Predestination paradox
A predestination paradox, also called a causal loop or causality 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 of the traveller killing his own grandfather before his parent is born, thereby precluding his own travel to the past by cancelling 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, not changing it. The Novikov self-consistency principle proposes that contradictory causal loops cannot form, but that consistent ones can.
Examples
A typical example of a predestination paradox is as follows:
A person travels back in time to discover the cause of a famous fire. While in the building where the fire started, he or she accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him or her, years later, to travel back in time.
Another example:
A man travels back in time and impregnates his great-great-grandmother. She would thus give birth to one of the man's great-grandparents, who would then give birth to his grandmother or grandfather, 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.
A variation on the predestination paradox which involves information, rather than objects, travelling 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 all three 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 travelled back in time but for the fire that he or she caused by travelling back in time. Similarly, in the third example, the man would not have overexerted himself but for the future information he receives. In the second example, the man's very existence would be pre-determined by his time traveling adventure. This also raises the paradox of which came first — the time travel or his existence (see below).
In most examples of the predestination paradox, the person travels back in time and ends up fulfilling his or her role in an event that has already occurred. In a self-fulfilling prophecy, the person is fulfilling his or her 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.
Fictional examples
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.
Prior to the use of time travel as a plot device, the self-fulfilling prophecy variant was more common, with one of the earliest and most famous examples being the ancient Greek legend of Oedipus. There, Laius's attempt to circumvent the prophecy that his son Oedipus would one day kill him by abandoning the babe as well as Oedipus's leaving home to avoid the prophecy that he would one day kill his father and marry his mother (unaware of his adopted status), would result in the fulfilment of both prophecies.
Literature
In Harry Potter and the Prisoner of Azkaban, Harry and Hermione travel back in time three hours to save Harry's godfather, Sirius Black, an innocent man about to be executed. Earlier, Harry saw someone he believed to be his father casting a Patronus spell saving him. Although hoping to see his father during this time journey, he discovers instead that it was himself that cast the Patronus. The film version of the book adds more examples, revealing that some stones that were mysteriously thrown into Hagrid's hut earlier were actually hurled by Hermione's future-self to warn them that Cornelius Fudge and company were arriving.
In Michael Crichton's Timeline, several graduate students who are excavating several medieval castles and towns from 14th century France are given the opportunity to travel back in time to the very place and time period they are studying. On a mission to rescue their Professor, who had left his time machine and gotten lost, the students end up causing some of the historical events they had studied.
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.
In the film Kate and Leopold, Kate McKay (Meg Ryan) lives in the present day (2001) and falls in love with a time traveller from 1876, Leopold (Hugh Jackman). After Leopold returns to his time, Kate also travels to 1876 to marry Leopold and consequently becomes the great-great-great-grandmother of her ex-boyfriend, Stuart (Liev Schreiber).
Back to the Future deals with a variant of the paradox. In it, Marty McFly (played by Michael J. Fox), travels back from the year 1985 to 1955. In doing so, he inadvertently 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 accommodate the paradox caused by Marty rather than the paradox being part of history to prompt the time travel, but the end result is the same. On the other hand, while in 1955, Marty discovers that he is the one who inspired Goldie Wilson, his town's African American mayor in 1985, to run for office by accidentally informing Wilson of his future in 1955. Also, by playing "Johnny B. Goode" at the 1955 high school dance, Marty becomes responsible for Chuck Berry's rock and roll composing the very song that Marty would learn to play. His friendship with his future parents led his mother-to-be into thinking that Marty is a nice name, which means that Marty inspired his own naming. The two sequels to the movie deal with similar variations of the paradox.
In Bill and Ted's Excellent Adventure, the jail break that allows Bill, Ted and the "dudes from the past" to escape relies on a series of booby traps that they have to remember to place in the future. There are similar scenes relying on predestination paradoxes throughout the film.
