On Bell's theorem\footnote{Based mainly in Ref. 1.}

Abstract

Bell's theorem is a crucial tool to solve the contradiction between local realism conceptions $\grave{a$ la} Einstein-Podolsky-Rosen and quantum mechanics. In this note we present three versions of the theorem: the original one of Bell of 1964, the Clauser et al stronger version of 1969, and the Wigner's version of 1970, and show how the simultaneous validity of EPR ideas and quantum theory leads to a contradiction with number theory. The quantum mechanical formula for the correlation between two spin 1/2 particles is derived in an appendix.