“I travel at the speed of light / or at a relativistic speed, I come back, I haven’t aged, yet Earth has. This is what I don’t understand.”
I too, have problems with that. Much because the speeds are relative. Me in a space craft is traveling at light speed relative to what? Apparently relative to the earth. So, from my point of view, I can think of myself as fixed in space, and the earth is moving away from me at relativistic speed. So observers both on the earth and on my space craft can think of themselves as stationary while the other is moving relative to their fixed position. When I land on earth, who is to say I am not the old man, and the earthlings are the young ones?
Why does movement and speed have anything to do with time.....I move at the speed of light.....so what? Time slows down for me?