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American Journal of Physics

Bell’s theorem: Local realism versus quantum mechanics

Miguel Ferrero, Trevor W. Marshall, Emilio Santos

Published Jul 1, 1990• 30 citations
Publisher

Abstract

Realism and locality are defined emphasizing the fundamental character of both principles. From this, the well-known expression proposed by Bell for calculating correlations is derived. Starting from this expression, the theorem of incompatibility is proved between local realism and quantum mechanics. An analysis is made of the experiments performed by Aspect and others, and it is concluded that, because photomultipliers and polarizing filters are not perfectly efficient, it is necessary to make subsidiary assumptions about how they operate in order to rule out local realism. It is argued that the subsidiary assumptions are not logically necessary and, consequently, local realism has not yet been refuted empirically.

DOI
10.1119/1.16400

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Realism and locality are defined emphasizing the fundamental character of both principles. From this, the well-known expression proposed by Bell for calculating correlations is derived. Starting from this expression, the theorem of incompatibility is proved between local realism and quantum mechanics. An analysis is made of the experiments performed by Aspect and others, and it is concluded that, because photomultipliers and polarizing filters are not perfectly efficient, it is necessary to make subsidiary assumptions about how they operate in order to rule out local realism. It is argued that the subsidiary assumptions are not logically necessary and, consequently, local realism has not yet been refuted empirically.
With Bell (1964) and his EPR-based mathematics contradicted by experiments, at least one step in his supposedly commonsense theorem must be false. Defining commonsense local realism as the fusion of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively), we eliminate all such contradictions and make EPR correlations intelligible by completing the quantum mechanical account in a classical way. Thus refuting the famous inequality at the heart of Bell's mathematics, we show that Bell's theorem is limited by Bell's use of naive realism. Validating the classical mantra that correlated tests on correlated things produce correlated results without mystery, we conclude that Bell's theorem and related experiments negate naive realism, not commonsense local realism.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., of the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of local realism. In this paper, Bell's inequality is derived in its traditional form, without resorting to the hypothesis of locality, the only assumption being that the probability distributions are nonnegative. These probability distributions are calculated, for a specific optical experiment, in the framework of quantum theory and it is shown that they can take on negative values. This can therefore be regarded as a rigorous proof that the hypothesis of locality is not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined.
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be estimated experimentally.Bell theorem will never address a real experiment because its assumptions cannot be strictly fulfilled. By an appropriate generalization of quantum framework and measurement postulates, in particular taking into account freedom of choice, local realism agrees with quantum mechanics and the performed experiments, also involving single qubit coherence and a weaker version of the Bell test, Einstein-Podolsky-Rosen steering.
An open letter to Bellians and the Annals of Physics' Editors re -- it's a proven scientific fact: a violation of local realism has been demonstrated theoretically and experimentally -- after AoP (2016:67). EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. Even more famously, Bell (1964) cried ‘impossible' against such variables; we give the shortest possible refutation of his claims. With EPR-based variables (and without QM), an old thought-experiment delivers a commonsensical locally-causal account of EPRB and GHZ in 3-space. We then name the flaw in Bell's theorem – Bell's error -- Bell's 1964:(14a) ≠ Bell's 1964:(14b) under EPRB. Thus, given Bell's (1988:88) gloss on a snippet of von Neumann's work, ‘There's nothing to Bell's theorem -- nor variants like CHSH (1969), Mermin (1990), Peres (1995) -- it's not just flawed, it's silly; not merely false but foolish.' In short, we show that the whole Bellian canon -- with its no-name brand of local realism -- is all of those, and misleading too. Under EPR, mixing common-sense with undergrad math/physics in the classical way so favored by Einstein, we interpret QM locally and realistically. We thus define a new brand of local realism -- CLR, commonsense local realism -- the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). Long may EPR rule OK we say.
Bell's theorem states that some quantum correlations can not be represented by classical correlations of separated random variables. It has been interpreted as incompatibility of the requirement of locality with quantum mechanics. We point out that in fact the space part of the wave function was neglected in the proof of Bell's theorem. However this space part is crucial for considerations of property of locality of quantum system. Actually the space part leads to an extra factor in quantum correlations and as a result the ordinary proof of Bell's theorem fails in this case. We present a criterium of locality in a realist theory of hidden variables. It is argued that predictions of quantum mechanics for Gaussian wave functions can be consistent with Bell's inequalities and hence Einstein's local realism is restored in this case.