The Problem With Quantum Mechanics

In the 1960s John Bell proved a mathematical result which showed that in certain kinds of experiments, pairs of particles can end up being very far apart. He took it for granted that the way in which we choose our measurement settings on one of the experiments can't affect the particle before it arrives there. So therefore he concluded and almost everybody else has concluded that what these correlations actually show is that quantum mechanics predicts that the world violates locality - it's non-local.