Realistic Quantum Theory and Relativity

Diederik Aerts, Sven Aerts

Euan J. Squires

Koji Nagata, Tadao Nakamura

Malley and Fine (Phys. Rev. A 2006 73 066102) discussed that all quantum observables would commute simultaneously if we accept a realistic theory of the Bell type (a local realistic theory) for quantum events, provided that all quantum events, including every quantum state and every observable (including every projector), are reproduced by a realistic theory of the Bell type for quantum events. We point out that their claim leads us to a contradiction. We study the relation between a local realistic theory and commutativity of quantum observables in a finite-dimensional space. We show that a realistic theory of the Bell type for quantum events does not impose the commutative algebraic structure into the set of all quantum observables if all quantum events are reproduced by a local realistic theory. We discuss that a violation of Bell locality is derived within a realistic theory of the Kochen?Specker type within quantum events.

Koji Nagata

Recently, [{arXiv:0810.3134}] is accepted and published. We would like to study the relation between a local realistic theory and commutativity of observables in a finite-dimensional space. We would like to conjecture that a realistic theory of the Bell type (a local realistic theory) for events would not imply the commutative algebraic structure into the set of all observables if all experimental events would be reproduced by a local realistic theory. We would like to suggest that a violation of Bell locality would be derived within a realistic theory of the Kochen-Specker type within quantum events.

Léon Brillouin