In Twelve Monkeys, James Cole (Bruce Willis) is the main protagonist who claims he traveled from the future to the present time to investigate the cause of an apocalyptic event that occurs in the near future. He apparently has bouts of memory loss and schizophrenic confusion and has recurring flashbacks of a man getting shot at an airport, an event which supposedly happened when he was a boy. At the end of the movie, the man who was shot turns out to be Cole himself. Although this event is not part of the main storyline, it lends credence to it because it suggests that Cole was not delusional after all and that the apocalyptic event is destined to occur. 12 Monkeys was inspired by the French film La Jetée, which featured the same paradox.
In The Butterfly Effect, when his teacher asks him to draw what he wants to be when he grows up, seven-year-old Evan Treborn (Logan Lerman) draws a murderer standing over two corpses with a bloody knife. He quickly "blacks out" the memory of having drawn the picture and never sees the drawing afterwards. In response to the picture, Evan's mother takes him to a doctor, who suggests he write about the incident in a journal. As an adult, Evan (Ashton Kutcher) uses the journal to return to the past and draw the picture. Also, seven-year-old Evan visits his father Jason in a psychiatric hospital and "blacks out" the few minutes that lead Jason to attack Evan until a guard accidentally deals a lethal blow to Jason's head. Later, in order to speak to his dead father, Evan uses his journals to relive the visit, during which he provokes the attack.
In a science fictional example of the self-fulfilling prophecy, in Star Wars Episode III: Revenge of the Sith Anakin Skywalker sees a premonition of his wife Padmé's death during childbirth. This incites him to try to keep her alive, which eventually results in him seeking the Dark Side. This in turn causes Padmé to lose her will to live, and she dies in childbirth as was foreseen.
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.
In "Roswell That Ends Well", an episode of Futurama, Philip J. Fry travels back in time and meets his future grandfather Enos and future grandmother Mildred. Fry accidentally gets Enos killed, and is shocked to discover that he continues to exist. He therefore is satisfied that Mildred is not his grandmother and has sex with her, only to have Professor Farnsworth point out later that Mildred is his grandmother, and therefore Fry has become his own grandfather.
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 he will clean up the timeline. How this is to be done, however, or whether the events of the episode will continue to exist if he does so, is never explained. Here, the paradox was called the Pogo paradox (after the phrase "We have met the enemy and he is us" from the Pogo comic strip).
In the Star Trek: The Next Generation episode "Captain's Holiday", Jean-Luc Picard is contacted by two Vorgons from 300 years in the future. They claim that he is destined to find a powerful weapon that was stolen and hidden in the past, the Tox Uthat. Compelled by this prophecy, Picard finds it, but on discovering that the Vorgons were the ones who stole it in the first place, chooses to destroy it instead. The Vorgons then admit that this was what history had actually recorded and their attempts to change it for their own gain failed.
In the movie Star Trek: First Contact, a Borg ship travels to to 2063 from the 24th century to prevent humans from making contact with aliens. The USS Enterprise follows the Borg into the past and destroys the ship. However, debris and some Borg survivors land in the Arctic where they go into suspended animation. Accidentally revived several decades later in the Star Trek: Enterprise episode "Regeneration", these Borg escape Earth and send a message to the Borg Collective of that period. It is implied that this signal may be why the Borg decided to invade the Alpha Quadrant in the 24th century.
In the Stargate SG-1 episode "1969", a wormhole transports the SG-1 team to 1969, 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 the 1973 Doctor Who serial 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 2005 episode The Parting of the Ways, the Doctor's companion, Rose Tyler, absorbs the energy of the spacetime vortex to save the Earth from the Daleks. She also uses the power to scatter the phrase "Bad Wolf" throughout history as clues, to lead her past self to the position where she will absorb the energy of the vortex to save the world.
In The Flipside of Dominick Hide, Dominick Hide is a time traveller assigned to learn about 20th century transport systems. Learning that his great-grandfather lived in the time and place he is studying (London in 1980), he breaks the rules of his job in order to track down his relative. Though he does not find him, he does have an affair with a woman which leads to her giving birth to a son, Dominick's grandfather. Thus the great-grandfather Dominick was searching for was in fact himself. It is eventually revealed that Hide's superior knew about the loop and deliberately allowed Hide to break the rules in order to fulfill it.
