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

Use of inequalities for the experimental test of a general conception of the foundations of microphysics. II

Bernard d’Espagnat

Published Jul 15, 1978• 5 citations
Publisher

Abstract

Some aspects of a previous article bearing the same title---hereafter referred to as I---are further developed and clarified. For reasons explained in the text, a variant of the set of assumptions used in I is also introduced. The Bell inequalities are shown to follow from that new set of assumptions as well. The derivation does not appeal to the concept of a density of probability in a supplementary variables space, and it is basically independent of the other modes of derivation of the same inequalities. Illustrations by means of model theories are given.

DOI
10.1103/physrevd.18.349

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Some aspects of a previous article bearing the same title---hereafter referred to as I---are further developed and clarified. For reasons explained in the text, a variant of the set of assumptions used in I is also introduced. The Bell inequalities are shown to follow from that new set of assumptions as well. The derivation does not appeal to the concept of a density of probability in a supplementary variables space, and it is basically independent of the other modes of derivation of the same inequalities. Illustrations by means of model theories are given.
It is pointed out that some already-known inequalities (Bell's inequalities) and some new ones presented here can be used to test experimentally the validity of a general conception of the foundations of microphysics. This conception mainly consists in considering sets of propositions (having the structure of lattices but possibly of non-Boolean ones) and in assuming that when a proposition is true on a system SSS this constitutes an intrinsic property of SSS, which can be neither imparted to SSS nor withdrawn from SSS as long as SSS is "isolated." It is shown that if experiments of the type of those used to test Bell's inequalities turn out to corroborate the quantum-mechanical predictions, such a result could be used in order to invalidate directly the general conception just described. This is done without reference to the general principles of quantum mechanics. More generally, our derivation does not depend for its validity on assuming the truth of any particular physical theory abstracted by induction from experimental knowledge.
Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and new inequalities are derived under general conditions. Published experimental evidence is reinterpreted under these results and found to be entirely compatible with local-realism, both, when experiments involve inefficient detection, if fair-sampling detection is assumed, as well as when experiments have nearly ideal detection and measurement crosstalk is taken into account.
In recent decades there has been a resurge of interest in the foundations of quantum theory, partly motivated by new experimental techniques, partly by the emerging field of quantum information science. Old questions, asked since the seminal article by Einstein, Podolsky and Rosen (EPR), are being revisited. The work of John Bell has changed the direction of investigation by recognising that those fundamental philosophical questions can have, after all, input from experiment. Abner Shimony has aptly termed this new field of enquiry experimental metaphysics. The objective of this Thesis is to contribute to that body of research, by formalising old concepts, proposing new ones, and finding new results in well-studied areas. Without losing from sight that the appeal of experimental metaphysics comes from the adjective, every major result is followed by clear experimental proposals with detailed analysis of feasibility for quantum-atom optical setups. After setting the appropriate terminology and the basic concepts, we will start by analysing the original argument of Einstein, Podolsky and Rosen. We propose a general mathematical form for the assumptions behind the EPR argument, namely those of local causality and completeness. That formalisation entails what was termed a Local Hidden State model by Wiseman et al., which was proposed as a formalisation of the concept of steering first introduced by Schrodinger in a reply to the EPR paper. Violation of any consequences that can be derived from the assumption of that model therefore implies a demonstration of the EPR paradox. We will show how one can then re-derive the well-known EPR-Reid criterion for continuous-variables correlations, and derive new ones applicable to the spin setting considered by Bohm. The spin set-up of the EPR-Bohm was used by Bell to derive his now famous theorem demonstrating the incompatibility of the assumption of local causality and the predictions of quantum mechanics. The inequalities which bear his name can be derived for any number of discrete outcomes, but so far there has been no derivation which can be directly applied to the continuous-variables case of the original EPR paradox. We close the circle by deriving a class of inequalities which make no explicit mention about the number of outcomes of the experiments involved, and can therefore be used in continuous-variables measurements with no need for binning the continuous results into discrete ones. Apart from that intrinsic interest, these inequalities could prove important as a means to perform an unambiguous test of Bell inequalities since optical homodyne detection can be performed with high detection efficiency. The technique, which is based on a simple variance inequality, can alsobe used tore-derive alarge class of well-known Bell-type inequalities and at the same time find their quantum bound, making explicit from a formal point of view that the non-commutativity of the local operators is at the heart of the quantum violations. Finally, we address the issue of macroscopic superpositions originally sparked by the infamous cat paradox of Schrodinger. We consider macroscopic, mesoscopic and ‘S -scopic’ quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size S of a (pure-state) su-perposition, with respect to an observable X, as being the maximum difference in the outcomes of X predicted by that superposition. Such superpositions are referred to as generalised S -scopic superpositions to distinguish them from the extreme superpo-sitions that superpose only the two states that have a difference S in their prediction for the observable. We also consider generalised S -scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalised S -scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing.
This article seeks to clarify certain key theoretical, conceptual and philosophical issues in the foundations of microphysics which, to judge from certain recent publications, continue to cause misunderstandings. In particular, we examine the Heisenberg indeterminacy relations, underlining that they are not univocally interpretable and that, at least in the interpretation following directly from the quantum formalism, they are not the target of Einstein, Podolsky and Rosen's criticism. We try to identify the essential goal and premises of this famous argument, with the help of a simple example. Finally, we examine briefly the Bell inequalities, emphasizing that, given their generality, the net consequence of their experimental violation cannot be circumvented neither by the abandonment of determinism nor by any local realistic reinterpretation of measurement results, as attempted in an article recently published in this journal.