Grounding Bohmian Mechanics in Weak Values and Bayesianism

Bohmian mechanics (BM) is a popular interpretation of quantum mechanics 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 Ṗ + ∇ · j = 0. In this article 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 quantum mechanics. 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 ẋ = j/P 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. PACS numbers: 03.65.Ta, 03.70.+k Grounding Bohmian Mechanics in Weak Values and Bayesianism 2