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Canadian Journal of Physics

An attempt to close the Einstein–Podolsky–Rosen debate

T Krüger

Published Jan 1, 2004• 6 citations
Publisher

Abstract

Based on a new rigorous ensemble approach to quantum mechanics, and without stressing any idea or concept of reality, the entire Einstein–Podolsky–Rosen (EPR) problem can be boiled down to the question of whether the separability principle of the natural sciences is universally valid. To give a precise answer first of all Bell's inequality is deduced from said ensemble point of view and with minimal requirements only. (In the final discussion of the results it turns out that Bell's inequality defines the upper bound for those basic correlations that are due to a mere conservation law.) Then, by use of Wheeler's gedanken experiment with coin halves, I show that the statistical operator representing an ensemble under investigation may be either separable (in a simplified sense) or not. The conceptual consequences of nonseparability are explained, and a general EPR-type experiment is re-examined. Thereby, it is proven that, if and only if, the statistical operator is nonseparable, Bell's inequality may be violated. Experimental evidence demands nonseparable operators. So, if quantum mechanics is assumed to make statistical statements on the results of measurements on ensembles only, there is no way to avoid acceptance of its (operationally) holistic character, and the question posed at the outset must be negated. PACS Nos : 03.65.Ta, 03.65.Ud

DOI
10.1139/p03-113

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Based on a new rigorous ensemble approach to quantum mechanics, and without stressing any idea or concept of reality, the entire Einstein–Podolsky–Rosen (EPR) problem can be boiled down to the question of whether the separability principle of the natural sciences is universally valid. To give a precise answer first of all Bell's inequality is deduced from said ensemble point of view and with minimal requirements only. (In the final discussion of the results it turns out that Bell's inequality defines the upper bound for those basic correlations that are due to a mere conservation law.) Then, by use of Wheeler's gedanken experiment with coin halves, I show that the statistical operator representing an ensemble under investigation may be either separable (in a simplified sense) or not. The conceptual consequences of nonseparability are explained, and a general EPR-type experiment is re-examined. Thereby, it is proven that, if and only if, the statistical operator is nonseparable, Bell's inequality may be violated. Experimental evidence demands nonseparable operators. So, if quantum mechanics is assumed to make statistical statements on the results of measurements on ensembles only, there is no way to avoid acceptance of its (operationally) holistic character, and the question posed at the outset must be negated. PACS Nos : 03.65.Ta, 03.65.Ud
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of (Bell-type) local realistic theories which could be consistent with a local quantum description for each subsystem. The relationship with criteria sufficient to prove entanglement is established, to show that any demonstration of EPR correlations will also signify entanglement. It is also shown how a demonstration of entanglement between two spatially separated subsystems, if not able to interpreted as a violation of a Bell-type inequality, may be interpreted as a demonstration of the EPR correlations. In particular it is explained how the experimental observation of two-mode squeezing using spatially separated detectors will signify not only entanglement but EPR correlations defined in a general sense.
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.
Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.
Bell inequalities are intended to formulate mathematically the argument of the thought-experiment proposed by Einstein, Podolsky and Rosen (EPR) in the Einstein-Bohr Debate. Devised to test Bell inequalities against quantum mechanics for resolving the Einstein-Bohr debate, Bell experiments are purportedly modern versions of the EPR experiment. However, there exists a fatal logical flaw in Bell experiments. Because of the logical flaw, Bell experiments differ essentially from the EPR experiment, and quantum correlation in the EPR experiment is not "quantum entanglement" in Bell experiments; the latter is not physically meaningful. In addition to the logical flaw in Bell experiments, a physical constraint imposed on measuring individual quantum objects is violated by all Bell inequalities, which makes Bell inequalities physically meaningless. Unlike Bell experiments, the EPR experiment will not violate any physical constraint, and the EPR argument has no logical flaw. Consequently, the experimental invalidation of Bell inequalities is not evidence for falsifying the two fundamental hypotheses for scientific research, i.e., locality and realism, underlying the EPR experiment, and by no means can Bell experiments resolve the Einstein-Bohr debate. Stemming from abandoning either locality or realism or both, the so-called new applications of quantum mechanics, including various quantum information technologies, are all ineligible and doomed to failure, for they attempt to exploit physically meaningless "quantum superposition" or "quantum entanglement", treating them as physical resources "out there" in the real world.
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.