Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

Abstract

Two aspects of the relativistic version of the Einstein-Podolsky-Rosen-Bohm (EPRB) experiment with massive particles are discussed: (a) a possibility of using the experiment as an implicit test of a relativistic center-of-mass concept, and (b) influence of the relativistic effects on degree of violation of the Bell inequality. The nonrelativistic singlet state average 〈\ensuremath{\psi}|a\ensuremath{\cdot}\ensuremath{\sigma}\ensuremath{\bigotimes}b\ensuremath{\cdot}\ensuremath{\sigma}|\ensuremath{\psi}〉=-a\ensuremath{\cdot}b is relativistically generalized by defining spin via the relativistic center-of-mass operator. The corresponding EPRB average contains relativistic corrections which are stronger in magnitude than standard relativistic phenomena such as the time delay, and can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with relativistic massive spin- particles. The degree of violation of the Bell inequality is shown to depend on the velocity of the pair of spin- particles with respect to the laboratory. Experimental confirmation of the relativistic formula would indicate that for relativistic nonzero-spin particles centers of mass and charge do not coincide. The result may have implications for quantum cryptography based on massive particles.