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AIP conference proceedings

The ESR Model: Reinterpreting Quantum Probabilities Within a Realistic and Local Framework

Claudio Garola, Guillaume Adenier, Andrei Yu. Khrennikov, PEKKA J. LAHTI, Vladimir I. Man’ko, Theo M. Nieuwenhuizen

Published Jan 1, 2007• 8 citations
Publisher

Abstract

Basing on known theoretical results (Bell's theorem, Bell–Kochen–Specker's theorem, etc.) most physicists believe that standard quantum mechanics (SQM) and local realism cannot hold together. Moreover, they also uphold that the experimental tests performed up to now confirm SQM and refute local realism. Some scholars, however, criticize this conclusion, yet maintaining that SQM conflicts with local realism. At variance with both viewpoints, an extended semantic realism (ESR) model has been worked out in Lecce which shows that, if quantum probabilities are interpreted as conditional rather than absolute, a picture of the microworld can be constructed that assumes local realism and embodies the mathematical formalism of SQM. We provide here a new synthetic and improved description of the ESR model, comment on its achievements and limits, and briefly compare it with other approaches.

DOI
10.1063/1.2827311

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Basing on known theoretical results (Bell's theorem, Bell–Kochen–Specker's theorem, etc.) most physicists believe that standard quantum mechanics (SQM) and local realism cannot hold together. Moreover, they also uphold that the experimental tests performed up to now confirm SQM and refute local realism. Some scholars, however, criticize this conclusion, yet maintaining that SQM conflicts with local realism. At variance with both viewpoints, an extended semantic realism (ESR) model has been worked out in Lecce which shows that, if quantum probabilities are interpreted as conditional rather than absolute, a picture of the microworld can be constructed that assumes local realism and embodies the mathematical formalism of SQM. We provide here a new synthetic and improved description of the ESR model, comment on its achievements and limits, and briefly compare it with other approaches.
Most physicists uphold that the tests of the Bell inequalities (BI) performed up to now confirm the predictions of standard quantum mechanics (SQM) and refute local realism. But some scholars criticize this conviction, defending local realism in various ways. We present here a new viewpoint based on an improved version of the extended semantic realism (ESR) model that has been recently worked out by one of the authors. The ESR model embodies the mathematical formalism of SQM into a more general framework in which not only local realism but also objectivity of physical properties holds, and the probabilities of SQM are reinterpreted as conditional instead of absolute. Hence the ESR model provides some predictions that are formally identical to those of SQM but have a different physical interpretation, and further predictions that differ also formally from those of SQM. In particular, we show here that the BI introduced by Clauser, Horne, Shimony and Holt (BCHSH inequalities) must be replaced by modified BCHSH inequalities. These depend on detection probabilities which may be such that the new inequalities are never violated by the conditional expectation values predicted by the model. The condition that no violation occurs implies the existence of upper bounds on detection probabilities, which makes the ESR model falsifiable. These results admit an intuitive explanation in terms of unfair sampling but basically differ from the seemingly similar results obtained by other approaches in which the efficiency problem is discussed in order to vindicate some kind of local realism.
The extended semantic realism (ESR) model, recently worked out by the author, embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework and reinterprets quantum probabilities as conditional instead of absolute. The predictions of the ESR model do not coincide with the predictions of QM, which makes the model falsifiable. In particular, the ESR model predicts that, whenever idealized measurements are performed, modified Bell–Clauser–Horne–Shimony–Holt (BCHSH) inequalities hold if one takes into account all individual systems that are prepared, standard quantum inequalities hold if one considers only the individual systems that are detected, and standard BCHSH inequalities hold at a microscopic (purely theoretical) level. These results constitute a first example of the unified perspective that can be attained by adopting the ESR model.
The extended semantic realism ( ESR ) model proposes a new theoretical perspective that embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute . We provide here a Hilbert space representation of the generalized observables introduced by the ESR model. By using this representation, we supply a straightforward generalization of the projection postulate and justify it in the case of discrete generalized observables by introducing a reasonable physical assumption on the evolution of the compound system made up of the (microscopic) measured system and the (macroscopic) measuring apparatus.
Most physicists uphold that the tests of the Bell-Clauser, Horne, Shimony and Holt (BCHSH) inequalities confirm quantum mechanics (QM) and refute local realism. Some scholars, however, criticize this conviction, yet maintaining that QM conflicts with local realism. At variance with both viewpoints one of the authors has recently worked out an extended semantic realism (ESR) model which shows that, if quantum probabilities are interpreted as conditional rather than absolute probabilities, a picture of the microworld can be constructed that is simultaneously consistent with local realism and QM. We show here that the BCHSH inequalities must be replaced, within the ESR model, by more general inequalities. These depend on parameters (detection probabilities) which may be such that the inequalities are never violated by quantum expectation values. The condition that no violation occurs implies the existence of upper bounds on detection probabilities, which makes the ESR model falsifiable. These results admit an intuitive explanation in terms of unfair sampling but basically differ from the seemingly similar results obtained by other approaches in which the efficiency problem is discussed in order to vindicate some kind of local realism.
Most scholars concerned with the foundations of quantum mechanics (QM) think that contextuality and nonlocality (hence nonobjectivity of physical properties) are unavoidable features of QM which follow from the mathematical apparatus of QM. Moreover these features are usually considered as basic in quantum information processing. Nevertheless they raise still unsolved problems, as the objectification problem in the quantum theory of measurement. The extended semantic realism (ESR) model offers a possible way out from these difficulties by embedding the mathematical formalism of QM into a broader mathematical formalism and reinterpreting quantum probabilities as conditional on detection rather than absolute. The embedding allows to recover the formal apparatus of QM within the ESR model, and the reinterpretation of QM allows to construct a noncontextual hidden variables theory which justifies the assumptions introduced in the ESR model and proves its objectivity. According to the ESR model both linear and nonlinear time evolution occur, depending on the physical environment, as in QM. In addition, the ESR model, though objective, implies modified Bell's inequalities that do not conflict with QM, supplies different mathematical representations of proper and improper mixtures, provides a general framework in which the local interpretations of the GHZ experiment obtained by other authors are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.
The belief that quantum mechanics (QM) does not admit a realistic interpretation is widespread. According to some scholars concerned with the foundations of QM all existing interpretations of this theory (except for the statistical interpretation) presuppose instead a form of realism which consists in assuming that QM deals with individual objects and their properties. We uphold in the present paper that the arguments supporting the contextuality and the nonlocality of QM are a significant clue to the implicit adoption of stronger forms of realism (realism of theoretical entities and realism of theories). If these kinds of realism are substituted by a simpler and more intuitive semantic realism one can contrive a noncontextual and local interpretation of the formalism of QM (SR interpretation). Moreover one can provide a model for such an interpretation (ESR model) in which local realism and QM do not conflict and some fundamental problems of the standard interpretation of QM are avoided.