Bell's theorem shows that no local hidden-variable theory can match all quantum predictions. Experiments violating Bell inequalities reveal entanglement and nonlocal correlations.
A preference for the latter resolution is supported by experiments suggested by Bell's theorem of 1964, which exclude some classes of hidden variable theory. Source: Internet
Bell's theorem is concerned with correlations defined in terms of averages taken over very many trials of the experiment. Source: Internet
For example, E. T. Jaynes citation claimed in 1989 that there are two hidden assumptions in Bell's theorem that could limit its generality. Source: Internet
Confident that this was as random as random gets, NIST has proceeded to use this test of Bell's theorem to pop out strings of numbers nobody could ever guess at a rate of 1,024 bits every 10 minutes. Source: Internet
Bell's theorem showed that the "entangledness" prediction of quantum mechanics has a degree of non-locality that cannot be explained away by any local theory. Source: Internet
Local realism The concept local realism is formalized to state and prove Bell's theorem and generalizations. Source: Internet