With quaternions, time plays a central role, and is in fact the center of the matrix representation. Time is isomorphic to the real numbers, so it forms a totally ordered sub-field of the quaternions. Events are not totally ordered, but time is. Squares of events are not totally ordered, but intervals are. Norms are totally ordered and bounded below by zero.
Time is the only element in the scalar of an event.
Time appears in different guises for the scalars of energy, intervals and norms. The richness of time is in the way it weaves through these other scalars, sharing the center in different ways with space. Approaches to Quantum Gravity Isham surveys the field. At this point I think I'll just explain my approach. It is based on a concept from general relativity.