics, and so on, so I do not doubt that it will also be possible for the world of the elementary particles. In astrophysics today, one comes upon pulsars and black holes, two regions in which gravitation becomes enormous, and perhaps a stronger force than all other forces. I could well imagine that in such black holes, for instance (if they exist), the spectrum of elementary particles would be quite different from the spectrum we now have. In the black holes, then, we would have a new area of physics, to some extent separated from that part which we now call elementary particle physics. There would be connections, and one would have to study how to go from the one to the other; but I do not believe in an end of physics.

Leon Rosenfeld
The Copenhagen interpretation of quantum theory, which grew out of discussions between Niels Bohr and Werner Heisenberg, included Leon Rosenfeld (1904- 75) as one of its major proponents. Born in Charleroi, Belgium, Rosenfeld made his intellectual home in the Copenhagen of Bohr. In addition to his discoveries in theoretical physics Rosenfeld became the major apologist of the Copenhagen school after Bohr's death.
Our interview with Professor Rosenfeld took place in Copenhagen and was one of his first activities after suffering a heart attack. Later we dined with the Rosenfelds and, after spirited discussions, toasted the memory of his friend and colleague Niels Bohr.
Rosenfeld's contribution to this book is important since it deals with the interpretation of quantum theory and is possibly his last exposition on this topic. In entering a world in which the properties of an object appear to change as a result of their observation, scientists were forced to abandon their comfortable belief in material 'entities' which 'possessed' particular properties. The Copenhagen interpretation is an attempt to give an account of this new world which is intellectually satisfying and avoids the pitfalls and paradoxes generated by earlier attempts to understand the quantum theory. Professor Rosenfeld discusses the way in which we must treat knowledge of the world below the atom.
From a historical point of view Rosenfeld makes interesting observations when he discusses the differences in approach between Bohr and Heisenberg, which may have led to subtle divergences in their interpretation of quantum theory. These differences are hotly denied by Heisenberg in his interview.

18 Leon Rosenfeld
PB Projcssor Rosenfeld, you worked closely with Niels Bohr for many years. Could H'l' beKin with some personal reminiscences (!(him?
When I first knew Niels Bohr in the 1930s there were not so many of us working in the institute, perhaps only half a dozen. He would come up every morning, since his house was near the institute, and if he met us on the stairs by any chance, the conversation could continue on the stairs for hours, or indeed at any place in the institute.
We learned that it was by those conversations that he could express himself. Whenever he had to write something down, being so anxious about complementarity, he felt that the statement contained in the first part of the sentence had to be corrected by an opposite statement at the end of the sentence. That made writing a paper a terrible business. But in conversation, it was easier: we could interrupt him, and put questions to him.
He would become completely lost in thought, even to the point of not realizing where he was. He took a walk with Klein on the day of Klein's wedding, and they nearly arrived too late! I remember I frequently travelled between Belgium, where I had my job, and Copenhagen, and once I had put my wife and child on the train, and I had the tickets in my pocket, when Bohr called to tell me an idea which he just had some hours before and which he wanted me to know before I departed. I was torn away from this conversation by the call of the station-master announcing the departure of the train. I still remember my wife's face!
PB What was your.first work with Bohr?
The first thing I did was to help him to write down his Faraday lecture. You see, his method was to dictate a sentence, as an experiment, and then this sentence was contemplated and criticized and changed and fussed over, and so on. I was supposed to react to each sentence, to criticize, etc. That was one kind of work I did for him.
Then, very soon afterwards, there came a paper by L. Landau and R.
Peierls which raised a very fundamental question about whether the field concept could be given a consistent meaning in quantum theory. In our work on this problem at first nothing could be written down, because we knew nothing at all in the beginning. We did not know whether the answer would be yes or no, and, in fact, we did not know that before the thirteenth or fourteenth proof. Every word was weighed, and every sentence has a subtle meaning, subtle in the sense that complementarity is always underlying the whole thing.
DP People speak about the Copenhagen inte1pretation with very different meanings. Could you outline what Bohr really meant?

19 Leon Rosenfeld
The phrase 'Copenhagen interpretation' is actually a misnomer, in the sense that there is only one interpretation of quantum mechanics. Bohr would rather say that quantum mechanics is a whole. It is a formalism of course, a mathematical formalism, but it is also a physical theory, and therefore definite physical meanings are attached to the symbols. It is only when you take the whole thing, that is, the formalism and the meanings attached to the symbols, that you have a physical theory. The misunderstandings that have been expressed so vociferously from various sides are based on a disregard of this circumstance. They take the formalism and then they try to put upon it what they call an interpretation, without reflecting that the way in which the equations are written already implies a definite interpretation, that is, a definite relationship between the symbols and physical concepts. It is not arbitrarily that Heisenberg constructed those matrix equations and those commutation rules. He was forced to those commutation rules. In fact, he did not know beforehand that such a non-commutative algebra would come out of his effort to give a mathematical form to a clear physical idea, that is, the idea of correspondence. Therefore, you can approach this conceptual aspect of quantum mechanics only historically, because it is very much conditioned by the way in which the pioneers (Heisenberg foremost, and then Dirac very soon afterwards, and Bohr) were led to this curious new use of mathematics in order to translate into mathematical language physical ideas which were clearer than the mathematics, and not the other way around.
You see, when you first approach quantum mechanics, as a student, it is reasonable that your first effort is to understand the equations and how to handle them. And then you ask: what is the meaning of all this? And if you are for some reason afraid of statistics or of probability, then you ask yourself: could it perhaps be otherwise? That was D. Bohm's way, actually. He gave a lecture on quantum mechanics (probably the first one that he gave on this subject) and he made a book out of it. This is a very good book, a very good exposition of quantum mechanics. But it was in the process of writing the book that he had doubts about the whole thing. However, his attitude was such that he put mathematics first and he tried to hang the physics onto the mathematics, without thinking that the natural process was just the opposite.
DP /don't think it would be fair to say that this has been Bohm 's view for the last ten years.
No. Bohm, because he is a very serious and honest thinker (and I respect him very much), at long last realized that his first approach simply did not work. But that did not mean that he was converted, like Paul on the road to Damascus. He had no such stroke as Paul had on that road. He kept his

20 Leon Roscnl'cld
original attitude of mind, and he is now trying something different, but still always with the same outlook, which I call an idealistic outlook. He gives primacy to building concepts out of nothing. I mean, the mind is able to build any constellation of concepts.
PB But it is ultimately based on experience too.
Of course, I quite agree. But those I call idealists do not go so far. They stop there; they stop at the concepts, and they say that these are the primary building-stones. This is an illusion. But that's Bohm's outlook and he is now trying to dig deeper into the analysis of the concept of space and time, based on altering events. This is certainly a very true analysis; at least it has a great element of truth, I think. Nevertheless, I believe it's not the way that has proved successful in getting to a new insight in physics.
DP Heisenberg and Bohr theories are spoken oftogether by many people as the Copenhagen interpretation. But I Jee/ there is a d/lJcrence.
Heisenberg had been trained in the German school by A. Sommerfeld, not only by Sommerfeld but by the whole German environment of the time, in which great weight was put on a philosophy - the Kantian philosophy - which happened to be the dominating philosophy, whereas Bohr was quite immune, that is, he had not been exposed to Kantian philosophy. However, he, also, had followed a course of philosophy at the university, which was given by Hoffding, a Danish philosopher. I would not call Hoffding an eclectic, but rather he looked upon philosophy as being au-dessus de la melee, that is, outside the province of philosophers. In fact, in the preface to his course he said: 'I am concerned in this course to present the philosophical problems, and not the solutions, because the solutions come and go, but the problems remain.' Bohr was therefore protected from any dogmatism or any reliance upon a priori ideas. He insisted upon first understanding the physics, and then trying to put it into a mathematical form.
s DP Did Bohr not have great respect for William James psychology?
Yes, but I think that Bohr knew very little - practically nothing - about William James until 1935 or 1936. I remember at that time he was great friends with one of his colleagues, Rubin, one of the Gestalt psychologists. In a conversation, Rubin said to him: 'what you tell me reminds me very much of William James.' It's simply a coincidence of attitudes. James came first of course. James had very much the same approach to psychology as Bohr had to physics; that's all one can say. So when Bohr got the copy of James's treatise from Rubin, and read the chapter on the stream of thought, he was quite enthusiastic about it. That I remember

21 Leon Rosenfeld
very vividly, because each one of us - at that time there were not so many - had to read the chapter and share his enthusiasm.
I knew James before because I had read about him and pragmatism and the rest of it. So for me this was rather natural; I had already noticed that Bohr's attitude was pragmatic.
DP I seem to remember some anecdotes about investigating the mind or thoughts, or thought examining itse(/: that Bohr used to tell his students.
At that time, Bohr thought very deeply about the expression of thought, that is, how we express thoughts, and how we use words. This is very characteristic, because it pervaded all his thinking in physics also. He liked W. Gibbs, because Gibbs started from a word of the common language, e.g. 'temperature,' which had a clear observational definition, and tried to connect it with an atomistic picture. That is an approach that Bohr liked, and when he thought about words and the way in which we use words in order to express our thoughts, he noticed that we use the same word in two very different meanings. We use a word to express our affections or emotions, e.g. we use the word anger when speaking of ourselves when we feel angry, also in describing a state of consciousness; but I can also say 'you look angry,' and there we use the word to describe not a state of consciousness, but a state of bodily activity and behaviour: the kind of behaviour which expresses anger. He noticed that this creates the risk of ambiguity, if you confuse the two; but a necessary ambiguity, because it is the only way for us to communicate our emotions; I can only know that you are angry if you tell me, or if you behave in a certain way which I interpret and identify with my state of consciousness concerning anger. It is a very deep feature of human language that it contains this ambiguity.
At that time, Bohr used a mathematical analogy with many-valued functions, a logarithmic function, for instance, which has a singular point at the origin. If you follow a path, as long as you do not go around the origin, you have a continuous variation, and you remain in the same sheet of the Riemann surface. But if you go around the origin, you reach another sheet of the Riemann surface, corresponding to a different set of values of the logarithmic function. So he said: when we discuss the state of behaviour, we must remain on the behaviour surface, and be careful not to spring over to the surface of consciousness, which is a different one. So, each word is a singularity, or is connected with a singularity, in our way of understanding existence.
PB It strikes me that what is implied here is the subject/object dichotomy.
That's it. This complementarity arises when we are the object of our own observation. We are at once subjects and objects. That is the very peculiar

22 Leon Rosenfeld
characteristic of consciousness. It is also connected with the problem of freedom of will. All the discussions about freedom of will are generally spoiled by this confusion: that will is the feeling that you have a free choice between different possibilities at the time you make a decision, but that happens on a different plane, and the concept of liberty is then no more applicable.
PB So, in .fact, Bohr ·s ideas in physics really had roots in philosophical perception.
Yes. He was well prepared to recognize the physics. A situation like that is completely alien to any Kantian attitude of mind.
PB Yet Heisenberg, even though a Kantian and perhaps even a Platonist, was able to understand, and was also ready.fi-o,n his point of view.for the problems in physics at that time.
That's all to the honour of Heisenberg, that he did understand Bohr at that stage, though not without a struggle. Heisenberg discovered the uncertainty relations; the background was the following.
They felt very strongly that, although quantum mechanics in the matrix formulation of Heisenberg was a complete theory, a complete logical scheme, it still did not provide a ready explanation of aperiodic phenomena. It was essentially a theory constructed for periodic systems or mul.1 tiperiodic systems. That is a point that Pauli insisted upon. And in fact Schrodinger, who came out of the blue to Copenhagen (I mean to the body of knowledge in Copenhagen), provided the answer unwittingly. He had quite different ideas. He thought that he had destroyed quantum mechanics, but Pauli was quick to see, and Bohr too then, that Schrodinger's formalism provided just the way to describe aperiodic phenomena. In fact the first application of quantum mechanics that Bohr made was to the study of collisions. The two schemes were equivalent. So that was the situation.
Heisenberg {it is very curious) did not recognize the situation for a while, because he was rather stubborn and he said 'my formalism is complete, nobody denies that, and therefore it must contain the answer to the question of what is observable and what is not.' He believed that he had put into his formalism only observable things and discarded things that were not observable, like the orbits of the electrons and so on.
But Pauli said: 'It is not true that orbits are not observable. The orbit of the moon is observable. So there is something missing in our understanding of what is observable and what is not.'
Then Heisenberg remembered a conversation he had with Einstein in which he tried to explain his theory of observables - that he had put only

23 Leon Rosenfeld

observables in his theory. To this Einstein retorted: what is observable or not is not for us to decide, but for the theory! So when he was confronted with this problem, he remembered that remark of Einstein, and by concentrating on it, he discovered that the answer given by quantum mechanics to the question 'what is observable and what is not?' is contained in the commutation rules from which we derive the uncertainty relations. They give the reciprocal limitation on the kind of things that one can observe.
When he had the commutation rules, he thought that he had solved the whole problem. But Bohr was not satisfied. Bohr was of course very much impressed by the uncertainty relations and he saw quite clearly that they provided essentially the answer to the problem. But it was not yet formulated with sufficient precision.
Heisenberg had tried to illustrate the meaning of the uncertainty relations by a famous microscope experiment, his gamma-ray microscope. He got the idea from a conversation with a colleague, while still a student. His friend asked: 'How could we see an electron?' - more or less as a joke. His argument, when he remembered this, was that if we look at an electron with gamma rays, then, by the Compton effect, the electron is scattered in a certain direction. Therefore, when we look at it, we disturb its momentum, we lose the momentum: that was one illustration that he gave.
Bohr seized upon that, because he saw that it was quite wrong. Bohr admitted that it was true that the electron gets a new momentum from the Compton effect, but he said that we can calculate the change of momentum, and therefore correct for it. So it is not something which we cannot know or observe.

DP Also, Heisenberg's argument presupposed the existence ofthe electron with a very precise momentum and position, which was disturbed by the observation.

Yes. Bohr immediately rejected that view. He showed by closer analysis of

the process that the uncertainty in the determination of the position was

due to the angular aperture of the beam which was necessary to form an

image, and that it was just this angular aperture which caused an uncer-

tainty in the direction in which the electron would be emitted. That

difference was the uncertainty in the momentum, and everything came

out all right.

•

DP At this point, it's not true to say the electron had an orbit or a path, in the classical sense ofthe words, which was implied in Heisenberg's work?

No, certainly not. It was an instantaneous state of affairs in which neither at the beginning nor at the end could you see a definite position or mo-

24 Leon Rosenfeld
mentum. This led Bohr to develop his analysis. He saw that the uncertainty relations implied two ways of looking at atomic objects which were mutually exclusive, when you pushed the idealization to the extreme.
DP This is analogous to the remark you made earlier about disrnssing thoughts.
Yes, he saw again the same mutual exclusiveness of points of view, which were both, of course, necessary. There was no question of eliminating one of them.
DP It would not be correct then to say that the electron had a path.
No. The first implication is that we cannot use mechanical and kinematical concepts as attributes of atomic objects. They express a relationship between the atomic object and a certain apparatus which we construct in such a way that the indication of the apparatus expresses, or defines, the concept in question. We have an apparatus from which we deduce what we call the position; we have another apparatus from which we can derive what we call the momentum. We can apply either apparatus to the object; that is our decision. We get the response. But if we have made it with one apparatus, we lose the possibility of controlling the complementary aspect.
DP More recently, Heisenberg speaks about potentialities. Again, thaf-isn 't the same as Bohr's interpretation, is it?
When you use such a vague word as potentiality, you can give it whatever meaning you like. The wave function or the state vector, whatever you call it, may be said to contain an infinity of potential answers to the question. Once you have made a measurement, let us say of position, then you get the wave function which is localized, which is a wave packet containing many values of the momentum, if you analyse it. Here one can use the word potentiality. Bohr was never acquainted with this idea of Heisenberg, but I can guess the way he would have taken it. He would have said: 'Well, that's a word, "potentiality"! If it is useful, all right, let us use it.' But I, personally, don't see this particular use.
DP When we were talking to Heisenberg recently, I made the same point: that I felt this was not quite the inference Bohr had in mind. Heisenberg said that he felt he and Bohr were in complete agreement. I think you 're implying that you don't feel that this is true.
Well, no. I can understand Heisenberg. He said the same to me once when we discussed the philosophical background. Because I have good relations with Heisenberg I could tell him that he was an idealist, and that I did not like that attitude. And he said: 'Yes, yes, I see; I can understand

25 Leon Rosenfeld
that you have a different attitude, but the interesting thing for me is that on physics we agree completely.' That is typical, I think, of the idealist. He tries to make a distinction between the way in which he behaves when he is a physicist, or biologist, or whatever, and what he talks about when he behaves as a philosopher. Pasteur used to say that when he entered his laboratory he left his religious faith in the cloakroom. I don't think it is a reasonable attitude at all. But Heisenberg has a right to say, according to his own attitude, that he felt in complete agreement with Bohr. I can understand that. The disagreement only starts when Heisenberg begins to talk about Plato and having rediscovered numerical relationships, fundamental symmetries, and so on.
DP Bohm has told me that nobody really understood Bohr's mind. It is a most subtle thing. The only person who could really tell you would be Rosenfeld.
I should say that Heisenberg could do it much better. But one who understood Bohr fully and deeply was Pauli. It is again a case of not separating the general, let us call it philosophical, from the scientific attitude. You cannot understand Bohr if you try to judge, or to analyse what he says, while projecting on to his statements postulates taken from Kantian philosophy, from the idea that things have attributes. That creates a sort of barrier between what you try to read and what Bohr wanted to express.
Bohr's approach always was to say: here we have a situation which is given to us as observers, that is, as beings reacting with the universe. We have developed what is called ordinary language, which is a system of concepts by which we describe our direct observations. It is perhaps refined in physics, in microscopic physics, in classical physics, by quantitative denominations and so on. Fundamentally it is always a system for the description of our perceptions and our reactions - in general, our experience. His attitude was to consider those things as given and therefore not to be discussed. Or, at least, their discussion was another matter; it was the job of the psychologists to analyse methods of perception and the function of the senses, etc. But the job of the physicist was to start from this given experience, this given knowledge, and then to organize it into a coherent whole by using logic, since logic also is given. After all, logic is the way in which we connect various statements according to rules which are such that the conclusion is inescapable when we apply the rules.
DP Did he mean logic in the sense ofa set ofrules which was observed to work in the classical world, or was it logic in the sense ofsomething to do with mental operations?
It is, of course, a mental operation; we are also part of the world. But there had been several attempts by J. von Neumann and others to say that

