I see some relatively comprehensive answers here but then I listen to this Don Lincoln presentation on the twin paradox which seems to be saying that the resolution to the paradox is more fundamentally due to the change in inertial reference frame, not the acceleration implicitly involved.
To try to clarify, let me pose that there are four observers in four distinct situations. At a particular instant in time, the four observers determine that they will all be stationary with respect to each other. The differences lie only in their accelerations and gravitational fields. The four situations are:
A) Zero velocity, zero acceleration, gravitational field and potential = 0
B) Zero velocity, acceleration=g (from rocket), gravitational field and potential = 0
C) Zero velocity, suspended in gravity=g (acceleration=0), potential=$\Psi$
D) Zero velocity, free-fall in gravity=g (acceleration=g), potential=$\Psi$
What can be said about the relative time dilations for these observers at this special instant in time?
[Edit] From the comments below, it looks like I also have to specify the relative positions. I'll say C and D are instantaneously in the same position above a large mass and A and B are instantaneously in the same position but at a distance X directly above them. I'll arbitrarily say the gravitational potential for A and B is still zero. I think I also need to say that the gravitational force and the acceleration act in the same direction.
