Science fiction has played with the grandfather paradox for decades. (If you're not familiar with the grandfather paradox, it's an argument put forth to demonstrate that time travel must be impossible, otherwise a person could travel back in time and kill off an ancestor before he/she reproduces, thereby causing the traveler not to exist--but then the traveler couldn't have prevented his/her own birth.) However, science has already come up with several answers to this paradox, including one listed in this article.
According to this article, time travel can occur along Closed Timelike Curves (CTC), a path in spacetime that returns to its starting point. The time travel happens by quantum teleportation (two particles that are entangled, or very closely linked, can affect each other instantaneously, even if they are separated. This means they seem to communicate faster than the speed of light, though no actual information is transmitted.) Before the quantum teleportation happens, post-selection is applied. This means only some types of quantum teleportation are allowed--the ones that are self-consistent. The whole idea seems like the Novikov self-consistency principle to me (basically, it's the idea that events leading to a time travel paradox aren't allowed.) However, it's interesting to see an actual physics paper supporting this idea. Unfortunately, quantum teleportation only works on the quantum level, not on the macro level where we exist. I suppose it's up to us science fiction writers to find ways to make time travel for humans plausible.