Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

Lad, Frank

doi:10.4236/jmp.2021.128067

Cited by 7 publications

(9 citation statements)

References 30 publications

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“…Hess found that it was also established in a random variables context by Vorobev [12]. Closely related results have been obtained in [13] [14], and possibly others, though they are little known to the community at large. While in the last line of (2.2) ( ) , C b b′ superficially appears to be the result of an independent measurement process and to have the same dependence on hidden variables as do the other correlations, its computation in fact reuses the data L. Sica from the previous correlations, data pair by data pair.…”

Section: The Constant In Bell's Inequality In Three Variablesmentioning

confidence: 69%

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

Sica¹

2023

JMP

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It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1's that are writable on paper. This surprising fact is not immediately obvious from Bell's inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.

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Section: The Constant In Bell's Inequality In Three Variablesmentioning

confidence: 69%

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

Sica¹

2023

JMP

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“…ations do not motivate a complete joint probability distribution for the polarization products constituting the linear combination that underlies Bell's inequality in a gedankenexperiment. The author of the present article has identified [2] precisely the four-dimensional convex hull of distributions that do cohere with the limited prescriptions of quantum theory in this regard. These do not specify a unique distribution for the gedanken quantity s which is defined as an unobservable combination of four polarization products on the same pair of photons.…”

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confidence: 86%

“…The substantive implications of quantum theory for the complete results of the experiment are imprecise. However, the author [2] has identified precise restrictions on distributions allowed by the theory that still respect local realism. These leave four free dimensions of agreeable probability vectors for the F. Lad imagined observation possibilities, and an identifiable convex hull of distributions within them.…”

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confidence: 99%

Further Investigations of the Aspect/Bell Error: Maximum Entropy Assessment

Lad¹

2023

JMP

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This article identifies the maximum entropy distribution among those in the polytope of probability distributions cohering with quantum theoretic prescriptions pertinent to Bell's inequality in the optical context. Perhaps surprisingly, the maxent distribution is not a uniform mixture of the extreme vertices of the convex hull of distributions agreeing with the theory. The expectation ( ) E s it supports equals 1.1296, within the permitted coherent interval of ( ]. The maxent mixture of the extreme agreeable vertices is compared herein with two other mixture distributions over the convex hull of those supported by quantum theory. One of these is a simple uniform mixture over the solution vectors to the appropriate linear programming problems that specify the polytope. The other is the mixture underlying simulated results of Aspect's experiments that have been shown to estimate ( ) E s as 1.7678. Further computations provide examples of the types of claims that would be entailed in a unique distribution within the cohering convex hull such as maxent. These defy quantum theoretic adherence to the general uncertainty principle which proclaims an agnostic position with respect to imagined joint observation operators that do not commute. They also display questionable implications of the "many worlds" proposal which the author does not favour. The article raises questions that deserve to be discussed concerning the general proposal that the maximum entropy principle should be employed to make precise probabilistic assertions about equilibrium phenomena when specific physical theory prescribes only an interval.

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“…Hess found it previously discovered by Vorobov [8] [9] in the context of random variables. It has been extensively discussed by Lad [10] who pointed out that four such relations can be obtained from the inequality since each one can be generated from the other three. (Depending only on basic algebra, consequences following from this were given in [13]).…”

Section: Sicamentioning

confidence: 99%

An Alternative View: Satisfaction of the Four-Variable Bell Inequality Using Quantum Correlations

Sica¹

2023

JMP

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The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness. The limits of the inequalities follow as mathematical consequences of their created algebraic structures independently of application to random or deterministic variables. The inequalities should be called identity-inequalities. A final correlation re-uses data from the previous correlations and thus leads to the inequality limits. It generally has a different functional form from the previous correlations, whether derived as a counterfactual mathematical result, or in a way enabling comparison with experiment. These algebraic facts and their consequences are central to understanding the inequalities' use, but have not been widely recognized. Logically consistent application of the inequalities to Bell experiments is challenging, given that the number of mathematically assumed random variables is greater than the number of physical variables produced per experimental realization. Given Bell's rejection of the use of sequential, alternative paths, three experimental runs are here considered to enable acquisition of data to be rearranged for computation of statistical cross-correlations. Predicted quantum mechanical correlations then satisfy the inequality. Since mathematically inconsistent use is sufficient to cause inequality violation, the conclusion that violation implies the nonexistence of underlying variables in the entanglement process does not follow.

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Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

Cited by 7 publications

References 30 publications

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

Further Investigations of the Aspect/Bell Error: Maximum Entropy Assessment

An Alternative View: Satisfaction of the Four-Variable Bell Inequality Using Quantum Correlations

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