26 Leon Rosenfeld
quantum mechanics necessitated a new logic. Bohr was always very much against such propositions.
He considered logic also as a part of experience. He was influenced in that by his brother, Harald, the mathematician, who was at that time very much involved with the famous quarrel among mathematicians, the formalists like Russell against L.E.J. Brouwer and the intuitionists. He did not mention Brouwer, but he was certainly very much against Russell.
He favoured the intuitionists, although I would not make too definite a statement about that. Anyway, it is again a pragmatic attitude, towards logic and mathematics, just as towards our physical experience or any experience whatsoever.
In order to understand complementarity, you must first put yourself at that starting-point; otherwise you miss the point. If you are a strict logician, you will say: if it is mutually exclusive, then one of the two is false, one is right. That is obviously not the case.
PB Historically, quantum physics comes after classical physics, and we have had several hundred years of Newton and Galileo. That's quite a long timejiJr the language to absorb all the implications andjimdamental meanings ofc/assical science. The transition from Greek to Newtonian physics was also d[fjicu/t, and required a great change in language; perhaps we could even predict eventually a quantum type language, in which such concepts as complementarity may disappear, or may be seen as something deeper.
Bohr once told me that he hoped that after a while, when people get used to it, as you say, complementarity would be something quite natural, taught in schools, etc.
DP I think Bohr had a rigorous view oflanguage - that it would never be possible to talk about experience other than with the language ofthe classical world, that it would never be possible to have an understanding ofquantum mechanics with a quantum mechanical language.
In a sense, it is simply a question of scale. We are macroscopic objects and therefore our only approach to atoms is by the intermediary of microscopic instruments. The eye can, at the limit, perceive two or three quanta, but that's an extreme case, and not the normal way in which we use our eyes.
DP So that language puts a barrier on any deeper, any further understanding ofquantum mechanics?
I would not say that. It makes the understanding non-trivial and different from the understanding of macroscopic phenomena. Bohr's aim - and I think he has attained it by introducing the idea of complementarity - was

27 Leon Rosenfeld
to make a full understanding, in the sense of description, of the behaviour of atoms possible for us.
DP Would it be true to ~ay that Bohr acrualfF pllf a limitation on the questions that we may ask, as a result o/"la11g11age?
No. His point was that there was no limitation to our possibility of describing the behaviour of atoms, provided we used the language at our disposal (the only language that is at our disposal), with due precautions which were indicated by the concept of complementarity and the interpretations.
DP When Einstein auempred to give an objective interpretation o,/rhe wave function, Bohr more or less took this as a limit on the sort o,/questions one can ask, did he nor?
Yes, surely. Complementarity implies that there are certain questions which become meaningless. For instance, 'what is the position and the momentum of a given particle?' - that is a meaningless question. But we know that it is meaningless beforehand; the theory tells us.
PB Is there a disti11crio11 between a meaningless question and an unanswerable one?
If it is meaningless, it is also unanswerable. But the fact that we cannot answer it does not imply any restriction upon our possibilities of accounting for all possible experience that we can have with atomic objects. Our experience of atomic objects is naturally limited by the difference of scale. There are only certain experiments that we can make. We cannot see an electron between our fingers of course.
PB I was thinking o,/'pure/y statistical questions, where for some reason ii becomes meaningless to try to describe the behaviour ofan individual in a ve,y large collection. That is, in a sense, an unanswerable question, and it's also meaningless, and yet does not introduce a quantum idea.
or It is not meaningless to say that you cannot describe a single particle in a
classical ensemble. I think meaningless is much more precise. fla statement is meaningless, its comradiction has no meaning also. Ifelt that Bohr was coming to the point ofsaying that some statements were meaningless.
PB In the sense of not being falsifiable.
He had no connection at all with K. Popper, or with positivism in general. I think it would be quite wrong to connect Bohr's attitude with positivism as it is practised by people called positivists.
DP Would it be tme to say that there are some statements which are meaningless: e.g. a square circle is a meaningless thing?

28 Leon Rosenfeld
Yes, but you see they are meaningless so far as they go against the scope of the theory. Here I must make a caveat, because we are not speaking of quantum mechanics as being the last word - that is obvious. It has limited scope; and Bohr always insisted on this. No theory is more than an idealization, good enough for a certain domain of experience; what happens beyond that is a quite different problem. Heisenberg expressed this idea once: in a certain sense, classical mechanics is a perfect theory, and an eternal truth which will never be questioned in any way, although we know that it is not correct for very large motions, or very fast motions.
But with regard to this meaninglessness: the fact that certain questions about the individuality of atomic particles are meaningless is not related, as Buckley said, to the quantum idea. But complementarity is not limited to the particular case of quantum mechanics. There is another complementarity between the direct macroscopic observation of thermodynamics on the one hand, and the atomistic description of the same system on the other. They are also complementary.
PB Because thermodynamics does not require any detailed molecular theoty.
Right, and it is there that the lack of individuality of the particles comes
in. It also comes in, of course, in quantum mechanics, and there have
been endless discussions among the younger generations as to whether the wave function describes a single electron or only an ensemble. Even Einstein raised that question. For Bohr, there was never any question; it was obvious that we are talking of an ensemble. As soon as we introduce statistics, we are talking of an ensemble, because statistics is made just for that. Probability implies a comparison of many similar cases with different outcomes. So there's no question; it's no problem.
DP It is meaningless to talk about the wave Jimction for one electron.
It refers to one electron put under certain conditions of observation, and
that is the important point to remember - that the apparatus is part of the description.
DP I felt from reading other people '.s intetpretations that Bohr had almost put a
limitation on what we could ask, and I consider that's not really true.
No, that's not true. Originally, Bohr thought that there was a limitation - he used the word resignation, which implies that you must abandon something about causality. That was, for some time, his idea, and even at the Solvay conference in 1927, where the famous confrontation with Einstein occurred, he used that point of view. But then he realized that the lack of deterministic causality does not mean lack of causality at all, but

29 Leon Rosenfeld
that a statistics is another kind of causality. Then he abandoned this misleading terminology.
Einstein played a very essential part there. He was dissatisfied with this apparent resignation, this apparent abandonment of causality. The only kind of causality which people inoculated with Kantian philosophy had was deterministic causality. So, at the Solvay conference in 1927 Einstein first tried to disprove both arguments, to find counter-examples. In the beginning, Einstein was in fact more ingenious than Bohr, in designing fancy gedanken experiments which would lead to conclusions contradicting the uncertainty relations. But Bohr learned the game very quickly, and he refuted all Einstein's proposals.
In the end, Einstein realized that there was no such trivial contradiction in quantum mechanics. In fact, he accepted quantum mechanics fully; that you can see from his letters, especially from his very interesting and revealing correspondence with Besso, which has just been published. So, if Einstein opposed quantum mechanics, it was not at all because he did not understand any point of it. But he said: 'Es widerspricht meinem innersten Geftihl' - it contradicts my innermost feelings. So he put the question in the domain of feelings, or philosophical prejudice.
PB Wouldn't you translate it as intuition?
Einstein did not use that word, and I don't think he wculd have, because we have no intuition of how atoms are going to behave, no intuition at all about atoms. Intuition is perceiving, in a single act, a wholeness with many relationships, which allows one to see relationships that others do not see.
I think intuition is actually a mental operation in the same way that logic is. It is a kind of short-cut that you can allow yourself when you see a whole network of logical relations. Then you have to work it out carefully to see that you have not missed anything. Intuition is a logical operation. Some people speak of having an intuition of how an electron will behave in certain circumstances, but that is a very abstract kind of intuition. It's not that they visualize the atoms in any way, but that they have a formal intuition of the workings of the differential equations.
PB Would you say that we have no intuition ofatoms, because ofthe nature of our language, which is a language ofeveryday objects?
Yes. Atoms are not part of everyday language; they are connected by specific definitions with concepts of ordinary language.
PB By the self-consistent approach which you and Professor Prigogine and others have taken, with regard to relations between dynamics and thermo-

30 Leon Rosenfeld
dynamics, dissipative structures and biological systems, you arc implying, in a sense, that all you can ever get is a se{[-consistent view ofthe world, rather than an Einsteinian one, which is almost a divine one. So it does connect up, doesn't it .1 Could you talk a little about your recent work in this _field?
What we try to do there is just to develop and to express in a precise formalism this complementarity between the thermodynamic or macroscopic aspect and the atomic one.
PB You ha1·e introduced the observer in the loop?
Yes, surely. This is not the first time that this connection has been attempted, but one has always done it by introducing brute force, let us say, a statistical element, which is called 'mixing' in the jargon. It comes from Gibbs's analogy - mixing milk and coffee and getting a homogeneous mixture, whereas one knows that the molecules are not at all homogeneously distributed. So the homogeneous aspect is macroscopic because we renounce a more detailed localization of the molecules, but only consider them from a distance, so to speak, and eliminate most of the parameters assigned to the individual molecules.
Now, that is a purely classical way of speaking, and it was good enough for classical statistics. But translating this into quantum theory is another thing. Von Neumann had tried it, and, one must say, had not actually succeeded. Localizing a quantum particle and introducing a momentum distribution at the same time - this gets you into conflict with the uncertainty relations. Of course, there are tricks. E. Wigner has introduced a very neat and elegant trick to get around that, but it is just a trick and does not give any satisfying solution.
Now, Prigogine's idea was to consider infinite systems so as to get rid of the periodicity which is inherent in the mechanical behaviour of finite systems. If it is infinite, then the period becomes infinite also. So you consider only a stretch, so to speak, a necessarily finite stretch of an evolution, which has no end in the finite. You can even push away the beginning to minus infinity, if you like. Then, if you try to determine the asymptotic behaviour of such an infinite system, you do find that the phase relations are automatically eliminated from the asymptotic density function without any necessity of explicitly introducing a statistical element. The statistical element is there, of course, but it is contained, inherently, in the whole description, so that the mixing is produced by the system itself and not by any imposed coarse-graining. The coarse-graining is inherent in the behaviour of the system itself. This puts the complementarity on a similar footing to the complementarity of quantum mechanics, where also it is not our doing that there is this complementarity

31 Leon Rosenfeld
between position and momentum; it is a consequence of the existence of the quantum of action, the fact that the atoms are not able to interchange action except in multiples of a unit.
PH How docs this complementarity tie in, now, with irrevi:'rsibility and time .flow? For instance, Weizsti"cker 's work introduces time on a ve1y.fi111damentaf level. This seems ve,y ne1r in physics.
Yes, we realize that the mixing, which in Gibbs's conception was the element producing this irreversible behaviour, occurs as a consequence of the dynamics of the system. The irreversibility which is a consequence of this mixing is inherent in the behaviour of the system - even in purely dynamical systems, in spite of the inherent reversibility pf the microscopic behaviour.
PB Because there are thresholds where order is possible?
Yes.
DP Is it rea/61 possible to talk about microscopic behaviour without at the same time specifying some microscopic system to which it refers?
That's a very involved question. When we describe atomic behaviour, we use a classical language, even if, or especially if, we speak of quanta( behaviour of the atomic system. In this part of the description, the reversibility of time is included. But then, by this asymptotic process, we destroy the invariance of the equation with respect to time-reversal. So the microscopic description that we obtain no longer has the character of reversibility in time. That is done by what we call a projection. That is a most technical detail, and a very abstract thing. It corresponds (to try to put it in ordinary language) to the fact that we eliminate most of the parameters which describe the behaviour of the atomic system. We only keep those that we decide are directly observable. I say 'we decide,' because, after all, we can, if we like, observe an atom by using a gamma-ray microscope, or that kind of apparatus. That is perfectly permissible, in the logical sense, even though we cannot build such instruments. But in bubble chambers, at Geneva and other places, there is apparatus which actually shows us individual atomic processes.
PB It's interesting that we interpret the microscopic bubbles in terms ofa path.
Yes, but we understand how this apparatus works:
PB At feast we can observe some atomic events.
Processes, yes. A bubble chamber picture is terribly complicated. Every bubble is a single experiment. But, then, thermodynamics is another

32 Leon Rosenfeld
mode of description that we have found useful (I'm becoming pragmatic again), and which consists in the elimination of most of the parameters and the retaining of only a sort of global effect which we call pressure, temperature, etc., which are averages over many atomic processes. Then we see that by coming from the atomic description to that new description by this elimination, we have also eliminated the invariance with respect to time-reversal.
DP This break with symmetries, though, is a characteristic ofthe classical world in many cases. Do you think that this is always true, that somehow the symmetry has been broken by goingji·om a system with a ve,y large number of variables to one with just a few classical variables?
That is certainly true in this case; I don't know how general it is. It is reasonable to expect that when we lose symmetries, we eliminate characteristics.
DP Heisenberg has a theo,y in which he has a Jimdamental symmetrical law and the world breaks the symmetry ofthe law. lnjact, this may be going to asymptotic states in which the symmetries, or the very fundamental particles, are all broken.
Yes, that may very well be. We are not that far yet.
DP Do you think, in this way, that it may be possible to have a theo,y of relativity, ofgeneralizing the gravitation by taking an asymptotic limit?
It may be that it will turn out like that, but we have no microscopic theories, so we can't say anything about that.
The kind of irreversibility we get depends on the questions we ask. Usually we are interested in the future, and therefore we have this aspect of dissipation, the reversibility getting worse and worse. But we are also perfectly able to look to the past and make retrodictions, which are also statistical of course. We can ask what the probability is that the present microscopic state of the system has arisen from a given configuration. We can also formulate the theory so as to get retrodiction.
DP Weizsiicker has said it isfimdamentally not correct to use the term probability in this sense, that is, to speak ofretrodictive probability.
PB They're all future-oriented, because, in a sense, you are putting yourself back in that supposed initial condition. In its formal sense of use, he's right, obviously.
Yes. He formulated that idea at a very early stage, in 1940 in a paper where he mentions that he received his inspiration from Gibbs. Gibbs

33 Leon Rosenfeld
says, if I may try to paraphrase his long and very complicated sentence, that in trying to make retrodictions about previous events, we are really able to disregard our knowledge of the probabilities of anterior events that have influenced those that we contemplate. I meant to mention only very trivial retrodictions, which we put ourselves in; the unrealistic situation of knowing nothing at all about the past of the system, which is of course never the case.
DP There is a search Jor.fi111damental particles- partons, quarks - continuaffy reinterpreting theory in terms ofmore particles. / 11·as wondering to what extent this is a Jailure to get rid q/'cfassical ideas and the notion qf'a particle, even a rsychological Jailure.
I think it is. I think the people doing the latest things in elementary particles are rather crude in their thinking. They are in danger of getting into a situation of infinite regress. If you introduce quarks, which must be very tightly bound together, what is then the field, or whatever, that binds them? And so you can go on indefinitely. So I think this is not a fruitful way to look at things.
PB What aboutfundamental symmetries?
The fundamental symmetries give a very strong indication that those things that we call elementary particles are actually structures consisting of elements which can arrange themselves indifferent ways. But that does not mean that those elements can be compared to the crude idea that we have of particles bound together by forces of another kind. That would lead us to an impossible problem. But they may stick together in the way that Heisenberg contemplates, by self-interaction.

David Joseph Bohm
David Bohm is .Professor of Theoretical Physics at Birkbeck College, the University of London. Born in Wilkes-Barre, Pennsylvania, in 1916, he gave some hint of his future scientific vocation when he displayed a childhood interest in mechanical devices and planned to make his fortune as a boy inventor. About this time he had sensations of the 'interconnectedness' of the world, a revelation which appears to have influenced his later thinking.
Bohm studied physics with Ernest Oppenheimer and, as a young research physicist, voiced his concerns over the foundations of scientific theories to Albert Einstein at Princeton. Bohm's early research on electron plasmas in metals is still considered a significant contribution to the theory of the solid state, but he was soon to leave 'conventional' research in favour of an investigation into quantum and relativity theories and the possibility of their unification.
Bohm has not yet been successful in formulating a more general theory of physics and it could be said that his greatest contribution has been in causing physicists to re-examine what it is they are doing and to question the nature of their theories and their scientific methodology.
Recently Bohm has become interested in education, its effects upon the developing individual, and the future of society. He has therefore become actively engaged in an educational experiment at Brockwood Park, England.
Bohm's passions are for conversation - he is an animated talker - and walking. A colleague who is fortunate enough to start David Bohm on a train of thought may find himself involved in a cross-country hike-cumdiscussion which will last for the remainder of the day! The following conversation with David Peat took place in London and for once did not involve any walking.

