Noncommuting local common causes for correlations violating the Clauser-Horne inequality

TL;DR

This paper demonstrates that in an algebraic quantum field theory setting, noncommuting local common causes can explain correlations that violate the Clauser-Horne inequality, challenging classical causal assumptions.

Contribution

It introduces the concept of noncommuting local common causes as a causal explanation for quantum correlations violating Bell inequalities.

Findings

Noncommuting common causes can explain Bell inequality violations.

Such causes are local and supported in the common past.

Classical commutative causality is not necessary for explaining quantum correlations.

Abstract

In the paper the EPR-Bohm scenario will be reproduced in an algebraic quantum field theoretical setting with locally finite degrees of freedom. It will be shown that for a set of spatially separated correlating events (projections) maximally violating the Clauser-Horne inequality there can be given a common causal explanation if commutativity is abandoned between the common cause and the correlating events. Moreover, the noncommuting common cause will be local and supported in the common past of the correlating events.