Von Neumann's `No Hidden Variables' Proof: A ReAppraisal
Abstract
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.
 Publication:

Foundations of Physics
 Pub Date:
 October 2010
 DOI:
 10.1007/s1070101094809
 arXiv:
 arXiv:1006.0499
 Bibcode:
 2010FoPh...40.1333B
 Keywords:

 Hidden variables;
 von Neumann’s proof;
 Foundations of quantum mechanics;
 Quantum Physics
 EPrint:
 8 pages, no figures