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A predestination paradox, also called either a causal loop, or a causality loop and (less frequently) either a closed loop or closed time 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 or her to travel back in time. This paradox is in some ways the opposite of the grandfather paradox, the famous example of the traveller killing his own grandfather before his parent is conceived, thereby precluding his own travel to the past by canceling his own existence.

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 as we know it, not changing it.

In physics, the Novikov self-consistency principle proposes that contradictory causal loops cannot form, but that consistent ones can. In a physical sense, a self-consistent causal loop of this kind is not actually a contradiction because it produces a logically consistent result rather than a contradictory one. It is only perceived as a paradox because it goes against conventional expectations and assumptions about causality.

A dual example of a predestination paradox is depicted in the classic Ancient Greek play 'Oedipus'

Laius hears a prophecy that his son will kill him. Fearing the prophecy, Laius pierces Oedipus' feet and leaves him out to die, but a herdsman finds him and takes him away from Thebes. Oedipus, not knowing he was adopted, leaves home in fear of the same prophecy that he would kill his father and marry his mother. Laius, meanwhile, ventures out to find a solution to the Sphinx's riddle. As prophesied, Oedipus crossed paths with Laius and this leads to a fight where Oedipus slays Laius. Oedipus then defeats the Sphinx by solving a mysterious riddle to become king. He marries the widow queen Jocasta not knowing it is his mother.

A typical example of a predestination paradox (used in The Twilight Zone episode "No Time Like the Past") is as follows:

A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time.

In the The Twilight Zone 2002-2003 revival, there is an episode in which the character goes back in time to assassinate Adolf Hitler while he is a baby. She kills the baby (whom she presumes to be actual Adolf Hitler), but the nanny (discovering the death), replaces the baby with a street gypsy's baby, and she presents this baby to the father as his own. The father proceeds to introduce this son to his guests as "Adolf", presumably the Adolf Hitler known to history in the first place.

A variation on the predestination paradoxes which involves information, rather than objects, traveling through time is similar to the self-fulfilling prophecy:

A man receives information about his own future, telling him that he will die from a heart attack. He resolves to get fit so as to avoid that fate, but in doing so overexerts himself, causing him to suffer the heart attack that kills him.

In both examples, causality is turned on its head, as the flanking events are both causes and effects of each other, and this is where the paradox lies. In the first example, the person would not have traveled back in time but for the fire that he or she caused by traveling back in time. Similarly, in the second example, the man would not have overexerted himself but for the future information he receives.

In most examples of the predestination paradox, the person travels back in time and ends up fulfilling their role in an event that has already occurred. In a self-fulfilling prophecy, the person is fulfilling their role in an event that has yet to occur, and it is usually information that travels in time (for example, in the form of a prophecy) rather than a person. In either situation, the attempts to avert the course of past or future history both fail.

Main article: Predestination paradoxes in fiction

Many fictional works have dealt with various circumstances that can logically arise from time travel, usually dealing with paradoxes. The predestination paradox is a common literary device in such fiction.

• In the beginning of the science-fiction film "Donnie Darko," Donnie is told while he is sleeping to leave his room and come outside by the voice of Frank. He does so and when he wakes up the next morning, he finds out that an airplane engine crashed into his room. Near the end of the movie, after discovering a universal truth, Donnie shoots Frank for running over his girlfriend in his car. On Donnie's way back home, he sees a portal opening above his house, and the plane flying over it. As the engine detaches from the plane and travels through the portal, time loops back to the night Frank saved Donnie. But since Donnie killed Frank, he stays in his room and dies. The people that he had affected continue on, with just a small recognition of what happened.

• DC Comics Character, the Flash (Barry Allen) was believed to be the fastest of all known Flashes, capable of running at the speed of light with little difficulty. In Flash #150, "straining every muscle," he ran at ten times the speed of light. However, when he pushed himself further (during the Crisis on Infinite Earths) he appeared to waste away as he was converted into pure energy, travelled back in time, and was revealed to be the very bolt of lightning that gave him his powers.

