Measurements are made at a particular time. In classical general relativity in curved spacetime, there are many possible metrics which might work, but no way to pick the appropriate one. Without a clear definition of measurement, the definition is non-physical. Fixing the metric cannot be done if the metric is subject to quantum fluctuations. 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.