Counterfactual restrictions and Bell's theorem

Jonte R. Hance

Tomasz Bigaj

Jonte R. Hance

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.

Jonte R. Hance

Counterfactual definiteness is shown from analysis of Bell's Theorem to be the factor separating classical from quantum theories. From this, it is shown that, by replacing it with 'counterfactual semi-definiteness', the definiteness of possible options available after a measurement event, some apt analysis of possible states can be kept. While not as solid as that forbidden by the EPR paradox and Bell's Theorem, it allows us to start investigating the physical implementation of possible states in a way that has rarely been done. Working from this, the idea of counterfactuality, and interaction between counterfactual possibilities, is developed further.

А. В. Белинский