My understanding is that pilot wave theory (ie Bohmian mechanics) explains all the quantum physics
This is only true if you don’t count relativistic field theory. Bohmian mechanics has mathematical troubles extending to special relativity or particle creation/annihilation operators.
Is there any reason at all to expect some kind of multiverse?
Depending on how big you expect the unobservable universe to be, there can also be a spacelike multiverse.
Could you illustrate the relativistic field theory issue (or link to illustration)? My blind assumption is that people did not try very hard to make it work.
(Spacelike multiverse seems like legit possibility to me.)
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 can help confirm that your blind assumption is false. Source: my undergrad research was with a couple of the people who have tried hardest, which led to me learning a lot about the problem. (Ward Struyve and Samuel Colin.) The problem goes back to Bell and has been the subject of a dedicated subfield of quantum foundations scholars ever since.
This many years distant, I can’t give a fair summary of the actual state of things. But a possibly unfair summary based on vague recollections is: it seems like the kind of situation where specialists have something that kind of works, but people outside the field don’t find it fully satisfying. (Even people in closely adjacent fields, i.e. other quantum foundations people.) For example, one route I recall abandons using position as the hidden variable, which makes one question what the point was in the first place, since we no longer recover a simple manifest image where there is a “real” notion of particles with positions. And I don’t know whether the math fully worked out all the way up to the complexities of the standard model weakly coupled to gravity. (As opposed to, e.g., only working with spin-1/2 particles, or something.)
This is only true if you don’t count relativistic field theory. Bohmian mechanics has mathematical troubles extending to special relativity or particle creation/annihilation operators.
Depending on how big you expect the unobservable universe to be, there can also be a spacelike multiverse.
Could you illustrate the relativistic field theory issue (or link to illustration)? My blind assumption is that people did not try very hard to make it work.
(Spacelike multiverse seems like legit possibility to me.)
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
I can help confirm that your blind assumption is false. Source: my undergrad research was with a couple of the people who have tried hardest, which led to me learning a lot about the problem. (Ward Struyve and Samuel Colin.) The problem goes back to Bell and has been the subject of a dedicated subfield of quantum foundations scholars ever since.
This many years distant, I can’t give a fair summary of the actual state of things. But a possibly unfair summary based on vague recollections is: it seems like the kind of situation where specialists have something that kind of works, but people outside the field don’t find it fully satisfying. (Even people in closely adjacent fields, i.e. other quantum foundations people.) For example, one route I recall abandons using position as the hidden variable, which makes one question what the point was in the first place, since we no longer recover a simple manifest image where there is a “real” notion of particles with positions. And I don’t know whether the math fully worked out all the way up to the complexities of the standard model weakly coupled to gravity. (As opposed to, e.g., only working with spin-1/2 particles, or something.)
Now I want to go re-read some of Ward’s papers...
(If you do go reread then I would love to read some low-effort notes on it similar to your recollection above.)