The Bell inequality is satisfied by cross-correlations of data sets assuming merely that they exist.

What is it about?

The Bell inequality was derived as a property of random processes. It is however, a fact of basic algebra and must be identically satisfied by assumed variables' data sets, either random or deterministic, each datum consisting of plus or minus 1. It is the mutual cross-correlation of such data sets that results in the inequality. In quantum mechanical experiments, the data have not been mutually cross-correlated, thus allowing for inequality violation. When non-commutation among the variables is taken into account, in either observation or prediction, the resulting correlations satisfy both quantum mechanics and the Bell inequality.

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Why is it important?

The Bell inequality is satisfied by quantum mechanical correlation functions, either measured or predicted, that result from cross-correlated data. The idea that any sensible concept of hidden variables is ruled out by experimental violation of Bell's inequalities has closed the door to creative research in the area for a half century. in addition, metaphysical ideas with which many physicists are uncomfortable are believed to be necessitated by experimental violation of the Bell inequality.