Bell inequality and common causal explanation in algebraic quantum field theory

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):404-416 (2013)
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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 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 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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Gábor Hofer-Szabó
Research Center For The Humanities, Budapest

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References found in this work

Algebraic quantum field theory.Hans Halvorson & Michael Mueger - 2006 - In J. Butterfield & J. Earman (eds.), Handbook of the philosophy of physics. Kluwer Academic Publishers.
Beables for quantum field theory.J. S. Bell - 1987 - In Basil J. Hiley & D. Peat (eds.), Quantum Implications: Essays in Honour of David Bohm. Methuen. pp. 227--234.
Events and processes in the quantum world.Abner Shimony - 1986 - In Roger Penrose & C. J. Isham (eds.), Quantum Concepts in Space and Time. New York ;Oxford University Press. pp. 182--203.
Stochastic Einstein Locality Revisited.Jeremy Butterfield - 2007 - British Journal for the Philosophy of Science 58 (4):805-867.

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