Bell's inequalities

Sica, Louis

doi:10.1016/s0030-4018(99)00417-4

Cited by 31 publications

(45 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall (see Section IV B) that the spin-1/2 operators that measure S 2 and S 3 do not necessarily commute. For completeness, we discuss an extended EPRB experiment 22 that could be used to check the violation of the CHSH inequality. The diagram of the experiment is presented in Fig.…”

Section: Extended Eprb Experimentsmentioning

confidence: 99%

“…Many aspects of all of this have been discussed in the literature by de la Peña et al 6 , Fine [7][8][9][10][11] , Pitowsky 12 , Hess and Philipp 13,14 , Khrennikov [15][16][17][18] , and many other authors [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] . The number of papers indicating dissent with Bell and his followers represents a rousing chorus and is still increasing.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended Boole-Bell Inequalities Applicable to Quantum Theory

Raedt¹,

Hess²,

Michielsen³

2011

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

We address the basic meaning of apparent contradictions of quantum theory and probability frameworks as expressed by Bell's inequalities. We show that these contradictions have their origin in the incomplete considerations of the premises of the derivation of the inequalities. A careful consideration of past work, including that of Boole and Vorob'ev, has lead us to the formulation of extended Boole-Bell inequalities that are binding for both classical and quantum models. The Einstein-Podolsky-Rosen-Bohm gedanken experiment and a macroscopic quantum coherence experiment proposed by Leggett and Garg are both shown to obey the extended Boole-Bell inequalities. These examples as well as additional discussions also provide reasons for apparent violations of these inequalities.

show abstract

Section: Extended Eprb Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended Boole-Bell Inequalities Applicable to Quantum Theory

Raedt¹,

Hess²,

Michielsen³

2011

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

show abstract

“…Sica [10,11] emphasized that Bell's inequalities are limits of arithmetic inequalities that must be satisfied by any cross-correlations of three or four finite data-lists (as appropriate), with data restricted to ± 1. Further, since experimental data are inherently finite, such data arranged in appropriate lists cannot violate the Bell inequality, no matter how exotic the statistics.…”

Section: A( a )B( B ) = −Cos(mentioning

confidence: 99%

“…2, the next section of the introduction will review an alternative derivation of the Bell inequality [10,11] in order to clarify the concepts used in this paper, which depart from those usually encountered in discussions of this subject.…”

Section: A( a )B( B ) = −Cos(mentioning

confidence: 99%

Bell's inequality violation due to misidentification of spatially non-stationary random processes

Sica¹

2003

Journal of Modern Optics

Self Cite

View full text Add to dashboard Cite

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information. They satisfy Bell's inequality and exhibit spatial non stationarity in angle. Correlations for three successive local spin measurements on one particle are computed as well. These correlations also exhibit non stationarity, and satisfy the Bell inequality. In both cases, the mistaken assumption that the underlying process is wide-sense-stationary in angle results in violation of Bell's inequality. These results directly challenge the wide-spread belief that violation of Bell's inequality is a decisive test for nonlocality. PACS number 03.65.Bz

show abstract

“…Indeed, minor modifications to the original model of Bell lead to the conclusion that there is no conflict [15,16,17]. In fact, Bell's theorem does not necessarily apply to the systems that we are interested in as both simulation algorithms and actual data do not need to satisfy the (hidden) conditions under which Bell's theorem hold [18,19,20]. Furthermore, we have given analytical proofs that two-particle correlations of the simulation models agree exactly with the quantum theoretical expression [21,22].…”

mentioning

confidence: 99%

Event-by-Event Simulation of Quantum Phenomena: Application to Einstein-Podolosky-Rosen-Bohm Experiments

Raedt¹,

Michielsen²,

Keimpema³

et al. 2007

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

We review the data gathering and analysis procedure used in real Einstein-Podolsky-Rosen-Bohm experiments with photons and we illustrate the procedure by analyzing experimental data. Based on this analysis, we construct event-based computer simulation models in which every essential element in the experiment has a counterpart. The data is analyzed by counting single-particle events and two-particle coincidences, using the same procedure as in experiments. The simulation models strictly satisfy Einstein's criteria of local causality, do not rely on any concept of quantum theory or probability theory, and reproduce the results of quantum theory for a quantum system of two S = 1/2 particles. We present a rigorous analytical treatment of these models and show that they may yield results that are in exact agreement with quantum theory. The apparent conflict with the folklore on Bell's theorem, stating that such models are not supposed to exist, is resolved. Finally, starting from the principles of probable inference, we derive the probability distributions of quantum theory of the Einstein-Podolsky-Rosen-Bohm experiment without invoking concepts of quantum theory.

show abstract

Bell's inequalities

Cited by 31 publications

References 13 publications

Extended Boole-Bell Inequalities Applicable to Quantum Theory

Extended Boole-Bell Inequalities Applicable to Quantum Theory

Bell's inequality violation due to misidentification of spatially non-stationary random processes

Event-by-Event Simulation of Quantum Phenomena: Application to Einstein-Podolosky-Rosen-Bohm Experiments

Contact Info

Product

Resources

About