• In the science-fiction film "The Matrix," the character Neo has a conversation with the Oracle, in which she tells him "Don't worry about the vase." Confused, Neo turns around, knocking over a vase. The Oracle then tells Neo that what is really going to "bake your noodle" is wondering whether he would have knocked it over if she hadn't said anything.

• In the popular web series Red Vs. Blue, Church travels back in time to prevent his commanding officer's heart attack by giving him aspirin-based blood thinners - forgetting that the CO is allergic to aspirin, and thus causes the heart attack he went back in time to prevent. Also, he inadvertently disables his team's tank's IFF system, causing his own death later in time.

• The entire plot of Bill & Ted's Excellent Adventure is a model example of a predestination paradox, wherein Bill and Ted are entrusted with the means to dramatically improve the entire universe of the future by a citizen (Rufus) of that very future. Near the end of the movie, Ted solves the problem of breaking into the jail by exploiting this paradox, demonstrating an unexpected (probably to himself as well) level of temporal insight. Knowing that time travellers (themselves) in the future world can provide aid to those in their current situation (as Rufus does originally), they resolve to help themselves break into the jail by stealing Ted's dad's keys from a couple of days ago and leaving them where they will be found at the exact moment of the resolution. This accordance with the Novikov self-consistency principle, suggests that there was never any possibility for Bill and Ted to fail.

• In the show Dexter's Laboratory movie Ego trip, Dexter battles robots from the future and said that he would "get revenge on whoever did this". As the movie comes to an end, him, his old selves and Mandark's old self vow revenge on Dee Dee (Dexter's sister and the hero of the future that they despise) so they send robots in the past to his laboratory to get her.

• In the movie Frequency, in which a father and son are allowed to speak on a HAM radio forty years apart, the father hides evidence from a murder under loose floorboards, and the son walks to the spot and recovers the evidence. This appears almost instantaneous due to the intercut scenes.

• In the episode "Roswell That Ends Well" of the animated television series Futurama, the main characters all travel back in time to Roswell in 1947. Once there, Fry becomes obsessed with protecting the man who would later become his grandfather, Enos. To this end, he shuts Enos in a deserted house in the middle of the desert, thinking that he would be safe and so would be able to have children and then grandchildren. However, Fry has in fact put Enos in a house on a nuclear testing site, and Enos is vaporized only minutes later by an atomic blast. Fry later comforts Enos' fiancée, no longer believing her to be his future grandmother since Enos died and Fry is still alive. He later has sex with her, only to realize afterward (thanks to the Professor) that she was/will be his grandmother after all because Fry had just made her pregnant with Fry's own mother, making him his own grandfather. (Later, when Fry observes that they're about to change history in order to return to the future, the Professor derisively says, "Oh, a lesson in not changing history from Mr. I'm-My-Own-Grandpa!")

• In Star Wars Episode III: Revenge of the Sith, Anakin has vision nightmares that his wife, Padmé will die in childbirth. In an attempt to prevent this, he turns to the Dark Side to gain the power to save her. However, by turning to the Dark Side he becomes corrupted and assaults her, which causes her to "lose the will to live" and she dies shortly after childbirth. In attempting to save her, he causes the very death he was trying to prevent.

• Shakespeare's Macbeth is a classic example of predestination. The three Weird Sisters give Macbeth a prophecy that he will eventually become king, but the offspring of his best friend will rule instead of his afterwards. Spurred by the prophecy, he kills Duncan, his king, and Banquo, his friend, something he never would have done before. In addition to these prophecies, other prophecies foretelling his downfall are given, such as that he will not be attacked, until a forest moves to his castle, and that no man ever born of a woman can kill him. In the end, fate (or predestination) is what drives the House of Macbeth mad, and, ultimately, kills them, as he is killed by a man who was never "born", having been torn from his mother's womb.

