Specifically, Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems. His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Stuart Freedman and John Clauser in 1972 and Alain Aspect's experiments in 1982. An early experimental breakthrough was due to Carl Kocher, who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied only upon (as cosine square of) the angle between the polarizer settings and decreased exponentially with time lag between emitted photons. Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine square dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles. All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.