Bell inequality and common causal explanation in algebraic quantum field theory

Szabó, Gábor and Vecsernyés, Péter (2013) Bell inequality and common causal explanation in algebraic quantum field theory. STUDIES IN HISTORY AND PHILOSOPHY OF MODERN PHYSICS, 44 (4). pp. 404-416. ISSN 1355-2198

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Abstract

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quan- tum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a ‘com- mon causal justification’ of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities.

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