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arXiv:quant-ph/0210145 · International Journal of Quantum Information

THE HESS-PHILIPP MODEL IS NON-LOCAL

D. M. Appleby

Published Mar 1, 2003• 1 citation
arXivHTMLPDF

Abstract

Hess and Philipp have constructed what, they claim, is a local hidden variables model reproducing the empirical predictions of quantum mechanics. In this paper explicit expressions for the conditional probabilities for the outcomes of the measurements at the two detectors are calculated. These expressions provide a conclusive demonstration of the falsity of the authors' claim. The authors give two different accounts of their model. The published version omits a crucial detail. As a result it disagrees with quantum mechanics. It also violates signal locality. The unpublished version agrees with quantum mechanics. However, it violates the condition of parameter independence, as Myrvold has previously shown.

DOI
10.1142/s021974990300005x

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Hess and Philipp have constructed what, they claim, is a local hidden variables model reproducing the empirical predictions of quantum mechanics. In this paper explicit expressions for the conditional probabilities for the outcomes of the measurements at the two detectors are calculated. These expressions provide a conclusive demonstration of the falsity of the authors' claim. The authors give two different accounts of their model. The published version omits a crucial detail. As a result it disagrees with quantum mechanics. It also violates signal locality. The unpublished version agrees with quantum mechanics. However, it violates the condition of parameter independence, as Myrvold has previously shown.
The hidden-variables model constructed by Karl Hess and Walter Philipp is claimed by its authors to exploit a “loophole” in Bell's theorem; according to Hess and Philipp, the parameters employed in their model extend beyond those considered by Bell. Furthermore, they claim that their model satisfies Einstein locality and is free of any “suspicion of spooky action at a distance.” Both of these claims are false; the Hess-Philipp model achieves agreement with the quantum-mechanical predictions, not by circumventing Bell's theorem, but via Parameter Dependence.
Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.
A recent Letter by Hess and Philipp claims that Bell's theorem neglects the possibility of time-like dependence in local hidden variables, hence is not conclusive. Moreover the authors claim that they have constructed, in an earlier paper, a local realistic model of the EPR correlations. However, they themselves have neglected the experimenter's freedom to choose settings, while on the other hand, Bell's theorem can be formulated to cope with time-like dependence. This in itself proves that their toy model cannot satisfy local realism, but we also indicate where their proof of its local realistic nature fails.
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This contradiction led many to question the underlying assumptions, viz. so-called realism and locality. The probability model underlying the Bell inequality is generally left implicit. We propose an explicit probability model for the CHSH version of the Bell experiment. This model has only two simultaneously observable detector settings per measurement, and therefore does not assume realism. The quantum expectation now becomes a conditional expectation, given the two detector settings. This probability model is in full agreement with both quantum mechanics and experiments. As a result, the model satisfies the Bell inequality; there are no so-called violations. We extend this model to include a hidden variable. This extended model is not Bell-separable. This non-separability implies that the model is non-deterministic or non-local (or both).
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.