• J. K. Rowling's book, Harry Potter and the Prisoner of Azkaban, also deals with causal loop paradoxes via a time travelling device called the Time-Turner. Rowling avoids making this obvious by making sure the early characters don't see any of the events changed, but rather hear things that could apply to either outcome. For example, Harry hears the "swish and thud of an axe", and assumes Buckbeak the hippogriff has been killed, but later discovers someone had swung the axe into the fence in frustration. In the movie based on the book, more direct paradoxes were added. When Harry, Ron and Hermione are about to be caught in Hagrid's hut, someone throws stones that break a container of flour and hit Harry on the back of the head, causing him to see the approach of Prof. Dumbledore with Cornelius Fudge and the executioner for Buckbeak. Later, we see it is Hermione, who had travelled back to save Buckbeak with Harry, who threw the stones when she realized they "weren't leaving." Also, Harry believes he sees his own father when he really sees himself travelled backwards in time.

• In the video game Final Fantasy VIII, after defeating the final boss, Sorceress Ultimecia, the main hero Squall Leonhart travels back in time and witnesses Ultimecia passing her powers on to Edea, thirteen years in Squall's past. He then informs Edea of the concepts of Garden and SeeD that she will create and which Squall will eventually lead.

• In the video game Shadow Hearts: Covenant, after the final boss, cinematics show the destruction of the world. Yuri is told that the only way to escape is to pray. It is then shown that everyone says goodbye to each other and each one's choice is obvious. Karin, however, wants to come with Yuri, as she has very deep feelings for him. Yuri, however, has never gotten over the death of his love, Alice. He decides to go back in time, where they first met, to experience the entire trip again. Karin, who wants to come along with Yuri and has no other place to go, as her hometown was destroyed, is caught in a paradox, where she was sent prior to Yuri's birth. She ends up meeting Ben (Yuri's father), with a picture of her, Ben and Yuri. This is shown in both bad and good endings. The conflicting part here is that it is suggested that Karin is Yuri's mother, but because, originally, Yuri and Karin are the same age and Yuri went back in time, he would eventually meet Karin again. Considering Karin is Yuri's mother, though her name is Anna (which is hinted to be Anastasia's doing, by her giving Karin a Russian passport with the name Anna on it) it would be conflicting when the original Karin would be born, which would mean that there were 2 Karins in the timeline. It is, however, not shown what happens to the Karin of Yuri’s timeline, when he goes back in time.

• In the Webcomic Irregular Webcomic space theme, (1623-1651) the characters Iki Piki and Serron travel back in time to save themselves from having their organs stolen. They then forget how their future selves got them out of it the first time round since they "should have written it down". The author also discusses at length in the annotations the paradoxes this creates. ("Iki Piki is assuming that the fact that his and Serron's future selves clearly exist means that they must somehow get out of their current life-threatening predicament. He hasn't reckoned with their ability to screw things up."

• In the Terminator series, John Connor sends Kyle Reese back in time with a message. Kyle recites this message to Sarah Connor, who later teaches it to John. Furthermore, Kyle is John's father, and thus if Kyle had not been sent back in time, John would not have been born. In an ironic twist, had the Terminator not attacked the police station in an attempt to kill Sarah Connor, the likelihood is that Kyle Reese would have been in jail. This would have fulfilled the ultimate goal of the Terminator's mission, the prevention of John Connor's existence, though in the same way, it would have prevented its own existence in doing so. It is later crushed in a hydraulic press, and leftovers of its own technology are sampled by Cyberdyne to create the machines it would later be based on.

• In Terminator 2, it is discovered that it is because of the original Terminator's CPU being partially recovered that SkyNet became possible in the first place, which leads to the creation of the Terminators and the technology to travel through time.

• In the Planet of the Apes film series, after the planet is blown up by an atomic bomb in the future, two apes escape to our time, and their intelligent offspring are oppressed, causing an uprising that would set the course for the beginning of the planet of the apes in the first place.

• In the episode of Mucha Lucha "Woulda Coulda Hasbeena", Señor Hasbeena remembers that a bizarre flash of light ruined his entire luchador career. Using a time machine first to travel into the past, Rikochet, Buena Girl, and the Flea attempt to stop him from ruining the future, forcing him to use his signature move, the Funky DiscoBall. But when he uses the move, he causes the bizarre flash of light that ruins his career.

