Grounding Bohmian mechanics in weak values and bayesianism

By Howard M. Wiseman. 2007

200 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Experimental and Cognitive Psychology, History and Philosophy of Science

View Paper: https://www.semanticscholar.org/paper/b99225fcc92ad6a0a86a11bd31ba356fb01b7d46

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In Atomic and Molecular Physics, and Optics

In Experimental and Cognitive Psychology

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Citations in the corpus

Bohmian Mechanics (2009, result): “A specific procedure [72, 32] of this kind, so-called weak measurements of the velocities, has been carried out experimentally [45], resulting in a picture similar to Figure 1.”
Do We Really Understand Quantum Mechanics? (2012, background): “Moreover, another argument in favor of the usual definition of the Bohmian velocity has been proposed in Reference [609].”
Nonperturbative theory of weak pre-and post-selected measurements (2011, methodology): “concerning the complementarity [177, 178]. Recently, weak PPS measurements were applied to obtain information on the wavefunction of a quantum particle [101, 102]. In particular, the proposal in Ref. [111] was realized in Ref. [101], where weak PPS measurements were used to obtain average trajectori”
Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer (2011, background): “It was recently pointed out that this procedure - weak measurement followed by “post-selection” - provides a natural way of operationally defining a set of average trajectories for a particle [11].”