2010/06/02 by Jeffrey Bub · 2 citations
Computer Science · Physics and Astronomy · Psychology · #Computability, Logic, AI Algorithms #Philosophy and Theoretical Science #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1007/s10701-010-9480-9
8 pages, no figures; for Peter Mittelstaedt Festschrift issue of Foundations of Physics
arxiv created 2010/06/02 · openalex publication_date 2010/06/10 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.