Current Status of Bohmian Mechanics

Bohmian mechanics has been thoroughly developed in the non-relativistic regime. There are existence/uniqueness results for the theory, proofs of the equivalence to the standard quantum formalism, extensions to spin and other value spaces, explanations for the Bose-Fermi alternative, and a host of other results.

As for relativistic concerns, there are proposals for dealing with nonlocality by use of additional structures. There is nothing mathematically that prevents this from being possible, but there has yet to be found a solution that feels natural.

As for quantum field theory, there seem to be a variety of ways of dealing with it from a hidden variables take on the fields to creation/annihilation of particles to even the Dirac sea. What is strongly lacking is a mathematically sound version of quantum field theory. Bohmian mechanics needs wave function evolution and needs it to be sensible. As of yet, most of quantum field theory seem to be approximations that work around the lack of a sensible wave function evolution.

Much needs to be done, but much has already been accomplished. The field is vibrant and alive though the attitudes towards it still make us recommend that those who wish to pursue it need to think carefully about how much they value their career. It is better to keep an eye on it, work on it in the dark, and be ready for the day it may become accepted.

There is no known argument that discounts Bohmian mechanics from being the foundations for quantum physics. And those who have studied will attest that it makes quantum mechanics as simple to understand as Newtonian mechanics. Even simpler, in some ways.