Bell's Inequality is a fundamental theorem in quantum mechanics that establishes a mathematical bound on correlations between measurements performed on separated entangled systems under the assumption of local hidden variables. Derived from John Stewart Bell's 1964 analysis, it formalizes the conflict between Einstein-Podolsky-Rosen (EPR) logic regarding locality and realism versus standard quantum mechanical predictions. The theorem dictates that if physical properties are determined by pre-existing local parameters ("hidden variables"), statistical correlations must satisfy a specific inequality which experimental observations of photon polarization consistently violate.
Any local hidden-variable model constrains correlations between distant measurements — in CHSH form |S| <= 2 — while quantum mechanics predicts up to 2*sqrt(2) for entangled pairs at suitable analyze…