Logic of Simultaneity

TL;DR

This paper explores a logical framework for spatiotemporal structures, emphasizing the importance of time intervals over points in distributed or relativistic contexts, leading to a connection with orthologic, a simplified quantum logic.

Contribution

It introduces a model that naturally derives orthologic from the structure of processes in space and time, especially in non-classical settings.

Findings

Time intervals are more fundamental than points in relativistic and distributed systems.

Orthologic emerges naturally from the set-theoretic modeling of spatiotemporal processes.

The logic governing such processes is non-Boolean, reflecting quantum-like properties.

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 real distributed 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. From this modeling process of spatiotemporal structures, orthologic, the most simplified version of quantum logic, emerges naturally.