Acuña, Pablo
(2021)
Must Hidden Variables Theories Be Contextual? Kochen & Specker meet von Neumann and Gleason.
European Journal for Philosophy of Science, 41.
ISSN 1879-4912
Abstract
It is a widespread belief that the Kochen-Specker theorem imposes a contextuali-ty constraint on the ontology of beables in quantum hidden variables theories. On the other hand, after Bell’s influential critique, the importance of von Neumann’s wrongly called ‘impossibility proof’ has been severely questioned. However, Max Jammer, Jeffrey Bub and Dennis Dieks have proposed insightful reassessments of von Neumann’s theorem: what it really shows is that hidden variable theories cannot represent their beables by means of Hermitian operators in Hilbert space. Hereby I show that i) the very same constraint can be derived from Gleason’s theorem, and that ii) if we consider the import of von Neumann’s and Gleason’s theorems, the relevance of the Kochen-Specker theorem for hidden variables the-ories gets substantially weakened: it does not force them to be contextual in any interesting sense of the term.
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