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Classicality and Bell's Theorem

Gomori, Marton and Hoefer, Carl (2023) Classicality and Bell's Theorem. [Preprint]


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A widespread view among physicists is that Bell's theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed is not a mark of the validity of classical physics, nor of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell's theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell's inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner's operational quantum mechanics and Robert Griffiths' consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell's theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell's theorem.

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Item Type: Preprint
Additional Information: Forthcoming in European Journal for Philosophy of Science
Keywords: classicality, Bell's theorem, Common Cause Principle, locality, conditional probability, interpretations of quantum mechanics
Subjects: General Issues > Causation
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Mr. Marton Gomori
Date Deposited: 26 May 2023 19:49
Last Modified: 26 May 2023 19:49
Item ID: 22150
Subjects: General Issues > Causation
Specific Sciences > Physics > Quantum Mechanics
Date: 2023

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