Logic of Simultaneity

Abstract

A logical model of spatiotemporal structures is pictured as a succession of processes in time. One usual way to formalize time structure is to assume the global existence of time points and then collect some of them to form time intervals of processes. Under this set-theoretic approach, the logic that governs the processes acquires a Boolean structure. However, in a distributed computer system or a relativistic universe where the message-passing time between different locations is not negligible, the logic has no choice but to accept time interval instead of time point as a primitive concept. The resulting logico-algebraic structure matches that of orthologic, which is known as the most simplified version of quantum logic, and the conventionality of simultaneity claim is reduced to the non-distributivity of the logic.