Bell's theorem, quantum mechanical non-locality and atomic cascade photons

Bell's theorem of 1965 is a proof that all realistic interpretations of quantum mechanics must be non-local. Bell's theorem consists of two parts: first a correlation inequality is derived that must be satisfied by all local realistic theories; second it is demonstrated that quantum mechanical probabilities violate this inequality in certain cases. In the case of ideal experiments, Bell's theorem has been proven. However, in the case of real experiments where polarizers and detectors are non-ideal, the theorem has not yet been proven since the proof always requires some arbitrary and {\em ad hoc} supplementary assumptions. In this paper, we state a new and rather weak supplementary assumption for the ensemble of photons that emerge from the polarizers, and we show that the conjunction of Einstein's locality with this assumption leads to validity of an inequality that is violated by a factor as large as 1.5 in the case of real experiments. Moreover, the present supplementary assumption is considerably weaker and more general than Clauser, Horne, Shimony, Holt supplementary assumption.