Question

Conceptual question about relativity: Imagine two events--
1. A photon hits a mirror
2. The same photon, after reflecting off of the mirror, hits some other surface.

These two events are separated in both space and time. However, the spacetime separation between the two events is zero.

What does this mean? Normally if the distance between two points is zero, it means that the two points are identical. Are these two events, in some sense, the same event?

Answer 1

They are not the same event in that they occur in different places and times in most frames of reference. In the photon's frame they are not separated in either space nor time because photons don't experience time and at least mathematically all points on the spacetime manifold are the same point to a photon.  What the zero spacetime interval can tell us though, is that the events are connected by a light beam (light-like separation). There is as much time between the events as there is space and one event can conceptually cause the other. They are on the cusp between time-like and space-like  events.