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arXiv:2305.06022

Interpretation of the superposition principle and locality loophole in Bell experiments

Sheng Feng

Published May 10, 2023• 0 citations
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Abstract

A connection is revealed between the superposition principle and locality. A self consistent interpretation of the superposition principle is put forth, from which it is shown that quantum mechanics may be a local statistical theory. Then it is shown how Bell experiments can be satisfactorily explained by assuming local nature for entangled particles, i.e., the violation of Bell inequality cannot distinguish between locality and nonlocality, which is referred to as locality loophole. Moreover, existing experimental results are presented indicating locality in quantum mechanics and new experiments are proposed so that the locality loophole may be closed.

DOI
10.48550/arxiv.2305.06022

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A connection is revealed between the superposition principle and locality. A self consistent interpretation of the superposition principle is put forth, from which it is shown that quantum mechanics may be a local statistical theory. Then it is shown how Bell experiments can be satisfactorily explained by assuming local nature for entangled particles, i.e., the violation of Bell inequality cannot distinguish between locality and nonlocality, which is referred to as locality loophole. Moreover, existing experimental results are presented indicating locality in quantum mechanics and new experiments are proposed so that the locality loophole may be closed.
Abstract Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work). It is therefore strange that there is non–locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell’s inequality is not conclusive about the non–local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell’s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.
In the usual derivation of Bell's inequalities, Locality is assumed to justify statistical independence of the outcomes of observations performed in remote stations; as the inequalities are observed to be violated, it is concluded that these outcomes are statistically dependent, and hence, that non-Local effects exist. Here it is shown that the simplest description of Bell's experiment according to the canon of von Neumann's theory of measurement assumes statistical independence of those outcomes. In other words, the straightforward description of Bell's experiment according to Quantum Mechanics (which, of course, violates Bell's inequalities) does not assume non-Locality. Summing up this and other related results it is concluded that, within the framework of Quantum Mechanics, there is no reason to believe in the existence of non-Local effects. In addition to its foundational significance, this conclusion has practical impact in the fields of quantum-certified and device-independent randomness generation and on the vulnerability of Quantum Key Distribution schemes, which are based on the existence of quantum non-Locality as an axiom.
Many Bell test results violate Bell's inequality. The premise of Bell's inequality is local determinism. We propose that, it can't be proved that something's mechanism isn't deterministic; if loopholes are not the reason of violation of Bell's inequality, violation of Bell's inequality illustrates that the mechanism isn't local. We propose a new explanation of Bell test, and the explanation illustrates the locality loophole is not closed by Weihs' experiment.
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.
It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space-time structure in the standard way then quantum mechanics might be consistent with Einstein's local realism. It shows that loopholes are unavoidable in experiments aimed to establish a violation of Bell`s inequalities. We show how the space-time structure can be considered from the contextual point of view. A mathematical framework for the contextual approach is outlined.