Hi Christopher, yep, I think I was a bit cryptic in that reply - sorry!

The underpinnings of "an inertial observer present at two events will always observe a shorter time interval between the two events than any inertial observer not present a both events" come from the Lorentz transform, but the simplest way to put is as follows.

The invariant spacetime interval is given by ds^2 = dt^2 - dx^2 for timelike intervals between two events. The observed (squared) time by any observer is hence: dt^2 = ds^2 + dx^2.

For an observer present at both events, dx = 0, so it is obvious that it gives the minimum value for dt (since ds is the same for all observers).

Hope this clears some of it, at least ;)

Regards,

Burt Jordaan (www.Relativity-4-Engineers.com)