Things like GPS and satelite communication wouldn't work if we didn't count for the diffrence in time caused by the diffrence in speed compared to here on earth.
Time travel is not only possible, but actualy already happening (although on a very tiny scale, and only towards the future).
If we could go near the speed of sound and we travel away from earth for 10 years and come back, we could be thousands of years in the future. Comming back aint really an option though.