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Particles can be distinguished by their trajectories in Bohmian quantum mechanics and there is no natural reason for imposing symmetrization (or anti-symmetrization) of the wave function of the particles (as opposed to the usual formulation of quantum mechanics where symmetrization is necessary).

I think it is very ad-hoc and unnatural to impose this property by hand as is explained in this introduction https://plato.stanford.edu/entries/qm-bohm/#IP.

Is this an objection to Bohmian quantum mechanics?

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"Is this an objection to Bohmian quantum mechanics?"

It's a very weak objection since it is not about failing to explain the data, it's just a complaint that the spin-statistics connection is unmotivated in the Bohmian framework. I am not actually sure this is true.

The fact that Bohmian mechanics requires a preferred frame of reference, and an ontological preferred gauge-fixing, in order to describe theories with relativistic or gauge symmetries, seems more serious to me. And even more serious is the challenge of describing a fermionic field. Reviving the Dirac sea seems to be the only idea anyone has.

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  • $\begingroup$ Thanks a lot, I didn't find a logical connection between symmetriation of the wave function and Bohmian mechanics in the literatures. I am not agree with you that this is just a complaint. It is related to some profound phenomena such as Bose-Einstein condensation, so Bohmian mechanics should explain this property (symmetrization of the wave function) from a fundamental point of view. Your concerns are very interesting, would you please show me some references on these subjects. $\endgroup$
    – reza-ebadi
    Commented May 18, 2022 at 6:58

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