the unresolved quantum dilemma

Pergamon Stud. Hist. Phil. Mod. Phys., Vol. 21, No. 3, pp. 389-395, 1996

Published by Elsevier Science Ltd. Printed in Great Britain.

1355-2198/96 $15.00 + 0.00

ESSAY REVIEW

The Unresolved Quantum Dilemma

Euan J. Squires*m

Andrew Whitaker, Einstein, Bohr and the Quantum Dilemma (Cambridge Uni- versity Press, 1995), xvii + 349 pp. ISBN 0521-48220-8 Hardback; 052 l-48428-6 Paperback.

In typical undergraduate courses on quantum theory students learn about solutions of partial differential equations, about linear vector spaces, about perturbation theory and other approximation methods, and maybe about elementary group theory. These are excellent topics, well worthy of attention, and they can certainly be of use in calculating the predictions of quantum theory, but they are not quantum theory. That is rather a set of rules, properties and ideas about the physical world, which is in many ways very contrary to the natural way we see that world. It is unfortunate that this important conceptual revolution that has been introduced into physics, and indeed the whole of science, by quantum phenomena is hardly mentioned, and that the still unresolved problems of the theory, problems that have occupied the attention of most of the greatest physicists of this century, are often simply ignored. Now there are reasons for this. Perhaps the strongest, and the one that would most often be quoted, is that students who are going to be practising physicists may need to know how to calculate things in quantum theory, and there the theory is unambiguous, so it is right that the calculational techniques should be taught. But in fact most students will not follow their undergraduate years with a career in quantum physics, and certainly for them, the interesting issues are surely of higher educational value.

Of course, I suspect the real motive for the selection of material is the need to examine the students at the end of the course so that they can be assessed, and it is much easier to test ability to repeat a simple calculation than to measure a level of understanding. Indeed this is what most students want; they expect a course to give them some skills that will enable them to answer examination questions, and do not really want to know about problems. An undergraduate spends his time at university struggling to follow most of the things he or she hears about-not really understanding what is going on, but just having enough

* sDeceased 6 June 1996; Department of Mathematical Sciences, University of Durham, Durham

DHl 3LE, U.K.

Sl355-2198(96)00010-X

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knowledge to answer a few questions-so students are not in any way surprised or impressed when they learn that there are things in the quantum world which are astonishing and apparently inexplicable. The same difficulty occurs in trying to explain quantum mysteries to non-specialists. The world is full of amazing phenomena they (rightly) believe, so why should they be particularly excited to learn about another, rather obscure, set of amazing things? Only in the context of the enormous amount that we do understand, can the problems of quantum theory be fully appreciated. Indeed, maybe this suggests one of the reasons why Einstein was the leader in recognising the inadequacy of quantum theory; he had himself provided an explanation of so many intriguing facts of the physical world, that he could never be happy with any sort of doctrine that seemed to say that there were phenomena for which no satisfactory explanation could be found! It is here that there does exist a very strong argument for not including conceptual issues too early in the teaching of quantum theory. The problems cannot be appreciated properly without a good knowledge of the experimental results and of the properties of quantum theory that, among other things, allows it to reproduce those results. The subject has suffered much from people writing on it, even claiming to solve its problems, without actually knowing quantum theory. (Examples range from worthy ‘amateurs’ to professionals of the eminence of Karl Popper.)

For all these reasons I welcome the fact that Andrew Whitaker begins his discussion of the conceptual issues surrounding quantum theory with a beautifully written account of modern theoretical physics-mechanics, thermodynamics and statistical physics, relativity and gravitation, and of course quantum theory. The material is presented with the care and attention to detail of one who must be an excellent teacher-he even takes the trouble to warn readers not to confuse Bohr, Bohm and Born! This account contains very little mathematics. My general view here is that the purpose of mathematics in physics (or indeed in anything else) is to make things easier, so it is often a mistake to try to teach physics without mathematics. However, in this book I did not get the impression that anything was being sacrificed. The absence of much technical detail is consistent with Whitaker’s aim, which is to show how physics allows us to understand the phenomena of the physical world. He attempts to take readers with very little knowledge (according to p. xiv only interest is needed) up to the stage where they can appreciate some of the problems that have baffled, and still baffle, experts who devote their careers to quantum mechanics. Others must judge how far he succeeds, but he certainly makes a bold and skilful attempt.

