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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 a person goes back in time to kill his grandfather before he had any biological descendant. If they succeed, one of their parents would never exist and they themselves would never exist either. This would make it impossible for them to go back in time in the first place, making them unable to kill their grandfather, who would continue to produce offspring and restart the situation. But if they fail, their grandfather would be alive and produce offspring, one of whom would eventually conceive the time traveler and the whole scenario would start over.
Temporal paradox has been used to argue that time travel must be impossible, because it is capable of resulting in a paradox. Kip 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, due to a distortion of probability. 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, despite the potential improbability of the situation.
Prior to 1986, DC published a number of Superman stories where he tried to alter the past, only to be defeated by the past protecting itself. (In one, Superman tries to prevent the assassination of Lincoln, only to come upon Lex Luthor who is also time traveling. Luthor exposes Superman to green kryptonite and this piece totally paralyzes Superman. The effect does not wear off until the dying president is carried out of Ford's Theater. )
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 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 guerrillas from the 22nd century, 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 (Sewashi) 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 Shizuka, the girl he likes (instead of the one he dislikes but conceived the father of his future grandson), what would happen to his grandson. Sewashi, 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.
In the game Soul Reaver 2 when Raziel and Kain travel to Nosgoth's past, a paradox occurs when Kain saves Raziel by removing the Soul Reaver from Raziel's body. This ends the time loop that Raziel endures because the soul devouring entity within the Reaver was Raziel's own soul, which he could not consume. Raziel's fate was to be absorbed by the blade, and in not being absorbed Raziel now has free will and can not spin within the Wheel of Fate. History attempts to protects itself from the paradox by creating a new enemy for the vampire race, known as the Hildan, leading into to the events of Legacy of Kain Defiance.
Novikov self-consistency principle 
This Novikov self-consistency principle says that anything a time traveler does in the past must have been part of history all along, so although the time traveler can have a causal influence on events in the past, it is impossible for anything the time traveler does to "change" history. So, for example, any attempt by the time traveler to kill one of his ancestors before they became a parent would be guaranteed to fail for some reason or another (perhaps the gun would jam, or perhaps the traveler would just have a change of heart), so the grandfather paradox would be avoided. This theory, however, is capable of causing bootstrap paradox.
An example of this is the Artemis Fowl series. In book 6, Artemis travels back in time, accidentally causing his younger self to eventually discover the fairies, setting the events of book one in motion. He also allowed mastermind Opal Koboi from the past to take over the house by traveling in same time stream that Artemis traveled back in. The book shows that if Artemis hadn't traveled back in the first place, he wouldn't have discovered the fairies and never have been able to go back at all.
Another possible example, could be of any Doctor Who episode where The Doctor and his companions travel to the past, at least for most of them, where anything they do in Earth's past, does not usually affect the future, they even seem to be already a part of history, even when The Doctor causes the volcano eruption of Mt. Vesuvius, they're obviously predestination paradoxes.
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 create his own parallel universe upon arrival in the past. So if he kills "his" grandfather, a paradox would not occur because the grandfather that he has killed is not his own grandfather from the universe from which he came, but that of the version of himself in the universe he is now 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.
Another example is in the manga/anime series Reborn!. A special weapon called the Ten-Year Bazooka (because anyone hit by it will be swapped with themselves from 10 years in the future for 5 minutes) allows Tsuna and his Guardians, as well as some of his other friends to travel into the future. However, due to a special device invented by Irie Shouichi, they are kept there for an extended period of time. They learn that this was because they possessed the Vongola Rings, which the Tsuna in that time period destroyed to avoid conflicts with rival mafia families. They learn that the rings power is necessary to defeat Byakuran, a man who, due to Shouichi's time-traveling, realized that he himself, and not merely a parallel version of himself, was present in all other multiple universes, referred to as parallel worlds. This allowed him to use knowledge far beyond what was present in any single one of those worlds, allowing him to take over all of them except for the future in which Tsuna traveled to. However, by defeating him in that universe, Tsuna killed all other instances of Byakuran in the other universes as well, as they were metaphysically the same person. Despite this, however, the universe in which Byakuran was defeated is still shown to exist.
Branching universe hypothesis 
This theory says that to travel back in time would cause time to branch.
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, she 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.
In Marvel Comics when the time-travelling villain Kang the Conqueror saves Princess Ravonna from being shot he creates a world in which he was killed instead. He discovers that due to his various travels through time he has created many Universes and versions of himself.
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. Also, in Source Code, a military officer is sent back in time to help prevent a bomb explosion. After the bomb is stopped, he still finds himself still in the past. In other words, a totally new universe.
In the Simpsons' Halloween show Treehouse of Horror V, there is TIME AND PUNISHMENT where Homer attempting to fix the toaster,accidentally creates a time machine and travels to the age of dinosaurs, inadvertently altering his time far for the worse. His attempts to rectify matters alter time over & over in amazing ways.
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.
Erased timeline hypothesis 
This hypothesis proposes that an individual can change the past, erasing their timeline, whilst continuing to exist in the new timeline. Therefore an individual who kills their grandfather will remain in the new timeline. This is seen in the 'Terminator' films, where characters are able to travel back in time to kill individuals and prevent/cause events, thus removing the need to time travel, but remain after doing so. If this theory is correct it would be possible to travel backwards in time but impossible to return to the timeline one originates from due to the butterfly effect. It would also be possible for an individual to repeatedly travel back in time converging with many versions of themselves, all of whom would have to exist together in the new timeline.
