In a recent preprint Gill and Lambare, criticize our paper published in Frontiers in Physics. Their criticism is unfounded and misleading. They define a probabilistic coupling, in which BI-CHSH hold for all finite samples. It does not mean, that BI-CHSH hold in our model, in which four incompatible experiments are described by setting dependent random variables implemented on 4 disjoint dedicated probability spaces. A joint probability distribution of these random variables does not exist and may not be used to derive inequalities. Moreover, their probabilistic coupling is useless, for a subsequent contextual model, which we construct to describe final data from Bell tests and to explain, in a locally causal way, the reported violations of inequalities and apparent violations of no-signaling. Neither quantum probabilistic model of an ideal EPRB experiment nor local realistic and stochastic hidden variable models may explain reported non-signaling Therefore; it is obvious that our model extends the set of probability distributions of possible measurements allowed in the standard hidden variable models. Gill and Lambare seem not understand , the main message of our paper, that the violation of BI-CHSH and Eberhard inequalities by finite samples in Bell Tests, no matter how well these tests are designed and performed, does not allow for doubt regarding the existence of objective external physical reality and causal locality in Nature. Our contextual model does not want to circumvent Bell Theorem. Therefore the title of Gill and Lambare paper and the conclusion: Kupczynski's escape route for local realism is not available are misleading and have nothing to do with the content and conclusions of our paper.
In a recent preprint Gill and Lambare, criticize our paper published in Frontiers in Physics. Their criticism is unfounded and misleading. They define a probabilistic coupling, in which BI-CHSH hold for all finite samples. It does not mean, that BI-CHSH hold in our model, in which four incompatible experiments are described by setting dependent random variables implemented on 4 disjoint dedicated probability spaces. A joint probability distribution of these random variables does not exist and may not be used to derive inequalities. Moreover, their probabilistic coupling is useless, for a subsequent contextual model, which we construct to describe final data from Bell tests and to explain, in a locally causal way, the reported violations of inequalities and apparent violations of no-signaling. Neither quantum probabilistic model of an ideal EPRB experiment nor local realistic and stochastic hidden variable models may explain reported non-signaling Therefore; it is obvious that our model extends the set of probability distributions of possible measurements allowed in the standard hidden variable models. Gill and Lambare seem not understand , the main message of our paper, that the violation of BI-CHSH and Eberhard inequalities by finite samples in Bell Tests, no matter how well these tests are designed and performed, does not allow for doubt regarding the existence of objective external physical reality and causal locality in Nature. Our contextual model does not want to circumvent Bell Theorem. Therefore the title of Gill and Lambare paper and the conclusion: Kupczynski's escape route for local realism is not available are misleading and have nothing to do with the content and conclusions of our paper.
In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring instruments and variables describing physical systems, at the moment of their interactions. These setting dependent variables may be correlated, but not necessarily due to spooky influences or superdeterminism. In several Bell Tests, two time series of distant clicks are converted into finite samples containing pairs of non zero outcomes. This data not only violates CHSH inequalities but also nonsignalling. Our model allows explaining both the raw and the final data in these experiments. Moreover, our model, does not compromise experimenters freedom of choice. The violation of nonsignaling is neither consistent with quantum description of an ideal EPRB experiment nor with standard local realistic and stochastic hidden variable models, thus the title of this article and its conclusion: Kupczynski escape route for local realism is not available are misleading.
