Bell Inequalities as Constraints on Unmeasurable Correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations . Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations...

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Bibliographic Details
Published in:Foundations of physics 2012-04, Vol.42 (4), p.544-554
Main Authors: Budroni, Costantino, Morchio, Giovanni
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Statistical Physics and Dynamical Systems
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Summary:The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations . Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈 A i 〉, 〈 B 〉, 〈 A i B 〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation 〈 A 1 A 2 〉 associated to different choices for B . The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-012-9625-0