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arXiv:2403.03780

Loophole-free Bell inequality violations cannot disprove local realism

F. De Zela

Published Mar 6, 2024• 0 citations
arXivHTMLPDF

Abstract

For almost three decades in the twentieth century, the physics community believed that John von Neumann had proved the impossibility of completing quantum mechanics by a local realist, hidden-variables theory. Although Grete Hermann had raised strong objections to von Neumann's proof, she was largely ignored. This situation lasted, until John Bell rediscovered that von Neumann's proof was flawed: a \emph{sufficient} condition for local realism had been taken as a \emph{necessary} one. Bell subsequently established various constraints on hidden-variables theories, in the form of inequalities that can be submitted to experimental test. All performed tests to date have opened some loopholes. The quest to close them motivated great technical achievements and ongoing efforts to improve what has already been reached. There is, however, a rather ironic twist concerning Bell inequalities. On deriving them, Bell also took a sufficient condition for local-realism, as if it were a necessary one. As a consequence, even completely loophole-free Bell inequality violations would not disprove local realism. We argue that Bell inequalities cannot follow from local-realism alone. The proof is given by constructing three local-realist models that entail Bell inequality violations.

DOI
10.48550/arxiv.2403.03780

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For almost three decades in the twentieth century, the physics community believed that John von Neumann had proved the impossibility of completing quantum mechanics by a local realist, hidden-variables theory. Although Grete Hermann had raised strong objections to von Neumann's proof, she was largely ignored. This situation lasted, until John Bell rediscovered that von Neumann's proof was flawed: a \emph{sufficient} condition for local realism had been taken as a \emph{necessary} one. Bell subsequently established various constraints on hidden-variables theories, in the form of inequalities that can be submitted to experimental test. All performed tests to date have opened some loopholes. The quest to close them motivated great technical achievements and ongoing efforts to improve what has already been reached. There is, however, a rather ironic twist concerning Bell inequalities. On deriving them, Bell also took a sufficient condition for local-realism, as if it were a necessary one. As a consequence, even completely loophole-free Bell inequality violations would not disprove local realism. We argue that Bell inequalities cannot follow from local-realism alone. The proof is given by constructing three local-realist models that entail Bell inequality violations.
An overview of the history of Bell’s inequality is given, beginning with the so-called EPR paradox originally put forward by Einstein, Podolsky and Rosen and the impossibility proof of von Neumann. Bell’s inequality, which ultimately shifted the discussion from arguments based on philosophically introduced postulates to the domain of experimental physics, is presented together with experimental attempts from the early 1970s to 2010s to violate this inequality. We introduce three historical loopholes in the experimental schemes which have prevented experimentalists from being able to fully disprove the possibility of a hidden-variables description of nature. Recent experimental data indicate that all the main loopholes are now closed for photons (albeit not simultaneously in one experiment). Besides the class of stochastic local realism that have been tested experimentally, some other possible classical interpretations are mentioned.
The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables level”. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell’s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell’s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment.
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.
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.
Abstract Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumption of the dependence of the decays on hidden variables, as well as the consideration of the statistical mixture of polarizations and the separation of local hidden variables for objects with spacelike distances. These violations closes the measurement-setting loophole once and for all. We propose to use the processes ηc→ΛΛˉ\eta _c\rightarrow \varLambda {\bar{\varLambda }}ηc​→ΛΛˉ ηc→ΛΛ¯ and χc0→ΛΛˉ\chi _{c0} \rightarrow \varLambda {\bar{\varLambda }}χc0​→ΛΛˉ χc0→ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.