Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

TL;DR

This paper demonstrates that in algebraic quantum field theory, the Weak Reichenbach's Common Cause Principle holds for local systems with certain causality and state properties, linking local causality to correlations.

Contribution

It proves that local primitive causality ensures the Weak Reichenbach's Common Cause Principle in algebraic quantum field theory.

Findings

Weak Reichenbach's principle holds under local primitive causality.

Correlations have common causes in regions within backward light cones.

Results connect local causality with quantum correlations.

Abstract

If \{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 (A(V_1),A(V_2),\phi) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A \in A(V_1), B \in A(V_2) correlated in the normal state \phi 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 (A(V_1),A(V_2),\phi) with a locally normal and locally faithful state \phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common Cause Principle.