Deterministic quantum mechanics

Question

I came across a very recent paper by Gerard 't Hooft The abstract says:

It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born's rule are features that strongly point towards determinism underlying quantum mechanics.

http://de.arxiv.org/abs/1112.1811

I am wondering why this view seems to unpopular?

Answer 1

It is unpopular among physicists because physicists, by definition, "like" theories and claims that correctly describe our world and Gerard 't Hooft's statements about the nature of the wave function are demonstrably invalid in the world around us, whether or not he may construct a contrived toy model where his claims are right and which has some vague features remotely resembling the real world.

The fact that the basic postulates of quantum mechanics are unavoidable has been known to physics at least from the late 1920s. For example, in his book on principles of quantum mechanics, Paul Dirac disproved all theories of 't Hooft's kind on the first three pages

http://motls.blogspot.com/2011/12/paul-diracs-forgotten-quantum-wisdom.html

and these early stages of the book – explaining that all the concepts and mathematical objects in the quantum theory have a new interpretation, one that doesn't coincide with anything we know in classical physics – are indeed a necessary pre-requisite for the reader to actually understand the rest of the theory.

Many other properties of quantum mechanics that couldn't be obtained from any classical theory compatible with relativity were obtained later, when physicists studied properties of entangled states. Bell's inequalities, Hardy's "paradox", GHZM states, Kochen-Specker theorem, free will theorem, and other results uniformly show that the natural phenomena we observe have features that can't be compatible with any theory of the type that Gerard 't Hooft is discussing. That's another set of rather good reasons for a physicist to treat such alternative theories as unpopular ones.

Answer 2

Thanks for the great question, I just skimmed the paper. My reaction: it is still a vague proposal, with hand-waving, ill-defined concepts, and not at all axiomatically 'clean'. For example, he never defines «probability.»

Weinberg and others agree with t'Hooft at least in how to pose the problem: derive the probabilities from the deterministic unitary evolution. There have been real physical models done and published with this end in view, and they tend to take a quantum statistical mechanical approach, so there is some point of contact with some of t'Hooft's attitudes. But the valuable work in this way, as I see it, is using Schroedinger's equation to analyse actual physical measuring devices, such as the important work by Balian and two others at

arXiv:cond-mat/0203460 « Curie-Weiss model of the quantum measurement process.»

: See http://arxiv.org/abs/quant-ph/0507017 for a much less realistic toy model, and my axiomatically clean treatment of it's implications for Hilbert's Sixth problem, the axiomatisation of physics, http://arxiv.org/abs/0705.2554 ,

and Prof. t'Hooft is not even attempting to do that. It seems strange to hope to analyse measurement without thinking of the physics of measuring devices, or solve an axiomatic difficulty about probability without giving it a physical definition. I leave aside rival approaches to the problem, such as the decoherence approach, which some physicists are interested in.

Now QM seems to me, and most physicists, correct physically: the measurement problem is merely an axiomatic problem. Most physicists don't believe there is any new physics to be discovered which is relevant to the issue of determinism or the measurement problem, nor do I. (There are important physicists who are an exception, e.g., I suppose, Penrose.) I believe that a careful axiomatic analysis would be interesting, most physicists do not. I do not see one in this paper.

Answer 3

My understanding is that the Copenhagen intepretation of quantum mechanics (ie. that particles have no definite position/momentum until they are observed) is just one of many interpretations, any one of which could be correct, and that we have no real reason for preferring one to another - they all produce the same results experimentally.

There is, in fact, a semi-popular deterministic interpretation called the De Broglie–Bohm theory. Unfortunately, it relies on an assumption that is even more unintuitive and terrifying (to physicists) than the Copenhagen intepretation: that all particles, everywhere in the universe, are connected by an invisible wave which acts at a distance instantaneously, no matter how large the distance. For obvious reasons, this is called a non-local theory.

Unfortunately, according to Bell's theorem, there can be no explanation of quantum-mechanics which is both local and deterministic. So we must accept that, if there is an underlying explanation for the weirdness of Quantum Mechanics, it must be either non-deterministic (like the Copenhagen Interpretation surmises) or non-local (like the De Broglie-Bohm theory).

For more information, see Nick Herbert's excellent book, Quantum Reality: Beyond the New Physics.

Answer 4

Even great physicists sometimes write weak paper, and this is the case. Any attempt to find some classical deterministic theory behind quantum mechanics failed, so far. And that is because there is not any.

Answer 5

One place to look is the homepage of Antony Valentini now at Clemson University. He claims that Born's probability rule is only an approximation. David Bohm first made this claim. One can show that entanglement can be used for faster-than-light and even retro-causal back-from-the-future delayed choice signaling once the shackles of Born's rule are cast away.