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Grounding Bohmian mechanics in weak values and bayesianism

H. Wiseman

Published 2007 in New Journal of Physics

ABSTRACT

Bohmian mechanics (BM) is a popular interpretation of quantum mechanics (QM) in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability density P(x). However, this ‘standard’ j is in fact only one of infinitely many that transform correctly and satisfy . In this paper, I show that a particular j is singled out if one requires that j be determined experimentally as a weak value, using a technique that would make sense to a physicist with no knowledge of QM. This ‘naively observable’ j seems the most natural way to define j operationally. Moreover, I show that this operationally defined j equals the standard j, so, assuming , one obtains the dynamics of BM. It follows that the possible Bohmian paths are naively observable from a large enough ensemble. Furthermore, this justification for the Bohmian law of motion singles out x as the hidden variable, because (for example) the analogously defined momentum current is in general incompatible with the evolution of the momentum distribution. Finally I discuss how, in this setting, the usual quantum probabilities can be motivated from a Bayesian standpoint, via the principle of indifference.

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