Grounding Bohmian mechanics in weak values and bayesianism

File Size Format
Title Grounding Bohmian mechanics in weak values and bayesianism Wiseman, Howard Mark New Journal of Physics Eberhard Bodenschatz 2007 Online IOP Publishing Ltd 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. Yes Yes http://www.iop.org/EJ/journal/NJP http://dx.doi.org/10.1088/1367-2630/9/6/165 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. 9 165-1 165-12 1367-2630 2008-02-25 en_AU Centre for Quantum Dynamics Faculty of Science, Environment, Engineering and Technology PRE2009-Theoretical Physics http://hdl.handle.net/10072/18286 Journal Articles (Refereed Article) c1