Response: Commentary: Is the moon there if nobody looks? Bell inequalities and physical reality

TL;DR

This paper defends the authors' original interpretation of Bell test experiments, emphasizing that their contextual probabilistic model explains quantum correlations and violations of Bell inequalities without assuming classical joint distributions.

Contribution

The paper clarifies misconceptions about Bell inequalities, demonstrating that their contextual model accounts for quantum violations while respecting locality and causality.

Findings

Bell inequalities are violated in experimental data.

Contextual probabilistic models explain quantum correlations.

Counterfactual models do not invalidate the original derivation.

Abstract

We reject unjustified criticism of our published article [2209.07992] by Gill and Lambare [arXiv:2211.02481, arXiv:2208.09930]. They completely misinterpret the content and conclusions of this article. They construct a counterfactual probabilistic model in which random variables representing outcomes of four experiments performed using incompatible experimental settings are jointly distributed. Thus, CHSH inequalities trivially hold for all finite samples generated by their model. Their model defines a probabilistic coupling for our model describing only the raw data from Bell tests. The existence of this coupling does not invalidate the derivation of the contextual probabilistic model describing the final data from Bell tests. Only these final data are used to test Bell inequalities. Inequalities cannot be derived because our model violates statistical independence. Our contextual model allows to explain in a local and causal way the violation of inequalities and the apparent violation of no-signaling reported in these experiments.