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A predestination paradox, also called a causal loop, is a paradox of time travel that is often used as a convention in science fiction. It exists when a time traveller is caught in a loop of events that "predestines" him to travel back in time. This paradox is in some ways the opposite of the grandfather paradox, the famous example being that of killing his own grandfather before his parent is born, in which a time traveller's acts preclude his own travel to the past by cancelling his own existence.
The Novikov self-consistency principle proposes that contradictory causal loops cannot form, but that consistent ones can.
Examples
A man travels back in time and impregnates his great-great grandmother. The grandmother would thus give birth to one of the man's great grandparents, who would then give birth to his grandmother or father, who would then be able to give birth to one of the man's parents, and finally to the man himself who would have to travel back in time in order to ensure his own existence. As a result, the man's very existence would be pre-determined by his time traveling adventure, and therein lies the paradox.
Examples in the media
Since it is impossible to practically experiment with time travel, a number of explanations have been given in various works of literature and film for various circumstances that can logically arise from such travel. Because of the possibility of influencing the past while time travelling, one way of explaining why history does not change is by saying that whatever has happened was meant to happen. A time traveller attempting to alter the past in this model, intentionally or not, would only be fulfilling his role in creating history, not changing it. This raises the issue of free will.
Literature
In Harry Potter and the Prisoner of Azkaban, Harry and Hermione travel back in time three hours. During this, Harry saves the life of his past-self, who mistakes his future-self for his father. However, when the time-traveling Harry goes to see his father perform the Patronus spell, he realizes that he had seen himself, not his father, do it. The film version adds three more examples, one being rocks mysteriously thrown into Hagrid's hut, which turn out be Hermione's future-self warning them Cornelius Fudge and company are arriving.
Film
Movies in the Terminator series deal with predestination paradoxes. In the first movie, Reese, the soldier sent back in time to protect Sarah Connor, the future mother of his commander John Connor, ends up fathering John Connor with her. Paralleling this, the Terminator cyborg sent back to kill Sarah is destroyed, but its components are salvaged to form the basis of the artificially intelligent computer network Skynet that will, in the future, send it back in time on its murderous mission.
The Back to the Future film deals with a variant of the paradox. In it, Marty McFly (played by Michael J. Fox), travels back from the year 1985 to 1955, and prevents his parents from meeting. This has the effect, via the grandfather paradox, of causing himself to start fading from existence. By the end of the movie he gets them back together, ensuring his own birth and becoming part of his own personal history. This is not a "pure" predestination paradox because history is changed to accomodate the paradox caused by McFly rather than the paradox being part of history to prompt the time travel, but the end result is the same. The two sequels to the movie deal with variations on the theme.
Television
The paradox shows up in two episodes of The Fairly OddParents cartoon series, namely The Secret Origin of Denzel Crocker and Father Time. In these episodes, the show's main character causes his later teacher's findings on fairy godparents to become public, and sees how his parents met for the first time, respectively.
A similar situation occurs in "Roswell That Ends Well", an episode of Futurama. In the episode, Philip J. Fry travels back in time and meets his future grandfather Enos and future grandmother Mildred. Fry accidentally kills his grandfather, and is shocked to discover that he continues to exist. He therefore decides that Mildred must not be his grandmother. Satisfied that this is the case, he has sex with Mildred, only to realize that she is his grandmother, and his grandfather is, in fact, himself.
In the Star Trek: Voyager episode "Relativity", Captain Braxton of the future timeship Relativity recruits Seven of Nine to prevent the USS Voyager from being blown up by a temporal intruder. Her first two attempts are unsuccessful, and she ends up recruiting Captain Kathryn Janeway to find the intruder who planted the bomb. The intruder turns out to be a future version of Braxton, seeking revenge against Janeway, whom he blames for interfering with the timeline on numerous occasions and causing him to endure a 30-year exile on 20th Century Earth. The First Officer on the Relativity arrests the present-day Braxton for "crimes he will commit," and promises Janeway that she will clean up the timeline. How this is to be done, however, or whether the events of the episode will continue to exist if she does so, is never explained.
In the Stargate SG-1 episode "1969", a wormhole transports the SG-1 team to the titular year, where they are arrested as communist spies. One of their guards, Lieutenant George Hammond, who will be their commanding officer in the future, finds a note in Samantha Carter's equipment. The note, in Hammond's own handwriting, states, "George, help them." Because of this, the younger Hammond helps SG-1 escape. In his relative future, General Hammond will remember the incident and write the note, giving it to Carter just prior to SG-1 leaving through the wormhole, thus closing the loop.
In one serial from the British science fiction television series Doctor Who, Day of the Daleks, guerillas from the 22nd Century travel back in time to prevent their own future from coming to pass. However, they discover that it is their actions that actually cause that future to happen. In that case, the loop is broken, not by them, but by the Doctor. As his existence is not dependent on the loop, he is not caught in the paradox and can act freely, his actions presumably causing that future to cease to exist.
In the animated series Gargoyles, Multibillionaire David Xanatos uses an artifact known as the Phoenix gate to travel back in time to the Dark Ages. There, he shows off his membership in the Illuminati to arrange that a single gold coin will be given to his younger self hundreds of years later. Xanatos used that same coin to build his fortune and get into the Illuminati, thereby making him a "self-made-man" in his own way.
Ontological paradox
The predestination paradox can also lead to a very closely related paradox, the ontological paradox. This paradox is best described by the following example:
On his 30th birthday, a man who wishes to build a time machine is visited by a future version of himself. This future self explains to him that he should not worry about designing the time machine, as he has done it in the future. The man receives the schematics from his future self and starts building the time machine. Time passes until he finally completes the time machine. He then uses it to travel back in time to his 30th birthday, where he gives the schematics to his past self, closing the loop. The paradox raises the ontological questions of where, when and by whom the schematics were created. Time loop logic operates on similar principles, sending the solutions to computation problems back in time to be checked for correctness without ever being computed "originally."
Other examples in science fiction include the antique eyeglasses Captain Kirk receives from Doctor McCoy in Star Trek II: The Wrath of Khan, which Kirk leaves in the 20th Century in Star Trek IV: The Voyage Home so it can be eventually bought by McCoy. Although the screenwriter's intent in Star Trek IV was to suggest a causal loop involving the glasses, the additional problem of the glasses aging by three centuries with each loop is never addressed. Similarly, Scotty and McCoy trade the formula for transparent aluminum with an engineer so that he can use it to build a whale tank for them. Scotty eases McCoy's concerns about changing history by asking, "How do we know he didn't invent it?" In neither case is there actual evidence seen of the loop, however - the characters merely assume it (see also transparent alumina).
Robert Heinlein's stories By His Bootstraps and "All You Zombies" also play with the ontological paradox, as do stories where a time traveller gives William Shakespeare a copy of his Complete Works. To use the example from the Television section, when the Doctor breaks the loop in Day of the Daleks, he creates an ontological paradox in the process of averting the predestination paradox. If the events that alerted him to the loop no longer exist, where did his knowledge of the loop come from? (Though his existence is not dependent on the loop, his knowledge is.)
Isaac Asimov's short story The Red Queen's Race used Lewis Carroll's example of the Red Queen's race in Through the Looking-Glass to illustrate the concept of a predestination paradox, even though the short story itself implies a resulting ontological paradox.
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