Contextual hidden variables theories and bell's inequalities

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when factorisability is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed.
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DOI 10.1093/bjps/35.1.25
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Soazig Le Bihan (2009). Fine's Ways to Fail to Secure Local Realism. Studies in the History and Philosophy of Modern Physics 40 (2):142-150.
Federico Laudisa (1996). Non-Locality: A Defence of Widespread Beliefs. Studies in History and Philosophy of Science Part B 27 (3):297-313.

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