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A Kantian Solution for the Freedom of Choice Loophole in Bell Experiments

R. Rossi, Patrícia Kauark-Leite

Published Jun 2, 2020• 1 citation
Publisher

Abstract

Bell’s theorem is based on the assumptions of local causality and measurement independence. The last assumption is identified by many authors as linked to the freedom of choice hypothesis. In this sense the human free will ultimately can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this assumption are known in the literature as “freedom-of-choice loophole” (FOCL). Although there is no consensus among the scientists that the measurement independence is linked to human choices, in a recent paper, published in a prestigious journal, signed by more than a hundred authors, this assumption was seriously taken for the first time in an experiment known as Big Bell Test (Abellán et al. 2018). Using photons, single atoms, atomic ensembles and superconducting devices, this experiment was performed in five continents, and involved twelve laboratories, adopting human choices to close the FOCL. Nevertheless, the possibility of human freedom of choice has been a matter of philosophical debate for more than 2000 years, and there is no consensus among philosophers on this topic. If human choice is not free, this solution would not be sufficient to close FOCL. Therefore, in order to support the basic assumption of this experiment, it is necessary to argue that human choice is indeed free. In this paper, we present a Kantian position on this topic and defend the view that this philosophical position is the best way to ensure that Big Bell Test can in fact close the loophole.

