2007/06/15 by H. M. Wiseman, H M Wiseman · 13 citations
Arts and Humanities · Physics and Astronomy · Psychology · #Philosophy and History of Science #Philosophy and Theoretical Science #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1088/1367-2630/9/6/165
published as New J. Phys. 9 165 (2007) · 11 pages
openalex publication_date 2007/06/15 · arxiv created 2007/06/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.