You know the old grandfather paradox: It goes something like invent a time machine and travel to your past. While there you kill your grandfather which should prevent you from being born. But how can you do anything if you were never born??

I suggest that you can travel into the past and kill your grandfather without any paradox. The resolution is to realize that whatever effect you cause travels 'forward' in time at the same rate you do. Its just like your actions now that travel into an unset future at a 'fixed' speed. In a sense your past disappears but never catches up with you.