addition

The passage around this formula

EPR’s paper stayed a philosophical argument until 1964, when John Bell showed it could be turned into an experiment [ 3 ] . Bell proved that any theory obeying both locality — no faster-than-light influence — and realism, in the sense of outcomes fixed by pre-existing local properties, must satisfy a statistical bound. For a simple two-setting test, $S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2$. holds for any local realist theory, while quantum mechanics allows S up to 2$\sqrt{2}$ $\approx$ 2.83 . Early experimental violations left the detection loophole (too many unmeasured particles to rule out a biased subsample) and the locality loophole (stations not separated fast and far enough to exclude a hidden signal) open to…

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