system
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human
Does the pilot-wave interpretation of quantum mechanics require an absolute reference frame that is incompatible with special relativity?

Hidden variables may not be impossible, but if they require a field that guides particles deterministically, shouldn't we be able to measure our movement through that field (the same way we should have been able to measure our movement through the luminiferous aether, if it existed)? Wouldn't that provide an absolute reference frame? I don't see how pilot wave theory can be made compatible with special relativity. Am I missing something?
gpt
It does require a preferred frame, which means there is only one foliation into spacelike hypersurfaces over which the particle trajectories are actually classically deterministic (which is the essential promise of the interpretation).  Working in other frames, the Bohmian trajectories zig and zag in random, unpredictable ways.  In particular, this can be understood via working out the pilot wave trajectories in EPR experiments.  If one could observe these trajectories, one could use these random zigs to figure out (by process of elimination) which frame was preferred.  But it is also a requirement of the interpretation that one can't ever access these trajectories at the level of granularity required to achieve this.  So strictly speaking it is not consistent with SR, but the problem can be kept under the rug for practical purposes. Whether this is philosophically acceptable is up to you. And pilot wave adherents tend to be willing to abandon exact Lorentz symmetry as a guiding principle.

But preferred frame aside, remember that the pilot wave interpretation is also presented in terms of fundamental particle-like entities, while the union of quantum mechanics and special relativity produces quantum field theory, where particles are not really fundamental in this sense. To the extent particles exist at all in QFT, they instead are more like structured patterns in the fields.  There is no broadly accepted or worked out pilot wave interpretation of quantum fields, and the idea is not particularly promising.  The basic problem is that in QFT there is no analogue of QM's position operator. In QM, particle position can make sense as the defining hidden variable in all cases.  In QFT, there is nothing that can perform this role.  

Additionally, there is no known way to do particle creation and annihilation in a classically deterministic way, even in a pilot wave interpretation. So when we demand this other important feature of QFT, the whole endeavor to save classical determinism fails anyway.