35 David Joseph Bohm
Most of the physicists with whom we hal'e had conversations have tended to accept quantum mechanics as it is. They are t1y111g to extend the formalism a little, either to unify it with relativity, or to attempt to provide an explanation for the elementary particles. I take it that you are not really satisfied with this approach.
Perhaps I should go back into the history of how my ideas came about. When I studied quantum mechanics I was fascinated with it. I felt it was a very deep, important study, but I didn't really understand it. Eventually I taught a course on the subject, and wrote a book on it, to try to understand it. After finishing my book [Quantum Theo,y. Prentice-Hall, 1951], I considered the matter again, and I felt that I still did not understand it. At that time, I began to think of different ideas than the usually accepted ones. I sent copies of the book to various physicists, including Einstein, who expressed interest in it. and we had some discussions. I think we agreed that one couldn't really understand what quantum mechanics was about. I also talked with Oppenheimer, but he was never critical enough to make possible a discussion at the level I would have liked. I sent my book to Pauli, who liked it, and also to Niels Bohr, but I received no comments from him.
Since I can't remember exactly how I thought at that time, I'll try to say what I now think the difficulties are. This is probably similar in essence to what I felt then. Any theoretical science has four aspects. These are: insight, to perceive the structure of new ideas; imagination, which projects a mental image of the whole idea, not only a visual image, but a feeling for it; reasoning, to work out the consequences logically; and, finally, calculation, to get numbers that make possible precise tests with experiment. Evidently all four were present in physics until quantum mechanics came in. In quantum mechanics people discovered that they could find no way of imagining the meaning of the theory. This was brought out most clearly and consistently by Niels Bohr. I'm not sure that any other physicist really understands exactly what Bohr meant to say, but I don't think we can discuss that here.
It is rather widely believed nowadays that science, at least physics, does not give much scope to imagination. Various imaginative pictures are used, like 'wave' and 'particles,' but they are in no sense regarded as a real description of what we are talking about. They are merely aids to calculation; we deploy our imaginative pictures so that we can calculate more efficiently.
What do you mean by understanding?
I mean to grasp the whole thing, to get a feeling for the whole thing. If I become proficient in calculating results, I don't feel that I necessarily

36 David Joseph Bohm
understand what it's about. By way of example, I might make a comparison with the Newtonian epoch. Let us say that Newton developed a calcu-
lus, and became very proficient at it. Every time you have the power x to the nth, you would replace it by nx"-1, and you can go through all sorts of
operations until you can finally say that you are proficient at working out these operations and can get numbers. Meanwhile, some other experimental physicist is proficient at manipulating his telescope, and he gets other numbers. If the two numbers agree, then everybody's happy. When the numbers disagree, they aren't happy and try again. That would have been the way quantum mechanics was done. I don't think Newton thought that way. He had some sort of imaginative overview of the whole meaning of the thing, of the universe.
Do you think this was why Newton was very concerned about gravitation, because he didn't really understand it?
That's right. For him it was only a means of calculating, and he was not satisfied. Modern physicists would say that they don't care, that's all a physicist wants to do. That is the change of attitude. I recall Feynman writing that imagination was the most important thing - and he is an imaginative fellow - but finally it always works out that the calculation is the main thing. I regard calculation as significant only to test the other aspects of physics. In itself, I regard it as rather insignificant. I don't think that the things physicists calculate are very interesting - e.g. how many Geiger counters are going to click; how many spots will appear on a photographic plate.
So it's really a test ofthe consistency ofyour own understanding.
Yes, and of the factuality of it also. ls it a real understanding? If you have an imaginative insight, you want to be sure it's not just imagination, you have to see that it's factual.
Wasn't it Goethe who attempted to postulate a physics based upon our everyday experience, rather than on making experiments and creating artificial situations?
When Roger Bacon originally suggested the form of modern science, he suggested that experience should play the key part in testing. Before that time people thought that Aristotle was the authority for what was true and, if you disagreed with Aristotle, you must be wrong. So it was a tremendously revolutionary idea to say that experience should be the test. This was later elaborated to say that one should try to arrange special experiences which are very simple. Ordinary experience is so complicated that it's very difficult to see just what it is testing. Then experiments were elaborated. This is a very powerful method but, at the same time, danger-

37 David Joseph Bohm
ous, because the experiments are developed on the basis of the theory; they are set up to answer the sort of questions that a certain theory asks. When experimental equipment was very cheap and simple, it didn't matter if one experiment or theory did not work out, because another theory could be considered, and one could try another experiment. But now it takes years to produce a big machine; it requires the cooperative work of many people and millions of dollars. People feel that once you have invested in this machinery, you had better use it. Theorists then feel impelled to develop theories that will raise questions that can be answered by this particular equipment, which in it's turn was set up to answer questions due to the previous theory. The result is that the experimental method, as it has developed, may tend to introduce a very conservative factor into physics whereas, in the beginning, it was quite radical and revolutionary.
Would you say that this is true ofthe particle accelerators, that they are perpetuating a fragmentary view ofnature?
I think a lot of people are questioning particle accelerators. The very fact that they are not supported now to the extent that they once were indicates that many physicists feel that they are not likely to produce the results that were expected. It was discovered by E. Rutherford that if you bombard atoms with alpha-particles, you can learn quite a bit about them. But that depends upon the idea that there is something stable about the atom, which remains while you are bombarding it. Now we are using such high energies that we literally disrupt everything and create all sorts of new things.
We could compare this to trying to study the structure of cities by bombarding them with higher and higher explosives and studying the fragments. If you bombard them with light, which doesn't destroy the cities, you learn something. If you use some sort of very fine shot, you might learn something, but as you raise the energy, you learn less and less rather than more and more.
You said that there was difficulty in understanding quantum mechanics.
Yes. I think that the difficulty is that we have no way of understanding what is actually happening, or what I call the actual fact. If I may paraphrase Bohr, we have only the phenomena, i.e. the observed phenomena, which are essentially classical in their description. Ordinary classical phenomena - the observation of a dot or a click - were previously understood to signify information about particles, and the particles were independent of these phenomena. Now, if you analyse the Heisenberg microscope experiment, you come to the conclusion that the experiment

38 David Joseph Bohm
cannot give you unambiguous information about the structures you are supposed to be observing. Therefore, there is no clear way of considering the unknown reality which is responsible for the experimental result.
Wouldn't Bohr have said that this is a Jimdamellfal property q/the world?
In effect he did say that. I don't think that he ever said it directly, but it was implied. But if he said that it is fundamental, then I ask: how does he know it's fundamental? It's only fundamental as long as the present theory works, and there are many ways in which it doesn't work, as we know. We certainly just can't accept it on authority that it is fundamental. We don't have Aristotle to tell us what is fundamental and what is not. Neither can our experiments tell us what is fundamental and what is not, because, as I've said, our experiments answer only the questions that we have already asked.
What about Bohr's view of language itself?
I would ask again: how does Bohr know that? I think the nature of language is even more unknown than the nature of particles. Bohr said that we are suspended in language and we literally don't know which way is up and which way is down; yet we are compelled to use language.
Our language has certain concepts in it and he believed that our language is committed to the concepts of classical physics, at least ultimately. That is, the ordinary ideas of place and time, and object and substance and matter, eventually, when refined, lead to the classical concepts of particles with certain positions and momentum. Bohr believed that the only way to get unambiguous communication is through classical concepts, and he takes it to be the task of physics to have unambiguous communications. But, contrary to Bohr, I say that physics is not primarily concerned with unambiguous communications; rather that all concepts are ambiguous, and that there are certain unambiguous abstractions that can be made from our ambiguous concepts. Those are the things that we use for tests. I think people get it upside down when they say that the unambiguous is the reality and the ambiguous is merely uncertainty about what is really unambiguous. Let's turn it around the other way: the ambiguous is the reality, and the unambiguous is merely a very special case of it, where we finally manage to pin down some very special aspect.
In his early works Wittgenstein said that words were justified by their relationship to facts in the world, but later he sa,d that it was in their use. Perhaps what Bohr said was too limited, and language is much more subtle than he believed.
First of all, you can't discuss language apart from thought. Language is only noises unless it is expressing thought. I don't think anyone would

39 David Joseph Bohm
presume to say that he knows the structure of thought. Not only is it unknown, but he would get into a terrible tangle, because of the very thought with which he is thinking about that structure: does he know that? Isn't there a danger that he is projecting some idea which he has in calling it the objective structure of thought? That's just the same problem as in machines. Machines have been built up in such a way that they lead us to ask only certain questions. If you have a theory of the structure of thought, you will project it into your thought and say that's what thought is. Then you will ask only questions about thought which are in your theory, and your thought will only answer the questions that you ask. So you are caught.
Are you saying that this is a limitation o/our knowing?
I'm saying that any idea which attempts to state that we know the structure of thought, or the structure of language, is suspect in my view. For example, N. Chomsky has stated that the structure of language is based, as I understand it, on our brain structure. He thinks he can connect it up. This may be insightful, but if he thinks he knows the ultimate structure of language, I think there is an extremely dangerous possibility of selfdeception.
The structure of language and the structure of thought are essentially one, inseparable. There are thoughts that go beyond language, but you cannot discuss the structure of language apart from the structure of the thought that language expresses. That is infinitely subtle, and I think Bohr might even have agreed with that. But Bohr made a still more subtle point - he was an extremely subtle person and very difficult to understand. Bohr said that he understood how subtle language is, but that physics is confined to dealing with unambiguous concepts, whose meaning cannot be doubted. Now I want to question that. Art is a field where ambiguous concepts are obviously the rule; you don't expect an image in art to definitely mean exactly this or that. But people think that physics means exactly such and such - at least that's the way that Bohr put it. I don't think that physics does mean that. Physics is a form of insight and as such it's a form of art. Every fundamental theory is an art-form in my view, and we can see how this art-form fits our general experience. No art-form fits it perfectly, so we go from one to another.
Classical physics led us to the ideal that we have a perfect correspondence between concept and fact, and thus no ambiguity. But when people study even classical physics carefully, they find contradictions. Zeno's paradox is a case in point. The most fundamental classical concept is an object moving through space, like a particle. As Zeno analysed it, a particle is in a certain position, then it's in another one, and another, and so

40 David Joseph Bohm
on; while it's in a certain position, it cannot be moving; when it's moving, it cannot be in a certain position. The concept of motion involves an essential ambiguity in the position. In fact, in our mathematics, if you take a certain point, according to the theory of continuity of a line there is no next point, it is ambiguous. But it follows that the present point is also ambiguous. What do you mean by the present moment? That's ambiguous because it's too fast. If you try to point to what it means, you don't get one moment, but you get some ambiguity as to exactly what it means.
You 're saying that physics has aspects ofan art:form, so what criteria do you use jar working in physics?
What criteria do you use in art? People have never been able to answer that question. I don't think you can answer it in physics. People are looking for complete security by saying they know a certain criterion by which they can judge what is good physics. But any attempt to make that criterion will just kill physics, because almost any new idea is bound to disagree with that criterion. The word art in Latin is based on a word meaning 'to fit, that which fits, that which is in harmony.' Ultimately, we have to see the harmony or fitting of our thoughts and our broader experience. If you have a preconceived idea of what constitutes fitting, then your mind is blocked. You may need something different.
You 're stressing the idea that science is a human activity.
It's a creative activity.
... and a personal activity.
Well, it's both personal and collective. But I would rather emphasize that it's creative and not mechanical. Something new has to be created. If you have a fixed criterion of what fits, you cannot create something new, because you have to create something that fits in with your old idea. If we say 'science is "X," science is something that fits a certain idea' - namely, what people have thought science is - then that limits what we can think.
If we have the concept of what fits, we 're limiting ourselves. Then how do we carry out this activity in our fives?
Is that a good question? When you ask the question 'how do we do it?' you're asking for a plan of how to go about things. This denies creativity. It is like saying 'how can I become a great and creative artist?' Can there be a technique, or a plan, or a criterion?
But you woufdn 't presumably go so far as to say that a critical analysis is not involved in the way your life is carried out?

41 David Joseph Bohm
Even that has to be creative. You can't take a fixed form of analysis. Any attempt to determine this thing beforehand is arbitrary. You are going to choose the criterion you prefer or enjoy, or the one that society enjoys or prefers.
But you must have some criterion. You 're claiming that people working with accelerators are doing things that don't fit.
I haven't stated a criterion. I'm just saying that if you look, you 'II see that it doesn't fit. How do you tell that there is a contradiction? Is there a rule for recognizing contradiction? It's the same as seeing that a picture is disharmonious or that a piece of music is not in harmony. What was once called disharmony in music later was called harmony. You can't fix the thing.
So the notion ofattempting to.fit a picture onto reality is complete(v alien to what you 're saying- I mean the notion ofa reality which exists independent <~/'man.
There is a reality which is beyond man, and includes man, but this is unknown. A man has certain ideas which dispose him to act in a certain way. If this action is harmonious, then he regards these ideas as correct. Our thought disposes us to act in a certain way. The word dispose means 'to arrange,' as a commander disposing his forces. If they are wrongly disposed, he will get into trouble, the worst trouble being the disposition of one-half of his forces against the other; that's a contradiction. For example, you are walking down the stairs in the dark and your body is disposed to expect another stair, but it happens to be flat. The whole movement is disorganized; it is not in harmony. Then suddenly you have the thought that this is flat and the entire disposition changes. I think that's the way all our thought works, including scientific thought. A certain way of thinking disposes us to act, in the laboratory or elsewhere, in a certain way. As long as we can find some general harmony in this action, we go on with it. When we find disharmony, we hold back and begin to look for another form of thought.
Would you say then that physics today Just doesn't fit, is not in harmony?
It's not in harmony. Quantum mechanics has no imaginative conception. If you are satisfied to say that physics is nothing but operating a formalism to get results, and operating equipment to get results, in order to obtain results which agree, all right. But if you say that physics aims to understand what's happening imaginatively, then I don't think that it's doing that. Neither relativity nor quantum theory is clear. And the relation between relativity and quantum theory is even less clear.

42 David Joseph Bohm
Was this lack offitting, this disharmony, true even before relativity, in the last century?
There was always trouble with classical physics but it was never quite so dramatic. There have been problems such as 'is there an ether?' or 'is there absolute motion?' Newton had the idea of absolute space, but it wasn't clear what he meant by it. He said the fixed stars are the frame of absolute space, but why should they be?
Have the experiments ofquantum mechanics and relativity actually exposed some long-term error in our way ofthinking abollt the world~
I don't think it was the experiments, but the theories themselves. The insight in the theories exposed an inadequacy in our way of thinking. It implied that we should have gone further to develop new ways of thinking, but this has not been done. As Bohr said, we have only classical concepts, they are the only unambiguous concepts. I believe that we cannot understand movement if we insist on unambiguous concepts.
Did the fundamental experiments of quantum mechanics really show the error ofthe notion ofman confronting nature as a separate object?
I think they do, but it's a very subtle thing to analyse. Bohr has given the most consistent analysis, but it's very hard either to understand or to express what Bohr meant. Generally the position is this. In classical physics, we say the world is made of separate objects, each a separate substance in mechanical interaction. The observing equipment is one of these objects, and therefore can be influenced by the other objects which it is observing. Evidently, you can maintain the separation of the observing equipment from the object observed and, in turn, the observing human being from the equipment, and so on. In quantum mechanics, one sees that the process by which these different things would interact cannot itself be analysed in detail. It is whole and indivisible. You cannot make a separation between the observing instrument and what is observed. For example, you are looking at this table; the form of this table has been built up by your experience which you are projecting into the table. ls the table you, or is it something separate from you? You appreciate it as a table with a certain form and a certain subsistence, but that form and that subsistence are as much you as the table. If you probed it with a very high energy machine, say with neutrinos, they would go right through, and the table would be a vaporous nebula. So the form of the table as a solid substance, or subsistence, comes from the human brain with its own particular mode of interacting. In a sense, the observer is the observed.
Something similar must occur in physics. We probe matter with certain ideas as to what to expect, and we make instruments in accordance with those ideas. In so far as the whole procedure works and fits, we say that is

43 David Joseph Bohm
what it is. But later on, we will say it is something else. We once said it was a little billiard-ball atom, and now we are saying it is something very different. The difficulty is that we see a lot of new things, but then try to explain them by particles. These particles would have to behave like waves at times; they would have to pass through barriers which are unpassable; they would have to spread out like a wave and suddenly condense; they would have to jump from one orbit to another without passing in between; and so on. They would have to do all sorts of things that particles can't do, yet we still call them particles. I think that most physicists believe that they are getting the ultimate constituent substances of the universe by discovering particles, although these particles behave in a way which would suggest that they are not that at all. By calling them particles you dispose your mind to think of them that way, in contradiction to some of the other properties that you 're ascribing to them.
So it is nccessa,y to engage in se(fexamination constantly flyou wish to pursue science.
You have to examine your thought, which is self-examination. People generally take their thought for granted. They pick up their way of thinking in school and from their parents. They say: 'we'll examine everything else, but we don't have to examine thought, we'll just think.'
By thought do you mean something different than logic?
Logic is only part of thought. Thinking is not only logical. In fact, thinking is usually not logical. People have to go to a great deal of effort to make their thought logical.
So science is not founded purely on logic.
Many would say that science is founded on logic and experiment, but I don't think that it's just logic and experiment.
Some feel that it's possible to build up quantum mechanics from logic. Would you care to comment on that?
It depends on what you mean by logic. The root of the word logic is the
Greek word logos, which is, according to the dictionary, the inner or essential thought of the thing. Many of our thoughts are just on the surface.
It has also to do with the idea, or the word. But the question is: what is the
relation between logic and reason? Reason is an activity. I call it perception through the mind. For example, when Newton saw universal gravitation as the reason for the behaviour of the planets, this was perception, it was not a deduction by logic from previous facts or ideas. Reason then is essentially perception through the mind. Logic is a way of trying to organize our thoughts so that they will be generally more harmonious. How-

44 David Joseph Bohm
ever, what we ordinarily mean by logic is a set of rules for organizing thoughts that are already in existence - arranging them, disposing them. But reason - perception through the mind - creates new orders of thought. Without this creation of new orders of thought, I think we wouldn't get anywhere.
But it may be possible to found an existing theory on logic or on logical structures.
You can examine its logical structure if you like, but that's not the foundation of it, you see.
Does the foundation lie in thought?
I would say that theory has no foundation. Any creative act or process has no foundation. If it has a foundation, it is not creative. If it comes from something that is already there, then it is merely the working out of what is already there, so it is not really the creation of something new.
Then what is the logical analysis oftheories?
You may analyse them to see whether your ideas are clear. Very often our theoretical ideas are confused in the sense that they may point in several directions at once without our knowing it. Perhaps a logical analysis can reveal confusion; it has done so on occasion. When you see confusion, that means that you should drop the theory and try another one. If logical analysis reveals confusion then it is valuable, but I don't think that it plays a fundamental role in the theory itself.
Would you comment on the work ofDavid Finkelstein* on logics in quantum theory?
I can't say that I fully understand the work, so I'm reluctant to comment. The ordinary logic of common sense, which, when put in mathematical form, has been called Boolean logic, implies that a proposition is either true or false. The word proposition is interesting. It is 'a proposal, something put forth.' If we took that literally, I think we could be much clearer. We could say that the function of thought is to propose, to put things forth. But there has to be an act of observation which disposes, that is, which judges between the true and the false. The judgment of a proposition should properly involve an act of observation, but in mathematics it is often an act of demonstration. This demonstration requires observation
• It was intended to include in this book a discussion with David Finkelstein on his attempts to derive space-time structure and the spectrum of the elementllry particles. In the course of the discussion Finkelstein was to have commented on Bohm 's reactions to his work. The proposed interview did not, however, take place.

