Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal

TitleVon Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Publication TypeJournal Article
Year of Publication2010
AuthorsBub, J
JournalFoundations of Physics
Pages1333 - 1340
Date Published2010/6/11

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 pre-measurement 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.

Short TitleFound Phys