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I would like to know if even bosons in the same quantum state, like in a BEC, can be discerned (by their positions) in Bohm's mechanics.

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Bohmian mechanics is basically unsatisfactory when discrete quantum numbers are involved. Bohm devised his pilot wave theory to provide an adequate alternative description of the motion of quantum-mechanical particles. It works for answering questions about the continuous observables $\vec{x}$ and $\vec{p}$ (and other things that can be constructed from these, such as the energy $H$).

However, as Bohm himself acknowledged, the pilot wave theory does not provide an adequate description of spin in quantum mechanics. There is no Bohmian mechanics of a pure angular system. The only known way to deal with angular motion is to introduce the discrete spin variables, in the way introduced by Uhlenbeck and Goudsmit. Bohm himself used the discrete spin variables to give the modern formulation of the Einstein-Podolsky-Rosen paradox. (The original description of the EPR paradox used position-momentum correlations, rather than anticorrelated spin states to produces the "spooky action at a distance.")

The description of quantum statistics is also ultimately a description in terms of discrete quantum numbers. There exists a set of single-particle states*, and an eigenstate of the theory is a set of occupation numbers, describing how many particles are present in each state of the spectrum. The full, many-particle wave function is therefore described by a discrete collection of states; there is a complex amplitude associated with every allowed set of occupation numbers (as determined from Bose-Einstein or Fermi-Dirac statistics). And just as in discrete-state spin systems, there is no adequate Bohmian formulation of this phenomenon.

*In an interacting theory, the single-particle states must be determined self consistently—but this is an irrelevant complication for the present purposes.

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