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EPJ Web of Conferences

Test of the Hypothesis of Realism Using a Modified Version of Wigner Inequality

N. Nikitin, K. S. Toms

Published Jan 1, 2019• 0 citations
Publisher

Abstract

In the current work we present a modified Wigner inequality for test of the hypothesis of realism. This modified Wigner inequality is suitable for test of realism not only in systems that obey the laws of non-relativistic quantum mechanics, but also in systems that obey the laws of quantum field theory. We show how this inequality can be violated in systems of neutral pseudoscalar mesons.

DOI
10.1051/epjconf/201922203003

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In the current work we present a modified Wigner inequality for test of the hypothesis of realism. This modified Wigner inequality is suitable for test of realism not only in systems that obey the laws of non-relativistic quantum mechanics, but also in systems that obey the laws of quantum field theory. We show how this inequality can be violated in systems of neutral pseudoscalar mesons.
We propose a Wigner-like inequality suitable for testing the hypothesis of realism. We show that this inequality is identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for testing realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett-Garg inequality in Wigner form, which was recently presented in the literature, for three and nnn distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Based on the Leggett-Garg inequality in Wigner form for nnn distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to ``freezing'' of the system in the initial state. It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.
Recently a new class of time-dependent Bell inequalities in Wigner form was introduced. The structure of the inequalities allows experimental studies of quantum and open quantum systems in external fields. In this paper, we study the properties of the time-dependent Wigner inequalities using the time evolution of neutral pseudoscalar mesons with CPCPCP-violation effects taken into account. It is shown that it is always possible to find a range of parameters to test for violation in an experimentally accessible area. The effect of the relaxation of the inequalities for large time scales is demonstrated.
In this paper we propose a time-independent equality and time-dependent inequality, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional probability and on Bayes' theorem in the framework of Kolmogorov's axiomatics of probability theory. The equality obtained is intrinsically different from the well-known Greenberger-Horne-Zeilinger (GHZ) equality and its variants, because violation of the proposed equality might be tested in experiments with only two microsystems in a maximally entangled Bell state $|{\mathrm{\ensuremath{\Psi}}}^{\ensuremath{-}}\ensuremath{\rangle}$, while a test of the GHZ equality requires at least three quantum systems in a special state $|{\mathrm{\ensuremath{\Psi}}}^{\mathrm{GHZ}}\ensuremath{\rangle}$. The obtained inequality differs from Bell's, Wigner's, and Leggett-Garg inequalities, because it deals with spin s=1/2s=1/2s=1/2 projections onto only two nonparallel directions at two different moments of time, while a test of the Bell and Wigner inequalities requires at least three nonparallel directions, and a test of the Leggett-Garg inequalities requires at least three distinct moments of time. Hence, the proposed inequality seems to open an additional experimental possibility to avoid the ``contextuality loophole.'' Violation of the proposed equality and inequality is illustrated with the behavior of a pair of anticorrelated spins in an external magnetic field and also with the oscillations of flavor-entangled pairs of neutral pseudoscalar mesons.
Many beautiful experiments have been addressed to test standard quantum mechanics against local realistic models. Even if a strong evidence favouring standard quantum mechanics is emerged, a conclusive experiment is still lacking, because of low detection efficiencies. Recently, experiments based on pseudoscalar mesons have been proposed as a way for obtaining a conclusive experiment. In this paper, we investigate if this result can effectively be obtained. Our conclusions, based on a careful analysis of the proposed set ups, are that this will not be possible due to intrinsic limitations of these kind of experiments.
We present a relativistic generalization of the Wigner inequality for the scalar and pseudoscalar particles decaying to two particles with spin (fermions and photons.) We consider Wigner's inequality with the full spin anticorrelation (with the nonrelativistic analog), as well as the case with the full spin correlation. The latter case may be obtained by a special choice of the plane of measurement of the spin projections on the direction of propagation of fermions. The possibility for relativistic testing of Bohr's complementarity principle is shown.
Some new temporal Bell inequalities are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive measurabilioty hypothesis advantegeously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be more severe than the similar violation in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations in which these inequalities could be tested are roughly considered.