Several foundational and information theoretic implications of Bell’s theorem (original) (raw)
Related papers
Bell's Inequalities — Foundations and Quantum Communication
Handbook of Natural Computing, 2012
For individual events quantum mechanics makes only probabilistic predictions. Can one go beyond quantum mechanics in this respect? This question has been a subject of debate and research since the early days of the theory. Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hiddenvariable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-thatlight-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind betterthan-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real me aning is, iť
Bell's theorem: A Faulty Logical Construct
Bell's theorem: A Faulty Logical Construct, 2025
It is proven that, several implicit assumptions used in the derivation of Bell's inequalities are making them universally valid and therefore, unsuitable either as a criterion for deciding between local realism and quantum mechanics, or as a tool that can be used to prove the existence of entanglement. It is further shown that Bell's theorem can be established only by asserting that the existence of an objective reality implies the exclusion of time from measurements and their outcomes. This exclusion of time is, however, in direct contradiction to the experimental results.
Bell's Theorem and Hidden Variable Theories
Alhun Aydın, 2011
Although standard quantum mechanics is compatible with experiments, it could not clarify some important unsolved problems like quantum reality and measurement process. Hidden variable theories provide solutions to these conceptual problems of standard quantum mechanics. We examine Bell's theorem, one of the most essential theorems about foundations of quantum mechanics, and Bell-test experiments which empirically rules out local hidden variable theories. Then we discuss pilot wave theory which is a non-local hidden variable theory and one of the most significant possible successors of standard quantum mechanics. Moreover, by touching upon also philosophical issues, we give the shape of the possible interpretation of quantum mechanics.
On the logical structure of Bell theorems
New Journal of Physics, 2006
Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory-nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of these novel designs fail in the most basic way, by not ruling out local hidden variable models, and we provide an explicit classical model to demonstrate this. They share a common flaw, which reveals a basic misunderstanding of how nonlocality proofs work. Given the time and resources now being devoted to such experiments, theoretical clarity is essential. Our explanation is presented in terms of simple logic and should serve to correct misconceptions and avoid future mistakes. We also show a nonlocality proof involving four participants which has interesting theoretical properties.
On Bell’s Theorem, Quantum Communication, and Entanglement Detection
AIP Conference Proceedings, 2009
A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and "free will". A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bell's theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states will be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.
The Bell's theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the Einstein-Podolsky-Rosen paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell's polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper we show, however, that the proof of the Bell's inequality involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, moreover, it might not be fulfilled in the experimental setup that tests the inequality. In fact, this assumption can neither be properly implemented within the framework of quantum mechanics. Namely, the proof of the Bell's theorem assumes that there exists an absolute preferred frame of reference, supposedly provided by the lab, which enables to compare the orientation of the polarization measurement devices for successive realizations of the experiment. The need for this assumption can be readily checked by noticing that the theorem does not hold when the orientation of one of the detectors is taken as a reference frame to define the relative orientation of the second detector, in spite that this frame is an absolutely legitimate choice according to Galileo's principle of relativity. We further notice that the absolute frame of reference required by the proof of the Bell's theorem cannot exist in models in which the hidden configuration of the pair of entangled particles has a randomly set preferred direction that spontaneously breaks the global rotational symmetry. In fact, following this observation we build an explicit local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell's states. 2
Bell’s theorem refuted as EPR and locality prevail
In a technical report under the auspices of The Nobel Committee for Physics, dated 4 October 2022, we find these claims: (i) Bell's first inequality was a spectacular theoretical discovery; (ii) Bell showed mathematically that no hidden variable theory would be able to reproduce all the results of quantum mechanics; (iii) Bell showed that all attempts to construct a local realist model of quantum phenomena are doomed to fail. Against such claims, and focussing on EPR's criteria, this personal note shows: (i) that all such claims are flawed; (ii) that Bell's theorem and Bell's inequality fall to straightforward considerations; (iii) that consequently, for their part in proving that EPR were right: we are indebted to those who develop the sources; hopefully en route to wholistic mechanics –– a commonsense quantum mechanics –– as we celebrate the birth of Olivier Costa de Beauregard, 111 years ago, 19111106, Paris. [This paper is a prelude to Watson (forthcoming): “On the Einstein-Podolsky-Rosen (EPR) paradox.” There, under EPR's criteria and avoiding Bell's errors, Bell's 1964 Eqs.1-3 are shown to lead to the correct quantum mechanical results. In this way, we refute Bell's theorem directly on Bell's terms.]
Comments on "Disproof of Bell's theorem
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 contextual hidden variables theories are not considered genuine physically theories and Bell's theorem's importance stems from its ability to be experimentally confirmed, then Joy Christian's counterexample does not diminish the importance of Bell's theorem. The implications of Joy Christian's counterexample are discussed in the context of information theory....