• In the second episode of the animated television series Time Warp Trio, the main protagonists Joe, Fred, and Sam travel to the year 2105. While there, they meet their own great-granddaughters Jodie, Freddi, and Samantha because the girls find a note in The Book which tells them to meet the boys under Roosevelt's statue in the park, a note which in the boys' era hasn't yet been written and put in The Book.

• In the online machinima comedy series Red vs. Blue, the character Church travels back in time to prevent his own death, and to avert the events and disasters that put the characters into their current situation. He ends up causing most of the problems and situations of the prior 48 episodes — including his own death — entirely by accident, and failing to prevent others' deaths, such as Tex's.

• Day of the Daleks, a serial of the BBC science fiction series Doctor Who, concerns freedom fighters from a future Earth that has been dominated by the Daleks. The freedom fighters travel back to the 20th century to assassinate the man history tells them was responsible for their predicament – the British ambassador who blew up a world peace conference and thus made the world susceptible to the Daleks. Due to the intervention of the Doctor and UNIT, one of their number eventually finds himself alone, injured and desperate to complete the mission, which he resolves to do with a bomb. The Doctor realises that the freedom fighters are caught in a paradox: the ambassador has always been innocent and they are responsible for the blowing up of the world leaders themselves, an event he is then able to prevent. It is implied: A) that the paradox would not be discernible/resolvable without the presence of a Time Lord such as the Doctor; and B) that the Daleks may have been the root cause of this disturbance in the web of time, since they have come back in time themselves to alter their own history and "invade Earth again" earlier and more successfully than they had originally.

• Blink, an episode of the BBC science fiction series Doctor Who, features a long and complex predestination paradox that centres around the character of Sally Sparrow and her contact with series protagonist the Doctor.

• The Parting of the Ways, an episode of the BBC science fiction series Doctor Who, also features a long and complex predestination paradox that connects the character of Rose Tyler and the Doctor with the words Bad Wolf.

• In the Philip K. Dick novel "Dr. Futurity", the main character is brought forward in time and is unsure why. He is sent to another planet to be sterilized (in accordance with the law of the time), but his ship crash lands on an unknown planet and the two pilots are killed. He wanders around the planet until he finds a stone tablet with instructions on how to pilot the ship. He takes the ship to a new destination to find the people who brought him forward through time. He learns that their intention was to save the leader of their clan. The other clan members went back in time several times previously in an attempt to save him, but he always wound up dead with an arrow in his chest. The main character then travels back with the clan members to observe the death. He eventually finds himself alone with the leader, who attempts to kill him. The main character kills the leader in self defense with an arrow. Subsequent events lead to the main character escaping back to his time and carving the ship's instructions onto the stone tablet, revealing that the planet he crashed on was Earth.

• In the video game Legacy of Kain: Soul Reaver, the main character, Raziel, was created as a vampire from a soul resurrected by his master, Kain. Later, when Kain betrays him, Raziel embarks on a quest for revenge, during which he finds out that in his previous life he was a human, and a member of the Sarafan (a group of humans bent on eradicating all vampires). In part 2, Raziel travels back in time and is attacked by a group of Sarafan, including his human self. Ultimately, the vampire Raziel ends up killing his human self, causing his own death, only to be later resurrected as a vampire by Kain.

• In Prince of Persia: Warrior Within, the Prince is stalked throughout the game by a mysterious wraith who at one point appears to attack him, just barely missing with the weapon he throws. The wraith is eventually killed by the Dahaka. Later, the Prince finds a mask that transforms him into the same wraith, and then uses the mask to occupy two places on the same timeline. He learns that the wraith (who he now understands to be his future self) was trying to protect him, rather than attack him. When he meets up with the Dahaka, however, the wraith-version of the Prince survives while the past version is now killed, creating a grandfather paradox as well. Also, in the Prince's main quest to prevent the Sands of Time from being created, he kills their creator, the Empress of Time, who then transforms into the Sands of Time, thus the Prince ends up causing the Sands' existence.

Prior to the use of time travel as a plot device, the self-fulfilling prophecy variant was more common.

