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 $\pscript$ 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 $Ω$ in $\pscript$ to obtain $Ω=Ω^{\rmant}\cupΩ^{\rmmix}\cupΩ^{\rmmat}$. We introduce a further classification $Ω^{\rmmix}=Ω_{\rmm}^{\rmmix}\cupΩ_{\rma}^{\rmmix}$ into matter-antimatter parts. Approximate classical probabilities and quantum propensities for these various classifications are considered. Some conjectures and unsolved problems are presented.

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