Coevents as Beables

TL;DR

This paper explores the logical structure of coevents in quantum histories, constructing a propositional lattice and relating it to traditional event lattices, with implications for topos theory applications.

Contribution

It develops a propositional lattice for coevents, compares it to traditional event lattices, and connects these structures to topos-theoretic truth value frameworks.

Findings

Simplified relationship between coevent and event lattices for multiplicative coevents

Identification of elements similar to topos truth values within the constructions

Potential application of topos theory to coevents in quantum histories

Abstract

Sorkin's coevents can be thought of as the `beables' of a quantum histories theory; in this paper we study the 'logical' implications of taking this claim at face value, constructing a propositional lattice for the space of coevents applicable to a given histories theory and comparing it to the more traditional propositional lattice of events. In particular we focus on multiplicative coevents, and find that the precise nature of their anhomomorphism leads to a particularly simple relationship between the two propositional lattices. Finally, we notice that our constructions contain elements intuitively similar to topos nations of truth values and use this to suggest a means of applying Isham's topos theoretic constructions to multiplicative coevents.