Misinterpretations and Contradictions of Bell Inequalities

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

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 premisses 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.

Colin James

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

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 1:he 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.

Mohammad Heshmatpour

Gordon Watson

Bell's famous inequality contradicts ours. But ours holds algebraically, experimentally, classically and quantum-mechanically: Bell's does not. So Bell's inequality is refuted on Bell's terms as we identify his naively-realistic error and correct it.

Alessio Avella, Marco Genovese