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

Quantum mechanics and hidden variables: A test of Bell's inequality by the measurement of the spin correlation in low-energy proton-proton scattering

Mohammad LAMEHI-RACHTI, W. Mittig

Published Nov 15, 1976• 237 citations
Publisher

Abstract

The inequality of Bell has been tested by the measurement of the spin correlation in proton-proton scattering. Measurements were made at ${E}_{p}=13.2 \mathrm{and} 13.7$ MeV using carbon analyzers of 18.6 and 29 mg/${\mathrm{cm}}^{2}$, respectively, accumulating a total of ${10}^{4}$ 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.

DOI
10.1103/physrevd.14.2543

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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.
Arising out of the EPR debate, the Bell and Wigner inequalities of quantum theory are experimentally testable relations which address the question of quantum completeness. This thesis provides feasibility results for a fermionic test of the Bell inequality, and the first known attempt to investigate the completeness question through the Wigner relation. Such a test is made possible by the production of an entangled p-p singlet at the KVI research facility in Groningen, the Netherlands, through the reactions 12C(d,2He)12B and p(d,2He)n. The p-p spin-correlations are analyzable via the KVI's 2-pi polarimeter acceptance, which eliminates loopholes common to previous experiments. The results distinguish between a hidden variables and quantum mechanical description of the universe. Also presented is a critique of the GHZ argument against the existence of local hidden variables.
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.
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.
Bell’s inequality is an expression which can be employed in order to test for the existence of hidden variables in a correlated system. The idea of hidden variables was introduced as a potential explanation for the quantum mechanical phenomenon of non-deterministic results of measurements. The existence of hidden variables can be tested experimentally. First, a particular measurement of one component of a correlated system must be associated with a positive or negative integer value. There must be an equal probability density of obtaining either measurement. Following this, an ensemble average of these measurements must be performed and Bell’s inequality must subsequently be employed. This theorem was essential in settling the EPR argument against quantum mechanical indeterminism, experimentally showing through violation of the inequality that there are indeed no hidden variables in a quantum system. For a system exhibiting classical behavior, Bell’s inequality should not be violated, provided the correlated system meets criteria appropriate to the assumptions underlying Bell’s theorem. A Mathematica model of Bell’s inequality was developed utilizing a Monte Carlo approach of randomizing parameters in order to test models of correlated systems. The model appears to agree with classical determinism within one standard deviation. It is possible to test both classical and quantum mechanical systems if properly correlated, and it is of future interest to test whether this extends to chaotic systems.