45 David Joseph Bohm
at the intellectual level, or perception. Science has generally accepted Boolean logic, but quantum mechanics has certain operators, whose value is either Oor 1, which could be used to describe a proposition being either true or false. Quantum mechanics has sets of operators, such that you can have one set of propositions all compatible with one another, and another set of compatible propositions, but the two sets are not compatible with each other. Quantum mechanics allows us to make a model of mutually incompatible propositions in terms of sets of operators that don't commute. You also find that when you have operators that don't commute, something more is needed, namely a discussion of the context in which any particular operator is the relevant one.
This is true in ordinary reasoning also. For example, the statement that the electron is either green or not green. We consider the context of what we know about electrons and find that this makes no sense; it doesn't fit the context at all; it is not a question that should be answered. Similarly, in quantum mechanics, questions could be asked about whether an electron is in a certain position or not; in another context, whether it has a certain momentum or not; but not both questions together. Consider spin for example: in one context, when our apparatus is oriented in a z-direction, we can discuss whether the spin is up or down; in another context, when our apparatus is oriented in the x-direction, we cannot discuss that, but only whether it is right or left. The two questions cannot be relevant together.
I don't detect in Finkelstein's work any real emphasis on this contextdependence. I think that this is a weakness. If you accept context-dependence, you can see that logic is in some sense empirical, that it is not purely a question of truth. (In fact, Finkelstein has said this himself.) Whether a certain set of propositions is relevant or not depends on the context, and that has to be seen in some broader way that goes beyond logic. One of the things that is missing is some broader imaginative concept which would show us why properties depend upon the context, or why propositions depend upon the context. I have developed an idea of this which I call the implicate, or enfolded order.
Can you give an example of what you mean by implicate and explicate order?
Take a jar of a very viscous fluid - say glycerin - and put a drop of insoluble dye into it. There is a device that turns the whole thing slowly, stirring the mixture until it becomes grey. Then you turn it around the other way, and slowly the thread of grey dye pulls together and makes the original drop again. While the fluid was grey- i.e., the dye was all spread out - the drop of dye was still there, in some form, but it was folded up into the whole liquid, or implicate. Implicate means, in Latin, 'folded up'

46 David Joseph Bohm
or enfolded. On the other hand, explicate order is the one that is unfolded. I can understand the quantum properties of these operators by considering that any phenomenon that is unfolded before us in a laboratory could be regarded as, generally speaking, folded up through all space.
Would this be analogous to illuminating a holographic plate and W!/olding the image?
That's right. In the holographic plate, the information about the image is present, folded up, all through the plate. Similarly, the information that determines how our apparatus is going to behave is contained, folded up, all through space. Therefore, you no longer have the model of localized objects, which are independent substances, as the explanation of everything.
/11 thermodynamics, people speak ofentropy as being related to disorder. Disorder, to you, would be a form ofimplicate order?
Yes. There is no disorder in the sense of absence of order, but rather there are different kinds of order.
So is entropy a measure ofimplication?
I should think that you could look at it as a certain kind of measure of implication, or 'enfoldment,' of the order. Since the enfolded does not appear obviously on the surface, you call it disorder because you don't see it. But, obviously, we can't say that anything that we don't see doesn't exist because we don't see it. I think that there is an order that we ordinarily don't see, because we are looking for something with unambiguous significance, that is, explicate. The fact that there are propositions which are not mutually compatible is a sign that the basic order is implicate. So that when one proposition is explicate, the other must be implicate, and vice versa. This would give you an imaginative understanding of why we use this logic.
Could this idea of one proposition being implicate and the other explicate be related to the uncertainty principle?
Yes. We say that all properties cannot be explicate together. But I would rather call it - as Bohr might have called it - the 'ambiguity principle,' not the uncertainty principle. The word uncertain implies that it exists in a definite form and that we are just not certain of it; we don't know of it. Rather, we should say that this property is not uncertain but ambiguous; that is, it has no clear meaning. We must give it a very complex representation in terms of many images.

47 David Joseph Bohm
Would you like to comment on the structure ofmind in relation to implicate and explicate order?
It suggests a structure in which mind and matter are not very different. Anyone can see that our thought has this character, that a large part of it is implicit or folded up. When one part is explicit, a tremendous amount is implicit. As we talk, the words are explicit, but the whole meaning is implicit; we couldn't pin it down. This implicate order is common to mind and to matter, so it means that we have much of a parallelism between the two sides. Naturally, this will require a great deal of development. The things which are well defined and explicate have to be seen as special features of the implicate order. The underlying reality is the implicate order, and the explicate order is a very special case of the implicate order.
Would you connect this with the quantum mechanical notion of wholeness and the absence offragmentation?
This idea of implicate and explicate order obviously involves wholeness, because, in the implicate order, everything has its origin in the totality; it is folded into the totality. Moreover, the separation of the observer and the observed is no longer basic in this view. The observer is essentially an implicate order, and so is the observed. Everything that is observed is really the intersection of two streams of energy: one stream which belongs to the thing observed, the other which belongs to the observer. The 'phenomena' are the result of the intersection of these two streams. Both streams come ultimately from the same total reality. There is a total reality which cannot be pinned down, it is ambiguous. It can be thought of as having many, relatively independent, streams of movement or energy. The physicist sends one stream of energy in the form of a beam of particles; the other stream is the target, which is more or less a stationary stream, moving only inwardly in the atoms; where these two intersect there arise phenomena.
The words and ideas you use have the sense ofthings coming into being, or time, but I think that you consider time in a very different sense?
I think that time is not the fundamental order, but a subsidiary order which man's thought has introduced. You can see that time is full of paradoxes. If we think of the past, the past is gone. We can never get hold of the past. The future is not yet, it hasn't come. We can never get hold of the future. The present is much too fast to get hold of; by the time you've said it, it's gone. So you can't grasp the past, the present, or the future. So what is time? Time is, at most, an abstraction introduced by thought. You cannot get any exact moment of time, except in your thought. If I

48 David Joseph Bohm
describe something as happening in time, whatever I describe has already happened; it's only present in my memory.
But the enfolding and unfolding which take place in nature surely take place in time?
We have to think that over carefully. Let's try to see what is difficult about the concept of time. Anything that I describe is gone. Of course, it may change slowly so that it is not too different, but in fact it is gone. We may expect that it hasn't changed very much, and in some sense that is true. But when it comes to anything which is really subtle and fast, for example elementary particles in physics, or the attempt to discuss the mind, then that short interval between the past which is gone and the present which is unknown may be all important. But all physics developed thus far depends upon the assumption that it is not important; but that's only an assumption.
We say that the function of physics is to predict. Present knowledge is actually knowledge of the past. Also, we are not predicting the future as it is, but the future as we shall see it in the future, which makes the future into the past of the future. We never predict from 'what is' to 'what will be,' rather from 'what has been' to 'what will have been.' Then we make the assumption that what has been is very close to what is, and that what will have been is very close to what will be. What we often fail to realize is that the assumption depends not only on the slowness of movement, but also on the metaphysics which says that everything is made of things, like particles, which don't change very much as they move, which move on a path that can be followed, and so on.
But aren't you using 'move' in two different senses, one in moving through time, and one in the movement ofthe implicate and explicate order?
So far I haven't tried to define what I mean by movement. There are various ideas involved. Classical physics has the idea of the orbit as a description of movement, but the orbit is an abstraction, you never see the orbit. The past positions may be plotted on a piece of paper, but they are not seen, they are gone. They may be present in your memory, but the orbit is an abstraction which exists, as far as we know, only in somebody's mind. Zeno's paradox raises that point too, because it says that when the particle is here at a certain moment, the past position is gone. So how can you define movement as the relation between the present position and the past position? You would be trying to define a property that exists as the relation between what exists and what does not exist.
Some have said that time is the fundamental thing and movement is derived. Are you saying the opposite?

49 David Joseph Bohm
Movement is fundamental and time is an order which we derive. Movement is the fact with which we begin. You cannot specify movement unambiguously; movement cannot be given an unambiguous description. Look at your own experience. Do you ever actually see time? You never do. You see the position of a clock. You may remember time, but you never perceive time. The memory of time is a set of images which is present now, but ordered by thought. And that's a clue. You do not actually experience movement by remembering a series of positions. If you are in a moving car, you feel that you are moving; you don't say I remember that I was there, there, there. And if you project a series of positions on a screen, they are not experienced as movement until they are so close that they are no longer unambiguously separated. Then you feel movement.
Do you think there is a danger in making an analogy between movement in space and movement through time?
But I don't know what movement through time means!
Well, people involved with relativity talk in terms ofa body moving through time.
That's what they say, but I don't know what it means. It's the same as for • quantum mechanics, I don't understand a great deal of what is done in relativity. If I project time t as an axis, certainly I can see the track as it's drawn on a piece of paper, but the track drawn on the paper is not the movement.
I ask: What is movement through time? What is time? Time exists only in the mind. Does the particle move through the mind? I don't get it! It is almost like treating time as a substance. If I say move through London, I see what that means, but move through time? First I'd have to see what time is, and then I would see a particle moving through it! But nobody sees that.
You 're saying that all these problems must be made clear before there's any chance ofmaking progress in physics?
Before fundamental progress is made, yes. I think that the main questions to be considered are: 'what is time?' 'what is movement?' and 'what is thought?' I believe that time is entirely constructed by our way of thinking. You find time only by recalling images of what has been. Those images must be based on what is in the brain, but the 'what is' is implicit or enfolded. Remembering the past consists of unfolding this image into a series, and we say 'that's the way it was.' The future consists of unfolding it in the way we expect it to be. But movement is not experienced as

50 David Joseph Bohm
moving through these images. That is merely a way by which we know something about it; through these images we can dispose our activities toward the next step.
Actually I would like to consider the notion of flow rather than movement. There is an unknown reality which can only be described as eternal flux or flow. Out of this appear various forms which can be perceived. When these forms have a certain persistence and stability, we can recognize them and we call them objects. But we must consider our attitude to these objects. Our attitude is that all objects, such as this table or this microphone, are not only forms, they are substances, and they exist independently. Therefore, the form belongs to the substance. The other attitude is to say that they are not substance, but they are subsistence, they have a certain stability. For instance, the vortex has a certain stability in water, but it is not an independent substance. Ordinarily, we take the view that water is the substance, but if we try to analyse water into atoms we get into trouble because of their quantum properties. So I would say that
the substance cannot be pinned down in any unambiguous way at all. It is
unknown. But we can abstract forms in the movement of this substance. The true substance, however, is that which determines its own form.
Are things really thought to be substantial essences?
In some sense, yes. The whole atomic theory is the idea of substantial essence. It says that every atom is a substance, and that it has a form which is the form of that substance. The world is full of independent substances, one for each atom. But that doesn't work you see. Every atom has been broken down into smaller particles and these into smaller. People call the latter particles partons. They hope that they have found the ultimate independent substance. I think we should coin a word, which I call the ultimon, the ultimate piece of independent substance, out of which everything is made. I think it's an illusion!
But classical physics was based on that sort ofillusion and it seemed to have worked quite well. People thought that they had an understanding ofnature.
Obviously it works. These forms do have subsistence and stability, so a possible explanation of this is to say that they are substances.
Yes, but at that time was there a harmony or a fitting?
All theories have this character, that there is harmony and fitting up to a point. When you push them further there isn't.
Music is an example. There was harmony and form; then it changed and we have a new harmony and a new form.

51 David Joseph Bohm
At least a search for a new harmony. Art is in much tile same position: it is in almost total chaos as people search for a new form of harmony.
Would it be naive to ask whether there is a progression orjusr a change?
I don't know. I think it's primarily a change, but it's hard to say in what sense; there's a progress in some senses, but not in others. To define progress you must define a direction. If you choose a direction, you may discover progress, but if somebody chooses another direction, he may discover no progress.
Progress implies a targC't, an C'nd-point.
Yes. I think there is no end-point and no target. The universe is an unending transformation in flux. Out of this appear these forms which have subsistence. The hardest thing of all is to see that we ourselves are only a form in this. The major reason, I think, why people find it difficult to accept this view is that it implies that we ourselves are only transient forms. The thought of the self has always been built around the idea that the self is an eternal substance. either material or spiritual, or both, and sometimes called the soul. I think that our views of matter and our views of ourselves are implicitly related. If a person is reluctant to believe that he is not a substance, he will be reluctant to believe that matter is not a substance.
This brings to mind what many mystics in the Middle Ages said about the spirit returning, rather than being permanent. Wasn't it MeistC'r Eckhart who believed that God was a Negative or a Nothing, and one returned to this?
Many religions have had that view, or something like it. In older times, people put their philosophical views in religious terms. The separation between art, science, and religion was a more modern development. Consider these ancient religious interests: one was the origin of things, the general structure; every religion had an explanation of this structure. First men see the world; then they see themselves as separate from nature in the world; then they somehow conceive a unity between the two in the process that created both nature and the world. This is the canonical form which people must come to. Then they invent various myths as to how this came 'about; they become attached to those myths; and the myths are overthrown.
Scientists have invented other, shall we say. myths as to how it came about, for example the astrophysical story. Eventually this will fade out into something unknown too. People are always trying to understand this wholeness which they seem to be separated from and trying to explain it. The way I think of it is this: suppose we take it hypothetically that when

52 David Joseph Bohm
man was just coming from the animal stage, he never thought of himself as a separate being, as separated from nature in any way. At some stage man began to think 'I am myself separate, I am a substance.' That may have given him some positive advantages but, at the same time, it gave him the negative feeling that he was separate from everything else, and he felt weak, lost, and alone. Therefore, man began to search to unite himself again with that from which he thought he had separated. In doing that, he invented various mythologies as to how man and the universe were created from some common source. Man is still pursuing this, but in scientific terms, rather than mythological. You notice that astrophysics gets tremendous support, not only because it's interesting, but also because it touches on this. It means a lot to these people that they are explaining their own origin in common with the origin of the universe. That gives them a tremendous impetus to do the work.
This reminds me ofthe celebrations in Washington 0973) for the 500th anniversary ofthe birth ofCopernicus [National Academy of Sciences, now published]. It was an almost mystical religious meeting in the end, the way that the scientists talked about Copernicus, as if he were a saint or a god.
One root of the word religion means 'to bind up, to unite'; the other is 'holy,' which has the same root as whole. Man feels separated from everything and he is always trying to bind himself back to it, to make it whole again. An ancient philosopher said that man's activities could be divided into three basic kinds: the scientific, the artistic, and the religious; science dealing with knowledge, art dealing with harmony or fitting, and religion dealing with this search for oneness. Scientists are still searching for oneness and so are artists in some way. Religion has become highly fragmented, and people no longer believe in mythology. The fact that people with religious intentions looked into these questions in the past is not at all surprising. In fact, there is no separation. I don't think that you will ever get rid of this search for unity, which was one side of what men meant by religion.
You mentioned the fragmentation ofthought which has taken place over the last few centuries.
Thought has a tendency to fragment, to look at the world in little pieces. The situation is very extreme now, with so many different subjects of study in the universities, and none of them connected. Some people try to make interdisciplinary subjects, which in turn become more fragments. I think the general fragmentation of knowlege is producing a problem today. Once there was the idea of the whole of knowledge, but that's obviously vanished long ago. Thought has an inherent tendency to produce