I am pleased that Whitaker reminds us that the conceptual difficulty which dominates quantum theory actually was present, at least to some extent, even before the theory had been introduced. When Sir William Thomson, lecturing in Baltimore in 1884, said ‘a real matter between us and the remotest stars I believe there is, and that light consists of real motions of that matter’(Thomson, 1884) he was defending a view that we should expect to be able to understand physical phenomena. He could see no sense in the idea of a wave travelling through space unless there was something that was waving. The fact that we were (most of

The Unresolved Quantum Dilemma 391

us) forced to abandon the idea that such a ‘real matter’ (an ether) existed, left a problem that the majority of physicists conveniently forgot. We really still do not know the correct way to answer questions like ‘what are electromagnetic waves?‘, or ‘what actually is waving’? With the advent of quantum theory the same question exists in a somewhat more subtle form; what is the wavefunction? Here I have one tiny quibble with Whitaker’s account. On p. 53 he suggests that Einstein’s introduction of the photon did away with the need for an ether. This of course is true if we can really accept that light consists of little objects (‘photons’) flying through space, but such a picture, as is explained very well in this book, cannot be correct, or at least cannot be the whole story. To William Thomson a wave equation would reflect the properties of some material carrying the wave. With the success of electromagnetic theory, Schrodinger would be free from such a prejudice, a fact which may well have been significant in that it allowed him to write down his wave equation without being able to ‘derive’ it.

Having provided the basic background, Whitaker goes on to what, as the title suggests, is the main topic of his book-the controversy over the meaning of quantum theory. He characterises this as a debate between the view of Einstein and the view of Bohr. With similar oversimplification it is possible to see it as being between the view that quantum theory is a satisfactory and complete theory (the Bohr camp) and the view that it is not (the Einstein camp). Whitaker notes that there is (or perhaps was) a majority consensus that Bohr won the argument. It is clear, however, that he does not accept this, but rather inclines to the belief that on the central issue-the adequacy or otherwise of quantum theory-Einstein was right.

It is unfortunate that, perhaps because Einstein almost single-handedly developed the theories of special and general relativity, his role in quantum mechanics is not always properly appreciated. He is seen as the great founder of relativity, who hovered a bit on the edges of quantum theory, making some important contributions, but never allowing himself to accept what it was telling us. Whitaker shows that, on the contrary, at almost every stage Einstein’s contributions were crucial. Others made significant individual steps, but Einstein saw more clearly than anyone the unfolding pattern. It was he, for example, who recognised the significance of the work of both Planck and de Broglie.

Whitaker makes the interesting suggestion that part of the reason why Einstein and Bohr failed to understand each other was that their motivations

were different. Bohr did not share Einstein’s ambition to understand what was happening. He was more pragmatic; he simply wanted a form of words that would allow physicists to develop quantum theory without being hampered by its apparent contradictions. He succeeded, in the sense that most physicists accepted this pragmatic stance; and the great progress of 20th-century physics is a tribute to the fact that this was a worthwhile aim. Unfortunately, however, Bohr went rather further than this. As Whitaker notes (p. 192), he tried to generalise the ideas he used in his effort to make sense out of quantum theory, in particular ‘complementarity’, which nobody has been able to make precise without making it either trivial or wrong, to other fields. Not surprisingly, this


met with no success. Also, at least some of those associated with the Bohr school, in particular Heisenberg, were so mesmerised by the anti-realist ideas that seemed to be supported by quantum theory, that they vigorously resisted attempts to provide understanding. This could have had a serious negative influence on the subject, because it is clear that the enormous progress that was made following de Broglie’s introduction of matter waves and Schrodinger’s subsequent proposal for a wave equation, which gave some measure of realism to the theory, could not have happened within the abstractions of ‘matrix- mechanics’ as it was then understood. Incidentally, I have always considered that the elementary calculation of momentum quantisation using the idea of standing waves around a classical particle trajectory is not given as much significance as it deserves in introductions to quantum theory. Although mathematically trivial, it is conceptually profound.

