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AIP conference proceedings

Some loopholes to save quantum nonlocality

Luigi Accardi

Published Jan 1, 2005• 47 citations
Publisher

Abstract

The EPR‐chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality.The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non‐Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to “reconstruct history” on the lines described by Orwell in “1984”.

DOI
10.1063/1.1874552

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•Jan 1, 2002•7 citations
The EPR‐chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality.The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non‐Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to “reconstruct history” on the lines described by Orwell in “1984”.
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.
On September 27 (2001), as a side activity to the "Japan-Italy Joint workshop on: Quantum open systems and quantum measurement", the first; public demonstration of the dynamical EPR-chameleon experiment was performed at Waseda University in order to give an experimental answer to a long standing question in the foundations of quantum theory: do there exist classical macroscopic systems which, by local independent choices, produce sequences of data which reproduce the singlet correlations, hence violating Bell's inequality? The EPR-chameleon experiment gives an affirmative answer to this question by concretely producing an example of such systems in the form of three personal computers which realize a local deterministic dynamical evolution whose mathematical structure is very simple and transparent. In the experiment performed on September 27 the local dynamics used was not a reversible one because the interaction with the degrees of freedom of the apparatus was integrated out giving rise to an effective Markovian dynamics which, although mapping probability measures into probability measures, did not preserve the +/- 1-values of the spin (or polarization) observables. This feature was criticized by some of the partecipants and the following two questions arose: i) is it possible to prove that the Markovian evolution, used in the experiment, is indeed the reduced evolution of a bona fide reversible evolution? ii) if the answer to question (i) is affirmative, is it possible to reproduce the EPR correlations by simply considering empirical averages of +/- 1-values, as one does in usual EPR type experiments? An affirmative answer to these questions was given in the paper [AcImRe01] and it is briefly reviewed in what follows.
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.
We prove that the structure of the classical dynamical system, constructed in [AcImRe01] to reproduce the EPR correlations, is a natural consequence of the combination of the general theory of classical dynamical systems with the extension of von Neumann measurement theory, proposed in [Ac93] to include in it the requirements of locality and causality.We then prove some a priori estimates which guarantee the convergence of the simulation procedure.The program to run the experiment is available from the WEB-page: http://volterra.mat.uniroma2.it.