Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

Abstract

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B