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

TL;DR

This paper investigates the validity of Reichenbach's Weak Common Cause Principle in algebraic quantum field theory with locally finite degrees of freedom, showing it generally fails but suggesting noncommutative solutions may still hold.

Contribution

It demonstrates the failure of the Weak Common Cause Principle in certain quantum field models and explores the potential for noncommutative common causes to restore the principle.

Findings

Weak Common Cause Principle is not valid in these models

Existence of states with no common cause in the union of backward light cones

Noncommuting common cause solutions can exist in these states

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.