Bell-CHSH inequalities are trivial algebraic properties satisfied by each line of Nx4 spreadsheets containing ±1 entries, thus it is surprising that their violation in some experiments allows to speculate about the existence of nonlocal influences in nature and casts doubt on the existence of external physical reality. Such speculations are rooted in incorrect interpretations of quantum mechanics and in a failure of local realistic hidden variable models to reproduce quantum predictions for spin polarisation correlation experiments (SPCE). In these models, one uses a counterfactual joint probability distribution of only pairwise measurable random variables (A, A’, B, B’) to prove Bell-CHSH inequalities. In SPCE Alice and Bob, using 4 incompatible pairs of experimental settings, estimate imperfect correlations between clicks registered by their detectors. Clicks announce detection of photons and are coded by ±1. Expectations of corresponding random variables: E (AB), E (AB’), E (A’B) and E (A’B’) are estimated and compared with quantum predictions. These estimates significantly violate CHSH inequalities. Since variables (A, A’) as well as (B, B’) cannot be measured jointly, neither Nx4 spreadsheets nor a joint probability distribution of (A, A’, B, B’) exist, thus Bell-CHSH inequalities may not be derived. Nevertheless, imperfect correlations between clicks in SPCE may be explained in a locally causal way, if contextual setting-dependent parameters describing measuring instruments are correctly included in the description. The violation of Bell-CHSH inequalities may not therefore justify the existence of a spooky action at the distance, super-determinism or speculations that an electron can be here and a meter away at the same time. In this paper we review and rephrase several arguments proving that such conclusions are unfounded. Entangled photon pairs cannot be described as pairs of socks nor as pairs of fair dice producing in each trial perfectly correlated outcomes. Thus the violation of inequalities confirms only that the measurement outcomes and `the fate of photons ` are not predetermined before the experiment is done. It does not allow for doubt regarding the objective existence of atoms, electrons and other invisible elementary particles which are the building blocks of the visible world around us including ourselves.
Bell's theorem states that no description of a Bell experiment can be simultaneously local, realistic in the sense of counterfactual definiteness, and free of conspiracy between settings and hidden state. The recent generation of experiments has confirmed the predicted violation of the CHSH inequality, so one of the assumptions must be abandoned. Which one, and how one reconstructs a coherent worldview after doing so, is a question on which many authors disagree. This paper is written by three such authors. All three reject both counterfactual definiteness and conspiratorial violation of statistical independence of setting choices and state. After a joint exposition of the classical half of Bell's theorem in the language of Pearl-style causal graphs, a joint summary of the loophole-free experiments, and a joint survey of the recent literature, each author states where they have presently arrived. Gill accepts irreducible and non-local quantum randomness and finds the choice between locality and realism a false dichotomy. In his later works, Bell derives counterfactual definiteness from classical local causality, and that is what has to go. The metaphysical concepts "realism", "locality", "causality" need to be reconsidered. Helland reconstructs the Hilbert-space formalism from a theory of accessible variables, and from this theory he concludes that every observer must be limited in a specific sense. Jongejan proposes a geometric hidden-variable construction in which the degree of violation of the CHSH inequality depends on the number of dimensions of space, Tsirelson's bound corresponding to three dimensions. The authors conclude with a discussion.
In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available.
Among the various "no-go theorems" in the foundations of quantum mechanics, Bell inequalities are among the few, which do not implicitly rely on the mathematical structure of quantum mechanics. Instead, Bell inequalities are commonly understood to rest on Kolmogorov's theory of probability and a "locality" assumption. Physical evidence supporting their violation is hence taken as evidence against at least one of these two assumptions.
This work provides a comprehensive analysis of the physical debate on Bell inequalities from the point of view of Kolmogorov's theory of probability, focusing on the Bell-Clauser-Horn-Shimony-Holt inequality (BCHSH inequality). The central contribution is the motivation and mathematical study of the notion of contextuality in Bell experiments: in so-called contextual Bell models the detectors themselves behave randomly and the distribution of the random detector parameters depends on the chosen detector settings. It is shown how even "classical" Bell experiments motivate such a description. The need to account for contextuality was pointed out before by de la Peña, Cetto, Brody, Lochak, Bohm, Hiley and others. A broad class of contextual models is proven to satisfy the BCHSH inequality, thereby generalizing a previous result by Gill and Lambare. Nonetheless, even under strong locality requirements, contextual Bell models may violate the BCHSH inequality: based on work by Popescu and Rohrlich, we consider a "proof of concept" example exhibiting the maximum possible violation.
Contrary to the much debated "loopholes" in empirical tests of Bell inequalities, contextuality thus reveals a conceptual misunderstanding in the physical conclusions commonly drawn from Bell inequality violations.