Grounding Bohmian mechanics in weak values and bayesianism

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Title Grounding Bohmian mechanics in weak values and bayesianism
Author Wiseman, Howard Mark
Journal Name New Journal of Physics
Editor Eberhard Bodenschatz
Year Published 2007
Place of publication Online
Publisher IOP Publishing Ltd
Abstract 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 \dot P + \del . j=0. In this article I show that there is a unique j that can be determined experimentally as a weak value using techniques that would make sense to a classical physicist. Moreover, this operationally defined j equals the standard j, so, assuming \dot x = j/P, the possible Bohmian paths can also be determined experimentally from a large enough ensemble. Furthermore, this approach to deriving BM singles out x as the hidden variable, because (for example) the operationally 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 derived from a Bayesian standpoint, via the principle of indifference.
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Copyright Statement Copyright 2007 Institute of Physics Publishing. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 9
Page from 165-1
Page to 165-12
ISSN 1367-2630
Date Accessioned 2008-02-25
Language en_AU
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject PRE2009-Theoretical Physics
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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