was predicted by local realism and those predicted by quantum mechanics. In theory, the results could be "coincidentally" consistent with both. To address this problem, Bell proposed a mathematical description of local realism that placed a statistical limit on the likelihood of that eventuality. If the results of an experiment violate Bell's inequality, local hidden variables can be ruled out as their cause. Later researchers built on Bell's work by proposing new inequalities that serve the same purpose and refine the basic idea in one way or another. Consequently, the term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden-variables theories; in practice, many present-day experiments employ the CHSH inequality. All these inequalities, like the original devised by Bell, express the idea that assuming local realism places restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated. To date, all Bell tests have supported the theory of quantum physics, and not the hypothesis of local hidden variables. These efforts to experimentally validate violations of the Bell inequalities resulted in John Clauser, Alain Aspect, and Anton Zeilinger being awarded the 2022 Nobel Prize in Physics. Conduct of optical Bell test experiments In practice most actual experiments have used light, assumed to be emitted in the form of particle-like photons (produced by atomic cascade or spontaneous parametric down conversion), rather than the atoms that Bell originally had in mind. The property of interest is, in the best known experiments, the polarisation direction, though other properties can be used. Such experiments fall into two classes, depending on whether the analysers used have one or two output channels. A typical CHSH (two-channel) experiment The diagram shows a typical optical experiment of the two-channel kind for which Alain Aspect set a precedent in 1982. Coincidences (simultaneous detections) are recorded, the results being categorised as '++', '+−', '−+' or '−−' and corresponding counts accumulated. Four separate subexperiments are conducted, corresponding to the four terms E(a, b) in the test statistic S (equation (2) shown below). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality. For each selected value of a and b, the numbers of