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The grandfather paradox is a paradox of time travel, supposedly first conceived by the SF writer René Barjavel in his book "Future times three" ("Le voyageur imprudent", 1943). Suppose you travelled 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 travelled 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 1.
The Novikov self-consistency principle and recent calculations by Kip S. Thorne indicate that simple masses passing through time travel wormholes could never engender paradoxes—there are no initial conditions that lead to paradox once time travel is introduced. If his results can be generalized they would suggest, curiously, that none of the supposed paradoxes formulated in time travel stories can actually be formulated at a precise physical level: that is, that any situation you can set up in a time travel story turns out to permit of many consistent solutions. Things might, however, turn out to be almost unbelievably strange.
There could be " parallel universes" 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. However, your existence is not erased from your original universe. Alfred Bester's short story "The Men Who Murdered Mohammed" uses this premise. It is also used in James P. Hogan's novel "Thrice Upon a Time", as well as Michael Crichton's novel "Timeline".
It could be that the universe does not have an absolute timeline that is permanently written after events happen (or, in the deterministic view, at the start of time). Instead each particle has its own timeline and therefore, humans have their own timeline. This might be considered similar to the theory of relativity, except that it deals with a particle's history, rather than its velocity.
Physical forces affect physical particles. If your body's physical particles go back in time, you will be able to kill your grandfather (no physical forces will mystically stop you) and nothing will physically happen to you as a result because there are no physical forces that can "figure out" what happened and this new timeline develops because the universe simply has no mechanism for unmaking it. Your younger self does not need to be born in order to fulfill a destiny of going back in time because there is no written-in-stone absolute timeline that needs to be followed. If you were able to find and observe the younger versions of the particles that make you up, they too would follow physical laws and hence wouldn't form into a younger version of you (because one of your parents wouldn't be there to form you).
This theory is similar to the parallel universes theory, except that it happens within one universe.
Another resolution, of which the Novikov self-consistency principle can be taken as an example, holds that, if one was to travel back in time, the laws of nature or other intervening cause, would simply forbid the traveller from doing anything that could later result in their time travel not occurring. For example, a shot fired at the traveller's grandfather will miss, or the gun will jam, or misfire, or some other event will occur to prevent the attempt from succeeding. In effect, the traveller will be unable to change history, because for him it has already occurred.
This theory might lead to concerns about the existence of free will (in this model, free will may be an illusion). This theory also assumes that causality must be constant: i.e. that nothing can occur in the absence of cause, whereas some theories hold that an event may remain constant even if its initial cause was subsequently eliminated. It is also possible that the time travelers' intended action might be completed, but never successfully enough to result in cancellation—see Novikov self-consistency principle.