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A Proposal for a New Interpretation of Bell's Inequality Proofs

Bardo ArtificialIntelligence

Published Dec 22, 2023• 0 citations
Publisher

Abstract

Bell's inequality proofs have been interpreted as demonstrating that quantum mechanics is incompatible with local realism. However, a new interpretation has been proposed that suggests that Bell's inequalities can be reconciled with local realism if we consider causality to be a property of classical space, rather than of the quantum world, ruled by probabilities.The linear flow of time is a subjective model of causality created by the human brain resulting in subjective interpretation of time travel into the past.

DOI
10.31219/osf.io/dqekx

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Bell's inequality proofs have been interpreted as demonstrating that quantum mechanics is incompatible with local realism. However, a new interpretation has been proposed that suggests that Bell's inequalities can be reconciled with local realism if we consider causality to be a property of classical space, rather than of the quantum world, ruled by probabilities.The linear flow of time is a subjective model of causality created by the human brain resulting in subjective interpretation of time travel into the past.
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].
A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory itself is both local and realistic when properly interpreted using a quantum Hilbert space rather than the classical hidden variables used to derive Bell inequalities. There is no spooky action at a distance in the real world we live in if it is governed by the laws of quantum mechanics.
Most physicists uphold that the tests of the Bell-Clauser, Horne, Shimony and Holt (BCHSH) inequalities confirm quantum mechanics (QM) and refute local realism. Some scholars, however, criticize this conviction, yet maintaining that QM conflicts with local realism. At variance with both viewpoints one of the authors has recently worked out an extended semantic realism (ESR) model which shows that, if quantum probabilities are interpreted as conditional rather than absolute probabilities, a picture of the microworld can be constructed that is simultaneously consistent with local realism and QM. We show here that the BCHSH inequalities must be replaced, within the ESR model, by more general inequalities. These depend on parameters (detection probabilities) which may be such that the inequalities are never violated by quantum expectation values. The condition that no violation occurs implies the existence of upper bounds on detection probabilities, which makes the ESR model falsifiable. These results admit an intuitive explanation in terms of unfair sampling but basically differ from the seemingly similar results obtained by other approaches in which the efficiency problem is discussed in order to vindicate some kind of local realism.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables -- impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality -- a few pairs of random variables (two dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) `` death of reality''; d) non-Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.