Bell test experiments or Bell's inequality experiments are designed to demonstrate the real world existence of certain theoretical consequences of the phenomenon of entanglement in quantum mechanics which could not possibly occur according to a classical picture of the world, characterised by the notion of local realism. Under local realism, correlations between outcomes of different measurements performed on separated physical systems have to satisfy certain constraints, called Bell inequalities. John Bell derived the first inequality of this kind in his paper "On the Einstein-Podolsky-Rosen Paradox". Bell's Theorem states that the predictions of quantum mechanics cannot be reproduced by any local hidden variable theory.
The term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden variables theories; in practice, in present day experiments, most often the CHSH; earlier the CH74 inequality. All these inequalities, like the original inequality of Bell, by assuming local realism, place restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated. A Bell test experiment is one designed to test whether or not the real world satisfies local realism.
Read more about Bell Test Experiments: Conduct of Optical Bell Test Experiments, Experimental Assumptions, Notable Experiments, Loopholes
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