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arXiv:2208.09930 · Quantum Reports

Kupczynski’s Contextual Locally Causal Probabilistic Models Are Constrained by Bell’s Theorem

Richard David Gill, Justo Pastor Lambare

Published Jun 6, 2023• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/quantum5020032

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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.

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The European Physical Journal Special Topics•Jul 4, 2025•1 citation
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.
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.
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model (called a violation of measurement independence (MI)) would mean a violation of experimenters’ freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thus they cannot depend on randomly chosen experimental settings. However, if hidden variables describing measuring instruments are correctly incorporated into a contextual probabilistic model a violation of inequalities and an apparent violation of no-signaling reported in Bell tests can be explained without evoking quantum non-locality. Therefore, for us, a violation of Bell-CHSH inequalities proves only that hidden variables have to depend on settings confirming contextual character of quantum observables and an active role played by measuring instruments. Bell thought that he had to choose between non-locality and the violation of experimenters’ freedom of choice. From two bad choices he chose non-locality. Today he would probably choose the violation of MI understood as contextuality.
Local realism reduces to the proposition that local determinate reality is the necessary and sufficient cause of every physical effect. By any standard account, quantum theory requires that local realism is false, because it embeds the famously spooky premise that some physical effects require causes that are instantly effective from arbitrarily far away. Nonetheless, quantum theory has replaced local realism as the foundation of science because, whereas local realism allegedly cannot violate the Bell inequality, quantum theory is taken to do so in accord with experiments. Here we prove, however, that an epistemic contextual model of local realism solves a puzzle about independent random measurements of local hidden variables in a way that causally explains observed Bell violations. We also reveal exactly how the Bell inequality fails to represent the local realistic prediction. Finally, we show that any theory that denies local realism comprises an unfalsifiable causal claim that is freely adjustable to make arbitrary predictions, which thus provide no validation of its causal claim. Results revitalize the hypothesis that local realism prevails. Keywords: Local Realism. Bell Violations. Photons. Entanglement. Quantum Physics.
In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word “local” applies to the way that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables (thought of as being located in the measurement devices and dependent on the measurement settings) is automatically covered, despite recent claims that Bell's conclusions can be circumvented in this way.
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.
Abstract Quantum theory has accounted for a wide range of physical effects in systems ranging from microscopic to macroscopic. However, it is associated with various paradoxes—such as the well-known EPR example. Einstein’s suggestion that the theory was incomplete has led to numerous attempts to underpin quantum theory by a hidden variable theory, including the Bell approach. This approach was originally based on certain assumptions: (i) realism (ii) locality and (iii) non-contextuality. In its developed form, the theory involved only probabilities for outcome values of system observables. For systems involving two sub-systems, the hidden variable theory predicted that correlations between measurement outcomes of observable pairs of from different sub-systems would satisfy certain—such as the CHSH Bell inequality. The inequality was inconsistent with quantum theory predictions and with experiment. Hence, the question arose: Which of the three assumptions was invalid? A widely held view is that a non-local theory is needed—another is that hidden variable theory should be contextual. In this article, derivations of the CHSH Bell inequality based on various combinations of locality/non-locality and non-contextuality/contextuality assumptions are outlined, leading to the conclusion that for a hidden variable theory to underpin quantum theory, it must be both non-local and contextual. Non-locality or contextuality alone is insufficient. However, it is also concluded that the realism assumption is questionable. At present an alternative approach of augmenting quantum theory by adding additional features—such as the deterministic trajectories of Bohmian mechanics (also a non-local theory) may be a better route for completeness.