A 1964 paper by John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. There is an ongoing and vigorous debate on whether he relied on an assumption of determinism, or instead, as he later claimed, derived determinism from assumptions of locality and perfect correlation. This paper aims to bring clarity to the debate via simple examples and rigorous results. It is shown that the weak form of locality used in Bell's 1964 paper (parameter independence) is insufficient for such a derivation, whereas an independent form called outcome independence is sufficient even when weak locality does not hold. It further follows that outcome independence, by itself, implies that standard quantum mechanics is incomplete. It is also shown that an appeal by Bell to the Einstein-Rosen-Podolsky argument to support his claim fails, via examples that expose logical gaps in this argument. However, replacing the reality criterion underpinning the argument by a stronger criterion enables a rigorous derivation of both weak locality and determinism, as required for Bell's 1964 paper. Consequences for quantum interpretations, locality, and classical common causes are briefly discussed, with reference to an example of local classical indeterminism.
A 1964 paper by John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. There is an ongoing and vigorous debate on whether he relied on an assumption of determinism, or instead, as he later claimed, derived determinism from assumptions of locality and perfect correlation. This paper aims to bring clarity to the debate via simple examples and rigorous results. It is shown that the weak form of locality used in Bell's 1964 paper (parameter independence) is insufficient for such a derivation, whereas an independent form called outcome independence is sufficient even when weak locality does not hold. It further follows that outcome independence, by itself, implies that standard quantum mechanics is incomplete. It is also shown that an appeal by Bell to the Einstein-Rosen-Podolsky argument to support his claim fails, via examples that expose logical gaps in this argument. However, replacing the reality criterion underpinning the argument by a stronger criterion enables a rigorous derivation of both weak locality and determinism, as required for Bell's 1964 paper. Consequences for quantum interpretations, locality, and classical common causes are briefly discussed, with reference to an example of local classical indeterminism.
Does determinism (or even the incompleteness of quantum mechanics) follow from locality and perfect correlations? In a 1964 paper, John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. Since then, a vigorous debate has rung out over whether he relied on an assumption of determinism or instead, as he later claimed in a 1981 paper, derived determinism from assumptions of locality and perfect correlation. This paper aims to bring clarity to the debate via simple examples and rigorous results. It is first recalled, via quantum and classical counterexamples, that the weakest statistical form of locality consistent with Bell’s 1964 paper (parameter independence) is insufficient for the derivation of determinism. Attention is then turned to critically assess Bell’s appeal to the Einstein–Rosen–Podolsky (EPR) incompleteness argument to support his claim. It is shown that this argument is itself incomplete, via counterexamples that expose two logical gaps. Closing these gaps via a strong “counterfactual” reality criterion enables a rigorous derivation of both determinism and parameter independence, and in this sense justifies Bell’s claim. Conversely, however, it is noted that whereas the EPR argument requires a weaker “measurement choice” assumption than Bell’s demonstration, it nevertheless leads to a similar incompatibility with quantum predictions rather than quantum incompleteness.
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.
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.
It is shown that when properly analyzed using principles consistent with the
use of a Hilbert space to describe microscopic properties, quantum mechanics is
a local theory: one system cannot influence another system with which it does
not interact. Claims to the contrary based on quantum violations of Bell
inequalities are shown to be incorrect. A specific example traces a violation
of the CHSH Bell inequality in the case of a spin-3/2 particle to the
noncommutation of certain quantum operators in a situation where (non)locality
is not an issue. A consistent histories analysis of what quantum measurements
measure, in terms of quantum properties, is used to identify the basic problem
with derivations of Bell inequalities: the use of classical concepts (hidden
variables) rather than a probabilistic structure appropriate to the quantum
domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument
for the incompleteness of quantum mechanics is the use of a counterfactual
argument which is not valid if one assumes that Hilbert-space quantum mechanics
is complete; locality is not an issue. The quantum correlations that violate
Bell inequalities can be understood using local quantum common causes.
Wavefunction collapse and Schr\odinger steering are calculational procedures,
not physical processes. A general Principle of Einstein Locality rules out
nonlocal influences between noninteracting quantum systems. Some suggestions
are made for changes in terminology that could clarify discussions of quantum
foundations and be less confusing to students.
Many of the heated arguments about the meaning of 'Bellʼs theorem' arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976.His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism.His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality.This is contrary to Bellʼs own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name).While there are other forms of Bellʼs theorems-which I present to explain the relation between Jarrett-completeness, 'fragile locality', and EPR-completeness-I maintain that Bellʼs two versions are the essential ones.Although the two Bellʼs theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities.For realists, the notion of local causality, ruled out by Bellʼs 1976 theorem, is motivated implicitly by Reichenbachʼs principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone.Operationalists pay no heed to Reichenbachʼs principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit 'principle of agent-causation', implies their notion of locality.Thus for operationalists, Bellʼs theorem is the 1964 one, and implies that it is determinism that must be forgone.I discuss why the two 'camps' are drawn to these different conclusions, and what can be done to increase mutual understanding.
In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle?
The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.