Universal homogeneous causal sets

TL;DR

This paper constructs a unique, universal, and highly symmetric causal set within the class of countable past-finite causal sets, serving as a fundamental model for discrete space-time in quantum gravity.

Contribution

It proves the existence and uniqueness of a universal homogeneous causal set in a specific class, and provides both probabilistic and explicit constructions.

Findings

Existence of a unique universal homogeneous causal set.

Construction methods include probabilistic and explicit approaches.

Universal causal set can embed all countable past-finite causal sets.

Abstract

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.