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A predestination paradox (also called causal loop, causality loop, and, less frequently, closed loop or closed time loop) is a paradox of time travel that is often used as a convention in science fiction. A temporal causality loop is a scenario in which some earlier event #1 is the cause of (or at least one of the causes of) some later event #2, and through time travel, event #2 is also the cause of event #1. The paradox occurs when a time traveler is caught in a loop of events that "predestines" or "predates" him or her to travel back in time. In this case, event #2 would be the event of the time traveler going back in time, and #1 would be something that time traveler did in the past that in turn influenced him or her to travel back in time. The paradox suggests that those people who travel back in time would have no way of changing a situation. One example would be a person who travels back in time to save a loved one from being hit by a car, then once in the past the person uses a car to try to reach the scene of the accident before it happened, and accidentally hits the very person they had come back to save, causing the death that had inspired their future self to travel back in time.
This theory is closely related to the ontological paradox in that something, in this case the reason for the trip in time, has no independent origin. The paradox does not necessarily imply a higher plan from some higher power. It merely affirms a belief that time is immutable. The series of events can still simply be from causality rather than from some form of higher plan, such as: Event A. Mad Scientist meets Delusional Madman mumbling about time travel mechanics; Event B. Mad Scientist devotes his life to proving time travel, ignoring his wife and kids who leave him; Event C. Mad Scientist decides to travel back in time to prevent this; Event D. Time travel turns Mad Scientist into Delusional Madman. Predestined in the sense that causality is immutable, not there was necessarily a plan involved.
Because of the possibility of influencing the past while time traveling, one way of explaining why history does not change is by saying that whatever has happened must happen. This means either that time travelers' attempts to alter the past in this model, intentionally or not, would only fulfill their role in creating history as we know it and not change it or that time-travelers' personal knowledge of history already includes their future travels in their own experience of the past (for the Novikov self-consistency principle).
In other words: time travelers are in the past, which requires that they were in the past before. Therefore, their presence is vital to the future, and they do something that causes the future to occur in the same way that they remember. It is very closely related to the ontological paradox and usually occurs at the same time.
Temporal causality loop
A temporal causality loop is a hypothetical event whereby a specific moment in time repeats itself continually inside an independent fragment of time. A temporal causality loop is a disruption of the space-time continuum in which a localized fragment of time is repeated, ad infinitum. In other words, a temporal causality loop is a theoretical phenomenon which occurs when a chain of cause-effect events is circular. For instance, if event A causes event B, and event B causes event C, and event C causes event A, then these events are said to be in a causality loop. Since the temporal causality loop is separated from ordinary space-time, time continues in a normal manner for those isolated from the anomalous event while those inside the anomalous event replay the same fragment of time on repeat. A temporal causality loop not only implies that the same events can be repeated identically and eternally, but also suggests that minor alterations can happen - and even multiply as the cycle progresses.
Examples and variations
A variation on the predestination paradoxes which involves information, rather than objects, traveling through time is similar to the self-fulfilling prophecy. For example, 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 these 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.
One example of a predestination paradox that is not simultaneously an ontological paradox is the following. In 1850, Bob's horse was spooked by something, and almost took Bob over a cliff, had it not been for a strange man stopping the horse. This strange man was later honored by having a statue of him erected. Two hundred years later, John goes back in time to sight-see, and sees someone's horse about to go over a cliff. He rushes to his aid and saves his life.
Another example was in the film Harry Potter and the Prisoner of Azkaban when Harry sees a figure save him and Sirius, believing the person to be his dead father until he and Hermione time travel and Harry realizes it was he himself who saved them.
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.
Examples from literature and fiction
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 and marry his wife. Fearing the prophecy, Laius pierces newborn 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 a wealthy man leading to a fight in which Oedipus slays him. Unbeknownst to Oedipus the man is Laius. Oedipus then defeats the Sphinx by solving a mysterious riddle to become king. He marries the widow queen Jocasta not knowing she is his mother.
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. Examples include Robert Heinlein's "—All You Zombies—", in which a young man is taken back in time and tricked into impregnating his younger, female self before he underwent a sex change, or The Man Who Folded Himself, a 1973 science fiction novel by David Gerrold that includes a series of similar paradoxes.
Prior to the use of time travel as a plot device, the self-fulfilling prophecy variant was more common. Shakespeare's Macbeth is a classic example of this. The movie Minority Report, imagined a world where prophecies were so reliable that they could be routinely used by police forces to eliminate crime.
In the Harry Potter Universe, a prophecy by Sybill Trelawney is partly overheard by Snape about the birth of a wizard, with the power to vanquish Voldemort. Snape then informs Voldemort about it. Aware of the prophecy, and assuming the baby to be Harry, he attacks the Potters, killing Harry's parents, but failing to kill newborn Harry, as his attack backfires, leaving him severely weakened and setting up the scenario in which Harry vanquishes him 18 years later.
The first Terminator movie relies on the predestination paradox. In the first movie, the cyborg T-800, sent back in time to assassinate the mother of Skynet's opponent, is destroyed, but its parts are salvaged, creating a timeline where the creation of a T-800 is possible. Additionally, in order to stop Skynet's assassination plan, Kyle Reese follows the T-800 back in time and winds up fathering the very opponent Skynet was trying to eliminate.
In Star Trek: The Next Generation episode "Cause and Effect", the destruction of the Enterprise near a distortion in the space-time continuum causes a temporal causality loop to form, trapping the ship and crew in time and forcing them to relive the events that led to their deaths.