Foundations of Physics 42 (2):241-255 (2012)

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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, B supported in spacelike separated double cones ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ , 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 ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ 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
Keywords Algebraic quantum field theory  Reichenbach’s Common Cause Principle  Ising model
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DOI 10.1007/s10701-011-9594-8
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References found in this work BETA

The Direction of Time.Hans Reichenbach - 1956 - Dover Publications.
Probabilistic Causality.Wesley C. Salmon - 1980 - Pacific Philosophical Quarterly 61 (1/2):50.
Probabilistic Causality.Wesley C. Salmon - 1980 - In Michael Tooley (ed.), Pacific Philosophical Quarterly. Oxford Up. pp. 137-153.
On Reichenbach's Common Cause Principle and Reichenbach's Notion of Common Cause.G. Hofer-Szabo - 1999 - British Journal for the Philosophy of Science 50 (3):377-399.

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Citations of this work BETA

Bell Inequality and Common Causal Explanation in Algebraic Quantum Field Theory.Gábor Hofer-Szabó & Péter Vecsernyés - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):404-416.
Relativistic Causality in Algebraic Quantum Field Theory.John Earman & Giovanni Valente - 2014 - International Studies in the Philosophy of Science 28 (1):1-48.
Characterizing Common Cause Closedness of Quantum Probability Theories.Yuichiro Kitajima & Miklós Rédei - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (B):234-241.
Distinguishing Causality Principles.Miklós Rédei & Iñaki San Pedro - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (2):84-89.

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