Coevents as Beables
Yousef Ghazi-Tabatabai

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.
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Taxonomy
TopicsQuantum Mechanics and Applications · Advanced Algebra and Logic · Logic, Reasoning, and Knowledge