This brings us to the final part of Whitaker’s book, where he discusses modern ideas on the interpretation of quantum theory, and in particular reviews possible solutions to the measurement problem. Quantum theory, as applied to single systems, is inadequate because it normally allows observation to have a range of possible results when in fact only one such result is experienced. That particular result is not, and indeed cannot be, distinguished in the theory. This is what is meant by the ‘measurement problem’ of quantum theory. In the context of this book it is convenient to classify possible solutions as being of three types: the complacent, the conservative and the radical. The complacent view is that basically everything is right with quantum theory; we just have to abandon a few prejudices which we acquired from classical physics or from our experience with the macroscopic world. This is the traditional ‘Bohr’ view, and is the one that perhaps most physicists who are familiar with, and who use, quantum theory actually hold. I do not believe that, today, it should be taken seriously. Although once it played a positive role in that it allowed people to develop applications of the theory, that stage has been passed, and complacency could well hinder the future progress of physics, which could, for example, come from attempts to find a proper understanding of the non-locality which is inherent in quantum theory, or a quantum theory of gravity, or even a quantum theory of the universe. Even contemporary workers whom I would classify as belonging to the complacent group, recognise that it is necessary to go beyond the Bohr-Copenhagen philosophy. Whitaker discusses two examples. There are those who emphasise the role of decoherence-something of which, I am sure, the early workers were fully aware [see, for example Bohm (1951; 1952)], but which is hailed almost as a modern discovery. Another area of work which has attracted much attention in recent years is the attempt to formulate precisely which set of observables at various specified times (‘histories’) can be given consistent (classical) probabilites. Although this might be an interesting problem in formal quantum theory, I share Whitaker’s opinion that the solution of the measurement problem is not to be found in this work.

The conservative view is to take seriously the empirical successes of quantum theory, but to recognise that since it does not contain the results of


measurements, something new is needed. An obvious possibility is to add, so- called, hidden variables. Whitaker describes the only really successful way of doing this, namely that due to Bohm (1952) (who improved on earlier attempts by de Broglie). He also gives a brief discussion of the alternative possibility, developed in particular by Pearle (1979) and by Ghirardi et al., (1986) where the Schrodinger equation is modified in such a way that the good predictions in microscopic physics are not spoiled, but collapse to specific results in measurement situations can occur very quickly. It is important to note that both these models are quite precise, with everything coming from the equations, and they do solve the measurement problem of non-relativistic quantum theory. Both are successful attempts to do things that many people believed to be impossible. What this implies, as John Bell emphasised, is that the resort to the linguistic contortions/anti-realism/abandonment of ordinary logic associated with the complacent view is, for those who wish to take it, a choice, and not something that is forced upon them by the experimental facts. One small qualification here is that, in both these models, there are also interesting issues related to psycho- physical parallelism that are different to those that occur in classical physics.

Given the interest in the foundations of quantum theory by so many brilliant scientists in the 1920s and 1930s it is perhaps surprising that these ‘solutions’ have been developed only more recently. There are lessons here for younger scientists. Whitaker notes that too often we believe things that are claimed to have been shown without actually having read, critically, the relevant papers. Bohr and Einstein were aware of Bohm’s work but were not particularly interested, and it is probably fair to guess that they would have taken a similar attitude towards the collapse models. Bohr had convinced himself there was no problem, so he was not looking for a solution. As we have seen, for pragmatic purposes this position was reasonable. Where Bohr probably went wrong was to allow the expediency of saying that we had mutually contradictory notions that could under certain circumstances be used to describe a range of phenomena, to develop into a dogma. On the other hand, Einstein made what Whitaker regards as a mistake, namely, the mistake of totally rejecting quantum theory as a candidate for a theory of individual systems. He was not interested in attempts to ‘cure’ the theory; rather he wanted to look elsewhere, to start again. He had not solved the problems of the perihelion of Mercury by looking for a few corrections to Newton’s laws of motion, or enabled us to understand the lack of an ether drift by fiddling with the lengths of rods moving through the ether, so he had reasons to be confident that such a procedure was correct and that it would succeed. Important issues for all research scientists are raised here. It is usually possible to write a paper, or at least a chapter of a thesis, by doing a ‘second order Born approximation’ to almost anything, but the result is unlikely to advance the course of science significantly, or to earn a Nobel prize. Where does a young research worker aim? I fear that the job situation, and the steady round of peer reviews and assessments to which most research is subject these days, is pushing everybody too far towards caution. It is sad that John Bell felt it necessary to tell Alain Aspect, even if only as a joke, not to spend time on


testing the Bell inequality unless he had a permanent job. Few more important experiments have ever been done!

