Against a minimalist reading of bell's theorem: Lessons from fine

Synthese 128 (3):343 - 379 (2001)
Abstract
Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/Aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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Reprint years 2004
DOI 10.1023/A:1011971808127
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Quantum Entanglement and a Metaphysics of Relations.Michael Esfeld - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (4):601-617.
On Minkowskian Branching Structures☆.Leszek Wroński & Tomasz Placek - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):251-258.
Quantum Entanglement and a Metaphysics of Relations.Michael Esfeld - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (4):601-617.
Towards a Theory of Limited Indeterminism in Branching Space-Times.Thomas Müller - 2010 - Journal of Philosophical Logic 39 (4):395-423.

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Contextual Hidden Variables Theories and Bell's Inequalities.Abner Shimony - 1984 - British Journal for the Philosophy of Science 35 (1):25-45.
Stochastic Outcomes in Branching Space-Time: Analysis of Bell's Theorem.Tomasz Placek - 2000 - British Journal for the Philosophy of Science 51 (3):445-475.
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Outcomes in Branching Space-Time and GHZ-Bell Theorems.T. Kowalski & Tomasz Placek - 1999 - British Journal for the Philosophy of Science 50 (3):349-375.

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