A histories approach to quantum mechanics

Abstract

A histories approach to quantum mechanics is formulated without the consistency requirement. Plausible, physically motivated axioms for a history structure are presented. In this structure, the consistency requirement is unnecessary because the joint sequential distributions are already probability measures. It is shown that the logic of a history structure is a temporal effect algebra and conversely, any temporal effect algebra is isomorphic to the logic of a history structure. When this general framework is specialized to a Hilbert space context, it reduces to a previously studied formalism.