Counterfactual restrictions and Bell's theorem

TL;DR

This paper demonstrates that counterfactual restrictions are essential for Bell's theorem, showing that violations of Bell inequalities can occur without full counterfactual definiteness, by restricting certain measurement choices.

Contribution

It introduces the concept of counterfactual restriction as a new way to interpret violations of statistical independence in Bell's theorem, linking it to contextuality.

Findings

Counterfactual restrictions are necessary for Bell inequality violations.

Counterfactual definiteness arises from statistical independence.

Counterfactual restriction offers an alternative interpretation to retrocausality or superdeterminism.

Abstract

We show that the ability to consider counterfactual situations is a necessary assumption of Bell's theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices be counterfactually restricted, rather than the full removal of counterfactual definiteness. We illustrate how the counterfactual definiteness assumption formally arises from the statistical independence assumption. Counterfactual restriction therefore provides a way to interpret statistical independence violation different to what is typically assumed (i.e. that statistical independence violation means either retrocausality or superdeterminism). We tie counterfactual restriction to contextuality, and show the similarities to that approach.