A Matter of Matter and Antimatter

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 $\text{pscript}$ of causets can be partitioned into three subsets $\pscript = (\rmant)\cup (\rmmix)\cup (\rmmat)$where$\rmant$isthesetofpureantimattercausets,$\rmmat$thesetofpuremattercausetsand$\rmmix$ the set of mixed matter-antimatter causets. We observe that there is an asymmetry between $\mathrm{a}nt$ and $\mathrm{m}at$ which may explain the matter-antimatter asymmetry of our physical universe. This classification of causets extends to the set of paths $\mathrm{\Omega }$ in $\text{pscript}$ to obtain $\Omega =\Omega ^{\rmant}\cup\Omega ^{\rmmix}\cup\Omega ^{\rmmat}$\mathrm{.}Weintroduceafurtherclassification$\Omega ^{\rmmix}=\Omega_{\rmm}^{\rmmix}\cup\Omega_{\rma}^{\rmmix}$ into matter-antimatter parts. Approximate classical probabilities and quantum propensities for these various classifications are considered. Some conjectures and unsolved problems are presented.