What is the difference between quantum mechanics and realism ? quantum mechanics states on statistics while the hardy assumption of EPR is that hidden variables may describe exactly the outcomes of each individual test. Bell refutes the last idea. But, he didn't need to refute the case where realistic outcomes are random because accepting this possibility would imply directly that the EPR assumption was wrong. Now, take the Bell demonstration. He integrated one application ( function defined for any input value with an unique outcome for each ). If the lambda function that results from the hidden variable is not a mathematical function ( hence having different outcomes for different tests ), the integral being not applicable, the demonstration would become invalid. Not saying invalid for the main purpose of the EPR-Bell discussion but not available to claim that the outcomes cannot be a result of randomness. Maybe it's true but the demonstration doesn't handle the case. ( And it's normal, this case is useless for the main discussion ) Is this reasoning exact ? Non-locality doesn't make any assumption on the existence or not of hidden variables. In general, it is the reverse. We say, since hidden variables are impossible to predict the individual outcomes, hence 1) we need a phenomenon to explain the correlations, 2) this phenomenon seems to be the non-locality. But never one demonstrated mathematically that a part of hidden variables and a part of randomness may not be statistically predictive. It's not the EPR assumption, nor its exact opposite. But to infer on a new kind of 'relation' between states of distant objects, the non-locality theorists needs also to exclude it. Else, a 'natural' explaination, even not realistic, would make the concept of non-locality useless. Am I wrong when saying that this demonstration doesn't exist ? if yes, please let me know its references. end of the post pure opinion now : It's not a pure original thought. I'm trying this explaination searching for an interpretation of the efficiency of some random algorithms ( that may be improved with math and/or machine powers ) giving so similar results, continuously from -PI/2 to PI/2.