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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Proposed experimental test of Bell’s inequality in nuclear beta decay

M. Skalsey

Published Apr 15, 1986• 1 citation
Publisher

Abstract

A \ensuremath{\beta} decay experiment is proposed for testing Bell's inequality, related to hidden-variables alternatives to quantum mechanics. The experiment uses Mott scattering for spin polarization analysis of internal conversion electrons. Beta-decay electrons, in cascade with the conversion electrons, are longitudinally polarized due to parity violation in the weak interaction. So simply detecting the \ensuremath{\beta} electron direction effectively measures the spin. A two-particle spin-spin correlation can thus be investigated and related, within certain assumptions, to Bell's inequality. The example of $^{203}\mathrm{Hg}$ decay is used for a calculation of expected results. Specific problems related to nuclear structure and experimental inconsistencies are also discussed.

DOI
10.1103/physrevd.33.2233

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A \ensuremath{\beta} decay experiment is proposed for testing Bell's inequality, related to hidden-variables alternatives to quantum mechanics. The experiment uses Mott scattering for spin polarization analysis of internal conversion electrons. Beta-decay electrons, in cascade with the conversion electrons, are longitudinally polarized due to parity violation in the weak interaction. So simply detecting the \ensuremath{\beta} electron direction effectively measures the spin. A two-particle spin-spin correlation can thus be investigated and related, within certain assumptions, to Bell's inequality. The example of 203Hg^{203}\mathrm{Hg}203Hg decay is used for a calculation of expected results. Specific problems related to nuclear structure and experimental inconsistencies are also discussed.
The inequality of Bell has been tested by the measurement of the spin correlation in proton-proton scattering. Measurements were made at Ep=13.2and13.7{E}_{p}=13.2 \mathrm{and} 13.7Ep​=13.2and13.7 MeV using carbon analyzers of 18.6 and 29 mg/cm2{\mathrm{cm}}^{2}cm2, respectively, accumulating a total of 104{10}^{4}104 coincidences. The experimental analyzing power, geometric correlation coefficients, and energy spectra are compared to the result of a Monte Carlo simulation of the apparatus. The results are in good agreement with quantum mechanics and in disagreement with the inequality of Bell if the same additional assumptions are made. The conditions for comparing the results of the experiments to the inequality of Bell are discussed.
In this paper, we present an analog of Bell's inequalities violation test for N qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict the results for different Bell's inequality tests, with distinct configurations and a larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality using a two-qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by the quantum mechanics theory and a local realistic hidden variables model (LRHVM) that was specifically developed for NMR. That is why we refer to this experiment as a simulation of Bell's inequality violation. Our result shows explicitly how the two theories can be compatible with each other due to the detection loophole. In the last part of this work, we discuss the possibility of testing some fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected.
In this talk given at the TAU92 Workshop, Columbus, OH, Sept. 92, we summarize results presented in more detail in a recent paper by S. Abel, M. Dittmar and the author where we gave a general proof that Bell's inequality can not be tested at a collider experiment. In particular, a measurement of correlated tau-spins at LEP does not constitute a test of local realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can always be described by a local hidden variable theory. In response to questions at the workshop we go beyond the paper and show that an old experiment involving the measurement of the correlated spins of the two photons emitted in positronium decay via Compton-scattering is also not a viable test of Bell's inequality.
We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin 1/21/21/2 hadrons from the decay of short-lived ($\ensuremath{\tau}<{10}^{\ensuremath{-}21}\mathrm{sec}$) 2He^{2}\mathrm{He}2He spin-singlet state, populated in the nuclear reaction $^{2}\mathrm{H}+^{1}\mathrm{H}\ensuremath{\rightarrow}^{2}\mathrm{He}+n$. The novel features of this experiment are (a) the use of an ``event-ready'' detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full $2\ensuremath{\pi}\text{ }\text{ }\mathrm{sr}$ acceptance with a random ``post selection'' of the reference axes. The spin-correlation function is deduced to be ${S}_{\mathrm{exp}}(\ensuremath{\pi}/4)=2.83\ifmmode\pm\else\textpm\fi{}{0.24}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.07}_{\mathrm{sys}}$. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of $|S|\ensuremath{\le}2$ at a confidence level of 99.3%.
All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described.
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the results obtained in photon experiments. In the tests of Bell inequalities in high energy physics, the early attempts of using spin correlations in particle decays and later on the mixing of neutral mesons used to form the quasi-spin entangled states are covered. The related experimental results in K^0 and B^0 systems are presented and discussed. We introduce the new scheme, which is based on the non-maximally entangled state and proposed to implement in ϕfactory, in testing the Local Hidden Variable Theory. And, we also discuss the possibility in generalizing it to the tau charm factory.