Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time

TL;DR

This paper analyzes the minimal causal violations needed to explain Bell experiment correlations, comparing the costs of violating locality, free choice, and arrow-of-time assumptions, including retro-causal models.

Contribution

It extends previous work by considering single-arrow violations and introduces a measure for the minimal violation frequency needed for simulation.

Findings

Locality and free choice assumptions are shown to be equivalent.

Retro-causal models can explain correlations with specific causal assumption violations.

The minimal violation frequency varies depending on the assumption violated.

Abstract

The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice, and arrow-of-time. It turns out that nature violates Bell inequalities, which entails the failure of at least one of those assumptions. Since rejecting any of them - even partially - proves to be enough to explain the observed correlations, it is natural to ask about the cost in each case. This paper follows up on the results in PNAS 118 e2020569118 (2021), showing the equivalence between the locality and free choice assumptions, adding to the picture retro-causal models explaining the observed correlations. Here, we consider more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics.