A theorem about possible theories is only half the story. The other half happened in laboratories, slowly, over half a century, as experimenters tried to give local hidden variables every fair chance and to close every gap through which they might escape.
The first tests
John Clauser, then a young physicist, read Bell's paper and realized that existing equipment could test it. In 1972 Stuart Freedman and John Clauser at Berkeley performed the first Bell test, using pairs of photons emitted by calcium atoms, and found a violation of the local limit in line with quantum mechanics. Other groups followed through the 1970s, most agreeing with quantum theory, though a few early results did not.
Aspect and the timing problem
These early experiments had a weakness. The filter settings were fixed long before the photons flew. In principle, some undiscovered signal could have told each photon how the other side's filter was set, so the correlation would not need to be mysterious at all. This is the locality loophole. To close the locality loophole, the settings must be chosen while the particles are in flight, so that no signal slower than light could carry the choice to the other side in time.
Alain Aspect, at the Institut d'Optique in Orsay near Paris, took this on. In 1982 Aspect, Jean Dalibard and Gérard Roger published a test in which the settings switched rapidly while the photons were traveling. The switching followed a regular pattern rather than a truly random one, so critics could still worry, but the violation of the local limit was clear.
In 1998 the group of the Austrian physicist Anton Zeilinger, then at Innsbruck, improved on this. Gregor Weihs and colleagues separated their stations by about 400 meters and chose the settings with fast random number generators, closing the locality loophole much more convincingly.
A better source of pairs
Later experiments used a cleaner way of making entangled photons. In spontaneous parametric down-conversion, a laser photon entering a special crystal occasionally splits into two photons of lower energy that are entangled. It produces pairs far more often and more controllably than atomic sources.
The detection loophole
A second gap concerned the detectors. If only a fraction of pairs are recorded, a clever local model could arrange for the detected pairs to be an unrepresentative sample that happens to violate the inequality. This is the detection, or fair sampling, loophole. To close the detection loophole, an experiment must record a large enough fraction of the particles that biased sampling cannot explain the results. In 2001 a team at the National Institute of Standards and Technology (NIST) in Boulder, Colorado, closed it using trapped ions, which can be detected almost every time, but their ions were far too close together to close the locality loophole as well.
2015: closing both at once
In 2015, three groups reported Bell tests that closed the locality and detection loopholes in the same experiment. At Delft University of Technology in the Netherlands, Ronald Hanson's team used electrons in diamond in labs 1.3 kilometers apart. Teams in Vienna, from Zeilinger's group, and at NIST in Boulder used photons with highly efficient detectors. All three found violations of the local limit.
The last escape route
One assumption cannot be fully tested: measurement independence. Perhaps the hidden properties of the particles and the choices of settings share some common cause in the distant past, so that the experimenters' free choices were never really independent. In the Big Bell Test of November 2016, about 100,000 volunteers around the world played an online game whose keystrokes supplied random choices for experiments in several laboratories. Other teams used light from distant quasars to pick settings. A view called superdeterminism, which holds that everything, including the choices, was correlated from the start, remains logically possible. Most physicists reject it, since it would undermine controlled experiments in every science.
The 2022 Nobel Prize
The 2022 Nobel Prize in Physics went to Alain Aspect, John Clauser and Anton Zeilinger for experiments with entangled photons that established the violation of Bell inequalities and pioneered quantum information science. Bell had died in 1990, and Nobel Prizes are not awarded after death, so the man who posed the question could not share in its answer.
Worked example: the Delft experiment
Each of two labs on the university campus held a tiny defect in a diamond, a spot where an electron's spin could be controlled with lasers and microwaves. Each electron was first entangled with a photon. The two photons traveled by optical fiber to a station in between, where a joint measurement, when it succeeded, signaled that the two distant electrons were now entangled with each other. That technique, called entanglement swapping, returns in Level 7.
Each lab chose its measurement setting with a fast random number generator and read out its electron's spin, which can be done reliably almost every time, closing the detection loophole. The labs were 1.3 kilometers apart, and each measurement finished in less time than light would need to cross between them, closing the locality loophole. Success was rare: over about 220 hours, the team gathered 245 successful trials. The result exceeded the local limit, by a modest statistical margin. Together with the Vienna and NIST results, the evidence was overwhelming.