I found someone’s thesis from 2020 (Hoi Wai Lai) that sums it up not too badly (from the perspective of someone who wants to make Bohmian mechanics work and was willing to write a thesis about it).
For special relativity (section 6), the problem is that the motion of each hidden particle depends instantaneously on the entire multi-particle wavefunction. According to Lai, there’s nothing better than to bite the bullet and define a “real present” across the universe, and have the hyperparticles sometimes go faster than light. What hypersurface counts as the real present is unobservable to us, but the motion of the hidden particles cares about it.
For varying particle number (section 7.4), the problem is that in quantum mechanics you can have a superposition of states with different numbers of particles. If there’s some hidden variable tracking which part of the superposition is “real,” this hidden variable has to behave totally different than a particle! Lai says this leads to “Bell-type” theories, where there’s a single hidden variable, a hidden trajectory in configuration space. Honestly this actually seems more satisfactory than how it deals with special relativity—you just had to sacrifice the notion of independent hidden variables behaving like particles, you didn’t have to allow for superluminal communication in a way that highlights how pointless the hidden variables are.
Warning: I have exerted basically no effort to check if this random grad student was accurate.
the problem is that in quantum mechanics you can have a superposition of states with different numbers of particles … If there’s some hidden variable tracking which part of the superposition is “real,” this hidden variable has to behave totally different than a particle!
Oh this seems like a pretty big ding to pilot wave if I understand correctly and it’s correct
I found someone’s thesis from 2020 (Hoi Wai Lai) that sums it up not too badly (from the perspective of someone who wants to make Bohmian mechanics work and was willing to write a thesis about it).
For special relativity (section 6), the problem is that the motion of each hidden particle depends instantaneously on the entire multi-particle wavefunction. According to Lai, there’s nothing better than to bite the bullet and define a “real present” across the universe, and have the hyperparticles sometimes go faster than light. What hypersurface counts as the real present is unobservable to us, but the motion of the hidden particles cares about it.
For varying particle number (section 7.4), the problem is that in quantum mechanics you can have a superposition of states with different numbers of particles. If there’s some hidden variable tracking which part of the superposition is “real,” this hidden variable has to behave totally different than a particle! Lai says this leads to “Bell-type” theories, where there’s a single hidden variable, a hidden trajectory in configuration space. Honestly this actually seems more satisfactory than how it deals with special relativity—you just had to sacrifice the notion of independent hidden variables behaving like particles, you didn’t have to allow for superluminal communication in a way that highlights how pointless the hidden variables are.
Warning: I have exerted basically no effort to check if this random grad student was accurate.
Oh this seems like a pretty big ding to pilot wave if I understand correctly and it’s correct