In order to understand nonlocal phenomena, the corresponding processes must be treated as scattering experiments and investigated in the frame of quantum eld theory. Quantum mechanics is not su cient for this task, because it is only concerned with the in uence of a potential on a physical object. But in processes with nonlocal e ects the role of interaction between physical objects must be su ciently respected. All this is shown rst of all for the special case of the spin-1/2-experiment, and then generalized to arbitrary scattering processes. 1. What is the problem? Nonlocal phenomena are discussed and analyzed, since Einstein, Podolsky and Rosen in their famous paper [1] have drawn attention to a di culty of quantum mechanics. By means of their also famous gedankenexperiment the three authors have demonstrated their thesis that quantum mechanics is incomplete. So called local theories were developed in order to repair this pretended fault. The work of Bell [2] consisted in describing mathematically a general kind of such theories, and inferring the inequality bearing his name from characteristic features of such theories by mere logical deduction. In quantum mechanics a corresponding condition can be given, too. These two inequalities are not compatible with one another. Hence it seems to be quite natural to decide between them by experiment. Since all results of experimental investigations from Aspect et al. [3, 4] up to Erven et al. [5] have shown that Bell's inequality is not compatible with the empirical results, local theories nowadays are quite generally refuted. On the other hand all these experiments are supporting the results of quantum mechanics. Hence one could infer that quantum mechanics is correct. But that would be an illegal conclusion, because the agreement with experiment is a necessary, but no su cient condition for the validity of a theory. Hence one would convert a double negation into a positive assertion. In this paper the thesis is claimed and proved that quantum mechanics, indeed, is incomplete, not on the philosophical level, where Bohr and Einstein were quarrelling, but in an immediately physical sense.
In order to understand nonlocal phenomena, the corresponding processes must be treated as scattering experiments and investigated in the frame of quantum eld theory. Quantum mechanics is not su cient for this task, because it is only concerned with the in uence of a potential on a physical object. But in processes with nonlocal e ects the role of interaction between physical objects must be su ciently respected. All this is shown rst of all for the special case of the spin-1/2-experiment, and then generalized to arbitrary scattering processes. 1. What is the problem? Nonlocal phenomena are discussed and analyzed, since Einstein, Podolsky and Rosen in their famous paper [1] have drawn attention to a di culty of quantum mechanics. By means of their also famous gedankenexperiment the three authors have demonstrated their thesis that quantum mechanics is incomplete. So called local theories were developed in order to repair this pretended fault. The work of Bell [2] consisted in describing mathematically a general kind of such theories, and inferring the inequality bearing his name from characteristic features of such theories by mere logical deduction. In quantum mechanics a corresponding condition can be given, too. These two inequalities are not compatible with one another. Hence it seems to be quite natural to decide between them by experiment. Since all results of experimental investigations from Aspect et al. [3, 4] up to Erven et al. [5] have shown that Bell's inequality is not compatible with the empirical results, local theories nowadays are quite generally refuted. On the other hand all these experiments are supporting the results of quantum mechanics. Hence one could infer that quantum mechanics is correct. But that would be an illegal conclusion, because the agreement with experiment is a necessary, but no su cient condition for the validity of a theory. Hence one would convert a double negation into a positive assertion. In this paper the thesis is claimed and proved that quantum mechanics, indeed, is incomplete, not on the philosophical level, where Bohr and Einstein were quarrelling, but in an immediately physical sense.
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.
The phenomenon of nonlocality in quantum mechanics is one of its most fundamental features and is most strikingly exemplified in the discussion of the Einstein, Podolsky and Rosen (EPR) type of experiment. The generality of Bell's inequality and the results of experiments done up to now show that local hidden-variable theories are ruled out as a means to resolve the famous EPR paradox. What remains for further consideration are the nonlocal and the Einstein-separable hidden-variable models. Finally, an alternative and possibly successful approach in trying to 'explain' nonlocality might involve ideas of backward causation.
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 argued 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. Wave-function 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.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
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.
Introduction Important advances in scientific knowledge may, not infrequently, be looked at from several angles. Here, in investigating the question the article title defines, part of our attention will have to be turned on the relationships of Bell's theorem to the old, but still not fully cleared up, question of the nature of causality. The word “nonlocality” means the violation of local causality, the initial meaning of whichwas that no influence, that is, no causal action , can be propagated faster than light. For a long time it was a received view that actions somewhat akin to the basically time-directed ones that living beings perform also take place within inanimate nature. This conception of causality may be called the causality–action theory . But later, having in view Hume's serious reservations concerning it, renowned philosophers of science claimed it might and should be dropped, since the effects it was meant to account for could be explained just as well by considering that what is at work is simply a conjunction of physical laws expressed by means of differential equations – a view that later Hempel and Oppenheim generalized and called the D-N (deductive–nomological) model of explanation (reprinted in [1]). Here the (widely accepted, as it seems) corresponding conception of causality will, for simplicity, be called the law-centered theory of causality . But does the latter theory subsume, at least within physics, all the meanings of the word ‘cause’ that true understanding calls for? Among philosophers the matter is not settled. Hempel himself granted that in several respects the D-N model is somehow inadequate for analyzing the cause–effect relationship [2]. And it seems indeed that a significant argument favoring a ‘no’ answer to the question might have been put forward as early as 1907 (although, to our knowledge, it was not), when Einstein pointed out that according to his then two years old special relativity (SR) theory, if we assumed an effect could follow its cause sooner than light velocity permits, then in some other frames of reference it would occur before its cause. For, concerning this consequence of the assumption, he wrote, “in my opinion, regarded as pure logic … it contains no contradiction; however it absolutely clashes with the character of our total experience, and in this way is proved the impossibility of the hypothesis” [3].