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Physics-Uspekhi

Bell's inequalities and EPR–Bohm correlations: working classical radiofrequency model

N. V. Evdokimov, Давид Николаевич Клышко, Владимир Павлович Комолов, V.A. Yarochkin

Published Jan 31, 1996• 30 citations
Publisher

Abstract

A description is given of an electron model which makes it possible to simulate pair correlation of random dichotomous signals of the Einstein–Podolsky–Rosen (EPR) type in the Bohm variant. This model can be used to demonstrate that Bell's inequality is satisfied in classical physics. Some features of parametric rf oscillators are used in the model. An analysis of the operation of the model helps one to understand the difference between quantum and classical correlations in EPR experiments. A specific mechanism is suggested for 'nonlocal' control of EPR-type correlations between distant observers, which applies to classical and quantum models. A controlled correlation between two random telegraphic signals is ensured by transmission, to two observers, of a sequence of pulses with the same random phase. An elementary derivation of Bell's inequality is given and an analysis is made of the logic of the use of the popular term 'quantum nonlocality' employed usually in the description of the quantum variants of the investigated experiment.

DOI
10.1070/pu1996v039n01abeh000129

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Kluwer Academic Publishers eBooks•Feb 24, 2006•13 citations
A description is given of an electron model which makes it possible to simulate pair correlation of random dichotomous signals of the Einstein–Podolsky–Rosen (EPR) type in the Bohm variant. This model can be used to demonstrate that Bell's inequality is satisfied in classical physics. Some features of parametric rf oscillators are used in the model. An analysis of the operation of the model helps one to understand the difference between quantum and classical correlations in EPR experiments. A specific mechanism is suggested for 'nonlocal' control of EPR-type correlations between distant observers, which applies to classical and quantum models. A controlled correlation between two random telegraphic signals is ensured by transmission, to two observers, of a sequence of pulses with the same random phase. An elementary derivation of Bell's inequality is given and an analysis is made of the logic of the use of the popular term 'quantum nonlocality' employed usually in the description of the quantum variants of the investigated experiment.
There is an opinion that the Bohm reformulation of the EPR paradox in terms of spin variables is equivalent to the original one. In this note we show that such an opinion is not justified. We apply to the original EPR problem the method which was used by Bell for the Bohm reformulation. He has shown that correlation function of two spins cannot be represented by classical correlation of separated bounded random processes. This Bell`s theorem has been interpreted as incompatibility of local realism with quantum mechanics. We show that, in contrast to Bell`s theorem for spin or polarization correlation functions, the correlation of positions (or momenta) of two particles, depending on the rotation angles, in the original EPR model always admits a representation in the form of classical correlation of separated random processes. In this sense there exists a local realistic representation for the original EPR model but there is no such a representation for the Bohm spin reformulation of the EPR paradox. It shows also that the phenomena of quantum nonlocality is based not only on the properties of entangled states but also on the using of particular bounded observables.
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.
Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell's inequality.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.
It is shown that the Einstein-Podolsky-Rosen (EPR) correlations for arbitrary spin s and the Greenberger-Horne-Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the information Bell inequalities. Relations between the randomness, the nonlocality, and the entropic information for the EPR and the GHZ correlations are established and discussed.
Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.