Foundations of Physics 32 (3):335-355 (2001)

Authors
Miklós Rédei
London School of Economics
Abstract
If $\mathcal{A}$ (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $\mathcal{A}$ (V 1 ), B∈ $\mathcal{A}$ (V 2 ) correlated in the normal state φ there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2 , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle
Keywords causality  common cause principle  quantum field theory
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Reprint years 2002
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DOI 10.1023/A:1014869211488
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Stochastic Einstein Locality Revisited.Jeremy Butterfield - 2007 - British Journal for the Philosophy of Science 58 (4):805-867.
Reconsidering Relativistic Causality.Jeremy Butterfield - 2007 - International Studies in the Philosophy of Science 21 (3):295 – 328.
Subsystems and Independence in Relativistic Microscopic Physics.Stephen J. Summers - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (2):133-141.

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