Temporal paradox
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A temporal paradox is an "impossible" situation in which a time traveler interferes with the timeline involved in his own existence.
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[edit] Example
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. This example is one type of causality loop.
A variation on this paradox was explored in the 1985 film Back to the Future in which the protagonist goes back in time and interferes with his parents' first romantic encounter, thus putting his own existence into jeopardy. In the episode Roswell That Ends Well of the American animated television series Futurama, the main character, Fry, actually becomes his own grandfather, much to the other characters' disbelief.
[edit] Theories in science fiction
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
Some believe that time itself would not allow such a transgression, and that the timeline would be preserved (perhaps by not allowing time travel in the first place). This is the "timeline protection hypothesis."
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. It is also possible that nobody with a time machine would actually attempt to cause any of these paradoxes out of fear that it would have dangerous results.
[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 world several thousand years later would be completely different from the future the traveler had left. This has been coined the "timeline corruption hypothesis."
[edit] Multiple universes hypothesis
Another hypothesis is that there are an infinite number of universes, one for each possibility. So one universe would have a live grandfather, and another universe would have a dead one. Or else, maybe 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 timeline of events throughout time is already set, i.e. if a time traveler is going to travel back in time, time has already taken this into account and the event of him arriving has already happened, on the grounds of all life is set indefinitely.
A theory similar to this is that the events of time can be considered set, yet changes can be made. For example, a person travels back in time and kills their own grandfather. To counter this paradox, the person is conceived under different circumstances, but lives exactly the same life and travels back in time to kill a man who is not in fact their grandfather. This works with the idea that the space-time continuum is flexible, capable of adapting to errors, paradoxes and changes to events. The aforementioned episode of Futurama could be an example of this; Fry uwittingly kills his 'grandfather', but circumstance plays out that he himself takes his grandfather's place to conceive his father.
[edit] Choice Timeline hypothesis
As soon as the time traveller decides to travel back in time, at that instant all history is changed, in result to what events happened when he arrived back in that time, on the grounds that history is made as we choose and decide what happens.
