In last month’s Insights column, we explored a puzzle that is a simple analogue of one of the most astonishing results of quantum mechanics — Bell’s theorem. Bell showed that if quantum mechanical predictions are correct, then we have to give up one of three reasonable assumptions about the world. In a recent Quanta article Natalie Wolchover explains how:
… when two particles interact, they can become “entangled,” shedding their individual probabilities and becoming components of a more complicated probability function that describes both particles together. This function might specify that two entangled photons are polarized in perpendicular directions, with some probability that photon A is vertically polarized and photon B is horizontally polarized, and some chance of the opposite. The two photons can travel light-years apart, but they remain linked: Measure photon A to be vertically polarized, and photon B instantaneously becomes horizontally polarized, even though B’s state was unspecified a moment earlier and no signal has had time to travel between them. This is the “spooky action” that Einstein was famously skeptical about in his arguments against the completeness of quantum mechanics in the 1930s and ’40s.
In 1964, the Northern Irish physicist John Bell found a way to put this paradoxical notion to the test. He showed that if particles have definite states even when no one is looking (a concept known as “realism”) and if indeed no signal travels faster than light (“locality”), then there is an upper limit to the amount of correlation that can be observed between the measured states of two particles. But experiments have shown time and again that entangled particles are more correlated than Bell’s upper limit, favoring the radical quantum worldview over local realism.
As Wolchover further describes in the article, there is a third possible assumption found in Bell’s analysis — “freedom of choice” — the assumption that the experimenters are free to place the polarizers at any angle that they want.
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