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International Workshop on Polarized Sources and Targets (PST)

Study of quantum spin correlations of relativistic electrons

Michał Drągowski, Marek Adamus, Paweł Caban, J. Ciborowski, M. Dehn, J. Enders, Yuliya Fritzsche, Jakub Rembieliński, Valery Tioukine

Published Sep 23, 2020• 0 citations
Publisher

Abstract

An experiment investigating quantum spin correlations of relativistic electrons is presented. The project aims at the first measurement of the quantum spin correlation function (and the corresponding probabilities) for a pair of relativistic particles with mass. The measurement will be carried out on a pair of electrons in the final state of Møller scattering. The detector consists of two Mott polarimeters, in which the spin projections of both Møller electrons are measured simultaneously.

DOI
10.22323/1.379.0004

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An experiment investigating quantum spin correlations of relativistic electrons is presented. The project aims at the first measurement of the quantum spin correlation function (and the corresponding probabilities) for a pair of relativistic particles with mass. The measurement will be carried out on a pair of electrons in the final state of Møller scattering. The detector consists of two Mott polarimeters, in which the spin projections of both Møller electrons are measured simultaneously.
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The relativistic spin correlation function was calculated for a pair of electrons originating from M\o{}ller scattering of two polarized electron beams. The results were discussed in view of a possible measurement of the correlation function and the corresponding probabilities. The special case of scattering off a stationary target (both polarized and unpolarized) was also analyzed. It was shown that the Clauser-Horne-Shimony-Holt (CHSH) inequality may be violated in the relativistic energy range when both scattering electrons are highly polarized.
In this paper we present and discuss the relativistic correlation function in a bipartite system of two electrons, originating from the ${e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ scattering of a polarized electron beam on an unpolarized target. We also calculate and investigate the probabilities of the definite outcomes of spin-projection measurements performed by two observers. The presented results might help in experimentally verifying whether relativistic quantum theory is able to reproduce the behavior of real quantum systems.
An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin correlation are then derived on the basis of a probability distribution function and its associated geometric representation, both for a pair of projections of a single-particle spin and for the bipartite system in singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical image of the electron spin, as discussed at the end of the paper.