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

Journal of Computational and Theoretical Nanoscience

Do Quanta Violate the Equation 0 = 0?

Elemér Elad Rosinger

Published May 1, 2017• 1 citation
Publisher

Abstract

Ever since the celebrated 1964 paper of John Bell, the statement that " Quantum systems violate the Bell inequalities " , [1,2], has a very large support among quantum physicists as well as others claiming some knowledge about quanta. Amusingly, it has so far escaped the general notice that, if indeed, quanta do violate that Bell inequalities, then-due to elementary facts of Logic-they must also violate all other valid mathematical relations, thus among them, the equation 0 = 0. Here the respective elementary facts of Logic are presented.

DOI
10.1166/jctn.2017.6820

Related papers

What If Quantum Theory Violates All Mathematics?

Elemér Elad Rosinger

Abstract It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.

Open Physics•Jan 1, 2017•0 citations

The Irrelevance of Bell Inequalities in Physics: Comments on the DRHM Paper

Elemér Elad Rosinger

It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems. This paper presents in more detail the surprisingly elementary, even if rather subtle related basic argument in DRHM, and does so together with a few comments which, hopefully, may further facilitate its wider understanding. 1.

Quantum Matter•Mar 25, 2014•4 citations

Hidden assumptions in the derivation of the theorem of Bell

K. Hess, Hans A. De Raedt, Kristel F. L. Michielsen

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

•Jan 1, 2012•17 citations

Hidden assumptions in the derivation of the theorem of Bell

Karl Hess, Hans A. De Raedt, Kristel Michielsen

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

arXiv:1108.3583•Physica Scripta•Nov 1, 2012•22 citations

Comment on "Bell inequalities and quantum mechanics" by J. H. Eberly

Luiz Carlos Ryff

Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use entanglement to obtain violations of Bell's inequalities. Even leading and outstanding physicists -- as certainly is the case of Prof. Eberly -- sometimes make elementary mistakes, and this by no means diminishes the importance of their scientific contribution. In general, this is a consequence of an excessive attachment to an idea (nowadays it has become fashionable to be against realism). This shows the importance of trying to keep an open mind.

arXiv:0902.1724•Feb 10, 2009•0 citations

Violation of Bell Inequalities: Mapping the Conceptual Implications

Brian Drummond

This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.

arXiv:2106.14767•Jun 28, 2021•3 citations
Ever since the celebrated 1964 paper of John Bell, the statement that " Quantum systems violate the Bell inequalities " , [1,2], has a very large support among quantum physicists as well as others claiming some knowledge about quanta. Amusingly, it has so far escaped the general notice that, if indeed, quanta do violate that Bell inequalities, then-due to elementary facts of Logic-they must also violate all other valid mathematical relations, thus among them, the equation 0 = 0. Here the respective elementary facts of Logic are presented.
Abstract It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use entanglement to obtain violations of Bell's inequalities. Even leading and outstanding physicists -- as certainly is the case of Prof. Eberly -- sometimes make elementary mistakes, and this by no means diminishes the importance of their scientific contribution. In general, this is a consequence of an excessive attachment to an idea (nowadays it has become fashionable to be against realism). This shows the importance of trying to keep an open mind.
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.