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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

When can hidden variables be excluded in quantum mechanics?

Baidyanath Misra

Published Feb 1, 1967• 34 citations
Publisher
DOI
10.1007/bf02771399

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The question of the possible existence of hidden variables is re-examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every other one. It is further shown that this property is in contradiction with empirical facts. The theorem which leads to this conclusion is a strengthening of the theorem of von Neumann on the same subject. The question is raised whether there exist perhaps quantum mechanical systems which admit approximate dispersion-free states.
Bell's theorem (1964) excludes local hidden-variable completions of quantum mechanics.This paper argues that the theorem does not exclude non-local ontological completion, andthat the Field component of the Field–Node–Cockpit (FNC) model satisfies the constraintsBell's result imposes on any viable hidden variable. The proposal is interpretive, notrevisionary: it does not modify quantum mechanical predictions but offers a frameworkwithin which quantum non-locality and phenomenal consciousness become aspects of asingle ontological structure. The paper distinguishes carefully between empirical claims (Bellviolations), ontological proposals (Field as ground), and phenomenological implications(consciousness as Field-access), arguing that these levels are compatible butmethodologically distinct.Keywords: Bell's theorem, hidden variables, non-locality, consciousness,Field–Node–Cockpit model, philosophy of physics
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no–go arguments against non–contextual hidden variables. All such arguments rely on choosing special sets of quantum–mechanical observables with measurement outcomes that cannot be simulated non–contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a non–contextual hidden–variable model. We show here by explicit construction that there are indeed such non–contextual hidden–variable models, both for projection–valued and positive–operator–valued measurements.