53 David Joseph Bohm
fragments, to focus on one thing and then on another, then another. That is even necesssary for good thought.
Could you connect this up with the idea ofimplicate and explicate order?
Various fragments are explicated by thought. In a hologram, you could fold up a tremendous number of pictures and any one could come out. That would be a fragment, and it would look like a whole, but it wouldn't be.
Is it true to say that conscious thought is explicate thought?
Yes, it is fragments being made explicate. You could say the unconscious is this vast background, which is ambiguous and cannot be defined.
Does consciousness necessarily imply fragmentation?
It depends on what you mean. The content of our thoughts involves many fragments. I think that is inevitable. We have got to focus on this problem or that, and we must separate one thing from another. We cannot try to do everything all at once. But our thought is not merely an image of things, it is also, more deeply, a disposition to act in a certain way. If we have fragments disposing us to act in different ways, that will start tearing us to pieces. We can see this happening in society, where all sorts of different views exist, and people are going in all sorts of different directions that are not compatible. Conflict arises either within one person or between people. At this point, people wish to establish wholeness, and they may try to impose it through some philosophy or some religion or some political theory as the order which will establish wholeness. It is actually only another fragment. What we want is to have wholeness in the activity of the human being, while the thought can fragment as much as it needs to, to deal with each particular aspect. At the same time, there will be all the different fragmentary views, and we must try to develop some broader views, not to impose them and say they are truth, but to see things more broadly, at the same time that we see them narrowly.
Historically we would probably say that this fragmented way ofthinking was an evolutionary process, as man confronted nature and tried to survive. Do you suggest a new evolutionary step in thought?
I don't say exactly that. Man had certain survival advantages by breaking things up, fragmenting them, treating them separately. But there are also disadvantages, as people are discovering. When you treat nature as fragmentary, dealing with one fragment after another, various problems occur, such as pollution or exhaustion of resources. It is not clear that fragmentation is an unalloyed means of survival. But this does not imply a

54 David Joseph Bohm
simple return to the time before man knew his separation from nature. Once man has had the thought that he is different from nature, he can never return. There is an inherent contradiction in the assumption that man can return to nature, which makes it impossible. If he tries, he will start with his mind, which is supposed to he separate and struggling to unite. But the very struggle to unite will be an expression of the fact that he believes himself to be still separate. This is the contradiction. What man can do is to get beyond that thought. Until man had the thought that he was different from nature, there was no fundamental disharmony. But the disharmony arose when man thought that he was different, isolated in some sense, and therefore in need of reuniting. If you think it over, what he is trying to do is to reunite what has never been separated.
There has to be a very big change in our way of thinking. I believe that quantum mechanics and relativity both point, to some extent, to what step is needed. Fundamentally, the step is to be free of this division between the self and the world, the observer and the observed. I think all our thinking tends to be based on the idea that thinking is carried out by an entity, who could be called a thinker, a self, or an 'I.' As Descartes said, 'I think, therefore I am.' He was only expressing what people had felt for a long time. He did not invent that. One view is to say that thinking is carried out by a mental or spiritual entity somewhere inside the body - the 'thinker'; that the thinker produces his thoughts, but is separate from this thoughts. Since the thinker has clear differences and properties from, say, the table, you must say that the thinker is a different kind of substance than ordinary material substance. That is what Descartes said. There are two kinds of substance: one is extended substance, ordinary matter; the other is thinking substance, which is mind. Once you have introduced this idea of separation and fragmentation, you must inevitably come to fragmenting the thinker from his thoughts, and from the world that he is thinking about.
But that separation is false and illusory, and the notion that there is a thinker inside who is producing the thought is merely imagination. What would be closer to the point would be to say that there is nothing but thought, and no 'thinker' to produce it.
So this whole process offragmentation is a process out ofnature?
But is it an actual process? ls it not an illusory process?
But there is pollution, exhaustion ofresources, and other problems.
Yes, but it is an illusion that there is any fragmentation in a fundamental sense. These problems are actually an expression of our oneness with nature, not of our difference. Man's thinking tried to be different from

55 David Joseph Bohm
nature and approached it in a fragmentary way, trying to treat it as pieces. But nature refuses to be treated as pieces. Man thinks these illusions, and his mind being disposed by the illusions, he creates real action which is out of harmony with reality.
So this.fantasy, this illusion, is turning inro a nightmare?
Yes, the fantasy produces real activities which are destructive. It is because man is one with nature that this happens.
Yes, but all these activities are part of rhe processes of nature.
Man's thought is part of nature, and when man's thought goes into fantasy and mistakes it for reality, that is also part of nature. The trouble is that man has the illusion that reality as a whole is fragmented, instead of seeing that it is his thought which is fragmented. Thought is like a bunch of maps. The maps are fragments, but you don't imagine that the world is fragmented because the maps are. It is useful to fragment these maps because it enables you to focus on details.
flpollution and so on are part ofthe illusion, then what you mean by reality is ve,y subtle.
Reality cannot be specified unambiguously. It is the flowing, an eternal transformation. Transformation cannot be pinned down unambiguously. It is movement, which means that any attempt to pin it down is an illusion. Thought makes these fragments which do appear to pin it down, and they are useful, but it is an illusion to suppose that the country doesn't
change because the map doesn't. If you have a map published fifty years
ago, and try to direct yourself through London, you will have trouble. These maps are fragmentary not only because they are broken up into pieces, but also because they are based upon the past, and the past is a fragment. The fifty-year-old map of London can give you only a fragmen-
tary picture of the situation now. If you supposed that the situation never
changed, then it would work.
Can our thoughts escape once they are tied to language?
Yes, they can, because we can look into the language. A language not only expresses our thoughts, but also helps work back on those thoughts, and gives them some fixity of shape.
But ifour language is inherently fragmented, it becomes increasingly difficult to free our thoughts.
I think that our thought is in fragments in the first place, and that is why our language is fragmented. I don't think that the trouble can be de-

56 David Joseph Bohm
scribed as originating in language. It originates in the very nature of thought. Language can be considered only as a secondary process. We have developed the language which emphasizes fragmentation by having one word for an object and saying that the object acts on another one and so on.
Is it possible, then, to understand quantum mechanics or the world within the language we use at present?
I think we can, although we might also change it. Language is always used figuratively and poetically, I think; we never use it literally. The attempt to give unambiguous significance to language will never work. It is inherently ambiguous, it is flowing, the meanings are flowing. If we think differently, we will find ourselves using the words differently. Perhaps, ultimately, we will change the formal structure as well.
You have worked with language structures yourself.
I made some experiments trying to change the structure of the language, just to see what would happen. I emphasized verbs instead of nouns, to emphasize the flowing movement. I saw that you could actually do quite a bit on that line, but I finally felt that you couldn't push it too far if you made a special language, because you would merely create another fragment. Special languages have been made and they have had a fragmentary effect.
I remember thinking that it seemed to be a language very constrained by sets of rules that you were developing.
It was more a mathematical kind of language. I was trying to 'mathemate' the language so that we would not have such a sharp separation between mathematics and ordinary language.
I never quite understood what your reservations on relativity were.
They are related to what I said previously about time and movement. First of all, relativity takes the space-time continuum for granted, which implies that time is a substance, or something you move through. I don't think that makes sense, you see. There are many ways in which relativity and quantum theory need to be changed together. There are two very elementary points which quantum theory does not deal with. One is the existence of things. Quantum theory says that nothing can be discussed except the probability of what will be observed when you have a piece of equipment. If we take the whole universe, we would have to suppose another universe of observing equipment, perhaps bigger than the first.

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Nevertheless, we must say that, in some sense, the universe does not require that universe of equipment; it is there without it. As Bohr said, classical mechanics did not explain that atoms are there, the most fundamental thing, the clue to something new. Quantum theory does not explain that matter is there without a tremendous amount of equipment to specify its state.
I think that every structure abstracts some things which are really folded up in the totality. They have some relative subsistence, but the attempt to say that it covers everything is going to make it impossible to be consistent.
The second thing that quantum mechanics does not discuss is the actual process. For example, if you take a single radium atom decaying into a Geiger counter, quantum mechanics proposes a wave function, half of which leaks out of the atom in two thousand years. However, in some cases something happens immediately. Let's say that it takes ten years to decay. Since the counter doesn't work for the first ten years, you know that nothing has happened, and that the wave function is entirely inside for the first ten or one hundred years, or whatever. And this contradicts the idea of Schrodinger's equation, which says that it was leaking out all the time.
The theory says that Schrodinger's equation is the most complete description possible. I say that must be wrong, and that Schrodinger's equation is an abstraction of a fragment.
At one time you tried to look at it using the notion ofhidden variables.
That is just one way of saying that there is more to it. That was perhaps too classical an approach. It was merely a way of getting insight.
Was there not some misinterpretation of what you were trying to do?
Yes. I think that some people thought that I was trying to return to classical concepts, but I was really using the hidden variables to get imaginative insight into what the theory meant. One could see that the hidden variables would have certain peculiar properties which suggested that you should look at it in another way. For example, one discovers that these hidden variables have properties which imply instantaneous connection of all parts of the universe, an extreme form of wholeness. Some people have said that it is so strange that they do not want to consider it. I don't think that it is sensible to say that as long as we do the computation, we don't have to imagine anything about it, so we are not disturbed by anything that happened. I don't understand the attitude which says that hidden variables have strange properties and therefore we would rather not use them. By using hidden variables, your attention is focused on these

58 David Joseph Bohm
strange properties, and by understanding quantum mechanics imaginatively, even if as not yet fundamentally, you begin to see that quantum mechanics implies something very new, which you are missing by just doing the computation.
At this paint a traditional sort o_(physicist would ask you to produce a new wediction.
That again is a sign of a certain attitude to physics, which says that the essential point about physics is to predict something. Why do you want to predict? You would think that there is a predictive instinct which must be satisfied. But this is obviously not the case. The reason why people want to predict is just to confirm that their ideas are on the right track. I am trying to say that in some cases you cannot predict; some things are ambiguous.
Trying to see the weakness of a theory in a traditional way is inadequate. The traditional scientific method is to say: wait until your experiments clearly show that you are wrong. But if you are going along with confused methods, no experiment will clearly show that you are wrong, because you can always modify your theory. This has often been done.
We must look at it differently, realizing that there is something wrong, which the present theory does not have in it, which requires understanding, namely, there is an actual individual event - the decay of the radioactive nucleus - which is simply not accounted for in the present theory. We must put in new concepts to account for it, and see what happens, even if we can't use them to predict anything more at the moment. I think that there is an overemphasis on prediction, on getting results, which is stifling physics. Many people don't fully and deeply realize that there is something missing. They are so used to doing statistical calculations, and saying that only statistics matters, that they do not notice that there is an actual, individual fact which is not accounted for.
Suppose we begin by saying that stationary states just simply exist, and that the world is very nearly in a stationary state, with some transitions. Now these stationary states make jumps from one to another. We haven't explained why that happens, we are only accounting for that fact, in which case we do not need equipment at all. We are not going to interpret quantum mechanics as what an observer would see, but as a process of jumping between quasi-stationary states. We now explain that we have what we call a material system, which is a stationary state of a large number of atoms. When you solve the many-body wave equation of quantum mechanics, you see that you cannot make this relativistic, you need to have one common time for the whole system. However, this material system is essential for relativity, because the theory presupposes some quasi-rigid material system as a frame from which to make observations. I

59 David Joseph Bohm
don't think that you could ever get any definite meaning to relativity for a single atom. You would not have a clear definition of properties such as direction in time for example.
I believe that Roger Penrose was trying to take collections ofatoms, and, in that way, he thought that he could define the direction.
Penrose is working on some particular mathematical structure to try to do something which may well be worth doing. I am trying to discuss something else. I think something has to happen at a lower level as it were. Physics has given us some facts, but the actual language of discussing these facts is confused.
I am saying we must consider that this piece of apparatus, this block of matter, exists, without any help, as it were, of observers, or anything. It is in a nearly stationary state, and it determines a frame. That is missing
from relativity theory; there is no clear definition of a frame. If it were not
for quantum mechanics, which makes matter stable, there would be nothing in relativity that would allow for the frame that measures anything. So there seems to be a deprivation of relativity in quantum theory.
To pursue this further, you find that, if you take stationary states in one frame and then move the system and accelerate it, the stationary states of that system are not compatible with those of the first. They are nonstationary, and they correspond to operators which are not compatible. So if you have one system in a stationary state, and another system moving, the moving system is not in a stationary state relative to the first system,
but it is relative to its own frame. If there were an observer inside, he
would be built out of atoms in those stationary states, and he would see everything relative to those stationary states, that is, as changing. So we have an interesting conception: a relativity of stationary states. What is stationary for one block of matter is not stationary for another. That concept has been missing. In fact, we have to give the same 'time' to all the atoms in one system, since we say there actually is a common time which is relevant for determining the stationary states of the first system, in technical terms, as the time-displacement operator for that system. Another system has another time-displacement operator and determines another set of states. The two systems are not stationary together.
Now, we get an extension of relativity, because we have introduced a new concept, which I call the material frame, or the natural frame for the stationary state. However, this means that Schrodinger's equation cannot be taken as a complete account any more, because each system has its own Schrodinger's equation, giving its own stationary states. One should not try to say that a single Schrodinger equation covers the whole universe.

60 David Joseph Bohm
We say that a particular material frame, or block of matter for example, is determined by solving Schrbdinger's equation for some atoms. This can be extended abstractly to the surrounding space, and another set of atoms which has its own frame. They may be related approximately but not exactly.
Then is space a relarional notion 1
Space comes out as relational space. Every particular block of matter has its space, which is extended abstractly into the surrounding region, and all these different spaces interpenetrate to form what I call a multiplex, that is, many spaces folded together. Rather than thinking of space as a single substance, we can think of it as an abstract relation of the multiplex, each element of it being a fragment that is based on one piece of matter. That is an order we are imposing on space and relating to matter.
These spaces are not all the same. We can approximately replace them by one bigger space, which some have done, and call this a real space. But I say that it is no more real than the smaller space, although it may be convenient for some purposes.
The total implications, or the metaphysics of quantum mechanics and relativity together, are utterly unclear. Every fact, you see, is presented in a framework of a set of concepts and ways of thinking. If you have a confused order of thinking, the fact will be confused. So I'm saying that the first step is to get a clear presentation of this fact. Then we can go on to develop mathematical methods of going further. When we have a set of facts, our next step is to develop a broader mathematical way of thinking, which will assimilate those facts as aspects of the mathematical concepts. I don't think the present fact is clear enough to assimilate into any mathematical system. That is one reason why so little progress has been made over the past forty years.

Carl Friedrich von Weizsacker
Professor Weizsacker 0912-) is Director of the Max-Plank Institute at Starnberg, Germany. He began academic life as a physicist and his abilities were soon recognized by Werner Heisenberg, who co-opted him to his team of brilliant young scientists. As a member of this research group Weizsacker was to make important contributions to the theory of nuclear structure.
Professor Weizsacker, like his mentor Heisenberg, has a deep interest in philosophy which has taken him to the Chair of Philosophy at Hamburg University. To the professions of philosopher and physicist can be added a third: political scientist.
We spoke with Professor Weizsacker at his institute, located beside Lake Starnberg in the mountains near Munich. Its tranquil setting seemed appropriate for a philosopher and physicist.
DP Professor Weizsacker, you begin a discussion ofquantum theory with a logic which emphasizes the distinction between past and.fitture. Would you elucidate this emphasis? Perhaps the right way of answering your question is for me to say two different things about the way in which I was induced to work in this field, first of all, long ago, in connection with thermodynamics and later on in connection with quantum theory. Now, when I studied thermodynamics in the university, I found it very difficult to understand how the irreversibility of actual events can be reconciled with the reversibility of events according to the basic laws of mechanics. I was informed by my teachers, and by the textbook, that this was done by introducing the concept of

62 Carl von Weizsiicker
probability, of statistics. And then I wondered how the concept of probability could introduce an asymmetry into time if it wasn't there from the beginning. The answer which I think I understood in the end, and which I think is correct, is that the asymmetry is brought into statistical thermodynamics by the fact that a probability of an event, in the direct sense, is always the probability of a future event. You ask 'how probable is it that it will be raining tomorrow?'; you don't ask 'how probable is it that it will be raining yesterday?' You cannot even express that in meaningful English. You can ask 'how probable is it that it was raining yesterday?' but that has a completely ditferent meaning; it means that you do not know whether it was raining or not, and you want to know how probable it is that you will find out that it was raining. So, again, it refers to the future.
DP Are there not events in the past which are no longer testable, but about which we can make statements in terms ofprobabilities?
Even there, I would say if they are actually not at all testable, it is meaningless to apply probabilities to them. If you are not able to test it now, and you say there is a probability of five per cent that it happened like that, and then by some good chance you find a way of testing it, then your probability applies. But I would say that I would be prepared to defend the view, in a discussion which would last two or three hours, that probabilities basically always refer to the future and all other uses of the term probability are made in a more or less oblique sense. The probability of a future event, in my analysis, would be the most primitive sense of probability.
Then, the next step was that I also had some difficulties in understanding the basic ideas of quantum theory. Of course, I could easily understand the mathematical formalism of it, but what it really meant - that was always the difficulty. I found again that the concept of probability was used, so I tried out the hypothesis that this would again mean that it actually refers to the future. And I think you can say so, because if you speak of the probability of finding an electron at a certain position, it is certainly the probability that you will find it there. I found that this gave a possibility of perhaps understanding the fact that the probability calculus of quantum theory actually differs from the probability calculus which we learn at school or in university, which rests on, for instance, Kolmogoroffs axioms. This is a fairly technical point, and in general, I think, our students are not told about it. The fact is that the axioms of probability, as we learn them in ordinary probability courses, are not in agreement with their use in quantum theory. In quantum theory we have the superposition of probability amplitudes, of which nothing is known in classical probability calculus.

