Counterfactual restrictions and Bell's theorem

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.