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

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 and , respectively, a correlating sta...

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Bibliographic Details
Published inFoundations of physics Vol. 42; no. 2; pp. 241 - 255
Main Authors Hofer-Szabó, Gábor, Vecsernyés, Péter
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.02.2012
Subjects
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Statistical Physics and Dynamical Systems
Algebraic quantum field theory
Ising model
Reichenbach’s Common Cause Principle
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Summary: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 and , 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 and 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.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-011-9594-8