, Volume 40, Issue 9, pp 13331340
First online:
Von Neumann’s ‘No Hidden Variables’ Proof: A ReAppraisal
 Jeffrey BubAffiliated withPhilosophy Department and Institute for Physical Science and Technology, University of Maryland Email author
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Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of premeasurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.
Keywords
Hidden variables von Neumann’s proof Foundations of quantum mechanics Title
 Von Neumann’s ‘No Hidden Variables’ Proof: A ReAppraisal
 Journal

Foundations of Physics
Volume 40, Issue 910 , pp 13331340
 Cover Date
 201010
 DOI
 10.1007/s1070101094809
 Print ISSN
 00159018
 Online ISSN
 15729516
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Hidden variables
 von Neumann’s proof
 Foundations of quantum mechanics
 Industry Sectors
 Authors

 Jeffrey Bub ^{(1)}
 Author Affiliations

 1. Philosophy Department and Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA