The grandfather paradox is a paradox of time travel, supposedly first conceived by the science fiction 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. In that case, your grandfather would still be alive and you would have been conceived, allowing you to travel back in time and kill your grandfather, and so on.

An equivalent paradox is known (in philosophy) as autoinfanticide — that is, going back in time and killing oneself as a baby — though when the word was first coined in a paper by Paul Horwich it was in the malformed version autofanticide.

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

Complementary time travel

Since quantum physics is governed by probabilities, an unmeasured entity (in this case, your historical grandfather) has numerous probable states; but, when that entity is measured, the number of its probable states singularises, resulting in a singular outcome (in this case, ultimately, you). Therefore, since the outcome of your grandfather is known, you killing your grandfather would be incompatible with that outcome. Thus, the outcome of one's trip backwards in time must be complementary with the state from which one left. (see Professor Dan Greenberger, of the City University of New York, quoted by Kettlewell, BBC, 2005, )

Novikov self-consistency principle

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 many consistent solutions. Things might, however, turn out to be almost unbelievably strange. For related information on unbelievably strange causality, see quantum suicide and quantum immortality.

Parallel universes resolution

There could be "an ensemble of 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. Parallel universes are also used in Michael Crichton's novel Timeline and Alfred Bester's short story "The Men Who Murdered Mohammed". The latter story starts with this premise, but proposes a timeline which is dependent on perspective, making such paradoxical changes self-limiting. Interestingly enough, Crichton's novel seems to imply that universes set in the past can affect the one we live in. The example given is when a professor trapped in the past sends a message to his graduate students at a medieval cathedral.

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).

The parallel universes theory obviates this problem of cause-and-effect.

This theory is similar to the parallel universes theory, except that it happens within one universe. If parallel universes cannot interact again after time travel occurs, then essentially the parallel universe resolution and the relative timelines resolution are the same as there is no way of proving a parallel universe still exists or ever did exist.

Author Orson Scott Card used this theory to allow his characters to travel back in time and prevent the European colonization of the New World in his novel, Pastwatch: The Redemption of Christopher Columbus. This model also appears in James P. Hogan's novel "Thrice Upon a Time", although Hogan confusingly uses the term "universes" to describe different moments on the same timeline rather than separate timelines.

In Anderson's Time Patrol, the Patrol's purpose is to prevent such changes in time, and when they have occurred, undo the changes as neatly as possible, to revert to the "normal" timeline. Such a Time Patrol, under one name or another, is a common feature in stories using this resolution.

In the television series Seven Days, NSA Agent Frank Parker uses a device called the chronosphere to go back in time, usually one week, to "undo" catastrophic events. This would only be possible if the relative timelines resolution holds, because if Parker succeeds, there would never have been any reason to send him back in time.

In the essay The Theory and Practice of Time Travel, Larry Niven proposes that, after some unknown number of revisions of history, the effect of some episode of time travel will be to create a universe where time travel, although possible, is simply never discovered. Such a timeline is stable, and in it no paradoxes occur, and so need no resolution.