The mathematics of causal sets

TL;DR

This paper surveys the mathematical foundations of causal set theory in quantum gravity, exploring how random partial orders model spacetime and discussing open problems in the field.

Contribution

It provides a comprehensive overview of the mathematical structures underlying causal set theory and connects theory with potential applications in quantum gravity.

Findings

Mathematical structures of causal sets are linked to models of spacetime.

Identification of open problems in causal set mathematics.

Translation of mathematical theory to physical applications.

Abstract

The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal set hypothesis, and describe how the mathematical theory can be translated to the application area. We highlight a number of open problems of interest to those working in causal set theory.