Unfaithful embedding of causal sets

TL;DR

This paper explores how unfaithful embeddings of causal sets can lead to phenomena like antiparticles and matter distribution, suggesting a new perspective on spacetime and matter emergence.

Contribution

It introduces the idea that unfaithful embeddings of causal sets can account for matter and interactions, expanding the causal set approach beyond faithful embeddings.

Findings

Unfaithful embeddings can produce matter and interaction fields.

Antiparticles and inhomogeneous matter distribution may result from unfaithful embeddings.

Faithful embedding is only necessary at coarse-grained levels for spacetime emergence.

Abstract

In the causal set approach, spacetime is a continuous approximation of a faithful embedded causal set. But the faithful embedded causal set describes the empty spacetime and cannot describe matter. Only faithful embedding of coarse grained causal set is necessary for the emergence of spacetime. The initial causal set can be unfaithfully embedded. The following properties of the universe can be the consequences of the unfaithful embedding: antiparticles, fields of interactions, the inhomogeneous distribution of the matter.