Whatever happened to Bohm?

Quantum Mechanics

September 29, 1995

The sociology of science, ie the study of science as a human activity, has become an area of controversy, as can be seen, for example, from discussions in The THES (November 1994), and in a recent issue of The Sciences, the journal of the New York Academy of Science. This is partly due to the rather absurd claims of some of its practitioners, who seem to deny that science is concerned with discovering the truth about the world, and see it as entirely the product of the cuture, race, class, even sex of the scientists; claims that can only be made by those without adequate knowledge of either science or the way it is done.

All this is rather sad because there are many issues worthy of study: why do certain ideas become acceptable at particular times, why do "fashions" come and go, even why do new questions suddenly become part of the scientific agenda?

James Cushing's book, subtitled Historical Contingency and the Copenhagen Hegemony, is a delightful example of what is needed. The author has an extensive knowledge of the relevant physics, and he tackles an important and intriguing question: why did a particular "interpretation" of quantum theory, associated mainly with Bohr and Heisenberg, and known as the Copenhagen interpretation, become the accepted orthodoxy? More specifically, Cushing asks why this particular interpretation, which three of the main contributors to the discovery of quantum theory, Einstein, de Broglie and Schrodinger, knew was fatally flawed, dominated over a rival interpretation which did not have the same defects.

Since its introduction by Planck at the start of this century, quantum theory has been an outstanding success. It has answered questions 19th-century physics could hardly even imagine; it has never been shown to be wrong, even where its predictions seem to violate commonsense; and the Schrodinger equation, which lies at its heart, has in its solutions all of atomic and solid state physics and the whole of chemistry.

There are observed phenomena in the micro world that are very bizarre, and which led people to speak of such weird, and essentially meaningless ideas as objects that are both particles and waves, or that can be in two places at once. Quantum theory provides, in the language of this book, an "explanation" of these phenomena, in the sense that it allows us to calculate, correctly, what will happen. It fails, however, to give us an "understanding".

The reaction of Bohr and Heisenberg was to assert that a set of rules that gives correct predictions is all we should expect from a theory, and that the desire for a realistic understanding was a hangover from the world of a more primitive (classical) physics. Such an instrumentalist, positivistic, approach was, of course, historically significant in that it allowed generations of physicists to use quantum theory with such success - simply by calling descriptions complimentary, they could forget that they were actually contradictory.

Ultimately, however, it was sterile because it discouraged all attempts to do better. Cushing is concerned with why this view was accepted when there was an alternative which gave identical results and which had a simple classical ontology, namely, the model introduced by de Broglie, and later, in a much improved form, by David Bohm.

The question seems to break into two, not necessarily related, parts. Although de Broglie's version had some technical problems, it was around from the early days, before any sort of interpretation had become established. Why was it not taken more seriously? Why did not people like Slater, who is quoted in Cushing's book as saying that Bohr's ideas are nothing more than "hand waving", work on de Broglie's model? The defects were cured in 1952 by Bohm, who actually succeeded in doing something that most quantum theorists, following a theorem of von Neumann, believed to be impossible. Why was this work, for so long, almost entirely ignored?

The central thesis of Cushing's book is that the answer to these questions lies in historical contingency - the order in which things happened. I am not convinced (and I guess the author would not expect me to be) that this is the complete truth, but the whole fascinating story is so well told that this hardly matters.

The historical sections are full of interesting anecdotes, and in the more technical parts, there are lots of things that even quantum physicists will profit from reading, for example, the excellent description of the measurement problem of quantum theory (which is widely misunderstood), and the details of many aspects of the Bohm model, including new material only previously available in journal articles.

The fact that the book contains an amazing range of quoted sources does not prevent it from also being rich in the author's own wisdom and insights.

I learned from this book that the dispute between the Copenhagenists and the others began very early in the story. The former did not approve of de Broglie's introduction of waves, even when they were used so successfully by Schrodinger in his equation. Having made non realism into some sort of dogma, they considered Schrodinger's work too pictorial, preferring instead the formal mathematical manipulations of matrix mechanics.

The later dominance of this school appears all the more surprising when we realise that at this level they were simply wrong. Although Schrodinger was able to show the equivalence of the two methods, the real difference between them was that his equation opened up the possibility of solving any problem, whereas the matrix theorists had no idea how to go beyond simple situations.

There are a few places where I would have done things differently. Like almost everybody else Cushing derives the Bohm model following Bohm's original paper, whereas it can be derived much more convincingly by starting with the requirement that it should give the statistical predictions of quantum theory for all position measurements.

With such a start we know that de Broglie could have answered Pauli's objections at the 19 Solvay conference, and we also know that attempts to distinguish the Bohm model from orthodoxy by measurements of tunnelling times are doomed to fail.

The attempts to change the Schrodinger equation so that it automatically gives the wave function "collapse" required to solve the measurement problem are treated too briefly, and some recognition should have been given to the fact that these models contain good physics, and indeed are the only real rivals to the Bohm model if we wish to have a theory that does not explicitly involve consciousness.

I was surprised that Cushing seemed to discuss determinism more in terms of what "I can calculate", than in terms of "what is", which is surely what Laplacian determinism, based on classical physics, is about, and to which chaos has no relevance.

One final point: suppose the historical order had been different and the problems of classical physics had been solved by the introduction of the extra force associated with Bohm's quantum potential. How long would it have been before we realised that the calculation of trajectories was actually unnecessary in comparing with experiments, and how would we have understood this apparently remarkable "accident"?

Euan Squires is professor of applied mathematics, University of Durham.

Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony

Author - James T. Cushing
ISBN - 0 226 13202 1 and 13204 8
Publisher - University of Chicago Press
Price - £51.95 and £21.50
Pages - 317

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