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

arXiv:2408.10256

Comment on the GHZ variant of Bell's theorem without inequalities

Joy Christian

Published Aug 12, 2024• 0 citations
arXivHTMLPDF

Abstract

I point out a sign mistake in the GHZ variant of Bell's theorem, invalidating its claim that the premisses of the EPR argument are inconsistent for systems of more than two particles in entangled quantum states.
DOI
10.48550/arxiv.2408.10256

Related papers

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

COMMENT ON "ON THE ROLE OF LOCALITY CONDITION IN BELL'S THEOREM"

Tomasz Paterek

In his paper,1 Razmi derives a Bell-like inequality without imposing the locality condition. Then he shows violation of this inequality by certain quantum predictions. Here we point at a loophole in Razmi's proof, which invalidates his inequality.

International Journal of Quantum Information•Aug 30, 2004•0 citations

Unconditional Quantum Correlations do not Violate Bell’s Inequality

Andrei Yu. Khrennikov

arXiv:1503.08016•Foundations of Physics•Jul 3, 2015•2 citations

Bell's Theorem Begs the Question

Joy Christian

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.

•Aug 7, 2024•0 citations

Bell's Theorem Begs the Question

Joy Christian

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.

•Jul 24, 2024•0 citations

Comment on ``Experimental Simulation of Two-Particle Quantum Entanglement using Classical Fields''

Aloysius F. Kracklauer

We assert that the reported results consitute an empirical counterexample to Bell's theorem

arXiv:quant-ph/0208099•Aug 15, 2002•0 citations
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.
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.