American Journal of Physics

What Bell proved: A reply to Blaylock

Tim Maudlin

Published Dec 14, 2009• 30 citations

Abstract

Blaylock argues that the derivation of Bell’s inequality requires a hidden assumption, counterfactual definiteness, of which Bell was unaware. A careful analysis of Bell’s argument shows that Bell presupposes only locality and the predictions of standard quantum mechanics. Counterfactual definiteness, insofar as it is required, is derived in the course of the argument rather than presumed. Bell’s theorem has no direct bearing on the many worlds interpretation not because that interpretation denies counterfactual definiteness but because it does not recover the predictions of standard quantum mechanics.

DOI: 10.1119/1.3243280

Related papers

EPR, Bell, and quantum locality

Robert B. Griffiths

Maudlin has claimed that no local theory can reproduce the predictions of standard quantum mechanics that violate Bell’s inequality for Bohm’s version (two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen problem. It is argued that, on the contrary, standard quantum mechanics itself is a counterexample to Maudlin’s claim, because it is local in the appropriate sense (measurements at one place do not influence what occurs elsewhere there) when formulated using consistent principles in place of the inconsistent appeals to “measurement” found in current textbooks. This argument sheds light on the claim of Blaylock that counterfactual definiteness is an essential ingredient in derivations of Bell’s inequality.

arXiv:1007.4281American Journal of PhysicsAug 19, 201167 citations

The EPR paradox, Bell’s inequality, and the question of locality

Guy Blaylock

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.

arXiv:0902.3827American Journal of PhysicsDec 14, 200959 citations

Bell inequalities, counterfactual definiteness and falsifiability

Justo Pastor Lambare

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical property of Bell’s probabilistic model. Although the amendment does not alter the relevance of the theorem regarding local realism, it brings back Bell theorem from the realm of philosophical discussions about counterfactual conditionals to the concrete experimental arena.

arXiv:1911.00343International Journal of Quantum InformationApr 1, 202111 citations

Quantum non-locality—it ainʼt necessarily so...

Marek Żukowski, Časlav Brukner

Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.

arXiv:1501.04618Journal of Physics A Mathematical and TheoreticalOct 9, 2014100 citations

Quantum Solipsism and Nonlocality

Travis Norsen

J.S. Bell's remarkable 1964 theorem showed that any theory sharing the empirical predictions of orthodox quantum mechanics would have to exhibit a surprising – and, from the point of view of relativity theory, very troubling – kind of nonlocality. Unfortunately, even still on this 50th anniversary, many commentators and textbook authors continue to misrepresent Bell's theorem. In particular, one continues to hear the claim that Bell's result leaves open the option of concluding either nonlocality or the failure of some unorthodox “hidden variable” (or “determinism” or “realism”) premise. This mistaken claim is often based on a failure to appreciate the role of the earlier 1935 argument of Einstein, Podolsky, and Rosen in Bell's reasoning. After briefly reviewing this situation, I turn to two alternative versions of quantum theory – the “many worlds” theory of Everett and the quantum Bayesian interpretation of Fuchs, Schack, Caves, and Mermin – that purport to provide actual counterexamples to Bell's claim that nonlocality is required to account for the empirically verified quantum predictions. After analyzing each theory's grounds for claiming to explain the EPR–Bell correlations locally, however, one can see that (despite a number of fundamental differences) the two theories share a common for-all-practical-purposes (FAPP) solipsistic character. This dramatically undermines such theories’ claims to provide a local explanation of the correlations and thus, by concretizing the ridiculous philosophical lengths to which one must go to elude Bell's own conclusion, reinforces the assertion that nonlocality really is required to coherently explain the empirical data. Introduction Fifty years ago, in 1964 [1], John Stewart Bell first proved the theorem that has become widely known as “Bell's Theorem” but that Bell himself instead referred to as the “locality inequality theorem” [2]. In Bell's own view, the theorem showed that the empirical predictions of local theories will be constrained by Bell's inequality (or as Bell himself preferred to call it, the “locality inequality”). Hence, nonlocality is a necessary feature of any theory that shares the empirical predictions of standard quantum mechanics.

Cambridge University Press eBooksAug 31, 201622 citations

Stop making sense of Bell's theorem and nonlocality? A reply to Stephen Boughn

Federico Laudisa

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.

arXiv:1705.01356May 3, 20171 citation