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DP So events in the ji1ture are described by this Temporal lo~ic, while events in the past have testable propositions.
You can say that for the past we have test,1ble propositions, we have facts, and facts are known or unknown. (Nobody would deny that a fact that is 1111known is a fact anyhow.) But for the /i1r11rc it would not be permissible to say that a future event. which is unknown, is an event anyhow. And this is precisely the point made by the so-called indeterminism of quantum theory: that if you assume that future events are objective, even as long as they are in the future, then you would have to presuppose the classical probability calculus, Kolmogoroff s axioms, the Boolean lattice of events, etc., which is not, in fact, the structure which quantum theory actually has. But if you say that a future event is actually not an objective event as long as it has not happened, but is a possible event (and possibility means something which is notjust 'actuality which is not known'), then you avoid every contradiction and you can interpret quantum theory in a common-sense way.
DP Are these future events the potentialilies that Heisenberg talks about?
Yes, I would say they are more or less the same thing.
PB Are they potentialities ralher than possibiliries? I mean by [Jossiblc cFc11ts those events which do nor necessarily have any direct causalities, or n,en ifthey do there is not necessarily anything implicit in the present which links tftl'm directly. I am thinking ofa seed thar grows into a tree, so I would say rhat rhe tree is a potentiality ralher than a possibi/iry.
If you offer this distinction, first I would ask you: would you take potentiality to be a special case of possibility? Would you say all potentialities are possibilities, but not all possibilities are potentialities?
PB Yes, I think I would.
In this case, I would say that the general theory of probabilities is a theory which refers to possibilities. Probability is a quantification of possibility, but where you have laws of nature which make it possible to predict probabilities from a given situation, this means that you have precisely that connection between present and future which you have been describing by saying potentiality. And in this sense, I would say here the word polentiab!y really applies.
DP You have made a distinction between past andjilture, yet you do not appear to have introduced time, in the ordinary sense, into your logic.
I have not introduced a metric of time, I have introduced an ordering in time, and this is a point which I think is quite important. To come to a

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more basic level of discussion, I feel that there is no possible use of concepts at all in the empirical world: there is not even a meaning to the word experience which would not presuppose the distinction between past and future. [f you speak about experience and say 'I learned that from experience,' this means from past experience, of course. Or you say 'this is a very experienced person,· and that means he has learned things in the past which he is able to apply in the future. But you can never apply anything you have learned in the past in the past~ That is meaningless. And you cannot have learned something from the future, except perhaps if you are a prophet. So I would say that the concepts which we use in common sense language when we speak about experience always presuppose the difference between past and future. Therefore I feel that whatever else we are going to introduce (like measurements, metric, space, objects) we always presuppose the difference between past and future. We presuppose it in such a manner that, in general, we are not even aware of our presupposing it. I call this structure by the name of time.
DP This theo,y seems to invofre a non-spatial aspect oftime.
Yes, I would say so. If you try to build ur a consistent axiomatic structure in physics, and begin with the quantum theory, I have not found it possible to write down axioms for quantum theory without using time in the sense in which I have used it now. But you can very easily build up quantum theory without any use of space. An axiomatics of quantum the()ry can be done in this way. You only speak about measurements and probabilities, predictions of probabilities, and laws for such predictions. Then you write down a correct theory of quantum probabilities which would include the superposition principle. It is never necessary to specify what sort of measurements they are and whether these measurements are made in space or in some other manifold of possible states. Ofcourse we know empirically that measurements are always made in space. and this must come out in the end, but the axiomatic structure of quantum theory can easily be made in such a manner that space is introduced at the very end.
I would say that time has a priority over space, but this priority is probably only possible as long as you speak in terms of quantum theory without relativity. The step which has not yet been taken in fundamental physics is not just to introduce a formalism which treats space and time on an equal footing, but also to understand how this happens.
DP It seems that the lense logic you are developing is more general than the propositional calculus.
First of all, you can say it is introduced as a variety of the propositional calculus. As soon as we go into the real mathematical problems - the

65 Carl von Weizsiicker
problem of mathematical logic - then I would say we come to a problem which can first be formulated by repeating an objection. The objection is this: von Neumann, you, and others are talking about quantum logic and calling it a tense logic. But this is nonsense, because it is derived from quantum theory, and quantum theory has been built up by means of classical logic. So, how can you get a result which implies a non-classical logic by means of classical logic? This seems somehow to be a vicious circle, or a vicious non-circle! I take this very seriously! I would not say that if the description given by my adversary were correct, I would still uphold the idea that there is a quantum logic; rather I would say this description is not correct in the following sense: quantum theory has not been built up by a consistent use of classical logic, but by a fairly inconsistent use of classical logic. This inconsistency has been discovered, and has been corrected by saying that, if we want to do it correctly, we must do it with quantum logic, with temporal logic, tense logic. But this means that quantum theory cannot be taken to be just the mathematical formalism, but the formalism with its semantics, and with its meaning, because the formalism in itself can certainly be described by classical logic as far as any mathematics can be described by classical logic. If this is so, the question is whether tense logic, temporal logic, is a special case of general logic, or whether general logic will have to be explained by, or be founded on, temporal logic. My proposal is that the latter is the case.
In this respect, of course, I am following the intuitionists. I say that if you wish to understand the fundamental problems of mathematics, you will have to decide how to treat infinite sets, and my personal predilection here is operationalism or intuitionism, saying that the actual meaning of infinite sets is only the possibility of having certain constructions. If I take this view of mathematics, I apply the concept of time to the foundations of mathematics because operations are done in time. So I would flatly deny the non-temporal nature of mathematics.
DP Time has been introduced into the theory in a very fundamental way. Could you explain how space is to be brought into quantum theory?
The question of introducing space is precisely an element in the theory which really has yet to be achieved. I am now entering a field in which I am offering my own hypothesis in physics. This hypothesis is that space is connected with metrical time; that measuring time is closely connected to measuring space, and that this is a different level in the construction of physics than the level at which we have just spoken about past and future.
I think the mathematical nature of what we call space in physics can be deduced from the quantum theory of what I like to call the simple alternative: the 'yes-no' decision. The quantum theoretical description of a simple

66 Carl von Weizsiicker
alternative is any experiment to which there are just two possible answers. Either the particular particle is a proton or a neutron. Or, there are two holes in a screen, and the particle which has gone through the screen has gone through either hole number one or hole number two. The quantum theory of simple alternatives is described by a two-dimensional complex vector space. This complex vector space is isomorphic, up to one sign, to three-dimensional real space. My hypothesis is that what we call space in physics, the space of possible positions of particles or fields, is deducible from quantum theory by being identical with Euclidean (or perhaps nonEuclidean) three-dimensional space, which corresponds to the two-dimensional vector space of the quantum theory of the simple alternative.
DP The idea ofa space built out ofsimple alternatives, binary logic, seems similar to Roger Penrose 's attempt to derive space from a matrix ofspinors which themselves have binary values.
I would say that it is very close to Penrose, and it seems to be independent. I always like to discover somebody else who did the same thing. The probability is a little bit greater, then, that it might be true.
DP So in the end you have a tense logic and a three-dimensional space. Do youjee/ it is necessa,y to go to the.four-dimensional space-time ofgeneral relativity?
You cannot say I have a three-dimensional space yet. First of all, I have quantum theory, including the concept of time in th~ sense of tenses, and I have two-dimensional complex vector spaces, and these can be somehow reduced to three-dimensional space.
OP Do you have a continuous metrical time?
If I accept quantum theory in the way in which it stands at present, I have a metrical time. I have not just[fied it, but I have it. And this is just one of the points which I try to clarify. How can I defend, in the end, the semantic consistency of speaking of metrical time which I did from the outset in building up quantum theory and an axiomatic system? I would propose that the parameter time, which we use in quantum theory, is only defined as a classical limiting case; it is not an observable; as we all know, we cannot describe it as an operator. If we speak about measuring time, and we describe that by real quantum theoretical measurements, probably the corresponding operator is not identical with the parameter time. The parameter time is always external to the system.
DP In the description ofexperiments involving very small distances, would your theory give results difjerent from conventional quantum theory?

67 Carl von Weizsacker
l would be very happy if I could answer your question and I hope to answer it in the end, but at present I would just say this: if I introduce space in the way I did it now, the real problem is not yet solved. This is just the first step, the step in which I show that in addition to the parameter time I can also introduce a parameter space.
But then I must speak about measuring time and measuring space. I would have to describe space as something (if I may use slightly picturesque language) which originates in the interaction of those physical objects which we then call particles. I would not say that there is space which can be subdivided indefinitely. In the parameter space, you can describe it like that of course, but that means that you have to produce more and more particles. As long as I have a finite number of particles, I have a limitation to th~ possible subdivision of space. For instance, if I say I have ten to the eightieth particles in the world, it would not be possible to define a smaller length empirically than ten to the minus ninety-three centimetres, because you would have to use all the particles in order to measure that.
PB What does the word fundamental mean to you? Can we talk about a .fimdamental level?
Fundamental is probably always a relative term; something is more fundamental than something else. That elementary particles are not fundamental is well known today, because they are changed into each other. I think that if we do not try to go beyond the frame of quantum theory, then the most fundamental physical objects would be objects which admit of only two possible answers to a question. I think that you.cannot subdivide quantum theoretical systems or objects beyond that. These most fundamental objects which are admissible within the frame of quantum theory would be the things we must study. In this sense, within the frame of quantum theory, I cannot think of anything more fundamental than a simple alternative. And this alternative is in the sense of being fundamental far beyond space. Space has to be built up from such alternatives, and not the other way around.
PB Why has it taken so long historically for man, who is totally enmeshed in time, to be brave enough to include time right in the very foundations of mathematics?
That is a most interesting question! Like all interesting questions, it probably has not precisely one answer; one must say several things. I would have two proposals; which are not contradictory but complementary to each other. One is, and this is true also in philosophy, that the simplest things are not conscious, are not in the conscious mind, but are presuppositions of which we are not even aware.

68 Carl von Weizsiicker
It is just the nature of time that whenever you try to say anything, what you have been doing is already presupposing some understanding of time. St Augustine said: 'if you do not ask me about time I think I know what it is, but if you ask me, I am not able to answer.' This is, I think, closely connected with the fundamental role played by time.
If you assume, as I do, that the concepts describing time belong to the most basic concepts, then it is not probable that it will be possible to explain them by reducing them to anything else, that is, to any other concepts. Rather, the other way round. Then one would expect that it would need a thoroughgoing analysis to come to a description of the structure of those most fundamental concepts which I suppose are closely connected with the concept of time.
This is only the one answer. The other answer is this. Certainly everybody has a good understanding of time, not perhaps to say what it is, but to use all the concepts correctly. Tenses, in Inda-European languages, are used quite correctly even by children, although the greatest logicians have great difficulty in explaining what the children are saying. There was, however, a particular step taken in Greek philosophy: the attempt to eliminate time from a fundamental role in it, and to replace it by concepts which are beyond time. This philosophy, which was closely connected, I think, with mathematics, was so successful that it influenced all later thought in a manner which has detracted awareness from the temporal relations which are involved in it. This is just one of the great steps in philosophy: that people learned to explain the world in a manner which tried to reduce it to something beyond time.
PB Human beings feel ;ime very deeply, yet the Greek ideal was to explain ourselves and the universe in non-temporal terms. This implies a perspective that isn't human: it does not contain man implicitly. It leads to equations and concepts which do not have a human.face, if/ may use a poetic image. But the quantum principle makes it more and more difficult to eliminate ourselves/ram the universe; and the introduction oftemporal logic, or time, into the very foundations ofmathematics seems to be bringing, in a strange way, human beings back into the universe.
Yes, I think that is a very good description. You could say that the Greek attempt is an attempt at divine knowledge, divine understanding, not human understanding. But that is not the whole truth, because, if you understand Plato or Aristotle, you find that they were fully aware of their own human nature, their limited understanding, and they were also aware of the very profound role of time. But time, as far as it enters that philosophy, I think, is always understood in the image of a circle, its returning into itself. The highest form of motion is circular motion, that is, a mo-

69 Carl von Weizsiicker
tion which never leaves itself. In this sense. it is an interpretation of time, but a special interpretation - an interpretation which does not take account of irreversibility, of what we call the second !aw, or of what we cal! evolution. That is one point.
Another point is that if there is a self-contradiction in classical metaphysics, which I think is absent from Plato but is very much present in much of later metaphysics, it is that these people think that, as human beings, they are able to see things with a divine eye and then able to formulate concepts which can be defended ·on the market' so to speak. I think this is somehow bringing the divine world-view too much into the human sphere, and forgetting our human limitations. In modern times both Hume and Kant, very different thinkers in very different traditions, have formulated quite clearly that our own theory of understanding must be a theory of a limited, finite understanding. Quantum theory is precisely the step in physics which makes it no longer admissible to forget about the human nature of the one who is making the theory - not only the observer, but the theorist. It might be that for a truly divine understanding it would still be true that there is a basic reality beyond time. But this cannot be formulated in all the nice little concepts of logic and mathematics which we are using. These concepts belong to human beings, and they belong to time.

Paul Adrien Maurice Dirac
In one of C.P. Snow's early novels a character in the scientific life of Cambridge is described as the successor of Newton. It can only be Paul Dirac (1902-). Like Newton before him Dirac has made contributions that are respected by his colleagues not only for their depth of insight and clarity but for the power and economy with which mathematics is brought to bear upon the problems of nature. Dirac's scientific papers have the polished and balanced appearance of a sculpture by Brancusi.
While Heisenberg was discovering the principles of quantum mechanics in his Helgoland retreat, Erwin Schrodinger followed a different path to derive his wave mechanics of the atom. Dirac was able to show that the two theories were equivalent, and in the process provided quantum theory with a sound mathematical footing. His contributions in physics also include the quantum theory of matter and radiation, the prediction of the spin of the electron, and the existence of the positron as well as an attempt to form a marriage between quantum theory and the theory of relativity. He was awarded the Nobel Prize in 1933.
Professor Dirac has retired from his position as Lucasian Professor of Physics, the chair previously held by Isaac Newton, and is at present at the Institute of Advanced Studies at Miami, where he was interviewed. At first Professor Dirac seemed reticent about his achievements in physics. However, when the topic of beauty in physical theories was raised, Dirac began to speak with animation. In addition to commenting on the current status of theories of physics he touches on the 'large number hypothesis,' which has occupied him in recent years. Dirac is concerned with the occurrence of large numerical constants in physical theories. Rather than ignore these numbers or ascribe the similarity of their values to mere coincidence Dirac has proposed that constants of nature are interrelated.

71 Paul Adrien Maurice Dirac
The large value of certain of these constants, Dirac supposes, is connected with the age of the universe.
DP Do youjel'I that thNe is thl' saml' l'XCitl'ment today in physics that thcrl' was in the twenties and thirties?
The problems are more difficult now and there is not the same hope of making rapid progress which there was in those days. Excitement is usually combined with the hope of making rapid progress, when any secondrate student can do really first-rate work. But the easier fundamental problems have by now all been worked out. Those that arc left are very difficult to work on, and one doesn't seem able to get the right basic ideas for handling them.
It is quite possible that they will require wholly new ideas. In fact it's pretty certain they will; otherwise they would already have been thought up.
PB But they wi/1 still be related to thl' existing development of theo,y in soml' sense at least.
Yes. The present theory must be an approximation to any improved theory which we get in the future.
DP Some people we've spoken to seem to think it's a matter for new experiments, partirnlarly in elementa1y particle physics.
If the theorists are not good enough to solve it on their own, that's what one has to do. It needs an Einstein, or someone like that. Einstein didn't depend on new experiments to get his ideas.
DP Do you feel that the progress in particle physics is.fruitful?
It's not really fundamental; it's collecting a mass of information and one doesn't know really how to get the basic ideas from it. Just like in the early 1920s one had a mass of spectroscopic information and it needed Heisenberg to find the real basis of a new theory from that wealth of material.
DP Do you think a umfication necessarily will have to include relativity?
I should think so, ultimately. Perhaps not gravitation in the first place; gravitation is rather separate from ordinary atomic physics and it plays very little role.
DP It seems to be an insurmountable problem to most people: the quantization ofrelativity. It is something you have worked on.

