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Journal of Modern Physics 2023年第6期14卷 802-817页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria USA

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.

关键词： Bell Inequality Bell Theorem Wigner Inequality Entanglement Locality Realism

Bell Correlations from Local Un-Entangled States of Light and Quantum Electro-Dynamics

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Journal of Modern Physics 2021年第1期12卷 10-21页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

Based on the Bell theorem, it has been believed that a theoretical computation of the Bell correlation requires explicit use of an entangled state. Such a physical superposition of light waves occurs in the down-converter sources used in Bell experiments. However, this physical superposition is eliminated by wave propagation to spatially separated detectors. Bell correlations must therefore result from local waves, and the source boundary conditions of their previously entangled state. In the present model, Bell correlations are computed from disentangled separated waves, boundary conditions of nonlinear optics, and properties of single-photon and vacuum states specified by quantum electrodynamics. Transient interference is assumed between photon-excited waves and photon-empty waves based on the possibility of such interference found to be necessary by the designers of Bell-experiment sources. The present model employs local random variables without specifying underlying causality.

关键词： Bell Correlation Bell Theorem Locality Wave-Particle Duality Entanglement Photon State

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

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Journal of Modern Physics 2016年第4期7卷 404-412页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

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.

关键词： Bell’s Theorem Bell Inequality Hidden Variables Correlations Commutation Noncommutation

Conditional Independence Leads to Satisfaction of the Bell Inequality without Assuming Non-Locality or Non-Reality

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Advances in Pure Mathematics 2022年第5期12卷 405-417页

作者： louis sica Institute for Quantum Studies Chapman University Orange USA Inspire Institute Inc. Alexandria USA

The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy the particles, the physical realization of three variables from an experiment producing two particles per trial requires two separate trial runs. One assumed variable value (for particle 1) occurs at a fixed instrument setting in both trial runs while a second variable (for particle 2) occurs at alternative instrument settings in the two trial runs. Given that measurements on the two particles occurring in each trial are themselves correlated, measurements from independent realizations at mutually exclusive settings on particle 2 are conditionally independent, i.e., conditionally dependent on particle 1, through probability. This situation is realized from variables defined by Bell using entangled particle pairs. Two correlations have the form that Bell computed from entanglement, but a third correlation from conditionally independent measurements has a different form. When the correlations are computed using quantum probabilities, the Bell inequality is satisfied without recourse to assumptions of non-locality, or non-reality.

关键词： Bell Theorem Bell Inequality Entanglement Cross-Correlations Conditional Independence

The Bell Inequalities: Identifying What Is Testable and What Is Not

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Journal of Modern Physics 2020年第5期11卷 725-740页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two entangled particles neglecting non-commutation. The assumed correlation functions, later confirmed for certain quantum measurements, violate the Bell inequality. The present paper reviews a more general derivation of the Bell inequality showing that it is identically satisfied by finite data sets whether deterministic or random, after assuming merely that they exist. It is thereafter concerned with the consequences of this result for interpretations of the inequality that result in its violation. A primary finding is that correlation functions have differing forms due to quantum commutation, non-commutation, and conditions of measurement, and result in satisfaction of the Bell inequality used consistently with its derivation. A stochastic process having the same correlation function for all variable pairs is shown to be inconsistent with experimentally reported data. The logic of the three and four variable inequalities is shown to be similar. Finally the inequalities in probabilities are shown to follow from those in correlations with quantum mechanical results satisfying either when properly implemented.

关键词： Bell Theorem Bell Inequality Entanglement Locality Correlations Hidden Variables Non-Commutation Commutation Cross-Correlations Non-Stationary

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

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Applied Mathematics 2014年第18期5卷 2899-2907页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

Based on the violation of Bell inequalities, it has been believed that the derivation of Bell correlations requires a quantum description that depends on entanglement. However, the present paper computes Bell correlations among polarization analyzer output intensities from two spatially separated sets of superposed random wave pairs. To obtain proper Bell correlations, the general statistics must be modified to represent single event pair selection. The correlations between analyzer output components are then in one-to-one correspondence with those computed from the entanglement formalism.

关键词： Bell Correlation Bell Theorem Locality Nonlocality Entanglement

Can a Photon Be Separated from Its Wave?

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Journal of Modern Physics 2018年第3期9卷 461-470页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

An experiment is proposed in which the overall path taken by a photon is indicated by the timing of a twin herald photon, while a particular segment of that path is determined by interference. The needed coincident pairs of photons are generated by type I spontaneous-parametric-down-conversion (SPDC) and diffraction-selected by a grating at the frequency of a two-photon state. This is to be divided into two one-photon states of high coherence length. Upon experimental confirmation that their count coincidences have been maintained, the two single photons are to be used as a timing herald and source for an unequal path interferometer. A photon’s path through the interferometer via a short arm is indicated by count synchronization with the herald. The exit output port used and resulting final detection location are determined by the phase in the long arm. If output port usage can be controlled by the phase in the photon-free arm, the path of the photon as particle will have been controlled by interference with an accompanying photon-empty wave.

关键词： Wave-Particle Duality Two-Photon State Which-Path Experiment Pilot Wave

Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems

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Applied Mathematics 2013年第10期4卷 90-94页

作者： louis sica Institute for Quantum Studies Chapman University Orange CA & Burtonsville MD USA Inspire Institute Inc. Alexandria VA USA

In eliminating the fair sampling assumption, the Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s historic conclusion that local hidden variables are inconsistent with the results of quantum mechanics. The GHZ theorem depends on predicting the results of sets of measurements of which only one may be performed. In the present paper, the noncommutative aspects of these unperformed measurements are critically examined. Classical examples and the logic of the GHZ construction are analyzed to demonstrate that combined counterfactual results of noncommuting operations are in general logically inconsistent with performed measurement sequences whose results depend on noncommutation. The Bell theorem is also revisited in the light of this result. It is concluded that negative conclusions regarding local hidden variables do not follow from the GHZ and Bell theorems as historically reasoned.

关键词： HZ-Theorem Bell-Theorem Noncommutation Counterfactual Hidden Variables Locality Nonlocality

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

Journal of Modern Physics 2023年第6期

作者： louis sica

来源：博看期刊评论

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