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The nonlocality of our physical world follows from a combination of a theorem proved by John S. Bell in 1964 and experimental results obtained since the early 1980s. His theorem builds on the puzzle about entangled particles pointed out by Einstein, Podolsky and Rosen in 1935. The EPR argument assumes that nature is local so that in particular a measurement (by, say, Alice) on one particle of a widely separated entangled pair cannot instantaneously alter the physical state of the faraway partner particle (which, say, Buzz can measure). They conclude that Buzz’s particle must already have determinate values for spins in every direction. Thus, quantum mechanics must be incomplete because it does not determine those values except to guarantee they will be consistent with whatever result Alice gets when she measures her particle.
Bell asked: supposing that Alice’s and Buzz’s entangled particles have determinate values, can such particles reproduce the results predicted by quantum mechanics for all the ways that Alice and Buzz might measure their particles? Recall that for particles with entangled spins, Alice and Buzz must each choose an axis to measure the spin along. Bell proved mathematically that if Alice and Buzz chose to measure along axes at angles such as 45 and 90 degrees from each other, their measurements from numerous runs of the experiment would produce a statistical distribution of results that disagreed with that predicted by quantum mechanics—no matter what distribution of determinate values the particles had.
Researchers carried out experiments using entangled photons instead of electrons (which alters the angles to use but makes the experiment technically much less difficult) and found results that conformed with quantum mechanics’s predictions. And so by Bell’s theorem there must not be any determinate values carried by those photons. And because that contradicts EPR’s conclusion, the assumption that nature is local is also wrong. And so the universe we live in cannot be local.