I remember reading a physics experiment a while back where sub atomic particles were accelerated at 300 times the speed of light, and they arrived at their destination at a point in time seemingly before they left to begin with. Don't ask me the details because particle physics is not my strong suit.
But as to the original question, I think time travel in the sense used by the original poster is impossible, and simply do not care to speculate. I have enough to worry about with weapons of mass destruction, overpopulation and environmental destruction, and simple fiscal mismanagement.