TY - JOUR AU - De Raedt, H. AU - Hess, K. AU - Michielsen, K. TI - Extended Boole-Bell inequalities applicable to quantum theory JO - Journal of computational and theoretical nanoscience VL - 8 IS - 6 SN - 1546-1955 CY - Stevenson Ranch, Calif. PB - American Scientific Publ. M1 - PreJuSER-14944 SP - 1011 - 1039 PY - 2011 N1 - Record converted from VDB: 12.11.2012 AB - 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 LB - PUB:(DE-HGF)16 C6 - pmid:18421121 UR - <Go to ISI:>//WOS:000290691900013 DO - DOI:10.1166/jctn.2011.1781 UR - https://juser.fz-juelich.de/record/14944 ER -