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Summarization and review:Bell-type space nonlocality

Jianlan Chen

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Like classical theory,quantum theory including non-relativistic quantum mechanics and relativistic quantum field theory has adopted locality description.But,essentially,quantum theory is a space nonlocality theory dressed by locality description.Since EPR paradox,Bell inequality,GHZ theorem,Hardy theorem and Cabello theorem were proposed,there have been a lot of theoretical and experimental works about the space nonlocality route along Bell-GHZ-Hardy-Cabello.Up to now the experimental results all support quantum theory.However,the essence of the space nonlocality characteristics of quantum theory has not been discovered yet,nor can the existence of hidden variables be denied,a situation that keeps attracting more attention and consideration to this hot issue.Here we generalize this route concisely and specify the related ideas,definition and theorem systemically.At last we give a detailed comment on this route.

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Like classical theory,quantum theory including non-relativistic quantum mechanics and relativistic quantum field theory has adopted locality description.But,essentially,quantum theory is a space nonlocality theory dressed by locality description.Since EPR paradox,Bell inequality,GHZ theorem,Hardy theorem and Cabello theorem were proposed,there have been a lot of theoretical and experimental works about the space nonlocality route along Bell-GHZ-Hardy-Cabello.Up to now the experimental results all support quantum theory.However,the essence of the space nonlocality characteristics of quantum theory has not been discovered yet,nor can the existence of hidden variables be denied,a situation that keeps attracting more attention and consideration to this hot issue.Here we generalize this route concisely and specify the related ideas,definition and theorem systemically.At last we give a detailed comment on this route.
The phenomenon of nonlocality in quantum mechanics is one of its most fundamental features and is most strikingly exemplified in the discussion of the Einstein, Podolsky and Rosen (EPR) type of experiment. The generality of Bell's inequality and the results of experiments done up to now show that local hidden-variable theories are ruled out as a means to resolve the famous EPR paradox. What remains for further consideration are the nonlocal and the Einstein-separable hidden-variable models. Finally, an alternative and possibly successful approach in trying to 'explain' nonlocality might involve ideas of backward causation.
A factual inconsistency of the nonlocality theory is demonstrated via a careful analysis of the conceptual and formal contents of Bell's theorem and the inequalities associated with it. The conceptual inconsistency of the theory follows from the consideration that it is, in principle, impossible to formulate quantum mechanics in terms of local hidden variables. The formal inconsistency of the nonlocality theory follows from the facts that: (i) nonlocality is not a physical property that can be represented by a function or an operator; (ii) it is impossible to derive Bell's inequality in a mathematically consistent way; and (iii) Bell's definition of locality is incorrect. Therefore, Bell's theorem cannot serve as the foundation for the introduction of the nonlocality notion in quantum mechanics.
Experiments motivated by Bell's theorem have led some physicists to conclude that quantum theory is nonlocal. However, the theoretical basis for such claims is usually taken to be Bell's Theorem, which shows only that if certain predictions of quantum theory are correct, and a strong hidden-variable assumption is valid, then a certain locality condition must fail. This locality condition expresses the idea that what an experimenter freely chooses to measure in one spacetime region can have no effect of any kind in a second region situated spacelike relative to the first. The experimental results conform closely to the predictions of quantum theory in such cases, but the most reasonable conclusion to draw is not that locality fails, but rather that the hidden-variable assumption is false. For this assumption conflicts with the quantum precept that unperformed experiments have no outcomes. The present paper deduces the failure of this locality condition directly from the precepts of quantum theory themselves, in a way that generates no inconsistency or any conflict with the predictions of relativistic quantum field theory.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
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.