von Neumann’s Theorem Revisited

Foundations of Physics 51 (3):1-29 (2021)
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Abstract

According to a popular narrative, in 1932 von Neumann introduced a theorem that intended to be a proof of the impossibility of hidden variables in quantum mechanics. However, the narrative goes, Bell later spotted a flaw that allegedly shows its irrelevance. Bell’s widely accepted criticism has been challenged by Bub and Dieks: they claim that the proof shows that viable hidden variables theories cannot be theories in Hilbert space. Bub’s and Dieks’ reassessment has been in turn challenged by Mermin and Schack. Hereby I critically assess their reply, with the aim of bringing further clarification concerning the meaning, scope and relevance of von Neumann’s theorem. I show that despite Mermin and Schack’s response, Bub’s and Dieks’ reassessment is quite correct, and that this reading gets strongly reinforced when we carefully consider the connection between von Neumann’s proof and Gleason’s theorem.

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Citations of this work

The Open Systems View.Michael E. Cuffaro & Stephan Hartmann - 2024 - Philosophy of Physics 2 (1):6:1-27.
Hilbert-style axiomatic completion: On von Neumann and hidden variables in quantum mechanics.Chris Mitsch - 2022 - Studies in History and Philosophy of Science Part A 95 (C):84-95.
Einstein Completeness as Categoricity.Iulian D. Toader - 2023 - Foundations of Physics 53 (2):1-15.
The Dual Dynamical Foundation of Orthodox Quantum Mechanics.Diana Taschetto & Ricardo Correa da Silva - 2025 - Studies in History and Philosophy of Science Part A 109 (C):89-105.

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