Temporal paradox
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Temporal paradox (also known as time paradox and time travel paradox) is a theoretical paradoxical situation that happens because of time travel. A time traveler goes to the past, and does something that would prevent him from time travel in the first place. If he does not go back in time, he does not do anything that would prevent his traveling to the past, so time travel would be possible for him. However, if he goes back in time and does something that would prevent the time travel, he will not go back in time. Thus each possibility seems to imply its own negation - a type of logical paradox.
A typical example of this kind is the grandfather paradox, where in a person goes back in time to terminate his grandfather before he had any biological descendant. If he succeeds, one of his parents would never exist and he himself would never exist either. This would make it impossible for him to go back in time in the first place, making him unable to kill his grandfather, who would continue to produce offspring and restart the situation. But if he fails, his grandfather would be alive and produce offspring, one of whom would eventually conceive the time traveler and the whole scenario would start over.
Solution
Temporal paradox has been used to argue that (backwards) time travel must be impossible, because it is capable of resulting in a paradox. Kip S Thorne, however, said that none of the supposed paradoxes formulated in time travel stories can actually be formulated at a precise physical level: that is, any situation in a time travel story turns out to permit many consistent solutions.
Time line protection hypothesis
This theory states that a time traveler, no matter what he had done, would not be able to create a time paradox. A person traveling back in time to terminate his grandfather, could have appeared in a wrong place, or had his gun jammed, thereby allowing his grandfather to have descendants. The natural law would prevent the traveler to alter the time travel he had done in the first place.
The animated television series Futurama shows a more lighthearted side of the paradox. In the episode "Roswell That Ends Well", the main character, Philip 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 does not disappear, he assumes that the man could not have been his grandfather and thus proceeds (unknowingly) to sleep with and (accidentally) impregnate a beautiful woman, who apparently is the younger version of his grandmother, thereby becoming his own grandfather.
In the 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. Because of those deaths, the Daleks were able to take over Earth in their time. However, a fellow guerrilla who was left behind was to blame, which was the true cause of their timeline ensuing.
In the game "Ratchet and Clank Future: A Crack in Time", Alister Azimuth tries to fix his mistake of causing the fall of the Lombaxes, but if he was successful in traveling to the past, time would rip itself apart and the universe would collapse on itself.
In the machinima series Red vs. Blue, Church is sent back in time via the combined energy of a bomb and a weather machine. He attempts to fix past events, as well as preventing the explosion, but his attempts are ultimately responsible for most of the events that took place beforehand in the series, including his own death.
In the Japanese manga Doraemon, the future grandson of the lead character—Nobita—comes back in time to meet his grandfather in his primary school days intentionally to change the life he is in. Nobita questions the existence of his grandson that if he did marry the girl he likes (instead of the one he dislikes but conceived the father of his future grandson), what would happen to his grandson. His grandson, along with Doraemon, replies that there are multiple paths leading to the same future, and they will still exist even if Nobita married another girl. The plot never explicitly told of when the history was altered, but later events in the plot did show a future where Nobita married the girl he likes and lived a better, wealthier life and yet, future characters showed no signs of remembering the original history. However, when being asked of Doraemon's reason of being in the past, he replies that his role is to make sure Nobita marries the girl he likes, which mentally still reserves logic.
In the television series Lost, Jack and Locke enter an underground research facility on the island in 2004, and watch an orientation film made by the mysterious DHARMA Initiative organisation in 1980. The film makes reference to an "incident" having occurred on the island at some point in the 1970s, necessitating the construction of the underground bunker, as a method of containing a limitless amount of electromagnetic energy, and preventing a global catastrophe. In the show's fifth season, some of the main characters begin moving erratically through time, before eventually becoming stuck in 1974. Three years later, these same characters unwittingly become the cause of the incident.
Novikov self-consistency principle
This theory says that anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency. In layman's terms, this is often called determinism. Succinctly, this explanation states that if time travel is possible, then actions are determined by history. Therefore, logically, it would be impossible to change the history. This theory, however, is capable of causing bootstrap paradox.
