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The British Journal for the Philosophy of Science

Bell's Inequalities and Quantum Non-separability

Shaurya Bhave

Published Dec 1, 1991• 0 citations
Publisher

Abstract

The separable hidden variables theory (Bhave [1986]) of Aspect's [1982] four single channel polarizers is developed further to consider possible modified Aspect's experiment with four double channel polarizers. It is shown that Aspect's commutator is not a truly stochastic commutator, and that until such a truly stochastic commutator is devised, experiments based on Bell's inequalities (like those of Aspect's) cannot be adequate experimental tests of quantum nonseparability.

DOI
10.1093/bjps/42.4.541

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The separable hidden variables theory (Bhave [1986]) of Aspect's [1982] four single channel polarizers is developed further to consider possible modified Aspect's experiment with four double channel polarizers. It is shown that Aspect's commutator is not a truly stochastic commutator, and that until such a truly stochastic commutator is devised, experiments based on Bell's inequalities (like those of Aspect's) cannot be adequate experimental tests of quantum nonseparability.
As a criterion between quantum mechanics and local hidden-variable theories, the so-called Einstein-Podolsky-Rosen paradox is mainly tested in the form of the statistical correlation between polarizations of photons issuing from a cascade transition. It has been stated more than once that an improved form of the test would make use of polarizers, the orientation of which would change randomly in a time comparable with the time of flight of the two photons; the Bell locality assumption could then be replaced by a weaker assumption also considered by Bell: The Einstein principle of separability. However, to our knowledge, no workable experimental scheme has yet been proposed, and we believe the one described in this paper to be a workable one. After explaining the difference between the Bell locality assumption and the Einstein principle of separability, we briefly discuss the theoretical implications of the modified experiment. The overall scheme of the apparatus we are proposing is described, and the generalized Bell inequalities, modified for our case, are derived. As in previous experiments, supplementary assumptions are made in order to derive experimentally testable inequalities. Finally, we describe the device we intend to use to carry out the proposed scheme.
It is shown that the following statements about a quantum correlation experiment are mutually equivalent. (1) There is a deterministic hidden-variables model for the experiment. (2) There is a factorizable, stochastic model. (3) There is one joint distribution for all observables of the experiment, returning the experimental probabilities. (4) There are well-defined, compatible joint distributions for all pairs and triples of commuting and noncommuting observables. (5) The Bell inequalities hold.
Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.
This paper discusses some tests of Bell-like inequalities not requiring entangled states. The proposed tests are based on consecutive measurements on a single qubit. Available hidden-variable models for a single qubit [see, e.g., J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)] reproduce the predictions of quantum mechanics and hence violate the Bell-like inequalities addressed in this paper. It is shown how this fact is connected with the state ``collapse'' and with its random nature. Thus, it becomes possible to test truly realistic and deterministic hidden-variable models. In this way, it can be shown that a hidden-variable model should entail at least one of the following features: (i) nonlocality, (ii) contextuality, or (iii) discontinuous measurement-dependent probability functions. The last two features are put to the test with the experiments proposed in this paper. A hidden-variable model that is noncontextual and deterministic would be at variance with some predictions of quantum mechanics. Furthermore, the proposed tests are more likely to be loophole-free, as compared to former ones.
Abstract It used to be assumed that the differences between “interpretations” of quantummechanics are philosophical and not physical. The experimental test of the original EPR “thought experiment” by Aspect et al., using the Bell inequalities, eliminatedthe Bohm-Aharanov local hidden variables, demonstrating that the so-called interpretations are distinct theories, amenable to experimental testing, and not merely philosophically different “interpretations”. In this paper I present a sequence of experiments, doable by current technology, to distinguish between various “interpretations” of Quantum Mechanics.