My understanding is that Bohmian Mechanics (pilot wave theory) is non-local, meaning that effects propagate faster than light. Are these effects in fact instantaneous in that model? How would an example pilot wave change over time (ie as the particle moves)?

Also, bonus question, what prevents using this behavior for super-luminal communication?

  • $\begingroup$ How do you square an assumed faster than light, or instantanous even, (take your pick) pilot wave with changes over time? What prevents any non local event from being used for comunication? physics.stackexchange.com/questions/200642/… $\endgroup$ – user140606 Jan 25 '17 at 23:16
  • $\begingroup$ @Countto10 There are many ways you can square that. The specific answer is something I'm looking for, but one possible thing I can think of is that the pilot wave's shape and position depends on the current state of its riding particle (eg momentum and position), and when that particle's state changes, its pilot wave would change instantaneously everywhere in the universe. But this is only one possible behavior, and my question is asking what behavior is actually suggested by the theory. $\endgroup$ – B T Jan 25 '17 at 23:35
  • $\begingroup$ If you downvote, please explain why $\endgroup$ – B T Jan 26 '17 at 2:07
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    $\begingroup$ The informative bit: I know you are not asking me personally, but I don't d\v because I don't know enough about the subject to judge. The preachy bit: I think you could expand on your subject a bit, especially with interpretation associated question (always dicey IMO), as in this case I might have given a bit of background. Best of luck with your question , though. I have Bohm's book on basic QM (it's 60 years old) and I think it's very good, he spends a lot of time on background. $\endgroup$ – user140606 Jan 26 '17 at 5:02

The "pilot wave" is the same as the multi-particle wavefunction in quantum mechanics, so it evolves according to the Schrodinger equation. Such a wavefunction is not a field in three-dimensional space, it is a field in 3N-dimensional space where N is the number of particles.

The equation of motion for the particles in three-dimensional space depends on the gradient of the complex phase in that 3N-dimensional space. This part is exactly the same as classical Hamilton-Jacobi theory, which is an alternative representation of the forces of classical mechanics. But building trajectories from the quantum-mechanical wavefunction adds an extra nonlocal force.

You can't send nonlocal signals in Bohmian mechanics because you can't do that in quantum mechanics, and Bohmian mechanics is just quantum mechanics plus particle trajectories. The reason you can't do it in quantum mechanics is because the nonlocal correlations it induces aren't strong enough, they are only strong enough to add a nonlocal extra to a local signal (see quantum teleportation, which requires a local signal to be performed).

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    $\begingroup$ I agree with what you are saying, but it is worth pointing out that in some versions of pilot wave theory the theory does allow for superluminal signaling(!), but it is statistically incredibly unlikely (similar to how in principle a broken egg can 'heal' itself in a Newtonian universe, it's just that probability theory basically says it'll never happen). [This is a particularly nice view point because in this case it is e.g. possible to derive Born's rule (in the same way that one can statistically derive the second law of thermodynamics in a time reversal-symmetric universe).] $\endgroup$ – Ruben Verresen Feb 1 '17 at 2:17
  • $\begingroup$ Interesting, I'm a little lost with 3N space and "extra nonlocal force". I'm still unsure whether the theory is really that the wavefunction changes throughout the entire universe instantaneously. For example, if two particles collide, the wave function changes beyond those particles' worldlines in ways that can't be calculated with information about the wavefunction locally in those places? $\endgroup$ – B T Feb 3 '17 at 0:27
  • $\begingroup$ @RubenVerresen Hmm, but we can theoretically create technology that will heal an egg. I've heard that the nonlocal signalling wouldn't be practical because any successful signal would not be able to be picked out from the noise. It certainly suggests that perhaps one day we'll find a way to send information instantaneously, even if matter will never move faster than light. $\endgroup$ – B T Feb 3 '17 at 0:30

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