Wow, how long have you got? Are you referring to Time Dilation or good old HG Wells "time machine" type stuff?
Time dilation, where time runs at a different speed for a body that is accelerating, is a proven (experimentally) effect. If you accelerate to close to the speed of light, you will "age" more slowly relative to a stationary object. Of course you have to consider who is actually moving, since the acceleration could be considered to be happening to either body (if you are standing on the accelerating body the stationary body will appear to be accelerating away from you). If you have a clock in both places, it will appear to be running slowly to an observer on the other body. Gravity can also cause time dilation - but that is not what the question is about.