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I find the de Broglie-Bohm pilot wave theory interesting but what I still feel missing in the descriptions I could find so far is that it reformulates what we already know but nobody speaks of new testable predictions that could eventually distinguish it from standard QT (such as a new phenomenon, new particles, etc.. that present QT does not predict or that it sheds light on anomalies, etc). Are there any?

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    $\begingroup$ Which anomalies? $\endgroup$ – Qmechanic Jun 5 '18 at 20:02
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    $\begingroup$ it is one of the "interpretations" of QM en.wikipedia.org/wiki/… , which means no new predictions afaik. In addition it cannot be exended into second quantization, Lorenz transformations etc, afaik again, $\endgroup$ – anna v Jun 8 '18 at 12:30
  • $\begingroup$ @anna v: "In addition it cannot be exended into second quantization, Lorenz transformations etc, afaik again" - it is rather annoying that I always have to tell people they should look into the papers on this subject instead of judging without knowing. Actually, extensions of that kind are discussed in many papers. (e.g.arxiv.org/abs/1307.1714) $\endgroup$ – Luke Jun 11 '18 at 11:08
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Bohmian mechanics contain an assumption that is not that well-known: quantum equilibrium. This basically says that the particles are distributed according to the square of the wave function. Obviously this is essential to reproduce Born rule but this is actually not a hypothesis in Bohmian mechanics: this is an emergent phenomenon. One can then wonder how quickly a system of particle relaxes to that quantum equilibrium. Various simulations shows this is very quick, $10^{-20}$ seconds, plus or minus a few orders of magnitude (!). But then one can entertain the question of what happened in the early universe… Very speculative, I agree, but compared to mainstream subject in theoretical physics, such as superstrings, not so much actually! Here is a reference:

Towler, M. D., N. J. Russell, and Antony Valentini (2012). “Time scales for dynamical relaxation to the Born rule”. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 468.2140, pp. 990–1013

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Actually, Bohmian mechanics is intended as a solution to the measurement problem, as a deeper theory that explains the measurement formalism of standard QM. As such, it is important that it exactly reproduces the predictions of non-relativistic quantum mechanics. And it is proven that it does so. A good reference with all details is here: https://arxiv.org/abs/quant-ph/0308038.

But there are some areas where the predictions of standard QM become ambiguous or, at the very least, hard to compute, e.g. with time measurements. (There is no time operator.) For predictions of arrival time statistics, Bohmian mechanics might give new results. There is a nice recent paper on https://arxiv.org/abs/1802.07141. But so far,the experiments to test this have not been carried out.

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  • $\begingroup$ The second paper you quoted led me to an interesting review of the subject: Muga, J.G. and C.R. Leavens (2000). “Arrival time in quantum mechanics”. In: Physics Reports 338.4, pp. 353–438. $\endgroup$ – frapadingue Jun 8 '18 at 17:36

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