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arXiv:1702.06617

Nonlocal single particle correlations and EPR state in the double-slit experiment

Oziel Ribeiro de Araújo, Alexander, Helder, Marcos Sampaio, Irismar da Paz

Published Feb 21, 2017• 0 citations
arXivHTMLPDF

Abstract

Quantum correlations of observables for two particle states have demonstrated the nonlocal character of the quantum mechanics. However nonlocality can be exhibited even for noncommuting observables of a single particle system. In this paper we show nonlocality of position-momentum correlations of a single particle in the double-slit experiment modeled by an initially correlated Gaussian wavepacket. The positivity or negativity of the Wigner function for the state of the particle at the detection screen is related with the $σ_{xp}$ covariances. A Bell's inequality is constructed from the Wigner function and it is violated for both the positive and negative cases. The case of positive Wigner function is the analogous of the original EPR state for a single particle.

DOI
10.48550/arxiv.1702.06617

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Quantum correlations of observables for two particle states have demonstrated the nonlocal character of the quantum mechanics. However nonlocality can be exhibited even for noncommuting observables of a single particle system. In this paper we show nonlocality of position-momentum correlations of a single particle in the double-slit experiment modeled by an initially correlated Gaussian wavepacket. The positivity or negativity of the Wigner function for the state of the particle at the detection screen is related with the σxpσ_{xp}σxp​ covariances. A Bell's inequality is constructed from the Wigner function and it is violated for both the positive and negative cases. The case of positive Wigner function is the analogous of the original EPR state for a single particle.
We study the slowing of the decoherence effect in the double-slit experiment by considering an initially correlated Gaussian state. The effects of the decoherence are included in a specific propagator which we use to obtain the density matrix at the detection screen. We calculate the uncertainties in the position and momentum for the density matrix as a function of the decoherence at the detection screen. We show that for a contractive initial state and specific times of propagation the state at the detection screen is squeezed in position in comparison with the standard Gaussian superposition. For this squeezed Gaussian superposition state, we observe that the fringe visibility is more robust to the decoherence in comparison with the standard Gaussian superposition. Then, we calculate the negativity of the Wigner function and study its behavior as a function of the decoherence and correlation parameters at the detection screen. We observe that the negativity decreases more slowly for the squeezed Gaussian superposition.
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.
Abstract We investigate whether negative values of Wigner functions purely coming from correlations are sufficient for observing nonlocal correlations. We employ a simple model for superpositions of coherent states and examine how the corresponding Wigner negativity of correlations relates to the violation of a CHSH inequality based on pseudo-spins. We find that a critical amount of this negativity is necessary to violate the inequality, making a nonzero negativity not sufficient for observing nonlocal correlations. Graphical Abstract
EPR paper contains an error. Its correction leads to a conclusion that position and momentum of a particle can be defined precisely simultaneously, EPR paradox does not exist and uncertainty relations have nothing to do with quantum mechanics. Logic of the EPR paper shows that entangled states of separated particles do not exist and therefore there are no nonlocality in quantum mechanics. Bell's inequalities are never violated, and results of experiments, proving their violation, are shown to be false. Experiments to prove absence of nonlocality are proposed where Bell's inequalities are replaced by precise prediction. Interpretation of quantum mechanics in terms of classical field theory is suggested. Censorship against this paper is demonstrated.
Abstract We investigate whether negative values of Wigner functions purely coming from correlations are sufficient for observing nonlocal correlations. We employ a simple model for superpositions of coherent states and examine how the corresponding Wigner negativity of correlations relates to the violation of a CHSH inequality based on pseudo-spins. We find that a critical amount of this negativity is necessary to violate the inequality, making a nonzero negativity not sufficient for observing nonlocal correlations.
We present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position–momentum correlations in the intensity, visibility and predictability of the wavepacket interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particle, atom or molecule interferometry and can be discussed in introductory quantum mechanics courses.