HoferSzabó, Gábor and Vecsernyés, Péter
(2012)
Bell inequality and common causal explanation in algebraic quantum field theory.
In: UNSPECIFIED.
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 quantum 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 'common causal justification' of these nonclassical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the nonclassical case, the Bell inequalities used in quantum theories cannot be derived from these nonclassical common causes. Just the opposite is true: for a set of correlations there can be given a nonclassical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the nonclassical case is wider than that restricted by the Bell inequalities.
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