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.
Another example is the movie Frequency, in which a man who grew up without a father sends information back in time to save his father's life. When the father survives, the son suddenly finds himself with a new set of childhood memories, while still remembering the original.
Frugal Lucre refers to this hypothesis in the Kim Possible episode 'The Big Job' when discussing Dr. Drakken's possible escape options.
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 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 
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-traveling 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." There is also the possibility that time travel into the past is only possible to the point where the time travel machine was 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?
This theory also happens in the TV series Lost when Desmond Hume, who can see into the future, sees Charlie Pace die when struck by lightning. Desmond saves him by building a big metal pole to absorb the shock instead. When Charlie doesn't die this way, Desmond sees him dying by trying to save Claire from drowning, trying to get Claire a bird, and while getting shot with an arrow from a trap in the jungle- all from which he is saved. Eventually Charlie accepts his fate and drowns in the DHARMA Initiative facility "the Looking Glass".
It's also shown in the Terminator film series, where in the second film, Sarah, John, and a second version of the type of terminator cyborg from the first film stop judgement day from happening, but in the third film, another terminator goes back in time, which leads to the explanation that Skynet is still invented and launched, just 10 years after it was originally, thus explaining that judgement day and Skynet can never be averted completely, just delayed. This also works as a way of explaining how John Connor can still be born, as his father, Kyle Reese, was born a decade, or two after he was, then traveled back in time to protect his mother, Sarah from an evil terminator cyborg in the 80's, then impregnates her and John is born after the terminator is defeated in the first film, thus solidifying his existence in the universe.
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.
A variation of this example occurs in the Season 3 finale of FRINGE when Peter Bishop uses the Doomsday machine. When he tells both Walter and Walternate he punched holes in both universes in the past and created a bridge between universes in order to repair the damage, Peter disappears because his actions caused the younger versions of himself in both of the new timelines to die in 1985.
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, though one might be able to change this fact slightly. If one were to go back and place a note in someplace one knew one's future self would find it and then subsequently stop an assassination one might be able to tweak this theory. If the specified note said to go back into time, stop the assassination, copy this note, and place it in the same spot it originally was, one might be able to intentionally stop the assassination.
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.
Changes allowed, without resolution to paradoxes 
Another theory, though much less commonly utilized, is one in which the altering of an event in the past would always be allowed, even if such alteration would logically cause a paradox.
Ad exemplum, a time traveler who embarks on a trip to the past would be able to kill his grandfather, even though such an act would prevent one of his parents from being born and thus prevent the time traveler himself from being born, without causing the resulting paradox to change any other part of the past. Though, with this theory, the time traveler, who would still remember having a grandfather and even parents, would appear to have not been born. This seems to generate a problem resembling the bootstrap paradox.
If the time traveler 'returned' to the future, it would be changed to accommodate him never existing and all effects that would have on time.
Doomed Timeline Theory 
This theory involves the universe incorporating a "fail-safe" by destroying any instance or timeline that deviates from a main timeline to prevent multiple universes from existing. Basically, any time travel deviating from a stable time-loop, paradoxical or not, is doomed to be destroyed. For instance, if a man goes back in time to prevent someone who's dead in the future from dying, succeeding will lead to that timeline ceasing to exist. However, there have been some who argue that this would refute the theory of relativity and the known laws of physics.
Multiple examples of this can be found in Andrew Hussie's webcomic Homestuck. Dave Strider, whose role as the Knight of Time allows him to utilize time travel on a frequent basis, has to be wary of keeping time loops stable. For instance, if he goes back in time to save himself, his past self will eventually become his future self that goes back in time to save himself. Any deviation from this will result in the creation of an alternate Dave. All alternate Daves are destined to die, and in this way, any alternate reality versions of the characters or universes are automatically destined to be destroyed.
Summerville's Timeline Theory 
This theory states that there is only one universe that would bend like a straightened paper clip by the events of time travel. When time travel occurs a chemical change occurs in the universe allowing the law of conservation of mass to be followed, (E.G. A time traveler materializes in the intended time out of the elements currently present in that time, or if a current version of him/herself exists they will transfer to the future consciousness) and the universe is forever changed. Any change or deviation from the original flow of events would not negate the existence of the traveler. The time traveler is real to that time and place as reinforced by the chemical change to the universe[clarification needed] that landed him at that point in the time line. Therefore if by time traveling into the past "the past self" is killed, "the future self" would live on because the past self is not him/her. It is another person from the point they entered that time. If the past self goes on to time travel, they create a cascade of time travel at the point they entered the past. Each journey into the past, no matter how similar, creates a different flow of events. Though it may mirror the events each time, this will continue until the flow of events affects the past self to the point they are no longer capable of or desire to follow that flow of events.
See also 
- Bootstrap paradox
- Chaos theory
- Cosmic censorship hypothesis
- Grandfather paradox
- Predestination paradox
- Science fiction
- Time loop
- Time travel