The GP coordinates version of Sch. metric uses a new time coordinate, t', which is the time read from a free-falling clock that was dropped from rest at large r and falls past the event we're measuring as it occurs.
I accept that coordinate time, so t' in this case, and proper time, τ, are different and I follow the mathematics needed to calculate t'. But I can't seem to understand conceptually how they are two different times?
Please can somebody enlighten me?