000014944 001__ 14944 000014944 005__ 20210129210618.0 000014944 0247_ $$2pmid$$apmid:18421121 000014944 0247_ $$2DOI$$a10.1166/jctn.2011.1781 000014944 0247_ $$2WOS$$aWOS:000290691900013 000014944 037__ $$aPreJuSER-14944 000014944 041__ $$aeng 000014944 082__ $$a570 000014944 084__ $$2WoS$$aChemistry, Multidisciplinary 000014944 084__ $$2WoS$$aNanoscience & Nanotechnology 000014944 084__ $$2WoS$$aMaterials Science, Multidisciplinary 000014944 084__ $$2WoS$$aPhysics, Applied 000014944 084__ $$2WoS$$aPhysics, Condensed Matter 000014944 1001_ $$0P:(DE-HGF)0$$aDe Raedt, H.$$b0 000014944 245__ $$aExtended Boole-Bell inequalities applicable to quantum theory 000014944 260__ $$aStevenson Ranch, Calif.$$bAmerican Scientific Publ.$$c2011 000014944 300__ $$a1011 - 1039 000014944 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article 000014944 3367_ $$2DataCite$$aOutput Types/Journal article 000014944 3367_ $$00$$2EndNote$$aJournal Article 000014944 3367_ $$2BibTeX$$aARTICLE 000014944 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000014944 3367_ $$2DRIVER$$aarticle 000014944 440_0 $$017841$$aJournal of Computational and Theoretical Nanoscience : for all Theoretical and Computational Aspects in Science, Engineering, and Biology$$v8$$x1546-1955$$y6 000014944 500__ $$aRecord converted from VDB: 12.11.2012 000014944 520__ $$aWe 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 000014944 536__ $$0G:(DE-Juel1)FUEK411$$2G:(DE-HGF)$$aScientific Computing (FUEK411)$$cFUEK411$$x0 000014944 536__ $$0G:(DE-HGF)POF2-411$$a411 - Computational Science and Mathematical Methods (POF2-411)$$cPOF2-411$$fPOF II$$x1 000014944 588__ $$aDataset connected to Web of Science, Pubmed 000014944 65320 $$2Author$$aBoole Inequalities 000014944 65320 $$2Author$$aBell Inequalities 000014944 65320 $$2Author$$aQuantum Theory 000014944 65320 $$2Author$$aEPR Paradox 000014944 7001_ $$0P:(DE-HGF)0$$aHess, K.$$b1 000014944 7001_ $$0P:(DE-Juel1)138295$$aMichielsen, K.$$b2$$uFZJ 000014944 773__ $$0PERI:(DE-600)2172443-X$$a10.1166/jctn.2011.1781$$gVol. 8, p. 1011 - 1039$$n6$$p1011 - 1039$$q8<1011 - 1039$$tJournal of computational and theoretical nanoscience$$v8$$x1546-1955$$y2011 000014944 909CO $$ooai:juser.fz-juelich.de:14944$$pVDB 000014944 915__ $$0StatID:(DE-HGF)0010$$aJCR/ISI refereed 000014944 9141_ $$y2011 000014944 9132_ $$0G:(DE-HGF)POF3-511$$1G:(DE-HGF)POF3-510$$2G:(DE-HGF)POF3-500$$aDE-HGF$$bKey Technologies$$lSupercomputing & Big Data $$vComputational Science and Mathematical Methods$$x0 000014944 9131_ $$0G:(DE-HGF)POF2-411$$1G:(DE-HGF)POF2-410$$2G:(DE-HGF)POF2-400$$3G:(DE-HGF)POF2$$4G:(DE-HGF)POF$$aDE-HGF$$bSchlüsseltechnologien$$lSupercomputing$$vComputational Science and Mathematical Methods$$x1 000014944 9201_ $$0I:(DE-Juel1)JSC-20090406$$gJSC$$kJSC$$lJülich Supercomputing Centre$$x0 000014944 970__ $$aVDB:(DE-Juel1)127467 000014944 980__ $$aVDB 000014944 980__ $$aConvertedRecord 000014944 980__ $$ajournal 000014944 980__ $$aI:(DE-Juel1)JSC-20090406 000014944 980__ $$aUNRESTRICTED