• In the ancient Greek legend of Oedipus, it is prophesied that the baby Oedipus will one day kill his father and marry his mother. His father, Laius, attempts to circumvent the prophecy by abandoning the baby in the wilderness, where he is found by another King and Queen and raised as their son. Years later, Oedipus — unaware that he was adopted — learns of the prophecy and leaves home to avoid it. He kills a man and marries the widow, but does not learn until later that they are, in fact, his biological parents. The attempts to avoid fate result in the fulfillment of the prophecy.

• In the ancient Indian story of Krishna in the epic Mahabharata, Kamsa, afraid of a prophecy that predicts his death at the hands of his sister Devaki's son, has her cast into prison where he plans to kill all of her children at birth. After Kamsa kills Devaki's first six children, Krishna is born. As his life is in danger he is smuggled out to be raised by his foster parents Yasoda and Nanda in the Gokul village. As a young man, Krishna returns to his kingdom to overthrow his uncle, and Kamsa is eventually killed by his nephew, Krishna. It is Kamsa's attempts to prevent the prophecy that lead to its fulfillment.

• In The Time Machine (2002 movie) remake the Professor's girlfriend dies as a result of a robbery attempt after he proposes to her. To prevent this, he builds a time machine and travels in time to stop the robbery from taking place. Although he manages to stop the event from taking place in the timeline, it is immediately followed by another more unfortunate one, rendering his efforts meaningless. It is later revealed to him in the future by the UberMorlock that he cannot succeed in saving her, because if it was not for her death, he would not have created the machine in the first place.

• In the Philip K. Dick short story "The Minority Report", on which the Steven Spielberg film Minority Report (film) is based, murders are prevented through the efforts of three "precogs", psychic mutants who can see the crimes before they are committed. When police chief John Anderton is implicated in a murder-to-be, he sets out on a crusade to figure out why he would kill a man he has yet to meet. Many of the signposts on his journey to meet fate were predicted exactly as they occur, and his search leads him inexorably to the scene of the crime, where he cannot stop himself from killing the other man. In the end, the prediction itself is what had set the chain of events in motion.

• In the video game Sonic the Hedgehog (2006 game), Shadow the Hedgehog and Silver the Hedgehog go back in time to witness the failure of the Solaris Project. While there, they discover Mephiles the Dark must be sealed in order to be defeated. When he is sealed by Shadow, he is given Shadow's abilities, and influences Shadow and Silver to go back in time in the first place.

• In the TV show Star Trek: Voyager, episode “Time and Again”, the crew of the starship Voyager investigates a planet that has suffered a horrendous fate. A 'polaric energy' power supply the planet's natives had used supposedly caused a planet-wide purge of all life from a polaric energy detonation. When an away team beams down, they find subspace fractures on the surface which are gateways in time to the day before, when the planet's people were still alive. Captain Janeway and Tom Paris end up back in the past, prior to the disaster but in the present, another Voyager away team is on the surface trying to use a subspace fracture to get them back. The crew keeps attempting to use a 'polaric beam' to open a fracture wide enough for Janeway and Paris to get back through. In the past, at the source of the planet's polaric energy supply, Janeway realizes that it is her crew's attempt from the future to rescue her and Tom Paris that is going to cause the disaster with the polaric energy. Janeway uses her weapon to close the rift, at which point the timeline is destroyed and the story appears to begin again. No such detonation is detected however, and in place of a devastated planet, a pre-warp civilization is discovered. No one except for Kes is aware of the events which took place in the alternate timeline.

• In Fallout 2, the character is able to get a random encounter where he can step into a portal. The portal takes him back in time to Vault 13, where his ancestor lived before being exiled. The player's actions cause the vault's water chip to malfunction, leading directly to the events of the first game which result in the player's current existence.

• In the television episode The Simpsons Treehouse of Horror XV, in the segment entitled "The Ned Zone", an old man falls into Ned's hands (literally). He receives a premonition of the man being consumed by alligators. Ned is so scared he drops the man into an open manhole, where the man is consumed by alligators.

• Newcomb's paradox
• Ontological paradox
• Time travel in fiction
• Grandfather paradox
• Self-fulfilling prophecy
• Causality
• Time
• Time loop
• The chicken or the egg