Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom

Abstract

In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A and B supported in spacelike separated double cones O(a) and O(b), respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of O(a) and O(b) and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models.

References in corpus (1)

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Cited by in corpus (6)

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• Noncommutative Common Cause Principles in Algebraic Quantum Field Theory
• Distinguishing Causality Principles
• On the concept of Bell's local causality in local classical and quantum theory
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• Characterizing common cause closedness of quantum probability theories