You can exist, because it's your present self doing the traveling. If you travel to before you were born, you haven't been born yet in that time stream, but your present self has. The 'future' would become your present self's past because you have already grown up and traveled time. They actually explained this really well on Lost. Well I never watched lost. You can travel back in time, you just can't change anything, because it's already happened, and nothing can change it. I forget exactly how it works. but they did explain time travel really really well on lost. Well if by someway you could travel into the past why couldn't you change anything? You are traveling back before something happened so you can change it since it hasn't happened. Unless you are going off the theory of fate. That no matter what you do you will end up doing what it was you were supposed to do for that event to take place. If the former is true though you couldn't return because the time you were trying to get to would no longer exist. Because what you did in the past has already been recorded now. So killing a butterfly would keep things normal just like not killing a butterfly. Well if you were recorded to have killed that butterfly then not killing it would change what happened. Though the 'rule of fate' kicks in again and you end up doing what you were supposed to do even if you were trying not to do it.