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

A Question About the Consistency of Bell's Correlation Formula

Han J.F. Geurdes, Koji Nagata

Published Jul 1, 2019• 0 citations
OpenAlex

Abstract

In the paper it is demonstrated that two equally consistent but conflicting uses of sign functions in the context of a simple probability density shows that Bell's formula is based on only one consistent principle. The two conflicting principles give different result. However, according to use of powers, i.e. $3\times (1/2)= (1/2)\times 3$, one must have the same result in both cases.

Related papers

Anomaly in Sign Function Probability Function Integration III

Han J.F. Geurdes

In the paper it is demonstrated that integration of products of sign functions and probability density functions such as in Bell’s formula for ±1 measurement functions, leads to inconsistencies. Keywords Inconsistency, Bell’s theorem.

•Feb 1, 2019•0 citations

Are there really two different Bell's theorems?

Travis Norsen

This is a polemical response to Howard Wiseman's recent paper, "The two Bell's theorems of John Bell". Wiseman argues that, in 1964, Bell established a conflict between the quantum mechanical predictions and the joint assumptions of determinism and (what is now usually known as) "parameter independence". Only later, in 1976, did Bell, according to Wiseman, first establish a conflict between the quantum mechanical predictions and locality alone (in the specific form that Bell would sometimes call "local causality"). Thus, according to Wiseman, the long-standing disagreements about what, exactly, Bell's theorem does and does not prove can be understood largely as miscommunications resulting from the fact that there are really two quite distinct "Bell's theorems". My goal here is to lay out what Wiseman briefly describes as an "alternate reading" of Bell's 1964 paper, according to which (quoting Wiseman here) "the first paragraph of Bell's `Formulation' section [should be seen] as an essential part of his 1964 theorem, the first part of a two-part argument." I will argue in particular that this "alternate reading" is the correct way to understand Bell's 1964 paper and that Wiseman's reading is strongly inconsistent with the available evidence.

arXiv:1503.05017•International journal of quantum foundations•Mar 17, 2015•16 citations

Epistemic values and realism in quantum mechanics: the case of contemporary solutions to the EPR controversy

Mathieu Guillermin, Tom Dedeurwaerdere

The EPR controversy between Albert Einstein and Niels Bohr about the completeness of the quantum mechanics is one of the most essential contemporary debates in physics with respect to the issue of realism. Initially considered as a though-experiment, the EPR paradox was meant to evidence the inadequacy of quantum mechanics with respect to the traditional leading principle of physics such as locality, independence of the system elements of reality with respect to the observer or semantic reference of theories to elements of the reality in itself. Bell’s mathematical inquiry opened the possibility to empirically discriminate between the view of Bohr and Einstein through the so-called Bell’s inequalities. Based on these inequalities, the experimental test provided in particular by the work of Alain Aspect settled the debate in favor of Bohr and the completeness of quantum mechanics. The previously evident assumption that physical theories are describing the reality in it-self can thus be questioned. Several approaches have been proposed to face that challenge, such as the orthodox quantum physics formulation coupled with the interpretation of Bernard d’Espagnat , the non-local theory of De Broglie-Bohm or the quantum mechanics approach with extended probability of James B. Hartle . In this paper, we consider the idea according to which the field of experiments and measurements on quantum systems is a research context where several epistemic values traditionally leading the scientific activity are in conflict. Instead of conceiving the transition from classical to quantum physics along Thomas Kuhns’ theory of revolutionary paradigm change , characterized by a strong incommensurability between the old and the new approaches, we argue that this epistemological shift could be rationally understood as an incremental evolution of the epistemic values leading scientific activity. As the analysis in this paper aims to show, such a rational reconstruction shows a process of gradual change, where core epistemic values are maintained, while others are broadened to account for the new scientific approaches. The settling of the EPR controversy could be understood as the indication that the previously assumed epistemic values cannot be consistently held together in the quantum context. The values of logical consistency and empirical adequacy remained universally shared, but the controversy leads to question the other traditionally admitted principles, such as the locality, the requirement of semantic references to the reality in itself and the independence of experimental results with respect to the observer, all tightly connected with the realistic conceptions of the world. This first part of the paper characterizes the selected contemporary approaches in quantum context with respect to the modification of the epistemic principles they adopt to restore their consistency. While the de Broglie-Bohm theory explicitly follows the requirement of referring to the reality in itself at the expense of the locality principle, the approaches of d’Espagnat and of Hartle give priority to the values of theoretical framework simplicity and predictive power. In the case of d’Espagnat, the descriptive purpose of the scientific activity remains, but only in a weak objectivity perspective, restricted to the “empirical reality” in which the observer is involved. In the case of Hartle, the extended probability formulation of quantum mechanics is conceived as “an extension of familiar probability theory that incorporates negative probabilities”6, which relies on the Bayesian conception of “probabilities as instruction for betting” (negative probability is thus associated to the instruction “don’t bet”). In a second part, the paper uses this reconstruction of the various theories in order to address the epistemic status of the principles of descriptive power and of independence of the observed system with respect to the observer. In particular, our analysis aims to assess if a reference to the observer is part of the reality description or if such reference is avoidable. This is of prior interest in exploring the main characteristics of a realistic approach that would be applicable in the context of experiments and measurements on quantum systems. In that perspective, we argue that the direct holistic realism, developed by Hilary Putnam in The Threefold Cord , could be a promising intermediate option between a classical realism, which assumes that theoretical structures are describing the reality in it-self, and a more instrumentalist view, focusing mainly on the modeling of the empirical reality as a result of experimental operations while rejecting access to the reality in itself.

