(The) contradiction between quantum mechanics and local realistic model and its experimental verification

Abstract

We introduce Einstein-Podolsky-Rosen (EPR) experiment and Bell``s inequality. Using these we prove Bell``s theorem, which says that quantum mechanics cannot coexist with local realism which has been very successful. This fact is surprising because both local realism and quantum mechanics are well founded. Only real experiments can determine which one is correct. We present current status of such experimental verifications and introduce detection loophole. Concerning detection loophole there still remain some controversies. We discuss the detection loophole in connection with Hardy``s nonlocality theorem. An inequality that must be satisfied in order that the Hardy nonlocality theorem avoids the detection loophole is derived. The minimum detection efficiency is calculated to be 2/3. It is shown that the minimum value theoretically obtainable using a version of Bell``s inequality is 2/3. We obtain explicit solutions for probability measures that reproduce quantum mechanical predictions for some spin-measurement directions for all entangled states. The necessity of negative probability in this case is shown. This constitutes another proof of Gisin``s theorem that all entangled states are incompatible with any local hidden-variable model. Finally, we discuss introduction of hidden variables in spin-measuring equipments in EPR-Bell experiment. We show why the original hidden variable λ is not the one to be considered to include hidden variables in spin-measuring equipments. On the one hand, when the hidden variables introduced in spin-measuring equipments have local correlations, Bell``s inequality is recovered. On the other hand, when they have nonlocal correlations, Bell``s inequality is not recovered. This is in accord with the fact that Bell``s inequality is derived for local realistic models.