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Cambridge University Press eBooks

Decoherence and hidden variables

Scott Aaronson

Published Mar 14, 2013• 0 citations
Publisher

Abstract

Why have so many great thinkers found quantum mechanics so hard to swallow? To hear some people tell it, the whole source of the trouble is that “God plays dice with the universe” – that, whereas classical mechanics could in principle predict the fall of every sparrow, quantum mechanics gives you only statistical predictions. Well, you know what? Whoop-de-doo! If indeterminism were the only mystery about quantum mechanics, quantum mechanics wouldn't be mysterious at all . We could imagine, if we liked, that the universe did have a definite state at any time, but that some fundamental principle (besides the obvious practical difficulties) kept us from knowing the whole state. This wouldn't require any serious revision of our worldview. Sure, “God would be throwing dice,” but in such a benign way that not even Einstein could have any real beef with it. The real trouble in quantum mechanics is not that the future trajectory of a particle is indeterministic – it’s that the past trajectory is also indeterministic! Or more accurately, the very notion of a “trajectory” is undefined, since until you measure, there’s just an evolving wavefunction. And crucially, because of the defining feature of quantum mechanics – interference between positive and negative amplitudes – this wavefunction can’t be seen as merely a product of our ignorance, in the same way that a probability distribution can.

DOI
10.1017/cbo9780511979309.013

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Why have so many great thinkers found quantum mechanics so hard to swallow? To hear some people tell it, the whole source of the trouble is that “God plays dice with the universe” – that, whereas classical mechanics could in principle predict the fall of every sparrow, quantum mechanics gives you only statistical predictions. Well, you know what? Whoop-de-doo! If indeterminism were the only mystery about quantum mechanics, quantum mechanics wouldn't be mysterious at all . We could imagine, if we liked, that the universe did have a definite state at any time, but that some fundamental principle (besides the obvious practical difficulties) kept us from knowing the whole state. This wouldn't require any serious revision of our worldview. Sure, “God would be throwing dice,” but in such a benign way that not even Einstein could have any real beef with it. The real trouble in quantum mechanics is not that the future trajectory of a particle is indeterministic – it’s that the past trajectory is also indeterministic! Or more accurately, the very notion of a “trajectory” is undefined, since until you measure, there’s just an evolving wavefunction. And crucially, because of the defining feature of quantum mechanics – interference between positive and negative amplitudes – this wavefunction can’t be seen as merely a product of our ignorance, in the same way that a probability distribution can.
Abstract Quantum mechanics, like other enormously successful physical theories, accurately describes how the natural world behaves. Its explanatory powers regarding the indeterminate behavior of the smallest constituents of nature have proven to be both profound and practical. Many technological devices from lasers to computer chips are based on quantum mechanics. Not surprisingly, the universe filled with microscopic random events revealed by quantum mechanics has generated wonder and interpretive bewilderment. Reactions to the unsettling revelations of quantum unpredictability have included appeals to unknown variables to preserve classical physics, and even wholesale theoretical dismissals. Far from proof of mathematical trickery or theoretical incompletion however, the now well-established and irreducible quantum randomness suggests a physical universe that is open to a future not determined by the past, and perhaps to a God that really does play dice.
Albert Einstein's comment that ‘God does not play dice’ sums up the way many people react when they first encounter the ideas discussed in the previous chapters. How can it be that some future events are not completely determined by the way things are at present? How can a cause have two or more possible effects? If the choice of future events is not determined by natural laws does it mean that some supernatural force (God?) is involved wherever a quantum event occurs? Questions of this kind trouble many students of physics, though most get used to the conceptual problems, say ‘Nature is just like that’ and apply the ideas of quantum physics to their study or research without worrying about their fundamental truth or falsity. Some, however, never get used to the, at least apparent, contradictions. Others believe that the fundamental processes underlying the basic physics of the universe must be describable in deterministic, or at least realistic, terms and are therefore attracted by hidden-variable theories. Einstein was one of those. He stood out obstinately against the growing consensus of opinion in the 1920s and 30s that was prepared to accept indeterminism and the lack of objective realism as a price to be paid for a theory that was proving so successful in a wide variety of practical situations. Ironically, however, Einstein's greatest contribution to the field was not some subtle explanation of the underlying structure of quantum physics but the exposure of yet another surprising consequence of quantum theory.
