Bell Correlations without Entanglement:  A Local Wave Model Using Gaussian-Poisson Statistics and Single Count-Pair Selection

Sica, Louis

doi:10.4236/am.2014.518276

Cited by 4 publications

(5 citation statements)

References 5 publications

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“…The creation of such counter examples has been claimed [17,18], but their discussion involves issues beyond the scope of this article.…”

Section: Discussionmentioning

confidence: 99%

The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′sassuming merely that they exist

Sica

2017

Open Physics

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Bell's stated assumptions in deriving his inequality were sufficient conditions. It is shown that a far simpler condition exists for derivation of the inequality: the mere existence of finite data sets regardless of their statistical or deterministic characteristics. When explicitly computing various quantum correlations, the noncommutation of some observables must be taken into account. The resulting variation in correlations among the observables leads to satisfaction of the Bell inequality. Bell's mistaken assumption of the same functional form for all correlations is the principal reason for inequality violation. Upon correction of this error, it is no longer necessary to invoke non-locality or non-reality to explain violation of the Bell inequality.

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“…The creation of such counter examples has been claimed [17,18], but their discussion involves issues beyond the scope of this article.…”

Section: Discussionmentioning

confidence: 99%

The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′sassuming merely that they exist

Sica

2017

Open Physics

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“…Logical flaws in the Bell theorem lead one to consider whether the entanglement predicted Bell correlation may be derived in other ways. The construction of a local probability model [20] shows that the entanglement derivation of the Bell correlation is not unique. Several other models have been proposed by researchers.…”

Section: Discussionmentioning

confidence: 99%

The Bell Inequality Is Satisfied by Quantum Correlations Computed Consistently with Quantum Non-Commutation

Sica¹

2016

JMP

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In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.

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“…The articles referred to are not physical derivations of the correlations, which are effectively limited by our unsettled understanding of photons and their relation to electromagnetic waves. However, derivations of Bell correlations based on more physical principles have also been given [22] [23].…”

Section: Computational Counter-examplementioning

confidence: 99%

“…The overall process is more complex than that implied by the Bell notation. The physical processes considered in [22] [23] are even more complex.…”

Section: Computational Counter-examplementioning

confidence: 99%

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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Bell Correlations without Entanglement: A Local Wave Model Using Gaussian-Poisson Statistics and Single Count-Pair Selection

Cited by 4 publications

References 5 publications

The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′sassuming merely that they exist

The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′sassuming merely that they exist

The Bell Inequality Is Satisfied by Quantum Correlations Computed Consistently with Quantum Non-Commutation

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

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