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. In another episode, Goliath is accused by two Gargoyles he had never met of being responsible of the disappearance of a third Gargoyle, Griff, during the Battle of Britain. In an attempt to discover the truth about the incident, he goes back in time, meets the Gargoyles, and ultimately becomes responsible for the disappearance when he's forced to take Griff back to 1994 with him.
In the Red Dwarf episode "Ouroboros" Lister encounters an alternate reality where Kochanski survived instead of him, after adding his contribution to an in-vitro tube he finds a supplies case labeled ouroboros (which was also written on the cardboard box he was abandoned in). He then realises that he is his own father, and when the child is 9 months old he goes back in time and places the child where he was left.
In the Twilight Zone episode "No Time Like the Past", the main character uses a time machine to go back in time to alter past events. After failing to warn a Hiroshima police captain about the atomic bomb, assassinate Adolf Hitler, and change the course of the Lusitania to avoid being torpedoed, he accepts that the past cannot be changed. He then uses the time machine to return to the town of Homeville in the year 1881. After reading in a history book that Homeville's schoolhouse will burn down because of a kerosene lantern thrown from a runaway wagon, he spots the wagon and attempts to prevent the fire, but instead causes the fire he intended to prevent.
In Babylon 5, it is established that the titular station's predecessor Babylon 4 vanished several years before. When it mysteriously reappears in the series' first season (taking place in 2258), it appears to have been dragged through time. The crew of Babylon 5 manage to evacuate those on Babylon 4 before it vanishes again ("Babylon Squared"). Two years later, led by a letter left in the distant past by a Minbari prophet named Valen, the crew of Babylon 5 realised that it was they who "stole" Babylon 4 in the first place to serve as a base of operations for a war a thousand years in the past ("War Without End"). They then travel back in time to accomplish this before Babylon 4 can be destroyed by their enemies, trying to avoid their earlier selves when the station gets shunted to 2258. The former Babylon 5 commander, Jeffrey Sinclair, stays behind and takes Babylon 4 back to 1260, where it fulfils its place in Minbari history. Sinclair is also transformed during the journey into a Minbari, and introduces himself to those he meets in the past as Valen, eventually leaving the prophecies that will guide his future friends and self full circle.
In an episode of The Powerpuff Girls, the professor informs the girls that he had a fleeting glimpse of something one day when he was a child, and then devoted his life to science trying to find what it was. The girls' nemesis, Mojo Jojo, learned of this, and travelled back in time to prevent this inspiration, and thus prevent the girls' creation. The girls followed him to the past, and the events led to the girls hovering over the young professor as he was regaining consciousness, becoming the glimpse that inspired him to create them.
In an episode of Darkwing Duck, Darkwing and the others are called to a lab where a scientist has discovered what appears to be Darkwing fossilized in amber. They travel to the past to investigate, only to eventually cause Darkwing to fall in some sap and get preserved in amber. The others then return to the moment they left the present and remove Darkwing from the amber.
In one of Ranger Gord's nature cartoons in The Red Green Show, Gord wants to save a burned forest, and says he will be building a time machine in the future and will bring it back to the present, which happens. Present-Gord and Future-Gord travel to the past and meet Past-Gord. The three stop what they believe causes the fire, and go back to the future to celebrate. Except when they warp, they create a spark that sets the forest ablaze.
Video games
In the first-person shooter TimeSplitters: Future Perfect, the player character Sgt. Cortez often meets a near-future version of himself who helps him progress with the game. Later on the player must perform that exact role to help his past self.
In the Legacy of Kain series, the character Raziel is born a human and lives the life of a religious zealot that, along with his Sarafan brethren, eventually meets his end at the hands of a demonic abomination. Raziel is resurrected as a vampire by Kain, who later sentences him to burn in the Abyss. Rising again, and following a quest for vengeance against Kain that covers the five games and time travel, Raziel discovers that it was he who killed himself and the other Sarafan, and that Kain had sentenced him to the Abyss to fuel the chase through time that would bring Raziel full circle for a larger purpose.