•Jan 1, 2012•0 citations

Levy-Lieb-Based Monte Carlo Study of the Dimensionality Behaviour of the Electronic Kinetic Functional

A. Seshaditya, Luca M. Ghiringhelli, Luigi Delle Site

We consider a gas of interacting electrons in the limit of nearly uniform density and treat the one dimensional (1D), two dimensional (2D) and three dimensional (3D) cases. We focus on the determination of the correlation part of the kinetic functional by employing a Monte Carlo sampling technique of electrons in space based on an analytic derivation via the Levy-Lieb constrained search principle. Of particular interest is the question of the behaviour of the functional as one passes from 1D to 3D; according to the basic principles of Density Functional Theory (DFT) the form of the universal functional should be independent of the dimensionality. However, in practice the straightforward use of current approximate functionals in different dimensions is problematic. Here, we show that going from the 3D to the 2D case the functional form is consistent (concave function) but in 1D becomes convex; such a drastic difference is peculiar of 1D electron systems as it is for other quantities. Given the interesting behaviour of the functional, this study represents a basic first-principle approach to the problem and suggests further investigations using highly accurate (though expensive) many-electron computational techniques, such as Quantum Monte Carlo.

Computation•Jun 10, 2017•1 citation

A Third Note on Bell's Theorem

Han J.F. Geurdes

In the paper it is demonstrated that Bell's formula for {+1,-1} measurement functions is inconsistent.

•Oct 1, 2018•0 citations

Is complex probability theory consistent with Bell's theorem?