72 Paul Adrien Maurice Dirac
One can deal with it up to a certain point, but one cannot complete the theory in a satisfactory way.
DP Could you summarize your thinking on the large numbers hypothesis~
The large numbers hypothesis concerns certain dimensionless numbers. An example of a dimensionless number provided by nature is the ratio of the mass of the proton to the mass of the electron. There is another dimensionless number which connects Planck's constant and the electronic charge. This number is about 137, quite independent of the units. When a dimensionless number like that turns up, a physicist thinks there must be some reason for it. Why should it be, well, 137, and not 256 or something quite different. At present one cannot set up a satisfactory reason for it, but still people believe that with future developments a reason will be found.
Now, there is another dimensionless number which is of importance. If you have an electron and a proton, the electric force between them is inversely proportional to the square of the distance; the gravitational force is also inversely proportional to the square of the distance; the ratio of those two forces does not depend on the distance. The ratio gives you a dimensionless number. That number is extremely large, about ten to the power thirty-nine. Of course it doesn't depend on what units you're using. It's a number provided by nature and we should expect that a theory will some day provide a reason for it.
How could you possibly expect to get an explanation for such a large number? Well, you might connect it with another large number - the age of the universe. The universe has an age, because one observes that the spiral nebulae, the most distant objects in the sky, are all receding from us with a velocity proportional to their distance, and that means that at a certain time in the past, they were all extremely close to one another. The universe started quite small or perhaps even as a mathematical point, and there was a big explosion, and these objects were shot out. The ones that were shot out fastest are the ones that have gone the farthest from us. That explains the relationship (Hubble's relationship) that the velocity of recession is proportional to the distance, and from the connection between the velocity of recession and the distance we get the age when the universe started off.
It's called the big bang hypothesis. There is a definite age when the big bang occurred. The most recent observations give it to be about eighteen billion years ago.
Now, you might use some atomic unit of time instead of years; years is quite artificial, depending on our solar system. Take an atomic unit of time, express the age of the universe in this atomic unit, and you again

73 Paul Adrien Maurice Dirac
get a number of about ten to the thirty-nine, roughly the same as the previous number.
Now, you might say, this is a remarkable coincidence. But it is rather hard to believe that. One feels that there must be some connection between these very large numbers, a connection which we cannot explain at present but which we shall be able to explain in the future when we have a better knowledge both of atomic theory and of cosmology.
Let us assume that these two numbers are connected. Now one of these numbers is not a constant. The age of the universe, of course, gets bigger and bigger as the universe gets older. So the other one must be increasing also in the same proportion. That means that the electric force compared with the gravitational force is not a constant, but is increasing proportionally to the age of the universe.
The most convenient way of describing this is to use atomic units, which make the electric force constant; then, referred to these atomic units, the gravitational force will be decreasing. The gravitational constant, usually denoted by G, when expressed in atomic units, is thus not a constant any more, but is decreasing inversely proportional to the age of the universe.
One would like to check this result by observation, but the effect is very small. However, one can hope that with observations that will be made
within the next few years, it will be possible to check whether G is really
varying or not. lfit is varying, then we have the problem offitting this varying Gwith our previous ideas of relativity. The ordinary Einstein theory de-
mands that Gshall be a constant. We thus have to modify it in some way.
We don't want to abandon it altogether because it is so successful. I have proposed a way of modifying it which refers to two standards of
length, one standard of length which is used in the Einstein equations, and another which is determined by observations with atomic apparatus. I
should say that the idea of two standards of length and of G varying with
time is not original. This sort of idea was first proposed by E. A. Milne about forty years ago. But he used different arguments from mine. His equations are in some respects similar to mine; in other respects there are differences. So this theory of mine is essentially a different theory from Milne's, although based on some ideas which were first introduced by Milne. One should give Milne the credit for having the insight of thinking that perhaps the gravitational constant is not really constant at all. Nobody else had questioned that previously.
DP This theory has an important consequence for the creation of matter.
Yes, the amount of particles - elementary particles, protons, and neutrons - in the universe is about ten to the seventy-eight, the square of the

74 Paul Adrien Maurice Dirac
age of the universe. It seems again one should say that this is not a coincidence. There is some reason behind it, and therefore the number of particles in the universe will be increasing proportionally to the square of the age of the universe. Thus new matter must be continually created.
There was previously a theory of continuous creation of matter called the steady state cosmology, but this theory of mine is different because the steady state cosmology demands that G shall be a constant. Every-
thing then has to be steady, and in particular G has to keep a steady value.
Now, I want to have G varying, and I also want to have continuous creation. It's possible to combine those two ideas and I've worked out some equations on possible models of the universe incorporating them.
PB One ofthe consequence's o(your theo,y is that it rule's ow an expandingcontracting universe.
That is so, yes, because in the theory there will be a maximum size. This maximum size, expressed in atomic units, would give a large number which does not vary with the time. Now, I want all large numbers to be connected with the age of the universe so that they will all increase as the universe gets older. If you have a theory giving you a large number, of the order of ten to the thirty-nine, which is constant, you must rule out that theory.
PB This implies a constantly expanding universe.
Yes. It must go on expanding forever. It can't just turn around and contract, like many people believe.
PB So that avoids the singularity at the end, so to speak.
Yes, that is avoided; there is just a singularity at the beginning.
PB There seems to be, or at least it's possible that one may observe such a thing as, a black hole, which is a theoretical consequence ofgeneral relativity. That is also a singularity, is it not?
It depends on what mathematical variables you use. It would be a very local singularity anyway, not a cosmological one.
PB But it seems staggering to the imagination that the mass ofthe star is concentrating into a smaller and smaller volume. I know there are repulsive forces that can stop it at various stages, but finally, I understand, with a star that is perhaps five or ten times the mass ofour sun, it need not stop.
That is what it seems, according to current theories.
PB It is difficult to imagine such an object, bllt I suppose that is not a necessary condition for doing physics.

75 Paul Adrien Maurice Dirac
If you can find equations for it, that's all the physicist really wants. It is quite likely that the laws will get modified under these extreme conditions; we 'II have to try to find out what the correct laws are.
PB But they need not contradict physical theo,y, wouldn't they simply be mod(fications?
They would be modifications, modifications holding under extreme conditions.
DP Would you comment on the divergences and infinities 1rhich occur in quantum/ield theo,y. Many think that they can be removed by renormali::.ation. Is this your.feeling?
It's just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.
DP Some people have suggested that by introducing curved space you can get rid ofthese in,/inities, Abdus Salam for example.
I know that he is working on that idea, but I feel that with a good theory these infinities would never arise in the first place.
DP The papers you produced have been unil'ersally considered beautijii!. Were you guided by notions of beauty?
Very much so. One can't just make random guesses. It's a question of finding things that fit together very well. You're solving a problem, it might be a crossword puzzle, and things don't fit, and you conclude you've made some mistakes. Suddenly you think of corrections and everything fits. You feel great satisfaction. The beauty of the equations provided by nature is much stronger than that. It gives one a strong emotional reaction.
DP Do you get this reaction from certain branches ofmodern physics today?
Not the renormalization theory, no!
PB / have a question about the interpretation ofequations. There are certain equations and certain theories where interpretations have been open to a great deal ofdiscussion. It is not quite clear what's really meant in non-mathematical terms; I'm thinking ofthe principle ofcomplementarity.
Yes, there is an uncertainty in the interpretation. But I don't feel it is too profitable to discuss the uncertainty because the basic equations them-

76 Paul Adrien Maurice Dirac
selves are uncertain, as I was trying to explain to you previously. If you don't have very great confidence in the basic equations, then there's not really much point in spending a lot of time on the interpretation of the equations, as you believe they will be superseded after a while in any case.
PB / was thinking of the uncertainty relations themselves. Do you believe that these will be superseded?
It's possible. You'd probably have to pay a price for it and give up some other cherished idea.
PB The problem of observation and measurement seems to be important.
Yes, but you're discussing these problems on the basis of our present theories, which are just, I believe, a transient phase of physics and will be superseded after maybe a few decades - or, well, one just doesn't know when they will be superseded. It is rather as though one tried to build up a new philosophy on Bohr's orbit theory. You might have gone a long way with it, but all that argument would have been completely valueless when Bohr's orbit theory was superseded.
DP lfyou were giving advice to young physicists today, which area would you suggest they look into?
I think perhaps they ought to avoid fundamental physics because all the worthwhile problems there have already been very thoroughly explored.
DP / mean in the sense of which area you think the breakthrough will come in?
I don't know.
DP You'd be there ifyou knew, I guess.
Yes.
PB Will it also depend on developments in mathematical theoty?
That's possible.
PB In the 1920s the mathematics had to be partially invented as well, along with the experiments.
The basic mathematical ideas were known previously to the mathematicians. They knew about Hilbert space; they knew about spinors. They had never thought that these things would ever have any physical application.
PB So it's quite possible that some branches of mathematics already known contain useful approaches.
Yes. However, an enormous volume of mathematics exists, and to look for which part is going to be useful in the future is pretty hopeless.

Roger Penrose
Roger Penrose's professional career began in pure mathematics. Born in Colchester, England, in I931, he obtained a doctorate in mathematics from St John's College, Cambridge. His interests turned to the study of space-time structure and he spent a number of years at several American universities before returning to England.
His contributions in theoretical physics reflect his mathematical background for he seems quite at home when moving through multidimensional spaces, projecting infinities, or dissecting hyperspheres. With his imaginative approaches he has established important theories on singularities in space-time which have bearing on the nature of black holes. His insights into the structure of space-time are a valuable addition to the understanding of the theory of relativity.
Penrose was interviewed by David Peat in London, where he held a professorship at Birkbeck College; he has since moved to the Rouse Ball Chair of Mathematics at Oxford. His discussions in this chapter range from an appraisal of relativity theory to an explanation of his attempts to probe the nature of space-time using spinors and twistors. When he touches on beauty in mathematics it is clear that he is talking about something which is very concrete for him. Roger Penrose's hobby is the constructing ingenious mathematical puzzles and games. Those who have watched him in the process of constructing a mathematical theory realize that fun should never be the exclusive province of children.
Many people working on space-time structure accept the general theory ofrelativity or, at most, they are prepared to extend some aspect of the theory. Your

78 Roger Penrose
mm approach is more rad,cal, jar you are seeking a ./imndation .for the
woperties o_/space and time.
I certainly think that one needs an explanation for the space and time that we sec. In the first place one may reasonably ask to explain why it is we see just three space dimensions and just one time dimension. Many people would probably say that this is not a really meaningful question. I don't like to take that point of view myself. I think that it is a question that should be completely answered. In order to explain this kind of thing, one has to develop the idea of space and time out of more primitive ideas. When I say 'primitive' I don't necessarily mean that these will be ideas seeming more obvious to people; I mean they will be concepts more basic to the physics in some deep sense.
Perhaps I could mention one of the basic motivations for the whole thing. It is that one should ultimately try to get rid of the concept of continuum altogether in physics. There are really two basic places where the continuum comes into physical theory. The first and most obvious is in the structure of space and of time. There is apparently this continuum of space-time. The normal picture that one has is that between any two points one can find others and one can go on subdividing ad infinitum. No matter how small the region of space examined it essentially looks the same as it did before. When you think of it, this is really an absurd idea physically; you take a ruler twelve inches long and you cut it in half and you keep on doing this until you get down to the atoms and fundamental particles; so you try to slice them up. But we have no real reason to believe that space at that sort of level - if there is such a thing as a space at that level at all - is really like the space that we're familiar.with. So I think that one really should question this use of continuum.
There is one other place where the continuum comes into physical theory in a really essential way, and that is in quantum mechanics. Here one has the complex continuum, where there are square roots of negative numbers in addition to real numbers.
Could you explain exactly how this comes into quantum mechanics?
I suppose the superposition principle is really the best way of expressing that. In quantum mechanics, if you have two states, you are supposed to be able to form other states which are physically admissible, by making combinations of these two states. So you can say, for example, if state A is allowable and state B is allowable, then state A plus state Bis also allowable. The thing is, in quantum mechanics, that you also have to allow complex combinations. You have to allow state A plus the square root of minus one times state B- that sort of thing. This may seem mysterious but it is

79 Roger Penrose
very essential in the theory. The occurrence of interference depends on this. Also Schrodinger's equation explicitly involves the square root of minus one. We would simply not get enough states to agree with observation if we were to use just real combinations.
So, we have this complex continuum arising in quantum mechanics and we have the real continuum arising in the structure of space-time. It always seemed to me that if we are going to get rid of the continuum in one place we have to get rid of it also in the other. So I tried to develop a theory where one builds up the idea of space and of quantum mechanics simultaneously, starting from combinatorial ideas - purely counting ideas to begin with. I always have had the feeling that counting and other combinatorial concepts are more likely to lie at the root of physics than concepts which depend on the idea of the continuum.
So as well as building up space and time Jiwn something more primitive you 're
(l:ving to get rid of the continuum. As I rC'Call, you chose, as your primitive objects, spinors. A spinor, which has a binary- or two-valuedness, is used in the mathematical description of the electron, but also has ajimdamental place in relativity theory.
The point is that spinors can be regarded as basic building-blocks. They are more primitive than vectors or tensors, you see. Vectors and tensors are used in many branches of physics and are quite familiar objects. Now a spinor is, in a certain sense, a square root of a vector. So we can go one step further and build up vectors and tensors out of these spinors. Once you have got the idea of spinors (and you really need spinors in order to describe electrons) they provide the additional advantage of having acertain universality, so that you can build the other objects out of them.
Yow·first model ofspace used networks ofspinors, didn't it?
The basic idea in that model was to use the concept of spin or angular momentum as the primitive physical concept. You do not initially have the concept of a space in the model.
We can consider two particles, for instance, each particle having a definite value for its spin. If these two particles combine into a single object, that object will have another value for its spin. These values, according to quantum mechanics, must be integral multiples of a basic unit, ½ h, the spin of the electron. The rules that are satisfied by spin can be put into a purely combinatorial form. This was really the first step, and it is essentially a matter of rewriting the standard formalism. The second step is then to try to use these combinatorial rules to build up an idea of space. Basically the question is how you define, from these purely combinatorial ideas, what you mean by a direction in space. You have no space to begin with, so you

80 Roger Penrose
cannot say that an object is srinning in a certain direction. What you can do, however, is take another object and try to define the angle between the spin axes of the two objects. Each object could be some conglomeration of particles which together form some system of a well-defined total spin. Then you can define this angle in terms of certain formalized experiments, the results of which can be treated according to a purely combinatorial calculus. Thus, having a concept of angle between spinning bodies, you can use the concept to build up the idea of physical space.
In this particular model you build up the concept of a three-dimensional Euclidean space, although strictly speaking this is not Euclidean space, but merely the directions in Euclidean space. All you can get from this model is the directions.
Is it mathematical(y possible to build up space with the notions ofdistanceJi·om two-valued objects, jar example spinors?
I don't see why not. This particular scheme of mine did not lead to the concept of distance, but it was clear that it was not going to by the way that it was set up. My later ideas are meant to take this into account. But also they are meant to do several other things all at once, so they do not just introduce distance. In particular, I had to make the scheme fit in with the ideas of relativity.
The primitive object in the .first theo,y was a spinor, but now you have developed a new mathematical oQject, a twistor. Could you explain what a twistor is, briefly?
The idea of a twistor is, as the name is supposed to suggest, a type of generalization of a spinor. It is, in fact, a type of spinor really, but not an ordinary space-time spinor. The motivation for developing the twistor theory was partly to improve on this model that I have just been describing in order to build up not only distances but also a proper relativistic space-time.
In the case ofa spinor, one can make a physical correspondence- the spin of the electron - to the mathematical oQject. ls there a physical representation ofa twistor?
You can get a picture of a twistor in physical terms, namely, as a particle of zero rest-mass, like a photon, or presumably a neutrino, which moves at the speed of light. If you count up the number of degrees of freedom for such a particle, including its spin, polarization, and location as well as its momentum, you find they are eight in number. These eight degrees of freedom can be conveniently represented mathematically as four complex degrees of freedom. One of the basic ideas in twistor theory is that the

81 Roger Penrose
complex numbers, which as 1 mentioned arise naturally in quantum mechanics, appear in the theory right in the beginning. Herc one describes space-time ideas, also, using complex numbers. So instead of describing our massless particles by means of an eight-real-dimensional abstract space (as I might have done had 1 chosen to) I use an equivalent fourcomplcx-dimensional space. This space is not the space we live in. That is to say a point in this space does not represent a point of the space we live in, but it represents the entire history of one of these zero-rest-mass free particles.
To most people. the point is the most primitive geomerric concepr: bll! in your rheo,y ir is a line.
That's right, because the normal picture of a zero-rest-mass particle, if you think in space-time terms, would be a straight line, for example a light ray. Strictly, for a spinning particle, the straight-line picture is not quite adequate but should be replaced by one of a certain twisting configuration. But let's not worry about that refinement.
This.four-dimrnsionaf complex space can be relared 10 vur/t11nifiar space-time, and this complex space is built essemia/(1· ow o_(/ines rarher rhan points.
That is one way of looking at it. You don't have points as the primitive concepts, you have these twistors, or, as you say, lines of zero-mass particles. If you wanted to find a point, you could do it, but you would have to go to a second step in the theory.
General relariviry prescribes the geodesics, or parhs rhe parricles will rravel on; gravirarionaljorces appear as rnrvarure q/'rhese parhs. How does rhis aspecr o/'rnrvarure arise in your complex space?
The twistor theory fits in very nicely with special relativity concepts, but at first you meet with stumbling-blocks if you want to fit twistor theory in with general relativity concepts. I think it docs lead to some interesting points of view to do with the nature of space-time curvature but I think it would be rather difficult to explain. In fact, it turns out that twist or theory seems to fit in better with quantum ideas of curvature than with classical ones.
One of the basic original motivations of twistor theory always was to try to make the quantum mechanics and the space-time geometry fit together in a much more intimate way; recall the use of complex numbers right at the beginning for the space-time descriptions.
Some people who rry ro Join quanwm rhe01y and relativiry use ordi11a1y ideas of conrinuous space-rime and apply quanrw11 ideas only to rhe concepr ofdisrance between poinrs, bur you are doing something rarher different.

