Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

A Proposal for Embodying Quantum Mechanics in a Noncontextual Framework by Reinterpreting Quantum Probabilities

Claudio Garola, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 5 citations
Publisher

Abstract

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.

DOI
10.1063/1.3109970

Related papers

Generalized observables, Bell's inequalities and mixtures in the ESR model for QM

Claudio Garola

The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of elementary QM. Basing on these results we prove that the Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality and quantum predictions hold together in the ESR model because they refer to different parts of the picture of the physical world supplied by the model. Then we show that a new mathematical representation of mixtures must be introduced in the ESR model which does not coincide with the standard representation in QM and avoids some deep problems that arise from the representation of mixtures provided by QM. Finally we get a nontrivial generalization of the Lüders postulate, which is justified in a special case by introducing a reasonable physical assumption on the evolution of the compound system made up of the measured system and the measuring apparatus.

•Jan 1, 2010•12 citations

The ESR model: A proposal for a noncontextual and local Hilbert space extension of QM

Claudio Garola, Sandro Sozzo

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.

Europhysics Letters (EPL)•Apr 1, 2009•30 citations

Reinterpreting Quantum Probabilities in a Realistic and Local Framework: The Modified BCHSH Inequalities

Claudio Garola, Sandro Sozzo

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.

arXiv:quant-ph/0703260•Mar 28, 2007•2 citations

Modified BCHSH Inequalities Within the ESR Model

Sandro Sozzo, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

The extended semantic realism (ESR) model reinterprets quantum probabilities as conditional rather than absolute probabilities, which provides a general framework that assumes local realism and incorporates the mathematical apparatus of standard quantum mechanics (SQM). We discuss expectation values, sequential measurements and correlation functions within this model. Then, we consider the standard Bell‐Clauser, Horne, Shimony and Holt (BCHSH) inequalities and show that they must be replaced by modified BCHSH inequalities. These contain detection probabilities that are not predicted by SQM and do not depend on features of the measuring apparatuses or environment. In order to avoid contradiction, the detection probabilities must satisfy some no‐violation conditions which can be experimentally checked, at least in principle, and make the ESR model falsifiable.

AIP conference proceedings•Jan 1, 2007•7 citations

Reconciling Local Realism with Quantum Mechanics: The Generalized BCHSH Inequalities

Claudio Garola, Sandro Sozzo

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.

•Mar 28, 2007•0 citations

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

Claudio Garola, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

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.

AIP conference proceedings•Jan 1, 2007•8 citations
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 which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of elementary QM. Basing on these results we prove that the Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality and quantum predictions hold together in the ESR model because they refer to different parts of the picture of the physical world supplied by the model. Then we show that a new mathematical representation of mixtures must be introduced in the ESR model which does not coincide with the standard representation in QM and avoids some deep problems that arise from the representation of mixtures provided by QM. Finally we get a nontrivial generalization of the Lüders postulate, which is justified in a special case by introducing a reasonable physical assumption on the evolution of the compound system made up of the measured system and the measuring apparatus.
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 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 reinterprets quantum probabilities as conditional rather than absolute probabilities, which provides a general framework that assumes local realism and incorporates the mathematical apparatus of standard quantum mechanics (SQM). We discuss expectation values, sequential measurements and correlation functions within this model. Then, we consider the standard Bell‐Clauser, Horne, Shimony and Holt (BCHSH) inequalities and show that they must be replaced by modified BCHSH inequalities. These contain detection probabilities that are not predicted by SQM and do not depend on features of the measuring apparatuses or environment. In order to avoid contradiction, the detection probabilities must satisfy some no‐violation conditions which can be experimentally checked, at least in principle, and make the ESR model falsifiable.
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.
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.