DOI
10.22034/jpiut.2024.62277.3802

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Bell’s theorem is based on the assumptions of local causality and measurement independence. The last assumption is identified by many authors as linked to the freedom of choice hypothesis. In this sense the human free will ultimately can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this assumption are known in the literature as “freedom-of-choice loophole” (FOCL). Although there is no consensus among the scientists that the measurement independence is linked to human choices, in a recent paper, published in a prestigious journal, signed by more than a hundred authors, this assumption was seriously taken for the first time in an experiment known as Big Bell Test (Abellán et al. 2018). Using photons, single atoms, atomic ensembles and superconducting devices, this experiment was performed in five continents, and involved twelve laboratories, adopting human choices to close the FOCL. Nevertheless, the possibility of human freedom of choice has been a matter of philosophical debate for more than 2000 years, and there is no consensus among philosophers on this topic. If human choice is not free, this solution would not be sufficient to close FOCL. Therefore, in order to support the basic assumption of this experiment, it is necessary to argue that human choice is indeed free. In this paper, we present a Kantian position on this topic and defend the view that this philosophical position is the best way to ensure that Big Bell Test can in fact close the loophole.
Bell's theorem is based on three assumptions: realism, locality, and measurement independence. The third assumption is identified by Bell as linked to the freedom of choice hypothesis. He holds that ultimately the human free will can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this third assumption are known in the literature as "freedom-of-choice loophole" (FOCL). In a recent publication, Abellán et al [2018] address this problem and follow this same strategy embraced by Bell [2004]. Nevertheless, the possibility of human freedom of choice has been a matter of philosophical debate for more than 2000 years, and there is no consensus among philosophers on this topic. If human choice is not free, Bell's solution would not be sufficient to close FOCL. Therefore, in order to support the basic assumption of this experiment, it is necessary to argue that human choice is indeed free. In this paper, we present a Kantian position on this topic and defend the view that this philosophical position is the best way to ensure that BigBell Test (Abellán et al. [2018]) can in fact close the loophole.
A Bell test can rule out local realistic models and has potential applications in communication and information tasks. For example, a Bell's inequality violation can certify the presence of intrinsic randomness in measurement outcomes, which can be used to generate unpredictable random numbers. Nevertheless, a Bell test requires measurements that are chosen independently of environment in the test, as would be the case if the measurement setting choices were themselves intrinsically random. Such situation seems to create a ``bootstrapping problem'' recently addressed in the BIG Bell Test, a collection of various Bell tests using human choices. Here, we report in detail our experimental methods and results within the BIG Bell Test, specifically for a special type of Bell inequality, known as the measurement-dependent local inequality. With this inequality, even a small amount of measurement independence makes it possible to disprove local realistic models. The experiment utilizes human-generated random numbers in selecting the measurement settings and is implemented with space-like separation between two distant measurement sites. The experimental result violates a Bell's inequality, which cannot be explained by local hidden variable models with independence parameter (as defined in [G. P\"utz et al., Phys. Rev. Lett. 113, 190402 (2014)]) $l>0.10\ifmmode\pm\else\textpm\fi{}0.05$. This result further quantifies the degree to which a local hidden variable model would need to constrain human choices, if it is to reproduce the experimental results.
Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no conspiracy. By imbedding the Bell causal structure in a larger causal network the authors correctly prove, that one can explain and quantify possible violation of measurement independence without evoking the super-determinism. They assume the independence of the variables that causally determine the settings and investigate how they might become correlated with hidden variables. Using their extended causal networks they derive a contextual probabilistic model on which their further correct results are based. The authors seem to ignore that contextual probabilistic model may be derived directly using only probabilistic concepts and incorporating correctly setting dependent variables describing measuring instruments. In these contextual probabilistic models experimenters freedom of choice is not compromised and the results of Bell Tests including an apparent violation of Einsteinian nonsignaling may be explained in a locally causal way. Talking about freedom of choice is misleading and is rooted in incorrect understanding of Bayes Theorem. We explain why freedom of choice should be called noncontextuality and why its violation in Bell Tests confirms only the contextual character of quantum observables. Therefore, contextuality and not experimenters freedom of choice are important resources in quantum information.
We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula E(AB∣a,b)=∫A(a,b,λ)B(a,b,λ)ρ(λ)dλE(AB|a,b) = \int A(a,b,λ)B(a,b,λ)ρ(λ) dλE(AB∣a,b)=∫A(a,b,λ)B(a,b,λ)ρ(λ)dλ follows from the logic of plausible reasoning (the objective Bayesian interpretation of probability theory) taken alone, without any further assumptions about realism. The space ΛΛΛ, usually interpreted as some space of `hidden variables', can be constructed for an arbitrary `field of discourse' using Stone's theorem. The rejection of superdeterminism follows from logical independence -- the non-existence of information which suggest a dependence -- of the free decisions of the experimenters from everything else. To prove the Bell inequality it is, then, sufficient to reduce this to E(AB∣a,b)=∫A(a,λ)B(b,λ)ρ(λ)dλ.E(AB|a,b) = \int A(a,λ)B(b,λ)ρ(λ) dλ.E(AB∣a,b)=∫A(a,λ)B(b,λ)ρ(λ)dλ. This follows for space-like separated measurements from Einstein causality alone. So, the consequence of the violation of Bell's inequality is that Einstein causality has been empirically falsified, without any loopholes left. We consider and reject the idea of weakening the logic of plausible reasoning could be used to create a loophole. Finally, we discuss what can be used to replace Einstein causality. While weak (signal) Einstein causality holds, it follows either from a notion of strong causality or from human inability to prepare states which violate quantum uncertainty, which makes it uninteresting for fundamental considerations. A notion of strong causality has either unacceptable causal loops or requires a hidden preferred frame. Given that a hidden preferred frame is completely compatible with modern physics, it is argued that this choice is preferable.
This Comment argues that two assumptions, which are presented as basic assumptions of Bell's theorem in [J. Handsteiner et al., Phys. Rev. Lett. 118, 060401 (2017)] and elsewhere, in fact follow from more basic premises. Measurement independence follows from (i) the use of free variables and (ii) the causal arrow of time. Determinism follows from (i) local causality and (ii) perfect correlations (predicted by quantum mechanics). In particular, it is pointed out that the measurement-independence violating toy model of [M.J.W. Hall, Phys. Rev. Lett. 105, 250404 (2010)], is based on a retro-causal model. While this may be controversial, it should be possible to achieve concensus on the much simpler matter of what the basic assumptions of Bell's theorem are.