Saul Youssef

arXiv:hep-th/9406184•Physics Letters A•Aug 1, 1995•10 citations
In the paper it is demonstrated that two equally consistent but conflicting uses of sign functions in the context of a simple probability density shows that Bell's formula is based on only one consistent principle. The two conflicting principles give different result. However, according to use of powers, i.e. 3×(1/2)=(1/2)×33\times (1/2)= (1/2)\times 33×(1/2)=(1/2)×3, one must have the same result in both cases.
This is a polemical response to Howard Wiseman's recent paper, "The two Bell's theorems of John Bell". Wiseman argues that, in 1964, Bell established a conflict between the quantum mechanical predictions and the joint assumptions of determinism and (what is now usually known as) "parameter independence". Only later, in 1976, did Bell, according to Wiseman, first establish a conflict between the quantum mechanical predictions and locality alone (in the specific form that Bell would sometimes call "local causality"). Thus, according to Wiseman, the long-standing disagreements about what, exactly, Bell's theorem does and does not prove can be understood largely as miscommunications resulting from the fact that there are really two quite distinct "Bell's theorems". My goal here is to lay out what Wiseman briefly describes as an "alternate reading" of Bell's 1964 paper, according to which (quoting Wiseman here) "the first paragraph of Bell's `Formulation' section [should be seen] as an essential part of his 1964 theorem, the first part of a two-part argument." I will argue in particular that this "alternate reading" is the correct way to understand Bell's 1964 paper and that Wiseman's reading is strongly inconsistent with the available evidence.
The EPR controversy between Albert Einstein and Niels Bohr about the completeness of the quantum mechanics is one of the most essential contemporary debates in physics with respect to the issue of realism. Initially considered as a though-experiment, the EPR paradox was meant to evidence the inadequacy of quantum mechanics with respect to the traditional leading principle of physics such as locality, independence of the system elements of reality with respect to the observer or semantic reference of theories to elements of the reality in itself. Bell’s mathematical inquiry opened the possibility to empirically discriminate between the view of Bohr and Einstein through the so-called Bell’s inequalities. Based on these inequalities, the experimental test provided in particular by the work of Alain Aspect settled the debate in favor of Bohr and the completeness of quantum mechanics. The previously evident assumption that physical theories are describing the reality in it-self can thus be questioned. Several approaches have been proposed to face that challenge, such as the orthodox quantum physics formulation coupled with the interpretation of Bernard d’Espagnat , the non-local theory of De Broglie-Bohm or the quantum mechanics approach with extended probability of James B. Hartle . In this paper, we consider the idea according to which the field of experiments and measurements on quantum systems is a research context where several epistemic values traditionally leading the scientific activity are in conflict. Instead of conceiving the transition from classical to quantum physics along Thomas Kuhns’ theory of revolutionary paradigm change , characterized by a strong incommensurability between the old and the new approaches, we argue that this epistemological shift could be rationally understood as an incremental evolution of the epistemic values leading scientific activity. As the analysis in this paper aims to show, such a rational reconstruction shows a process of gradual change, where core epistemic values are maintained, while others are broadened to account for the new scientific approaches. The settling of the EPR controversy could be understood as the indication that the previously assumed epistemic values cannot be consistently held together in the quantum context. The values of logical consistency and empirical adequacy remained universally shared, but the controversy leads to question the other traditionally admitted principles, such as the locality, the requirement of semantic references to the reality in itself and the independence of experimental results with respect to the observer, all tightly connected with the realistic conceptions of the world. This first part of the paper characterizes the selected contemporary approaches in quantum context with respect to the modification of the epistemic principles they adopt to restore their consistency. While the de Broglie-Bohm theory explicitly follows the requirement of referring to the reality in itself at the expense of the locality principle, the approaches of d’Espagnat and of Hartle give priority to the values of theoretical framework simplicity and predictive power. In the case of d’Espagnat, the descriptive purpose of the scientific activity remains, but only in a weak objectivity perspective, restricted to the “empirical reality” in which the observer is involved. In the case of Hartle, the extended probability formulation of quantum mechanics is conceived as “an extension of familiar probability theory that incorporates negative probabilities”6, which relies on the Bayesian conception of “probabilities as instruction for betting” (negative probability is thus associated to the instruction “don’t bet”). In a second part, the paper uses this reconstruction of the various theories in order to address the epistemic status of the principles of descriptive power and of independence of the observed system with respect to the observer. In particular, our analysis aims to assess if a reference to the observer is part of the reality description or if such reference is avoidable. This is of prior interest in exploring the main characteristics of a realistic approach that would be applicable in the context of experiments and measurements on quantum systems. In that perspective, we argue that the direct holistic realism, developed by Hilary Putnam in The Threefold Cord , could be a promising intermediate option between a classical realism, which assumes that theoretical structures are describing the reality in it-self, and a more instrumentalist view, focusing mainly on the modeling of the empirical reality as a result of experimental operations while rejecting access to the reality in itself.
We consider a gas of interacting electrons in the limit of nearly uniform density and treat the one dimensional (1D), two dimensional (2D) and three dimensional (3D) cases. We focus on the determination of the correlation part of the kinetic functional by employing a Monte Carlo sampling technique of electrons in space based on an analytic derivation via the Levy-Lieb constrained search principle. Of particular interest is the question of the behaviour of the functional as one passes from 1D to 3D; according to the basic principles of Density Functional Theory (DFT) the form of the universal functional should be independent of the dimensionality. However, in practice the straightforward use of current approximate functionals in different dimensions is problematic. Here, we show that going from the 3D to the 2D case the functional form is consistent (concave function) but in 1D becomes convex; such a drastic difference is peculiar of 1D electron systems as it is for other quantities. Given the interesting behaviour of the functional, this study represents a basic first-principle approach to the problem and suggests further investigations using highly accurate (though expensive) many-electron computational techniques, such as Quantum Monte Carlo.