Grandfather paradox

The grandfather paradox is a proposed paradox of time travel first described (in this exact form) by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (The Imprudent Traveller). Nevertheless, similar (and even more mind-boggling) paradoxes had already been described, for instance by Robert A. Heinlein in "By His Bootstraps". The paradox is this: suppose a man travelled 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 means 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.

Despite the name, the grandfather paradox does not exclusively regard the impossibility of one's own birth. Rather, it regards any action that makes impossible the ability to travel back in time in the first place. The paradox's namesake example is merely the most commonly thought of when one considers the whole range of possible actions. Another example would be using scientific knowledge to invent a time machine, then going back in time and (whether through murder or otherwise) impeding a scientists' work that would eventually lead to the very information that you used to invent the time machine.

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 he used the term 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, the idea that the time traveller will end up in a parallel timeline, while the timeline in which the traveller was born remains independent or the possibility of the time traveller saving his grandfather's life instead of killing him so that he could later be born and travel back in time so that he could save his grandfather's life, exactly the opposite of the original paradox.

Scientific theories

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 traveller does in the past must have been part of history all along, and the time traveller can never do anything to prevent the trip back in time from being made since this would represent an inconsistency. In laymen's terms, this is often called determinism. It conflicts with the notion of free-will. Succinctly, this explanation states that if time travel is possible, then actions are determined by history.

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. Succinctly, this explanation states that: if time travel is possible, then multiple versions of future exist in parallel universes.

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 traveller ending up in a different branch of history than the one he departed from. See also quantum suicide and immortality.

• M-theory is put forward as a hypothetical master theory that unifies the six 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. 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 traveller 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, or at least not unlimited). 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-traveller'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 the 2002 film The Time Machine, this scenario is shown where the main character builds a time machine to save his girlfriend who got killed by a robber, yet she still dies, only from a car crash instead. In some stories it is only the event that precipitated the time traveller'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 Doctor Who role-playing 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?

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, such as the final episode of Star Trek: The Next Generation. A less destructive alternative of this theory suggests the death of the time traveller whether the history is altered or not; an example would be in the first part of the Back to the Future trilogy, where the lead character's alteration of history results in a risk of his own disappearance, and he has to fix the alteration to conserve his own existence. In this theory, killing one's grandfather would result in the disappearance of oneself, history would erase all traces of the person's existence, and the death of the grandfather would be caused by another means (say, another existing person firing the gun); thus, the paradox would never occur from a historical viewpoint.

Temporal Modification Negation Theory

This theory is partially similar to other theories on time travel. While stating that if time travel is possible it would be impossible to violate the grandfather paradox, it goes further to state that any action taken that itself negates the time travel event cannot occur. The consequences of such an event would in some way negate that event, be it by either voiding the memory of what one is doing before doing it, by preventing the action in some way, or even by destroying the universe among other possible consequences. It states therefore that to successfully change the past one must do so incidentally.

For example, if one tried to stop the murder of one's parents, he would fail. On the other hand, if one traveled back and did something to some random person that as a result prevented the death of someone else's parents, then such an event would be successful, because the reason for the journey and therefore the journey itself remains unchanged preventing a paradox.

In addition, if this event had some colossal change in the history of mankind, and such an event would not void the ability or purpose of the journey back, it would occur, and would hold. In such a case, the memory of the event would immediately be modified in the mind of the time traveller.

An example of this would be for someone to travel back to observe life in Austria in 1887 and shooting five people, one of which was one of Hitler's parents. Hitler would therefore never have existed, but since this would not prevent the invention of the means for time travel, or the purpose of the trip, then such a change would hold. But for it to hold, every element that influenced the trip must remain unchanged. This would void someone convincing another party to travel back to kill the people without knowing who they are and making the time line stick, because by being successful, they would void the first party's influence and therefore the second party's actions.

A humorous treatment of this issue occurs in an episode of Futurama, in which Fry travels back in time and inadvertently causes his grandfather's death before he marries his grandmother. His distraught grandmother then seduces him, and upon returning to his own time Fry learns that he is his own grandfather.

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".

Another theory suggests that the time machine requires a receiving end machine and thus it is impossible to travel before the time of the first invention of a time machine.

See also

• Chronology protection conjecture
• Ontological paradox
• Predestination paradox
• Time travel in fiction
• The chicken or the egg
• Temporal paradox
• Time loop
• Achron - an upcoming video game notable for being the first game to handle the grandfather paradox as a gameplay mechanism
• Back to the Future - a motion picture that deals with this paradox, when the protagonist accidentally intervenes with his parents first meeting.
• The Terminator series - in which terminator machines from the future traveled to present time in order to kill the future resistance leader and his mother.