Multiple universes hypothesis
This theory states that there are infinite number of universes, all-together known as multiverse. If a person is about to travel back in time, he will end up in a parallel universe. So if he kills "his" grandfather, a paradox would not occur because the grandfather that he had killed is the grandfather who lives in the universe he currently is in.
An example of this occurs in the Japanese anime series Dragonball Z in which Trunks, the son of Vegeta and Bulma, comes from the future. In the present, Trunks was not even born. He warns of the arrival of androids which are more powerful than even Goku and Vegeta, and forewarns the death of Goku in his past. However, by giving the medicine which can cure Goku and undertaking extensive training, Trunks and the Z Fighters manage to defeat the androids as well as Cell. When Trunks returns to his present, though, his universe is still the same with Goku and other Z-fighters still dead, the only difference being that at that point of time, Trunks, because of his training with the Z-fighters, had become strong enough to defeat the androids and Cell of his own time. According to fan speculation, this is because Goku must have died somewhere in the time difference between present and future.
Branching universe hypothesis
This theory says that a backwards time travel would make the universe branching.
An example of this occurs in The Legend of Zelda. Toward the middle of The Legend of Zelda: Ocarina of Time, the protagonist, Link, is sealed in slumber for seven years. When he awakens, he finds the world in a ruined state. At the end of the game, the antagonist, Ganon, is defeated and sealed within the Sacred Realm. Princess Zelda, then, sends Link into the past to right the wrongs Ganon created. By doing so, he creates two worlds, one in which Ganon is sealed away in the Sacred Realm, and one in which Ganon was merely imprisoned by the King. Additional evidence is stated by Eiji Aonuma when conversing on timeline placement of The Legend of Zelda: The Wind Waker and The Legend of Zelda: Twilight Princess, where he says that the games are parallel.
This was also in a DC anthology, which included among other series, one comic with Superman. In the comic, Superman attempts to change many of the world's great events, including Lincoln's assassination. When he comes back to his own time, nothing had changed. However, he discovers a parallel version of the world with the altered history.
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 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. There's also the Ray Bradbury science fiction short story "A Sound of Thunder", in which the butterfly effect is caused by a real butterfly.
Note that the timeline corruption hypothesis is not intended to solve the temporal paradox. It seems to be part of the multiple universes hypothesis, in which a change in the timeline creates a new universe.
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 siblings). 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 (the youngest of the three). This allows Marty to correct the error and restore the timeline, albeit with a few minor changes that are due to his interference. This effect has one contradiction - If a person, somehow, causes himself to not be born in the past, then he would not have been able to do the thing that caused him to not be born for he would have not existed, thus causing time to corrupt.
This theory also figures prominently in the 1989 sequel Back to the Future Part 2 in which McFly's enemy, the now-elderly Biff Tannen, travels from 2015 back to 1955 to give his younger self a copy of a sports almanac with the final scores of professional sports games from 1950 to 2000. The younger Biff uses this information to change history, so when Doc and McFly return to 1985 from their own mission in 2015, they find Hill Valley drastically changed. Marty proposes going back to 2015 to stop Biff from going back to 1955, but Doc explains that it would do no good since they were on a different timeline and 2015 would also be different. The only way to restore the timeline is to return to 1955 and take the almanac away from Biff so he will not use it to change history. Note that this does not create a bootstrap paradox because Biff, from timeline A, traveled back in time and created timeline B, thus there is a clear(ish) logical reason as to where the almanac came from.
This idea also appears in a Family Guy episode, in which Peter goes back in time with the help of "Death" so that he can relive his teen life. When he arrives in the past, rather than spending time with his present-day wife, Lois, Peter ignores her. His actions cause a corruption in the timeline, and when Peter returns to the present day, all of reality is radically different.
