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0 pointsbkcooper11y ago0 comments

What's the current status of Bohm's hidden variable theory? Does it stand up in light of the Bell test?

Yes. Bell's theorem doesn't forbid hidden variable theories (in fact, he has a publication preceding his famous result explicitly demonstrating a hidden variable theory that could reproduce QM measurements on a two-level system), just local hidden variable theories. In his collected papers, Bell often remarks that he feels Bohm's interpretation should be more widely studied.

It's a good question why it's not. My understanding, though I'm not well versed in the subject, is that there are some pretty severe shortcomings to it, particularly when you start considering systems with many particles. I've read some of Bohm's writings to try to understand it and as far as I got I found it pretty underwhelming; it seemed more like a bookkeeping trick than any sort of real insight.

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jostylr11y ago

Try reading some of the stuff from http://www.bohmian-mechanics.net/ I was a student of Sheldon Goldstein of that group and can attest that it has no problems with many particles.

In fact, part of my thesis was explaining how identical particles are handled in Bohmian mechanics. Basically, one considers a configuration space whose points are sets of points in physical space rather than some arbitrarily ordered points. One then immediately gets bosons and there is a principle which guides one to fermions. This works beautifully with spin as well, where the spin is associated with the physical point in space, not with the particle label as is usually done. I find it to be very elegant.

There is also an extension to quantum field theory in which the particle creation and annihilation operators actually represent those events with the Bohm particles. So that is not a problem either. It becomes an indeterministic theory at that point (creation is a random event while annihilation is simply when the particles collide).

The main conceptual question is dealing with instantaneousness of the theory. It is a merit of BM that it brings this to the forefront. One can always put in an arbitrary (hidden) foliation of space-time to deal with it, but it is a bit distasteful even if, as there are, foliations that can be derived the other existing structures.

One final note is that Bell was a very strong proponent of Bohmian mechanics even when Bohm had forgotten about it for a time. Bell's formulation was based on the first order probability flow and not the quantum potential. Bell's version works for spin while the quantum potential does not (sadly for numerical work).