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arXiv:1010.4412 · Physics of Particles and Nuclei

The locality problem in quantum measurements

D. A. Slavnov

Published Jan 1, 2010• 10 citations
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Abstract

The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler’s delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpretation for these experiments, which does not contradict the classical ideas, is given.

DOI
10.1134/s1063779610010077

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The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler’s delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpretation for these experiments, which does not contradict the classical ideas, is given.
The problem of wave-particle duality is considered within the framework of the algebraic approach. Contrary to the widespread belief, we demonstrate that wave-particle duality can be reconciled with the assumption that there exists some local physical reality determining the results of local measurements. A number of quantum experiments—double-slit electron scattering, Wheeler’s delayed choice experiment, the past of photons passed through the interferometer—are discussed using the concept of locality. A clear physical interpretation of these experiments that does not contradict classical concepts is provided.
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.
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.
In recent notes by Einstein, Podolsky and Rosen and by Bohr, attention has been called to the fact that certain results of quantum mechanics are not to be reconciled with the assumption that a system has independently real properties as soon as it is free from mechanical interference. We here investigate in general, and in abstract terms, the extent of this disagreement. When suitably formulated, such an assumption gives to certain types of questions the same answers as does quantum mechanics; this is true of the formulas usually given in discussions of the theory of measurement. There exists, however, a general class of cases in which contradictions occur. That such contradictions are not restricted to the abstract mathematical theory, but can be realized in the commonest physical terms, is shown by the working out of an example..
This work presents a conceptual and semi-formal analysis of quantum entanglement, locality, and determinism, motivated by a thought experiment involving double-slit measurements performed on entangled particles at spacelike separation. While quantum correlations appear instantaneous, the paper demonstrates that no superluminal information transfer or causal influence is required to explain observed outcomes.Building upon the Einstein–Podolsky–Rosen framework and Bell’s theorem, the study distinguishes between local dynamical processes and nonlocal informational correlations encoded in the global quantum state. It argues that measurement outcomes are locally realized yet globally constrained, leading to an effectively deterministic universal description while preserving epistemic uncertainty for observers.The paper reframes quantum nonlocality as a manifestation of global consistency rather than physical influence, offering insights into the relationship between realism, free will, and relativistic causality. The discussion is interpretational in nature and does not introduce new experimental claims, aiming instead to clarify foundational assumptions underlying quantum theory.This work is intended for researchers and students interested in quantum foundations, the philosophy of physics, and the conceptual structure of modern physical theories.