"Gravitational time dilation" explains things much better than "twin paradox", even though the article never really explained what causes gravitational time dilation.
#1 Basically acceleration by any force is the same as gravitational acceleration because of the fact that inertial mass always equals gravitational mass for any object.
#2 An object experiencing greater gravity than another object experiences slower passage of real time (not really explained though it's suggested that it has something to do with the change in the frequency of light, i.e. gravitational red shift and blue shift)
#3 An object experiencing acceleration from any force would in effect experience the effects of a gravitational field, which because of point #2 would cause its personal time to slow down relative to the rest of the universe.
So basically the twin that went away aged really slowly only when the ship was turning around.
I have no idea how this is supposed to relate to how the two watches work though.
The article also basically said that light does not always move at the speed c but this only happens when you can't observe that light (since physical contact is needed to observe light when you can see it, it's moving in the same reference frame as you). It's like being invisible only when no one is looking.
Well, basically this thread discusses time travel... Thanks for clearing the matter up.