The timeline corruption hypothesis is also used in the Red Dwarf episode, "Tikka to Ride", when the Red Dwarf crew travels back in time (with Lister's intention of ordering 500 curries) and accidentally kills Lee Harvey Oswald, saving Kennedy's life. Three years later, in an alternate reality, it is revealed that through a series of chain events, the USSR won the Space Race and put the first man on the moon, meaning that the Dwarfers never travelled into deep space in the first place, trapped in an alternate 1966. The Dwarfers manage to correct this by trying to make Oswald shoot from a different floor, before making an impeached Kennedy assassinate himself, as the man on the grassy knoll.
Philip K. Dick also explored timeline corruption paradoxes. In the story "Orpheus with Clay Feet", Slade, a character from the future, goes on a time travel vacation to the past where he can visit famous science fiction writer Jack Dowland and become his muse. Slade, however, fails to inspire Dowland as he had hoped, and Dowland never becomes the master he should have been.
Timeline corruption is an important motif in Star Trek: Enterprise. Captain Archer and the Enterprise crew become embroiled in an ongoing Temporal Cold War with the Suliban Cabal, a race of hostile aliens from the future who deliberately manipulate the timeline for their own ends. One of the results was that Earth's early 20th-Century history was changed so that the Nazis controlled much of Europe and proceeded to invade North America. Of course, the humans had to find a way to stop the Suliban and restore the timeline. Similar events occur in other Star Trek series.
In the videogame World of Warcraft, the Bronze Dragonflight (tasked with the safety of the timelines) frequently asks the heroes (players) to help them fight the Infinite Dragonflight, who would want to change important events of the past. Although this may vary depending on the point of the view of the player, most of the events are negative ones - Thrall's escape from his prison, leading to the formation of the new Horde, enemies of the Alliance; the opening of the Dark Portal, in which a corrupted Medivh opens up a link with the world of Draenor, starting the orcish invasions of Azeroth and ensuing wars; and the Culling of Stratholme, a defining moment in which Prince Arthas's fall to madness leads to the rise of the undead Scourge and his eventual merge with the Lich King - but they insist that the outcome of preventing such events would be "much worse".
The videogame series Command & Conquer contains a miniseries called Red Alert, whose three games depict what "happened" when Albert Einstein traveled back in time to prevent Hitler from rising to power. This resulted in the Nazi regime never coming to power, allowing the Soviet Union to become a formidable threat to the Allied Nations; instead of just tension during the Cold War, the Soviets launched a full-scale invasion against the United States. Later in the series, the Soviets steal the time-travelling technology for themselves to kill Einstein, preventing his technology from helping the Allies; however, this leads to Japan's Empire of the Rising Sun emerging as a new superpower.
In the videogame The Journeyman Project, a Temporal Distortion Wave threatens to alter the present. The player is tasked with retrieving a CD-ROM disk that has the correct timeline stored on it. Upon returning to the present from the far distant past, it is revealed that the timeline has indeed been corrupted by four key events in the recent past. This idea of avoiding corrupted timelines is seen throughout the Journeyman Project Trilogy. Although, it is only a story element in the later games as opposed to a major gameplay moment.
Realistically, there is absolutely no way to travel into the past without causing irreparable damage to the timeline as there are far too many variables. Example: One atom travels back in time one million years. Its slight gravitational effect changes the position of every subatomic particle in the universe to eventually move less than a micron. That change may be enough to cause a neuron in one person's brain to fire or not fire causing or preventing a cascade effect. This changes what this person thinks and does thus altering far too many variables to list therefore changing the entire course of history. The effects of any larger object would be far more devastating. If the theory of temporal corruption is correct, time travel would be extremely impractical to say the least.
Temporal merging hypothesis
This is the opposite of the multiple universes hypothesis, in that each action committed in time travel actually overlaps one reality with another. For instance, if a time traveler were to meet his double from another time, the double would merge with the time traveler, making the traveler a part of the time he is visiting. The same would hold true for events. Two events would merge 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 seen in the film The One, in which a character travels across time or dimensions, destroying copies of himself to cause them to merge — thus increasing power for the original character. A similar idea is seen in Margaret Peterson Haddix's book series, The Missing, in which any records of original time are kept in tracers, and those traveling back in time can merge with their own tracers.
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. This theory is the most consistent with our understanding of the dimension of time.
