Note that this being a work of mathematics, nothing has been really proven. But if validated, it lays an excellent foundation for experimentation, and finally, building the Time Travel device of my dreams. I'm coming to kill you, great-great-grandfather!
-Ralf Maximus
I would hate to shatter someone's dreams, but the type of time travel you imply is probably not possible.
If it were possible, we would know it was already, from the evidence of people from the future doing it and traveling to our time or earlier. How could we not know about it going on? As humans, we are bound to blab our secrets when we shouldn't, so some time traveler would have spilled the beans about it. It's our nature. We screw things up.
The fact we have no proof in our current time that there are time travelers in the future that have visited the past, leads me to believe one of 3 things are true:
A. Time travel, of the type you imply, isn't possible.
B. Humans become extinct before they discover how to do it.
C. The evidence of time travelers is being hidden in the biggest global conspiracy/cover-up of all time.
C is a bit far fetched, because like I said...we can't keep secrets that well.
B...I don't want to think about, even if it is true...so I'll just believe in A.
Of course a 4th possibility could be true:
D. People will someday figure out how to travel to the future but never how to travel to the past. (but then that would mean one-way tickets, we would have no proof that it worked since the traveler could never come back and tell us, and we would assume it just messed up and killed him, and abandon the project before anybody else got hurt.)