Time dilation is the result of velocity. Your time would appear slower as measured by an earth bound observer. From your point of view, however, the clocks on earth appear to be moving more slowly than yours.
I believe that special relativity is so called because it is a special case of the general theory.
I understand that any observer can consider themself at rest as they watch someone else whiz by. Theoretically when I coast by the earth at .99c it is just as reasonable for me to assume I’m standing still and the earth is cruising by at .99c.
However, if I synch up two atomic clocks on earth and then take one with me on my spaceship won’t the two clocks disagree when I return to earth? Won’t the clock on the spaceship look as if it’s been running slow while I was away on my jaunt through the solar system?
I have explanations of the twins paradox dancing in my head but I don’t think I ever really was able to grasp that one fully and don’t know if that’s what applies here
The sync’d atomic clocks example is one where you’ve introduced accelerated frames of reference- to return to earth, you’ve got to accelerate (or deccelerate) to turn around. As Saltire aptly put it, it becomes “more complex, to somewhat understate the situation.”
The twins paradox. Velocity is relative; acceleration is not. My understanding of SR is better than my grasp of GR. The best I can tell you is that the travelling twin’s situation is not an inertial frame.