Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as `strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as `weakly objective,' that is, each correlation function pertains to a different set of particle pairs.
It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).
I identify a number of errors in Richard Gill's purported refutation (arXiv:1203.1504) of my disproof of Bell's theorem. In particular, I point out that his central argument is based, not only on a rather trivial misreading of my counterexample to Bell's theorem, but also on a simple oversight of a freedom of choice in the orientation of a Clifford algebra. What is innovative and original in my counterexample is thus mistaken for an error, at the expense of the professed universality and generality of Bell's theorem.
In a couple of recent preprints Moldoveanu has suggested that there are errors in my disproof of Bell's theorem. Here I show that this claim is false. In particular, I show that my local-realistic framework is incorrectly and misleadingly presented in both of his preprints. In addition there are a number of serious mathematical and conceptual errors in his discussion of my framework. For example, contrary to his claim, my framework is manifestly non-contextual. In particular, quantum correlations are understood within it as purely topological effects, not contextual effects.
Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam …
We investigate the connection between quantum no-cloning theorem and Bell's theorem. Designing some Bell's inequalities, we show that quantum no-cloning theorem can always be certified by Bell's theorem, and this fact in turn reflects that our physical world is essentially nonlocal.
Recently, Colbeck and Renner (2011) [arXiv:1005.5173] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is more significant than the other variations of Bell's theorem that have been published in the 50 years since Bell's theorem. Colbeck and Renner themselves do not relate their theorem directly to Bell's theorem, so here I present a version of the Colbeck-Renner theorem that makes the relationship explicit.
Nieuwenhuizen argued that there exists some "contextuality loophole" in Bell's theorem. This claim is unjustified. In Bell's theorem non-contextuality is not presupposed but derived from Einstein causality using the EPR argument.
It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences from observations formulated within classical automata theory. Similarities between the assumptions underlying classical automata theory and those underlying universally-unitary quantum theory are discussed.
Bell's theorem is reformulated and proved in the pure mathematical terms of automata theory, avoiding any physical or ontological notions. It is stated that no pair of finite probabilistic sequential machines can reproduce in its output the statistical results of the quantum-physical Bell test experiment if each machine is independent of the respective remote input.
This paper implements in a simple but rigorous fashion a model of particle interaction involving all paths within a quantum system, both for configuration space and for spin. The model, which we call the space of all paths, leads to a locally explicable conceptual framework for quantum mechanics. Using it we present two counterexamples to Bell's theorem. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternativel…
In a recent paper [arXiv:1703.11003] on this journal Stephen Boughn argued that quantum mechanics does not require nonlocality of any kind and that the common interpretation of Bell theorem as a nonlocality result is based on a misunderstanding. In this note I argue that the Boughn arguments, that summarize views widespread in certain areas of the foundations of quantum mechanics, are based on an incorrect reading of the presuppositions of the EPR argument and the Bell theorem and, as a consequence, are totally unfounded.
This note shows how one can be led from considerations of quantum steering to Bell's theorem. The point is that steering remote systems by choosing between two measurements can be described in a local theory if we take quantum states to be associated many-to-one with the underlying "real states" of the world. Once one adds a third measurement this is no longer possible. Historically this is not how Bell's theorem arose - there are slight and subtle differences in the arguments - but it could have been.
Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of Bell-type inequalities fail if non-Newtonian hidden variables are taken into account. From the non-Newtonian perspective, Bell's inequality is a property of a limited and unphysical class of hidden-variable models. An explicit counterexample to Bell's theorem can be easily constructed.
An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell's theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d'Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inc…
It is demonstrated that a recently suggested model for the EPR-Bohm spin experiment, based on Clifford algebra valued local variables and observables, runs into very serious difficulties and can therefore not be taken as constituting a viable counter-example to Bell's theorem.
Bell's theorem admits several interpretations or 'solutions', the standard interpretation being 'indeterminism', a next one 'nonlocality'. In this article two further solutions are investigated, termed here 'superdeterminism' and 'supercorrelation'. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be violated, even if they…
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is cla…
In a recent article (Found Sci (2020) https://doi.org/10.1007/s10699-020-09666-0) Marek Czachor claims that the Bell inequality cannot be proved because variables of complementary measurements cannot be added or multiplied. Even though he has correctly identified the problems existing with the orthodox interpretation of the Bell inequality and dealt with them in an original way, the interpretation he addresses do not pertain to the original formulation given by John Stewart Bell.
In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory. If Bell's theorem's importance is to rule out contextual hidden variable theories obeying relativistic locality, then Joy Christian's counterexample achieves its aim. If however cont…
Four critical elementary mathematical mistakes in Joy Christian's counterexample to Bell's theorem are presented. Consequently, Joy Christian's hidden variable model cannot reproduce any quantum mechanics results and cannot be used as a counterexample to Bell's theorem. The mathematical investigation is followed by a short discussion about the possibility to construct other hidden variable theories. A tutorial section on relevant Clifford algebra topics was added at the end to help interested readers decide for themselves the validity of Joy's claims. Also an appendix section discusses recent …
Meyer，Kent and Clifton（MKC）声称已经否定了Bell-Kochen-Specker（Bell-KS）定理。的确，它们使KS对该定理的物理含义的解释无效。然而，它们并没有使贝尔的观点无效，即量子力学与经典假设不一致，即测量告诉我们系统先前拥有的属性。经典测量思想的失败，也许是量子力学唯一最重要的含义。在传统的着色中，有一些剩余的白色斑块。MKC填补了这些斑块，但代价是引入了颜色变得“病态”不连续的斑块。这种不连续性意味着这些斑块中的颜色是经验上不可知的。我们证明了一个一般定理，表明它们的程度至少是一样大的补丁的白色在一个传统的方法。该定理不仅适用于MKC着色，而且适用于任何其他试图绕过Bell-KS定理的尝试（例如Pitowsky着色）。我们继续讨论其影响。MKC不使Bell-KS定理无效。然而，它们确实表明，到目前为止，我们还没有正确地理解这个定理。由于这个原因，他们的结果（以及皮托夫斯基早期的结果）是非常重要的。