In Clive Barker's Undying, the character Patrick Galloway discovers a journal that mentions a powerful mystical weapon, the Scythe of the Celt, which was stolen from a now-ruined monastery hundreds of years in the past, and describes a means of travelling in time via a magical portal. The journal writer intended to use the portal to take the Scythe before it was stolen but was mortally injured before he could do so. Using clues in the journal, Galloway travels back to a time when the monastery was intact and populated and steals the Scythe, becoming the very thief mentioned in the journal. The theft of the Scythe also releases energy that causes the destruction of the monastery whose ruins Galloway finds in the present day.
In Shadow of Memories, the predestination paradox and many other time travel concepts are explored as the protagonist is murdered by a mystery assailant and he is empowered to prevent his own demise via time travel.
In The Prince of Persia (Ubisoft), "The Sands of Time" and "Warrior Within", the Prince is able to manipulate time, and the effects and/or causes of time travel are explored (with a light air in Sands of Time, and with a more far-reaching philosophical logic in Warrior Within) and the very nature of casuality is questioned. However, all manipulations seamlessly integrate themselves into the timeline, such that when one is sure that one has just cheated fate (the main theme in Warrior Within), one finds oneself merely fulfilling one's own destiny. Also seen is a self-fulfilling prophecy by the "Empress of Time" that predicts that the Empress will die at the Prince's hand, prompting the Empress to decide to engage the Prince in battle to try and prevent her own death by killing the Prince first. She underestimates the Prince and is killed, and the same event releases the "Sands of Time" that start the Prince's ordeal in the first place.
In Legend of Zelda: Ocarina of Time, the main character Link, who is the destined "Hero of Time," goes back and forth between a seven-year time period to save Hyrule from the evil Ganondorf. There are various points in the game where Link must fight both in the times when he was a child and a teenager in the same place for the same goal.
In Final Fantasy VIII, the main character, Squall, ends up in the past for a short time in front of the orphanage he grew up in. By speaking to the caretakers for one moment about his origins, he ensures the creation of Garden and his appointment as commander of the SeeD forces.
In the PC game Escape From Monkey Island, the player character Guybrush Threepwood travels through a special time-travel-inducing swamp. There, he meets his future self, who hands him three items and speaks certain phrases to him. The object of this part of the game is to ensure the proper conversation and item-exchanging occur in the same order both when the player is controlling past-Guybrush, and later when the player controls future-Guybrush. Otherwise, a time storm erupts. The three items, of course, are trapped in an endless loop of changing-hands.
Machinima
In the machinima comedy web series Red vs Blue: The Blood Gulch Chronicles, the character Church and the robotic body his ghost is possessing are thrown nearly two thousand years into the past by a massive explosion. After travelling forward again, but to his recent past, he attempts to prevent the events of the previous series, primarily the deaths of himself and his on-again-off-again girlfriend Tex. Most of his efforts backfire, and he not only is unable to prevent Tex's death, but also becomes responsible for practically every event that occured during the series (including his travel through time as well).
Ontological paradox
A very closely related paradox, usually occurring at the same time as a predestination paradox, is the ontological paradox:
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.
Another example, involving more than one person:
A professor travels forward in time, and reads in a physics journal about a new equation that was recently derived. He travels back to his own time, and relates it to one of his students who writes it up, and the article is published the same journal which the professor reads in the future.
The paradox raises the ontological questions of where, when and by whom the schematics were created or the equation derived. 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."
Robert Heinlein's stories By His Bootstraps and "—All You Zombies—" also play with the ontological paradox, (indeed, the ontological paradox is sometimes called the "bootstrap paradox" in that story's honor) as do David Gerrold's more complex The Man Who Folded Himself and 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.)
In By His Bootstraps, the protagonist is asked to go through a time portal by a mysterious stranger, a second stranger tries to stop him, and all three get into a fight which results in the protagonist being pushed through anyway. Ultimately, it is revealed that all three are the same person: the first visitor being his future self and the second an even older future self trying to prevent the loop from occurring. The onotological paradox here is in where and how the loop started in the first place. "—All You Zombies—" involves an even more convoluted time loop involving kidnapping, seduction, child abandoment and gender reassignment surgery, resulting in the protagonist creating the circumstances where he becomes his own mother and father.
