In quantum mechanics, a local hidden variable theory is one in which distant events are assumed to have no instantaneous (or at least faster-than-light) effect on local ones.
According to the quantum entanglement theory of quantum mechanics, on the other hand, distant events may under some circumstances have instantaneous correlations with local ones. As a result of this it is now generally accepted that there can be no interpretations of quantum mechanics which use local hidden variables. The term is most often used in discussions of the EPR paradox and Bell's inequalities. It is effectively synonymous with the concept of local realism, which can only correctly be applied to classical physics and not to quantum mechanics.
Read more about Local Hidden Variable Theory: Local Hidden Variables and The Bell Tests, Bell Tests With No "non-detections", Optical Bell Tests, Generalizations of The Models
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