A Matter of Matter and Antimatter

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.