Temporal paradox
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A temporal paradox is a paradoxical situation in which a time traveler causes, through actions in the past, the exclusion of the possibility of the time travel that allowed those actions to be taken.
The typical example is that of the grandfather paradox, wherein a time traveler goes back in time and kills his grandfather before his father is conceived. It is a paradox because if this occurs, he will never be born, and therefore never be able to travel back in time to kill his grandfather, thus allowing himself to be born. This example is one type of causality loop.
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[edit] Theories
Currently, temporal paradoxes are the domain of science fiction and philosophy. Various schools of thought exist as to what would happen in the grandfather paradox were a time travel device ever invented.
[edit] Timeline protection hypothesis
The timeline protection hypothesis posits that a time traveller would be incapable of causing a paradox, as the natural continuity of the timeline would cause any such interaction to fail. For example, he would appear in the wrong place (or fail to go anywhere at all), various twists of fate would conspire to impede him, or his actions would instead be responsible for the history he remembers.
A similar theory states that time travel may in fact be a factor in making the universe the way it is today; actions of time travelers are responsible for the present situation. Alternatively, any time traveller would take the utmost care in avoiding such paradoxes, inspired by the fear of the damage they could cause.
The animated television series Futurama shows a more lighthearted side of the paradox. In the episode "Roswell That Ends Well", the main character, Phillip J. Fry, travels back in time with his friends to 1947 in Roswell, New Mexico. Remembering that his grandfather works at the base, and told that killing the man would nullify his own existence, Fry becomes obsessed with protecting him. Fry's efforts prove counterproductive: he locks the man in a shack to protect him, failing to realize that an atomic bomb is being tested on the grounds. When he doesn't disappear, he assumes that the man could not have been his grandfather (the man indicates himself to be a homosexual numerous times anyway), and thus proceeds to sleep with and impregnate his grandmother, thereby becoming his own grandfather.
1972 "Doctor Who" adventure Day of the Daleks. Sir Reginald Styles is targeted by 22nd Century guerrillas, who believe he's behind the deaths of VIP delegates. Due to their deaths, the Daleks were able to take over Earth in their time. In truth, a fellow guerrilla who was left behind was to blame, which was the true cause of their timeline ensuing.
[edit] Timeline corruption hypothesis
Another idea is that any change in the timeline, even without personal interaction, while allowable, would cause a "butterfly effect" in the timeline. All history after the time the traveler visited would be affected by minute changes the traveler had made in the past, and the history, depending on how severe the time traveller's actions were, would sooner or later be completely changed. This has been coined the "timeline corruption hypothesis." The 2004 film The Butterfly Effect and the Multiverser RPG system prefer this view. See also the Ray Bradbury science fiction short story "A Sound of Thunder", in which the butterfly effect is caused by a real butterfly.
The most well-known example of this theory is the 1985 film Back to the Future, in which the protagonist Marty McFly goes back in time and interferes with his parents' first romantic encounter, thus erasing his own existence (as well as that of his family). However, the effect only happens gradually, exemplified by a family photo in his possession: each of his siblings begins to disappear limb by limb, starting with the oldest and working down to him (Marty is the youngest of the three). This allows Marty to correct the error and restore the timeline, albeit with a few minor changes due to his interference.
[edit] Temporal merging hypothesis
This is the opposite of the multiple universes hypothesis, in that each action done in time travel actually overlaps one reality with another. For instance, if a time traveller was to meet their double from another time, the double would merge to the time traveler, making the traveler a part of the time they are in. A similar thing would happen with events, merging the two events into the nearest event which does not produce a paradox (a dead grandfather in one universe but not in another would either create a dead grandfather in both universes, but alter the person's heritage so as to allow this, merge both timelines so that the person would fade from all timelines upon return, or produce a mean between life and death such as a coma).
An example of this is shown in The One, when a person travels in time or dimensions, destroying copies of himself to cause them to merge, so as to gain power.
[edit] Multiple universes hypothesis
Another hypothesis is that there are an infinite number of universes, one for each possibility. Here, should the time traveller kill his grandfather, one universe would have a live grandfather, and another universe would have a dead one. Failing that, the universe would annihilate itself, for such a paradox would defy its laws.
Another theory concerning the classic grandfather paradox is that such an event would create a new universe, one in which the aforementioned deed was committed. This would not affect the committer's universe, nor the committer himself.
[edit] Set timeline hypothesis
The set timeline hypothesis defines the timeline as preset, preventing any interference in events: for example, the invention of time travel and the subsequent abuse of it would ultimately fail, because the time traveler has no choice but to establish history as it has been written, on the grounds of all life is set indefinitely.
This theory is similar to the timeline protection hypothesis, in that a time traveler can in no way cause a paradox without either resolving it or failing. The above-mentioned Futurama episode would fit into this: Fry, despite his efforts, does exactly what he was supposed to do in the timeline.
[edit] Choice timeline hypothesis
In the choice timeline hypothesis, history changes the instant the time traveler decides to travel back in time, thereby rendering his actions in that regard pre-destined.
Bill & Ted's Excellent Adventure, as well as its sequel and animated adaptation, feature numerous uses of this hypothesis. Bill and Ted, constantly realizing that their plans are foiled by the lack of a certain item, decide to later travel back in time and deliver themselves the necessary item, often indicating a specific place in which the item will appear. Upon searching the location, the item is invariably there. This is used to somewhat ridiculous proportions in the second film, where the characters quite literally make objects appear out of thin air with this method.
[edit] Can-Not Because Has-Not theory
This theory states that the present is not the forefront of time, and so we are our future selves' past. Thus, if sometime in the future a time travel device were created, someone from the future would have already brought it back to us. thus establishing itself as "already" existing in our time as a result - and likely copied and recopied. Since our present selves are still wondering about time travel, this theory states that we will never be able to build a time machine, because if we are still wondering, then no one from the future has built a time machine and brought it back with them to us, and if no one in the future has built a time machine, then we in the future will not build a time machine, and no one can ever build a time machine because no one in the future has built one. This theory, however, creates a Causality Loop.
[edit] Temporal Disinterest Hypothesis
This hypothesis states that if someone builds a time machine for a specific purpose, and fulfills this purpose by means of time travel into the past, the resulting being (the maker of the time machine) would be satisfied and not have a reason to create a time machine, thus causing yet another paradox.
