Take that, Bell’s Inequality!

Bell’s inequality was tested using the CHSH method. Entangled photons were produced from two different laser beams by passing light from Type I BBO crystals and detected using avalanche photodiodes. Values for S as high as 2.30 were obtained. Background One of the major differences between quantum mechanics and previous physical theories is its probabilistic nature. If the state of a classical system is completely known at some time then, in principle, it is possible to develop equations of motion for that system that will determine the values for any observable quantity at any time in the future. However, the most that quantum mechanical equations of motion can provide is the probability that a given observable will take a particular value. This led some of the pioneers of the field to suspect that quantum mechanics was an incomplete theory, and that there were other, ”hidden”, variables that would allow one to completely determine the final state of a quantum system in the same way as a classical one. In support of this view, Einstein, Podolsky, and Rosenberg proposed a thought experiment in 1936 using the phenomenon of entanglement. Quantum mechanics allows two particles that interact with each other to be put into a state in which the two particles cannot be treated as separate entities. Measurements of a property of one of the particles will still be probabilistic according to quantum mechanics, but they will be absolutely correlated with properties of the other particle. This condition persists even if the particles are subsequently separated from each other. The argument is this, then: assuming the laws of physics are locally deterministic, that is, that the behavior of an isolated system will only depend on the state of the system, then any correlation between two isolated systems must be the result of some other information stored in the two systems. In other words, since two entangled particles separated by a large distance cannot communicate with each other, there must be some hidden variables responsible for the correlations seen when the particles are measured. Since the wave functions of quantum mechanics do not provide this information, quanum mechanics must be an incomplete theory. In 1964, John Stewart Bell published a method to determine the validity of this argument. He showed that, in any physical system governed by local variables, the correlations