Grandfather paradox

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The grandfather paradox is a paradox of time travel, first described by the science fiction writer René Barjavel in his 1943 book "Le Voyageur Imprudent" ("The Imprudent Traveller"). The paradox is this: suppose a man traveled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension, the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which in turn implies the grandfather would still be alive, and the traveller would have been conceived, allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.

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 version autofanticide.

The grandfather paradox has been used to argue that backwards time travel must be impossible. However, a number of possible ways of avoiding the paradox have been proposed, such as the idea that the timeline is fixed and unchangeable, or the idea that the time traveler will end up in a parallel timeline, while the timeline in which the traveler was born continues to exist.

Scientific theories

Complementary time travel

Since quantum mechanics is governed by probabilities, an unmeasured entity (in this case, your historical grandfather) has numerous probable states. When that entity is measured, the number of its probable states singularises, resulting in a single 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.

Novikov self-consistency principle

See the Novikov self-consistency principle and Kip S. Thorne for one view on how backwards time travel could be possible without a danger of paradoxes. According to this hypothesis, the only possible timelines are those which are entirely self-consistent, so that anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from being made since this would represent an inconsistency.

Parallel universes/alternate timelines

There could be "an ensemble of parallel universes" such that when the traveller kills the grandfather, the act took place in (or resulted in the creation of) a parallel universe in which the traveller's counterpart will never be conceived as a result. However, his prior existence in the original universe is unaltered.

Examples of parallel universes postulated in physics are:

• In quantum mechanics, the many-worlds interpretation suggests that every seemingly random quantum event with a non-zero probability actually occurs in all possible ways in different "worlds", so that history is constantly branching into different alternatives. The physicist David Deutsch has argued that if backwards time travel is possible, it should result in the traveler ending up in a different branch of history than the one he departed from. See also quantum suicide and quantum immortality.

• M-theory is put forward as a hypothetical master theory that unifies the five superstring theories, although at present it is largely incomplete. One possible consequence of ideas drawn from M-theory is that multiple universes in the form of 3-dimensional membranes known as branes could exist side-by-side in a fourth large spatial dimension (which is distinct from the concept of time as a fourth dimension) - see Brane cosmology. It is theorized that when two branes collide it sends a massive ripple of heat and energy throughout the two. This is a possible explanation of what caused the big bang according to the ekpyrotic scenario and the cyclic model. However, there is currently no argument from physics that there would be one brane for each physically possible version of history as in the many-worlds interpretation, nor is there any argument that time travel would take one to a different brane.

Theories in science fiction

Parallel universes resolution

The idea of preventing paradoxes by supposing that the time traveler is taken to a parallel universe while his original history remains intact, which is discussed above in the context of science, is also common in science fiction - see Time travel as a means of creating historical divergences.

Restricted action resolution

See also: Predestination paradoxes in fiction

Another resolution, of which the Novikov self-consistency principle can be taken as an example, holds that if one were 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 the grandfather will be injured but not killed, or the person killed will turn out to be not the real grandfather, or some other event will occur to prevent the attempt from succeeding. No action the traveller takes to affect change will ever succeed, as there will always be some form of "bad luck" or coincidence preventing the outcome. In effect, the traveller will be unable to change history from the state they found it. Very commonly in fiction, the time traveller does not merely fail to prevent the actions he seeks to prevent; he in fact precipitates them (see predestination paradox), usually by accident.

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.

Closely related but distinct is the notion of the time line as self-healing. The time-traveler's actions are like throwing a stone in a large lake; the ripples spread, but are soon swamped by the effect of the existing waves. For instance, a time traveller could assassinate a politician who led his country into a disastrous war, but the politician's followers would then use his murder as a pretext for the war, and the emotional effect of that would cancel out the loss of the politician's charisma. Or the traveller could prevent a car crash from killing a loved one, only to have the loved one killed by a mugger, or fall down the stairs, choke on a meal, killed by a stray bullet, etc. In some stories it is only the event that precipitated the time traveler's decision to travel back in time that cannot be substantially changed, in others all attempted changes will be "healed" in this way, and in still others the universe can heal most changes but not sufficiently drastic ones. This is also the explanation advanced by the Dr. Who roleplaying game, which supposes that Time is like a stream; you can dam it, divert it, or block it, but the overall direction it is headed will resume after a period of conflict.

It also may not be clear whether the time traveller altered the past or precipitated the future he remembers, such as a time traveller who goes back in time to persuade an artist -- whose single surviving work is famous -- to hide the rest of the works to protect them. If, on returning to his time, he finds that these works are now well-known, he knows he has changed the past. On the other hand, he may return to a future exactly as he remembers, except that a week after his return, the works are found. Were they actually destroyed, as he believed when he travelled in time, and has he preserved them? Or was their disappearance occasioned by the artist's hiding them at his urging, and the skill with which they were hidden, and so the long time to find them, stemmed from his urgency?

Relative timelines resolution

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. 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.

Destruction resolution

Some science fiction stories suggest that causing any paradox will cause the destruction of the universe, or at least the parts of space and time affected by the paradox. The plots of such stories tend to revolve around preventing paradoxes.

Observation resolution

Some speculations suggest that, under no circumstances whatsoever you would be able to "kill your grandfather". The only result of the time travel would be your knowledge that you've caused some event in the past. For example, if a protagonist kills his grandfather, it would turn out that the victim is not his grandfather at all.

Other considerations

Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible, on the same order as round squares. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, where he wrote:

Nobody has ever built a time machine that could take a person back to an earlier time. Nobody should be seriously trying to build one, either, because a good argument exists for why the machine can never be built. The argument goes like this. Suppose you did have a time machine right now, and you could step into it and travel back to some earlier time. Your actions in that time might then prevent your grandparents from ever having met one another. This would make you not born, and thus not step into the time machine. So, the claim that there could be a time machine is self-contradictory.

However, some philosophers and scientists believe that time travel into the past need not be logically impossible provided that there is no possibility of changing the past, as suggested, for example, by the Novikov self-consistency principle. Bradley Dowden himself revised the view above after being convinced of this in an exchange with the philosopher Norman Swartz.

Consideration of the possibility of backwards time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion. He seems to have been suggesting something along the lines of the block time view in which time does not really "flow" but is just another dimension like space, with all events at all times being fixed within this 4-dimensional "block".

See also

• Causality
• Chronology protection conjecture
• Time loop
• Predestination paradox
• Ontological paradox
• Time travel in fiction
• The chicken or the egg