Bill & Ted's Excellent Adventure, as well as its sequel and television spin-offs (Bill & Ted's Excellent Adventures - both animated and live-action), 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.
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 is demonstrated in an episode of the TV show Big Bang Theory where Leonard and Sheldon sign a roommate agreement that states if either one of them ever invents time travel their first trip back would be to their present location 5 seconds after the signing of the contract, they are subsequently disappointed when the 5 seconds pass and nothing happens. This theory, however, creates a Causality Loop. Also if it is that any time machine made will allow only one way travel, i.e. into the future, or if it is that we can go into the future, but while returning, we can only return to the present (i.e. not set the dial to go back more than we used to go into the future, or before the time machine is invented), this theory fails. Wormholes, which are suggested to allow backwards time travel, demonstrate this, as you cannot go further back in time than when the wormhole was created.
There are also other possibilities: someone in the future will build a time machine and many people will use it to travel back in the past, but we do not know this because: "no one can travel so far in the past to reach our time" or "no one has revealed that time-travelling is possible" or "no one that revealed that time-traveling is possible, was trusted" or "anyone with the knowledge to sufficiently understand temporal mechanics enough to build such a device, will also be enlightened enough not to interfere with the known written past" or "the time machine will be destroyed if you go back before it is created."
Self-Healing hypothesis
This theory states that time would heal itself from the paradox. A person is about to alter an event in the present by traveling back to the past and altering the events that cause the events in the present day to happen. Then there will be another set of events that will cause the present-day events to happen, and so there will be reason for him to travel back in time, and thus the paradox would never happen.
An example of this can be seen in the film The Time Machine, where the main character creates a time machine to save his dead fiancé, but upon doing so, she is killed another way. When traveling to the future, he finally finds out that if she did not die he would never create the time machine. Thus it is impossible to save her. Even though this does not create a physical paradox, it creates a mental one in which the time traveler, who still builds the time machine for the same reason, remembers a different cause for that reason.
Another example is the TV series Doraemon, where in one episode the main character travels back in time to save someone from being hit by a car. Doraemon then states that 'if history is altered, it will always repeat itself to make up for the event that did not occur'. However he also states that 'the event might happen on another person, or be a completely different event altogether', raising the question how did the time traveler know about what was supposed to happen in the first place?
Destruction resolution
This theory states that any paradox would cause the destruction of a universe, or at least the part of the time & space affected by the paradox. In this hypothesis, if a person travels back to kill his grandfather before one of his parents is conceived, then it will cause himself to disappear. History would erase all traces of the person's existence, and the death of the grandfather would be caused by another reason. Thus, the paradox would never occur from the historical viewpoint.
Temporal Modification Negation Theory
This theory is partially similar to other theories on time travel. While stating that if time travel is possible it would be impossible to violate the grandfather paradox, it goes further to state that any action taken that itself negates the time travel event cannot occur. The consequences of such an event would in some way negate that event, by either voiding the memory of what one is doing before doing it, by preventing the action in some way, or even by destroying the universe among other possible consequences. It states, therefore, that to successfully change the past one must do so incidentally.
For example, if one tried to stop the murder of one's parents, he would fail. On the other hand, if one traveled back and did something to some random person that as a result prevented the death of someone else's parents, then such an event would be successful, because the reason for the journey, and therefore the journey itself, remain unchanged preventing a paradox.
In addition, if this event had some colossal change in the history of mankind, and such an event would not void the ability or purpose of the journey back, it would occur, and would hold. In such a case, the memory of the event would immediately be modified in the mind of the time traveler.
An example of this would be for someone to travel back to observe life in Austria in 1887 and while there shoot five people, one of whom was Hitler's parent. Hitler would therefore never have existed, but since this would not prevent the invention of the means for time travel, or the purpose of the trip, such a change would hold. Also for it to hold, every element that influenced the trip must remain unchanged. This would void someone convincing another party to travel back to kill the people without knowing who they are and making the time line stick, because by being successful, they would void the first party's influence and therefore the second party's actions.