Entanglement, Microcausality and Gödel’s Theorem

Abstract

Abstract One of the key points of Pauli’s proof of the spin-statistics theorem is the principle of microcausality, which essentially states “that all physical quantities at finite distance exterior to the light cone (for | x o ′ − x o ″ | < | x ′ − x ″ | ) are commutable”. Indeed, Pauli was aware that if it were not valid then neither was his version of the spin-statistics theorem. In this presentation, we explore the relationship between entanglement and microcausality and point out that in the case of spin-singlet states, microcausality does not apply. Consequenly, we revise the spin statistics theorem to incorporate entanglement and to suggest some refinements to the axiomatic structure of quantum mechanics. Ironically, singlet states are SL(2,C) invariant as is the Minkowski metric of special relativity, although the singlet state is often used to convey “spooky action at a distance” as if it were in violation of special relativity, which it is not. We also pose the question whether the paradoxes associated with “entanglement” can be understood as a special case of Gödel’s theorem.