Hidden variables and the two theorems of John Bell

1993/07/01 by N. David Mermin · 2 voices · 71 citations
Arts and Humanities · Chemistry · Physics and Astronomy · #History and advancements in chemistry #Philosophy and History of Science #Quantum Mechanics and Applications #physics.hist-ph #quant-ph

paper · pdf · doi:10.1103/revmodphys.65.803

openalex publication_date 1993/07/01 · arxiv published 2018/02/27 · arxiv updated 2018/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• On the Problem of Hidden Variables in Quantum Mechanics
• On the Einstein Podolsky Rosen paradox
• The Problem of Hidden Variables in Quantum Mechanics

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• The Logic of Consistent Histories: A Reply to Maudlin
• On the Unconditional Validity of J. von Neumann's Proof of the Impossibility of Hidden Variables in Quantum Mechanics
• Throwing bridges: where and how can classical and quantum view be connected?
• Non-locality, Contextuality and Transition sets
• Ontological models and the interpretation of contextuality
• Generalized parity proofs of the Kochen-Specker theorem
• Correspondence between quasiparticle dissipation and quantum information decay in open quantum systems
• Common Denominator for Value and Expectation No-Go Theorems
• Quantum realism and quantum surrealism
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• Maximum Bell Violations via Genetic Algorithm Search
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Discussions

• Consider the Hilbert space $$\mathcal{H} = \mathrm{span}\left( \{ |0\rangle\ |0\rangle, |0\rangle\ |1\rangle, |1\rangle\ |0\rangle, |1\rangle\ |1\rangle \} \right) \cong \mathbb{C}^4$$ of (pure) state [stackexchange, 4 points]
• Quantum Contextuality was discovered concomitantly by Kochen-Specker , with their set of 117 directions , and by John S. Bell , in his article about hidden variables [1] . This Bell article is very we [stackexchange, 2 points]

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