82 Roger Penrose
It certainly is not just doing that, that's quite right. One of the basic things is to get rid of the concept of point as the most primitive concept. When you try to fit general relativity into this scheme you find that you arc almost forced to think of it in quantum mechanical terms rather than as classical general relativity. Perhaps I should not say it quite so strongly, because there are more recent points of view which suggest that perhaps classical general relativity can also be fitted into twistor theory more clearly than I had thought previously. But there is the suggestion that it's very much a quantum general relativity which arises naturally in twistor theory. One of the things that happens once you have general relativity and quantum mechanics coming together in twistor theory is that the points in space cease to have precise meaning - they become smeared. Thus you don't even have points to have distances between. You develop quite different ideas of the basic space concepts.
So rhar, in a sense, space is builr in a quanrum mechanical way. Would ir be r,w! ro say rhar?
That would be the idea, yes. But the theory is still in a somewhat preliminary stage.
I Think ir 's inreresring rhar we have d/fjiculry speaking abow rhis. This may
refteu rhe.fimdamental ic:'l'e/ ar which you 're working, or rhe presenr incom-
plereness of rhe rlu.>01:v. Do you feel rhar ir would be easier ro speak about it [l
rhe rheory was comp/ere, or is ir olnecessiry d/fjiculr ro speak abour things like this?
1 think it's difficult anyway. One doesn·t know where the theory is leading; it may lead to a very simple concept that could be said in a few words. But on the whole it tends to involve ideas which are not easy to express, mathematical ideas which are not very familiar to most people.
Including physicisrs?
I think so.
Would if be true ro say rhar you have begun a program which artempts to find a foundation for relativity rheo,y within quanrum theory?
To some extent that's true. It is really a new way of combining quantum mechanics and relativity. In the first instance, it's a reformulation of existing theory. Much of what I do in this connection is simply rewriting established theory in a completely different language. At first sight, you might think that you're not doing anything new, but different things suggest themselves, and when you get stuck the mathematics guides you. You have to think of how to express certain ideas which you take from con-

83 Roger Penrose
ventional theory and you hit on a certain formula which describes these ideas. Then this formula allows generalizations in certain very natural ways, whereas the old formalism wouldn't have suggested that at all. So, very often, although a reformulation is doing nothing more than reexpressing the same physical content in a different language, you find that it leads to something very different. The suggestions as to where to go next can be completely different from the ones in the old language.
You are beginning with a different philosophy, a different view ofspace-time and mauer. Conventional quantum theo,y involves elementary particfes which are beginning to look less elementary because they can always be split up. You have quite a different concept ofa particfe.
Perhaps I should make the point that in twistor theory, although I've been speaking about a twistor as though it were a zero-rest-mass particle, in fact it is really more like the square root of a zero-rest-mass particle. Twistors are definitely not to be identified with actual physical particles. This leads to a new way of looking at actual particles as entities built up from something more primitive, namely from the twistors themselves.
I was speaking about zero-rest-mass particles; for them a one-twistor description will suffice, but there are other kinds of particles in nature. In fact, the particles we 're most familiar with are not of zero rest-mass. They are massive particles, and for massive particles a description in terms of two or more twistors is necessary. There are certain very simple particles called leptons - these include electrons, positrons, and µ.-mesons - and my present view is that a two-twistor description is appropriate for them. The internally more complicated hadrons, such as protons, neutrons, and 1r-mesons, would require a three-twistor description at least. Now in ordinary theory we can talk about particles which are built up of other particles, such as quarks or partons, but these are still always particles of a kind. In twistor theory, however, the components of the particles are not particles but twistors. In fact, it is really rather misleading to refer to particles as composed of twistors; the difference lies in the way twistors are used. Their role is more like the role of points in conventional theory. And you don't normally talk about particles being composed of points. The points are what you describe the particles in terms of. Similarly, in twistor theory, particles are to be described in terms of a certain number of twistors rather than being thought of as composed of these twistors.
In addition to having a theory which explains elementary particles, do you also explain their interactions in a unified way?
That is the intention. All interactions, according to the twistor point of view, would ultimately find expression in terms of basic interchanges of

84 Roger Penrose
twistors, although that's perhaps a slightly simple-minded way of looking at it.
The new theory you are developing begins with twistors, mathematical representations ofzero-rest-mass particles. A theory which involves only massless objects has a very special symmetry or invariance, doesn't it?
Since in twistor theory one starts from zero rest-mass rather than finite rest-mass, one is led to consider conformal invariance. This is a type of invariance which is broader than the invariance in special relativity, where you just consider observers in uniform motion to be equivalent to each other. Suppose we envisage only zero-rest-mass particles or zero-restmass fields; take photons as an example - these are particles of light. If you consider light on its own, without any other particles, you are talking about the electromagnetic field and this has a larger invariance group than the invariance of special relativity. Perhaps the easiest way to describe this conformal invariance is to note that what photons don't have is a scale. You can imagine the space-time to be altered by a rescaling at each point. As far as the photons are concerned, nothing has been altered. This would not be true of massive particles.
Perhaps a good i({ustration, in two dimensions, would be to imagine the chanl(es in geometry ofthe su,:face ofa balloon as you inflate it.
Yes. You can blow up the balloon uniformly until it's twice as bi.g, or non-uniformly, so that some parts of it stretch more than other parts. Suppose there's a little circle drawn on the balloon: If it gets stretched into an elliptical shape, that's not a conformal transformation. If the circle remains a circle, that is a conformal transformation.
In two dimensions, the circle must remain a circle when stretched. Now you deaf with stretchings in space-time and the extension ofthat circle would be the fight radiating through space and in time, the so-ca({ed light cone.
That's right. Instead of talking about little circles what you talk about are light cones. You can imagine the space being stretched at different points by different amounts, but the stretching has to be isotropic; that is to say, so that the light-cone structure is preserved.
So ifyour space is.filled only with a massless.field, i.e. light, then it will be conformally invariant and not possess any scale.
You conformally stretch your space by different amounts at different points and the electromagnetic theory is insensitive to such transformations so there's no way of telling what the local scale is purely by electromagnetic means. There is no way of telling distance.

85 Roger Penrose
The twistor theory is based, in the first instance, essentially on this type of geometry, which is insensitive to the stretchings; the concept of distance is not put in right at the beginning. That is, you can put the distances in, there's no problem in doing it, but the theory most easily describes these conformally invariant ideas. So, things like electromagnetism, i.e. photons and massless neutrinos, arc described very naturally in the theory. Things which involve mass and the breaking of conformal symmetry, though they can be put into the theory, don't fit into it at quite the same basic level as do the conformally invariant ideas. Gravitation theory, I should say, is not a conformally invariant theory, although it has many conformally invariant aspects, and is, in fact, more conformally invariant than one might have thought.
Has this breaking ofco,1/ormal invariance somethin1:; to do with interaction?
Yes, I should think that's fair. The gravitational self-interaction, if you like, where gravitation acts on itself, is not conformally invariant. It is sensitive to the scale.
You could have self-interacting theories which are conformally invariant, and those which are not. There's the so-called massless </>4 theory • which is conformally invariant, a self-interacting theory which has a very special interaction. On the other hand you can have self-interacting theories, such as Einstein's gravitation theory, which are not conformally invariant, where there's a scale built into the theory.
Now conformal invariance can be removed by certain self-interactions, but the massive particles also break conformal invariance. Do you view mass as produced by the self-interaction ofmassless objects?
I think one would regard mass more as a result of the interactions of a particle with all kinds of particles including itself.
When quantum mechanics first treated the electron, it was interpreted as a particfe moving at the speed oflight but 'jitterbugging' about so its average motion in any direction was much slower. Is there any connection here with your ideas?
I used to think so, for whenever you observe the velocity of an electron, you find it's the speed of light. The electron can be sitting there not seeming to be going at the speed of light because its jiggling around all the time. You can decompose the wave function for the electron so that it appears as two particles, one flipping into the other and back, and so forth. But, certainly, it would be inaccurate simply to think of this particle jiggling around like that. It's inaccurate for the same reason that all these pictures of point particles are inaccurate.

86 Roger Penrose
Could I ask, when you 're 1rorking 011 rhesc rlungs, which sound incrccliblv absrracr (rhe square roors </(paruclcs, ere.), do you acruallv u•ork in a risual sense.''
Very much. There arc so many things that can be interpreted in geometrical ways, even though they're not geometrical things to begin with. The geometrical mode of thought is a very powerful one. Some people may not agree, and I wouldn't want to claim that one way is necessarily better than another, but it is often very helpful to put a problem, which may not be initially a geometric one, into geometrical language and visualize what's going on. You can often circumvent a great deal of complicated calculations by means of simple pictures.
So alrhough it sounds so absrracr to me, you, injact, have rC'ly real pictures.
Yes, apparently concrete pictures. But they are the translations of translations of translations of concepts which may be quite different from the pictures that one ends up with.
What is acsrhetics in marhematics and how does it play a role?
I think it's not essentially different from aesthetics in art. It is a feeling for the beauty of the subject and for such qualities as simplicity, universality, and elegance. I think that one's aesthetic judgments in mathematics are very similar to those in the arts. But in mathematics aesthetics ,is not only an end in itself, but it is also a means. In solving a problem it often turns out that the direct approach -just slugging away, sorting it out - will not get you anywhere, unless you know how to solve it anyway. If you want to find a new way of solving a problem, you must feel your way around, in a sense, and look for pleasing and aesthetically attractive solutions. So in that way aesthetics can be a means towards solving a problem, rather than an end in itself. Of course, it is an end too: one really studies the subject of mathematics mainly for its beauty!
Bur relativity isn't quire mathemarics; it's also parr ofphysics.
Of course. But when you approach relativity from the mathematical point of view these aesthetic criteria are important. Of course, you also want to explain what's going on in nature, and aesthetics comes in there too, because an explanation tends to be suecessful only if it's pleasing as well.
I wouldn't like to say that the aesthetics are really the only thing in relativity. The subject certainly has a great aesthetic appeal, but any theory must stand or fall by experimental tests. There's no doubt that if experiments did turn against it, the theory would have to be thrown out. It can't survive as a physical theory by aesthetics alone.

John Archibald Wheeler
John Wheeler is a physicist whose mind has the combination of inventiveness and independence that seems so characteristic of American men of talent. Born in Florida in 1911, Wheeler studied with two of the greatest men of science, Albert Einstein and Niels Bohr. Those who knew Bohr say that Wheeler's combination of courteous attention and encouragement to others, no matter if they are established scientists or students at the start of a career, is a reflection of his teacher.
In addition to making contributions in the fields of nuclear physics, atomic structure, and relativity theory John Wheeler has encouraged a generation of young scientists to become independent and creative thinkers. A conversation with Wheeler, or the hearing of one of his lectures, is an exhilarating and entertaining experience. Ideas and examples follow one another until, by a masterly sleight of mind, they condense into a coherent picture and a hint at a theory to come. Wheeler has never been afraid to take his ideas to their theoretical conclusions or to probe the fantastic and imaginative theoretical aspects of our universe. It is perhaps not surprising that on the occasion of his sixtieth birthday he was presented by fellow scientists with a copy of Alice in Wonderland.
A few years ago John Wheeler took the courageous step of abandoning geometrodynamics, the approach to relativity theory which had occupied him for many years. In its place he could not yet put an idea, but simply the 'idea for an idea.' After our interview he told us that he looked forward to the years ahead. He would begin again and explore new scientific Paths: there would be so much to discover and much to learn.
DP I'd like to begin by recalling the title ofa book you wrote, Einstein's Vision. Einstein and Bohr are two great historicalfigures behind science today.

88 John Archibald Wheeler
Could you rel/ us, jirsr ofall, whar you fee{ Einsrein 's vision robe, and how it
has been rrdlecred in your own work?
Einstein's vision really goes back to the earlier days of William Kingdon Clifford, who proposed that a particle is nothing else but a kind of hill in the geometry of space. When a particle moves from one place to another, it's just as if a hill in the geometry of space, or a wave on the surface of water, moved from one location to another. It was impossible to do anything with an idea so abstract and ethereal until the time came for Einstein's theory of gravity. Now gravity was reduced in its explanation to nothing else but the curvature of the space caused by the sun or any other centre of attraction. With this geometrical picture of gravitation, the door was opened to a much deeper understanding of what goes on, and somehow this genie, which had been introduced solely as a kind of slave to carry force from one mass to another, took on a life of its own. Geometry acquired degrees of freedom of its own; the universe, made up of a kind of curved-up sphere of geometry, turned out not to be able to sit statically, quiet, but was forced to be dynamic. This was so preposterous that Einstein himself, who had brought this genie into being following these earlier free views of Clifford, tried to cork the genie back up in the bottle by introducing some new term that would prevent the universe from being dynamic and expanding. He called it a cosmological term.
Then, twelve years later, Edwin Hubble, the great astronomer, showed that indeed the universe is expanding. This, then, is the greatest, most preposterous prediction that physics has ever made in any time past, confirmed - fantastic evidence of the predicting power of the human mind. To think of this geometry as not only the framework of the universe, but as even supplying the 'hills' that Clifford had talked about, rhar today is still an unrealized dream. But it's an attractive dream, and part of what I called Einstein's vision.
DP Einsrein realty did not have much success in reducing marrer ro geomerry. Marrer and graviry coexisr in a rather uncomfortable way in his rheory. Your own work has been direcred ro removing marrer complere{y inro geomerry.
I was trying every possible lead that I could see open, to pursue further this great dream of Clifford and Einstein; to visualize matter as in some way built out of geometry. The new feature that came on the scene in my own thinking, as contrasted with that earlier work, was the quantum principle. One could say, in fact, that the relativity principle of Einstein and the quantum principle of Niels Bohr are the two overarching principles of the physics of the twentieth century, and without taking both into account one can well believe he can account for nothing.

89 John Archibald Wheeler
This quantum principle says that geometry, far from being smooth at very small distances, is instead like the surface of the ocean, which may look smooth to an aviator miles above it, but is seen to be covered with waves as he comes down a few hundred feet above the surface. Then, if he is precipitated into a lifeboat floating on the surface, he sees even those waves breaking into foam, in the same way that at small distances, by the quantum theory, space is predicted to have irregularities in its structure, so that if one gets down to sufficiently small distances the irregularities become so gigantic that it's like the foam on the surface of the ocean from the waves breaking. Space is built of a kind of foam-like structure.
Now this really reverses one's view of where particles fit into the scheme of things. Before this time, one thought of particles in space as really important and the space around as relatively unimportant. But now we come to realize that the amount of disturbance that's going on everywhere in space all the time is so great compared to the extra disturbance which a particle makes by being there that it's quite wrong to think of particles as the natural starting-point for the description of nature. You and I look at the sky and we see this and that putfy white cloud floating here and there; the clouds look like the only thing that's important. Yet when we go to study in more detail, we realize that the water vapour in the clouds is a thousand times more tenuous than the air, and that the proper starting-point for the description of the sky is not the clouds but the physics of the air. In the same way, the proper starting-point for the description of particles is all this activity, all the time and everywhere, throughout space.
DP When Newton proposed his ideas ofabsolute space, they were criticized by Leibniz in letters to Samuel Clarke. Leibniz conceived ofspace in a relational sense as defined by material bodies. Has Leibniz's idea been completely abandoned with this new fimdamental conception ofspace and geometry?
Of course this idea of Leibniz - that in some sense space is not a thing in itself but is a way in which we summarize our knowledge of the relationships between objects - is really, in one sense, played out in mathematical detail in Einstein's already existing theory of relativity. That is to say, in Einstein's theory the geometry is not something which goes its own merry way, but something which is governed in its curvature and its constitution by the location of energy. Where there's energy, space is curved more. In this sense, we have really a relativity: we have a picture of geometry as tied to the location of matter. However, we are certainly not assuming anything like the Newtonian picture - that space is, so to speak, a Godgiven perfection standing high above the battles of matter and energy - but that space is itself a dynamic participant in the world of physics.

90 John Archibald Wheeler
It's quite a marvellous thing how, in all the long history of mankind, the dream has always been held alight by one or another great thinker that somehow we'll manage to reduce all of existence to a mathematical expression in some very deep and marvellous and beautiful sense. Einstein's picture of geometry has been able to carry us towards this vision: that not only space is geometry, but also matter is geometry. I, myself, today, don't believe that it's a sound principie to think of space as the ultimate building material. I think it's not simple enough, and at the same time not complex enough. It's not primitive enough. But right now the more natural thing to do, I think, is to celebrate how absolutely wonderful it is, and how far it's carried us - this idea of interpreting gravitation as simply curvature of empty space. It's preposterous! The only thing that could be more preposterous is how successful it's been!
PB Do you believe that this approach eliminates man? Are you flying to ./ind, or was Einstein t1ying to find, a description ofthe universe, shall we say, from outside, that excludes man? It looks as if one is trying to find a perspective which one properly associates with another sort ofbeing.
The one reason above all others that Einstein could never bring himself to accept quantum theory, which he himself had done so much to bring into the world, was his feeling that somehow it denied the existence of an objective world; somehow it seemed to make what happens in the world depend upon we who observe it. This seemed to Einstein in contradiction to the objective spirit of science which we've all thought about for so long. In this sense, Einstein was really seeking an objective description of nature, if you want to call it that, one in which man's part in bringing about what happens is put aside. He really did object to anything that was not objective.
I can remember, myself, trying to persuade him of the correctness of the quantum principle when one of my students, Richard Feynman, had come up with a still newer and simpler way of seeing the content of it. After spending twenty minutes speaking about it to Einstein, and saying how marvellous it was, and asking 'do you not agree, Professor Einstein, that this makes it much more reasonable to accept the quantum principle?' he laughed and said that he had earned the right to make his mistakes, and that he could not believe that God plays dice. In this he was referring to the fact that in the quantum principle we're instructed that the actual act of making an observation changes what it is that one looks at. To me, this is a perfectly marvellous feature of nature. We had this old idea, that there was the universe out there, and here is me, the observer. safely protected from the universe by a six-inch slab of plate glass. Now we learn from the quantum world that even to observe so minuscule an