Correlation functions, Bell's inequalities and the fundamental conservation lawsC. S. Unnikrishnan
Gravitation Group, Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai-400 005, India
received 2 July 2004; accepted in final form 7 December 2004
published online 14 January 2005
I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum-mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates Bell's inequalities. Taken together with Bell's theorem, this result has far-reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden-variable theories are incompatible with fundamental symmetries and conservation laws.
03.65.Ta - Foundations of quantum mechanics; measurement theory.
03.65.Ud - Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).
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