Grandfather paradox

The grandfather paradox is a paradox of time travel. Suppose you traveled back in time and killed your biological grandfather before he met your grandmother. Then you would never have been conceived, so you could not have traveled back in time after all. Now did you travel back or not?

The grandfather paradox has been used to argue that backwards time travel must be impossible. However, other resolutions have also been advanced.

For instance, there could be "parallel universes" (see Everett many-worlds interpretation) and when you travel back in time and kill your grandfather, you do so in a parallel universe in which you will never be conceived as a result. You continue to exist in your original universe however.

Another resolution holds that, when you travel back in time, the laws of nature simply forbid you from doing anything that could later result in your time travel not occurring, free will being an illusion.