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arXiv:quant-ph/0105020

Does Bell's theorem apply if perceived pseudo-Euclidean space is emergent?

Bart Jongejan

Published May 6, 2001• 0 citations
arXivHTMLPDF

Abstract

Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot coexist, then predictions about those can neither. Using an EPR-inspired experiment with distantly separated measurements on pairs of entangled spinning particles, Bell proved that no local hidden variable (HV) theory can describe reality in more detail than QM. However, it is possible to conceive a viable HV theory based on the assumption that the perceived structure of spacetime is emergent from a hidden curved spacetime. According to this theory, locality can be maintained for each of the measurements while what is perceived as non-locality can be ascribed to the emergence of spacetime correlations between the instruments of the two parties. The theory predicts correlations that agree with QM, provided that the hidden spacetime has three spatial dimensions. If it had fewer than three dimensions, the CHSH inequality would not be violated and if more, Tsirelson's bound would be violated. According to this HV theory, the laboratory frame of reference is a corollary of correlations of the type that are the subject of Bell's thought experiment.

DOI
10.48550/arxiv.quant-ph/0105020

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Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot coexist, then predictions about those can neither. Using an EPR-inspired experiment with distantly separated measurements on pairs of entangled spinning particles, Bell proved that no local hidden variable (HV) theory can describe reality in more detail than QM. However, it is possible to conceive a viable HV theory based on the assumption that the perceived structure of spacetime is emergent from a hidden curved spacetime. According to this theory, locality can be maintained for each of the measurements while what is perceived as non-locality can be ascribed to the emergence of spacetime correlations between the instruments of the two parties. The theory predicts correlations that agree with QM, provided that the hidden spacetime has three spatial dimensions. If it had fewer than three dimensions, the CHSH inequality would not be violated and if more, Tsirelson's bound would be violated. According to this HV theory, the laboratory frame of reference is a corollary of correlations of the type that are the subject of Bell's thought experiment.
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to the customary a priori given frame of reference of the laboratory when describing real EPR experiments. J.S. Bell has argued that local hidden parameter theories that reproduce the predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning leading to Bell's conclusion is physically meaningless if the frame of reference that is based on EPR-correlations is accepted as the backdrop for EPR-type experiments. The refutal of Bell's proof opens up for the construction of a viable hidden parameter theory. A model of a spin h/2 particle in terms of a non-flat metric of space-time is shown to be able to reproduce the predictions of quantum mechanics in the Bohm-Aharonov version of the EPR experiment, without introducing non-locality.
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.
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.
Einstein, Podolsky, and Rosen (EPR) have designed a gedanken experiment that suggested a theory that was more complete than quantum mechanics. The EPR design was later realized in various forms, with experimental results close to the quantum mechanical prediction. The experimental results by themselves have no bearing on the EPR claim that quantum mechanics must be incomplete nor on the existence of hidden parameters. However, the well known inequalities of Bell are based on the assumption that local hidden parameters exist and, when combined with conflicting experimental results, do appear to prove that local hidden parameters cannot exist. This fact leaves only instantaneous actions at a distance (called "spooky" by Einstein) to explain the experiments. The Bell inequalities are based on a mathematical model of the EPR experiments. They have no experimental confirmation, because they contradict the results of all EPR experiments. In addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions; for instance, he assumes that the hidden parameters are governed by a single probability measure independent of the analyzer settings. We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.
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 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality. He also showed that QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review, we will discuss various foundational as well as information theoretic implications of BI. We will also discuss about some restricted nonlocal feature of quantum nonlocality and elaborate the role of Uncertainty principle and Complementarity principle in explaining this feature.