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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Experimental consequences of objective local theories

John F. Clauser, Michael Horne

Published Jul 15, 1974• 1,537 citations
Publisher

Abstract

A broad class of theories, called "objective local theories," is defined, motivation for considering these theories is given, and experimental consequences of the class are investigated. An extension of previous analyses by Bell and by Clauser et al. shows that predictions of objective local theories and of quantum mechanics differ, and that an experimental test of the entire family of objective local theories can be performed. The experimental requirements are given. Objective local theories satisfying a plausible but experimentally untestable supplementary assumption are shown to be incompatible with existing experimental data.

DOI
10.1103/physrevd.10.526

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A broad class of theories, called "objective local theories," is defined, motivation for considering these theories is given, and experimental consequences of the class are investigated. An extension of previous analyses by Bell and by Clauser et al. shows that predictions of objective local theories and of quantum mechanics differ, and that an experimental test of the entire family of objective local theories can be performed. The experimental requirements are given. Objective local theories satisfying a plausible but experimentally untestable supplementary assumption are shown to be incompatible with existing experimental data.
ABSTRACfObjective local theories of reality are defined, and shown to lead to predictions which are distinctly different from the predictions by quanttnn mechanics.Experiments may thus be performed which will either disprove the predictions by quanttnn mechanics in at least one application, or show that nature cannot be viewed as both objective and consistent with macrocausality.The experimental requirements are presented.The demonstration is done through a generalization of analyses by Bell, Clauser, Horne, Shimony, and Holt.The present analysis will be based solely on the phenomenology of correlation experiments, and thus will constrain the most general theories of this type.
The study of hidden-variable interpretations of quantum mechanics was transformed by two papers of Bell. In his 1966 paper in Reviews of Modern Physics [1] he analysed the argument of von Neumann [2] and the more powerful arguments of Jauch and Piron [3] and of Gleason [4], all leading to similar conclusions about the nonassignability of simultaneous values to all the observables of a nontrivial quantum system; and he showed that these arguments do not exclude what may be called “contextualistic” hidden-variable theories, in which the value of an observable O is allowed to depend not only upon the hidden state λ, but also upon the set C of compatible observables measured along with O . In Bell's 1964 paper in Physics [5] (written later than the other, in spite of the earlier publication date) he gave a new kind of argument against a hidden-variable interpretation of quantum mechanics, by showing that no hidden-variables theory which satisfies a certain condition of locality can agree with all the statistical predictions of quantum mechanics. The main purpose of this lecture is to discuss an experiment, designed by Clauser, Horne, Holt and myself [6], which is based on Bell's proof of the incompatibility of quantum mechanics and local hidden-variable theories. Before doing this, however, I wish to make several comments.
Recent experiments of Gröblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Gröblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Gröblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class.
Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve this goal. Our conclusions are based on a straightforward statistical analysis of the outcomes of these experiments. The key tool in our study is probability theory and, in particular, the concept of sample space for the dichotomic random variables that quantifies the outcomes of such experiments. We also show that an experimental proof of Bell's theorem is not, in principle, impossible, but it would require a completely different experimental apparatus than those commonly used to allegedly achieve this objective. The main consequence of our work is that we cannot dismiss local realistic hidden variable theories on the basis of currently available experimental data.