Of course, in this last instance, Einstein failed. And, in retrospect, it seems unlikely that he was even looking in the right place. But does that mean that his basic instinct was wrong? As Whitaker explains very convincingly, he regarded quantum theory as being nothing more than a theory of ensembles, rather like thermodynamics. And it is certainly true that we would not have discovered statistical mechanics by adding small corrections to thermodynamics, or by adding hidden variables that were in some way ‘guided’ by the free energy, or some other thermodynamic quantity. We would have had to forget thermodynamics and look elsewhere. This of course, leads us to the third possibility for solving the measurement problem-the radical one, where we start afresh. Einstein’s ambition to understand what was happening in the quantum world, noted above, led him to seek this radical solution.

I believe that ultimately we will learn that Einstein was right, and indeed this is the most exciting thing about working in the foundations of quantum theory. When we find the solution of the measurement problem it will surely lead us into really new territory. However, at least for those of us who lack Einstein’s creative talents, it may be that the best place to look for clues about the way to proceed, is to ‘play around’ with the two solutions we have. If either of them is in some way correct then surely they are part of a bigger structure than we know at present-involving relativity, gravity etc.-but without them we would have little chance of finding what it is.

It is appropriate here to ask about the status of the, so-called, ‘many-worlds’ interpetation of quantum theory, a term that tends to mean something different to everyone who writes about it! The paper of Everett (1957) that began it, is very much in the ‘complacent’ camp, in that it does not introduce any extra, hidden, variables, and asserts that there is no collapse of the wavefunction which at all times obeys the linear Schriidinger equation. Everett emphasised that this was perfectly compatible with the results of a sequence of observations being consistent with the Born rule. Since this fact would surely have been known to anyone who had thought about it, it is perhaps curious that Everett’s paper has inspired such an enormous amount of activity. The paper contains some nice examples of formal quantum theory, but nothing really new, and I guess that this is another example of a paper often quoted but seldom read! As has been noted many times Everett still leaves us with an incomplete theory, which must be supplemented by some discussion of what it means for me to observe a particular result, with Born rule probability. Most people who have tackled this problem, who wish to remain within the spirit of what Everett was saying, try to solve it by introducing consciousness in some fundamental way This puts the interpretation firmly in the ‘radical’ camp, and indeed takes it beyond what at present we should regard as physics.

I approached W&taker’s book with a slight feeling of doubt as to whether we needed yet another lengthy discussion on a debate which has now been poured over for half a century. The book is so well written, with occasional flashes of


quiet humour, and many novel insights, that this feeling was totally overcome. Whitaker gives an excellent, balanced and well-referenced guide to the debate, and something of its historical context. [In at least two instances (pp. 106 and 245) we are reminded of the sad fact that even physicists are unable to rise above racial and political prejudices.] Anybody interested in the foundations of quantum theory, or in the history of science in this century, or in the personal stories of those involved in one of the greatest scientific endeavours of all time, will appreciate it. I would especially recommend it to new students of university physics.

References

Bohm, D. (1951) Quantum Theory (Englewood Cliffs, NJ: Prentice-Hall). Bohm, D. (1952) ‘A Suggested Interpretation of Quantum Theory in Terms of Hidden

Variables’, Physical Review 85, 166-179. Everett, H. (1957) ‘Relative State Formulation of Quantum Mechanics’, Reviews of

Modern Physics 29, 454465. Ghirardi, G. C., Rimini, A. and Weber, T. (1986) ‘Unified Dynamics for Microscopic

and Macroscopic Systems’, Physical Review D34,4701191. Pearle, P. (1979) ‘Towards Explaining Why Events Occur’, International Journal qf

Theoretical Physics 18, 489-5 18. Thomson, W. (1884) Lectures on Molecular Dynamics (Baltimore, MD: John’s Hopkins

University Press).

the unresolved quantum dilemma

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