Bell's theorem is an exercise in the statistical theory of causality

TL;DR

This paper derives Bell-CHSH inequalities using modern statistical causality theory with graphical models, clarifying the causal assumptions behind Bell's theorem and addressing recent claims about hidden variables.

Contribution

It presents a novel derivation of Bell's inequalities through graphical causal models, emphasizing the role of causal assumptions and addressing setting-dependent hidden variables.

Findings

Bell-CHSH inequalities derived from causal graphical models

Causal interpretation clarifies the assumptions behind Bell's theorem

Contextual hidden variables do not circumvent Bell's conclusions

Abstract

In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word "local" applies to the way that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables (thought of as being located in the measurement devices and dependent on the measurement settings) is automatically covered, despite recent claims that Bell's conclusions can be circumvented in this way.