Return to interval (thing)
As all observers, no matter their state of motion, agree about the distance between two points in Classical dynamics (and in "common sense") so, in Relativity theory, the interval between two events (such as two shots being fired) is commonly agreed. It is, for relativity theory, the invariant analogous to distance.
The reason for this is easy to see: The interval between two events is numerically equal to the proper time separating the events. For example, if a pistol, with a clock tied to it, moving at constant velocity, is fired twice: once when the clock reads t1 and again when it reads t2; then everyone must agree that the proper time separating the two explosions is t2 - t1. This equals the interval between the events.
If a particular reference frame measures the distance between two events to be x, y & z (i.e. forward, sideways & up) and the time gap to be t. Then the interval separating the two is:
s = sqrt(x2 + y2 + z2 - c2t2)
(Where c is the velocity of light in a vacuum.)
(Sporus is not the greatest expert in the universe on this one but the above seems reasonable enough.)