Consistent Histories as Valuations

TL;DR

This paper explores the consistent histories approach in quantum mechanics through the lens of truth valuations, connecting it with Sorkin's coevent interpretation and topos theory to provide a logical framework.

Contribution

It introduces a novel formulation of consistent histories using truth valuations, linking it with coevents and topos theory for a unified logical perspective.

Findings

Consistent histories valuations relate to Sorkin's multiplicative coevents.

A topos-theoretic framework effectively describes these valuations.

The approach offers a new logical foundation for quantum histories.

Abstract

Sorkin's coevent interpretation shifts the focus of quantum logic from the structure of a propositional lattice to the nature of truth valuations thereon. We apply this shift in emphasis to a simple formulation of the consistent histories approach, expressing it in terms of truth valuations which are brought together in a logical framework. We see that these consistent histories valuations are related to Sorkin's multiplicative coevents, and that they can be naturally described by an adaptation of Isham's early topos-theoretic approach.