A Matter of Matter and Antimatter

TL;DR

This paper introduces a quantum gravity model using causal sets, classifies them into matter, antimatter, and mixed types, and explores asymmetries that could explain the universe's matter-antimatter imbalance.

Contribution

It extends causal set theory with a novel classification into matter and antimatter causets, providing a framework to analyze matter-antimatter asymmetry in quantum gravity.

Findings

Causets are partitioned into matter, antimatter, and mixed sets.

An asymmetry between matter and antimatter causets is observed.

Probabilities and propensities for different causet classifications are analyzed.

Abstract

A discrete quantum gravity model given by a quantum sequential growth process (QSGP) is considered. The QSGP describes the growth of causal sets (causets) one element at a time in discrete steps. It is shown that the set $\pscript$ of causets can be partitioned into three subsets $\pscript = (\rmant)\cup (\rmmix)\cup (\rmmat)$ where $\rmant$ is the set of pure antimatter causets, $\rmmat$ the set of pure matter causets and $\rmmix$ the set of mixed matter-antimatter causets. We observe that there is an asymmetry between $\rmant$ and $\rmmat$ which may explain the matter-antimatter asymmetry of our physical universe. This classification of causets extends to the set of paths $\Omega$ in $\pscript$ to obtain $\Omega =\Omega ^{\rmant}\cup\Omega ^{\rmmix}\cup\Omega ^{\rmmat}$. We introduce a further classification $\Omega ^{\rmmix}=\Omega_{\rmm}^{\rmmix}\cup\Omega_{\rma}^{\rmmix}$ into matter-antimatter parts. Approximate classical probabilities and quantum propensities for these various classifications are considered. Some conjectures and unsolved problems are presented.