Another example is the antique pair of eyeglasses Admiral Kirk receives from Doctor McCoy in the 23rd Century in Star Trek II: The Wrath of Khan, which Kirk leaves in the 20th Century in Star Trek IV: The Voyage Home, implying that they would be a gift again. Although presumably 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.
A similar paradox (and unexplained problem) occurs in the film Somewhere in Time, when an elderly Elise McKenna gives Richard Collier a pocket watch which he then takes in time to hand it to her younger self, who will then, decades later, return it to him.
Also in Star Trek IV, Scotty and McCoy also trade the formula for transparent aluminum to an engineer for materials needed to build a whale tank. Scotty eases McCoy's concerns about changing history by asking, "How do we know he didn't invent the thing?" In neither case presented in the movie is there actual evidence seen of the loop, however; the characters merely assume it (see also transparent alumina). It is possible, of course, that no such causal loops are formed: the eyeglasses may not be destined to be the exact same pair McCoy gifts to Kirk, and the engineer might fail in his attempt to invent transparent aluminum. It is worth noting, however, that in the novelization of the film, Scotty recognizes the engineer's name as that of the inventor.
In The Terminator, Kyle Reese, having traveled forty-five years into the past, gives Sarah Connor a message from his commander (and, unbeknownst to him, son) John Connor. In Terminator 2: Judgment Day, John says that his mother made him memorize the message — which, ironically, says that the future can be changed — in order to give it to his father, so that his father might then pass it on to her. At no point do we learn when or how the message was originally composed. In addition, Kyle shows Sarah how to fight Terminators. Sarah teaches the same to John, who trains Kyle in the future.
In the 2002 Doctor Who webcast Real Time, Dr. Reese Goddard, a Cyberman from an alternate 1927 where the Earth had been infected by a virus that turned people into Cybermen, came to the planet Chronos to stop the Doctor from giving the Cybermen the virus in the first place. Goddard brought a modified version of the virus deadly to Cybermen, which the Cybercontroller captured and reverse engineered to create the virus which infected Earth. It also transpired that the Cybercontroller infected the Doctor's companion Evelyn Smythe with the virus, so that when she travelled into the past she would begin the infection and eventually become the Cybercontroller herself.
In Bill and Ted's Excellent Adventure, future Bill and Ted introduce their past selves to Rufus. He never actually tells them his name.
In a section of The Legend of Zelda: Ocarina of Time, the player character, Link, enters a windmill where he meets an organ grinder who tells him that seven years ago, a child came to the windmill and played a song, causing the windmill to go out of control (and opening a gameplay area). He teaches Link the Song of Storms, after which Link goes back in time and becomes his younger self, who goes to the windmill and plays the song, causing the effects and planting the melody in the organ grinder's mind.
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.
In a storyline in the daily comic strip Calvin and Hobbes, Calvin attempted to create an ontological paradox by travelling two hours into the future to retrieve a story he had to write for homework and did not want to do. He reasoned that by that time it would be done and he could then bring it back to the past and spend the time goofing off instead of working. Of course, the future Calvin didn't have the homework either, having decided two hours previously to time-travel instead of doing it. Calvin eventually ended up fighting with two of his future selves, while Hobbes and his future self wrote a story based on the whole predicament. The story (which was about Hobbes saving the day) received an A+.
In the anime series Generator Gawl, the genetic code that led to the creation of the generators is taken from Gawl, a generator who had traveled back in time to change the past.
In the Red Dwarf episode "Stasis Leak", Rimmer encounters the future holographic version of himself who tells him that the future crew had traveled back in time through a stasis leak found on one of the lower levels of the ship. He writes this in his diary. In the future, Lister reads Rimmer's diary and looks for the leak, which the crew finds and uses to travel back in time, where future Rimmer tells past Rimmer about the leak. The paradox not only involves the knowledge of the leak, but also the fact that the phenomenon itself is called a "stasis leak".