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.Comment: 22 pages, including 1 figur