The paradox issue of travelling back in time is easily solved if you accept the many worlds theory of quantum physics. For every event, from the most insignificantly small sub-atomic interaction to the gigantic collision of galaxies every possible outcome actually becomes reality in its own universe. Basically, anything that is possible is real, but it may not exist in your universe. This means there are an infinite number of universes constantly branching into an infinite number of new directions in time. You can travel back in time and kill your grandfather because in the universes that move forward from that moment you won't be born, but there are alreay an infinite number of universes where you already were. Confusing, isn't it?