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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2$\begingroup$ Which anomalies? $\endgroup$– Qmechanic ♦Jun 5, 2018 at 20:02
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1$\begingroup$ 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 vJun 8, 2018 at 12:30
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$\begingroup$ @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) $\endgroup$– LukeJun 11, 2018 at 11:08
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$\begingroup$ @annav Being an interpretation does not imply that it can make no new predictions. The fact that the interpretation requires different axioms from the standard formalism means that in principle different predictions are possible. The very fact that de Broglie-Bohm theory predicts continuous trajectories is itself a "new prediction." The important question is whether a prediction is testable. $\endgroup$– The LedgeMay 1, 2020 at 19:10
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$\begingroup$ @TheLedge whether a prediction is testable." if there were testable predctions it would no longer be an interpretation. Special relativity can be considered at low velocities as an interpretation of Galilean realtivity, i.e. mathematical model that gives the same measureable results. But it is a new theory because its hive velocity predictions are validated. (in my physics vocabulary ofcourse) $\endgroup$– anna vMay 2, 2020 at 3:20
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3 Answers
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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. $\endgroup$ Jun 8, 2018 at 17:36
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I know this is already a few years old, and I think the answers given are good. I just wanted to add one more idea to the list.
In his 1993 book The Undivided Universe: An Ontological Interpretation of Quantum Theory, David Bohm talks about active information--information which governs or "informs" the behavior of a system, but which need not impart energy to the system for the effect to take place. As an illustrative example he asks the readers to consider a radio-controlled boat. Its movement is controlled by the information contained in a radio wave, but this effect is independent of the amplitude of the wave. Thus the wave is important only as a carrier of information, not as a carrier of energy. As another example he mentions DNA. DNA carries information which governs our organism, but the energy required to carry out its instructions comes not from the DNA but from some ingested outside source.
Bohm shows how the wave function can be seen as active information, governing the movement of particles by its form but not its amplitude, with the particles getting the energy necessary to carry out its instructions from some other source (he talks about where they might get this energy in the book). Quoting from the book:
. . . we can go once again into the example that we gave earlier of the electron in an interference experiment. [. . .] As the particle reaches certain points in front of the slits, it is 'in-formed' to accelerate or decelerate accordingly, sometimes quite violently.
Although [the equation of motion for the particle] may look like a classical law implying pushing or pulling by the quantum potential, this would not be understandable because a very weak field can produce the full effect which depends only on the form of the wave . . .
The fact that the particle is moving under its own energy, but being guided by the information in the quantum field, suggests that an electron or any other elementary particle has a complex and subtle inner structure.
The full discussion can be found on pages 35-38 (section 3.2).
I don't think that this idea (that "elementary particles" are not elementary, but have internal structure) has ever been formalized, but it certainly is not predicted by the standard quantum formalism. If one could use some rigorous mathematical formalism to describe the manner in which an electron is decomposed (presumably involving unfathomabe energies), this prediction would be testable (in principle).
