I'm no theoretical physicist or physicist of any kind, but I have some basic grasp of how the universe works and after thinking long and hard about time travel, I don't think we have to worry about the paradoxes which are inherent to time travel when time traveling into the past. If we are to believe that time is relative like Einstein has stated in his equations, such as the twin brother paradox (where one brother stays on Earth while his twin brother goes off in a rocket and comes back to find his brother on Earth has aged into an old man, but he has remained the same as when he left), then I would imagine that something fairly similar would occur when a time traveler time travels into the past. For instance, let's say that a time traveler from the far future goes back in time via starship traveling faster than light with the Alcubierre warp drive bubble to prevent his birth from occuring by killing his grandfather and succeeds. His grandfather is now dead, but the time traveler continues to exist, he does not literally disappear like Marty McFly in Back To The Future because that would violate the laws of energy conservation, so that's out. Just like the twin brother scenerio, the paradox is a real one, but the time traveler's existence is never compromised (unless of course he's caught, arrested and brought on charges for murder). Since Einstein believed that the past, present and future is happening all at the same time, one can say that there is only one timeline but once a time traveler time travels either into the past or future, they are basically parallel timelines/universes that do not affect one another, they are all relative. Hence, if you're in the past you can change history without compromising the present or future. By the same token, if you're in the present you can change history without compromising the future and vice-versa. This is somewhat different than the parallel timeline/universes that we are accustomed to seeing on shows like Star Trek and Stargate SG-1 where a time traveler changes the past and in that instant a parallel timeline/universe is created. This is not possible because just like the disappearance of Marty McFly, it violates the laws of energy conservation. The fact is, mass like energy cannot be created or destroyed. Therefore, if parallel timelines/universes do exist, they must have been created at the exact same time as when our universe was created. Thoughts anyone? See the attached diagram I created in Illustrator to see what I mean.