Albert Einstein's comment that ‘God does not play dice’ sums up the way many people react when they first encounter the ideas discussed in the previous chapters. How can it be that some future events are not completely determined by the way things are at present? How can a cause have two or more possible effects? If the choice of future events is not determined by natural laws does it mean that some supernatural force (God?) is involved wherever a quantum event occurs? Questions of this kind trouble many students of physics, though most get used to the conceptual problems, say ‘Nature is just like that’ and apply the ideas of quantum physics to their study or research without worrying about their fundamental truth or falsity. Some, however, never get used to the, at least apparent, contradictions. Others believe that the fundamental processes underlying the basic physics of the universe must be describable in deterministic, or at least realistic, terms and are therefore attracted by hidden-variable theories. Einstein was one of those. He stood out obstinately against the growing consensus of opinion in the 1920s and 30s that was prepared to accept indeterminism and the lack of objective realism as a price to be paid for a theory that was proving so successful in a wide variety of practical situations. Ironically, however, Einstein's greatest contribution to the field was not some subtle explanation of the underlying structure of quantum physics but the exposure of yet another surprising consequence of quantum theory.
We have learned a lot about quantum mechanics already. We learned it is probabilistic and that it can have indeterminate behavior until measured. The Nobel Prize winner, Richard Feynman, summed this up the best with the following quote from his famous The Feynman Lectures in Physics: “We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! Physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible-that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it ⋯\cdots ⋯ So at the present time we must limit ourselves to computing probabilities. We say ‘at the present time,’ but we suspect very strongly that it is something that will be with us forever-that it is impossible to beat that puzzle-that this is the way nature really is.” Physicists are troubled that this is the way the real world is, but we have come to accept it so we can learn more about the mysteries of the real world. We examine advanced ideas surrounding the Stern-Gerlach experiment and its extensions including delayed-choice experiments, interaction-free experiments, and Bell experiments.
Two mysteries -loosely connected?The Authors who have suggested a deep connection between the solution of the mind-body problem and the understanding of quantum mechanics are too numerous to list.But what exactly would be the alleged structural fit between these two deeply puzzling theoretical issues?Can a genuine philosophical issue -which by its very nature is conceptual in nature -ultimately be resolved by advances in the empirical sciences?The connection is all too often asserted to lie in the subjects confounding natures, but the mere fact that two problems are of equal impenetrability to the human mind does not imply that there is a profound interdependence between the two.There is however an obvious way in which quantum mechanics might have a bearing on the philosophical mind-body problem: if quantum mechanics implies that for some physical events there is no physical cause, then at least the very strong variants of the so-called "principle of causal closure" of the physical realm lose much of their corroborative underpinning in physics as practiced by real physicists as such, and are thus constrained to the speculative physicalism advanced by metaphysicians.However, unless one assumes a strong version of the principle of sufficient reason, which would exclude chance events in principle, even events supposedly not caused by some physical cause are not immediately thereby caused by some nonphysical cause.Moreover the fact is that not all of the interpretations of quantum mechanics imply indeterministic 'choices' of events: neither the many-worlds interpretation nor a Bohmian hidden variable interpretation assume indeterminism.Even in the most obvious theoretical nexus
In previous chapters we presented and discussed the standard, generally accepted Copenhagen interpretation of quantum mechanics according to which there exists in nature at the most fundamental level an irreducible and ineliminable indeterminism. Although we saw that what historically constituted the Copenhagen interpretation of quantum mechanics is difficult to specify with precision, three central commitments do characterize it. (1) In general, no particle trajectories can exist in a space–time background. (2) No deterministic description of fundamental physical phenomena is possible. (3) There exists in the laws of the fundamental physical phenomena of nature an essential and ineliminable indeterminism or probability (unlike the probability of classical physics, that there reflects our ignorance of the finer details of complex physical phenomena). A flavor of these features of the Copenhagen interpretation of quantum mechanics can be gotten from the quotations at the beginning of Part VIII ( Some philosophical lessons from quantum mechanics ). On this view, it is in principle impossible to predict, say, the exact future behavior of an electron (that is, to give its position and velocity as functions of the time). According to the Copenhagen school, there can be no causal description of microphenomena in terms of a continuous space–time background (as there is in classical physics). It is generally believed that a causal interpretation of quantum mechanics is impossible, although no proof of this exists.