As I understand it, EPR proposed their entanglement thought experiment as a means of demonstrating that Quantum Mechanics was incomplete, and hence that the Copenhagen interpretation (which says that the wave function is a complete description of the state of a system) was wrong. They postulated the existence of hidden variables as a way of 'completing' the theory. Here 'hidden' just means 'not in any way reflected in the wave function'. Bell proved that any extension of QM that uses hidden variables will predict correlations for measurements of entangled particles that differ from what QM predicts, if the principle of locality is to be maintained. Aspect et al showed, subject to various minor loopholes on which most people seem to place not much reliance, that experimentally observed correlations follow the QM predictions rather than those predicted by a hidden variable theory that preserves locality. From this we inductively conclude that there is no valid hidden variable theory that preserves locality. Various presentations of this topic suggest that the tests of Bell's theorem have shown that we cannot maintain both locality and something else, where that something else is variously described as realism, counterfactual definiteness, or other similarly vague-seeming terms. This seems consistent with EPR's and Bell's original ideas, which were to challenge or defend the Copenhagen interpretation that a particle does not have a definite position and momentum unless it is in an eigenstate of one of the two operators. But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments. The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval. I realise that this is a hand-wave rather than a mathematical proof, but I find myself unable to imagine what sort of a theory (extension of QM) or interpretation could remain consistent with the Bell results while still preserving locality. I would be grateful for any light that contributors are able to shed on my fog of puzzlement.