A temporal paradox, time paradox, or time travel paradox is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time and time travel. In physics, temporal paradoxes fall into two broad groups: consistency paradoxes exemplified by the grandfather paradox; and causal loops. Other paradoxes associated with time travel are a variation of the Fermi paradox and paradoxes of free will that stem from causal loops such as Newcomb's paradox.
A causal loop is a paradox of time travel that occurs when a future event is the cause of a past event, which in turn is the cause of the future event. Both events then exist in spacetime, but their origin cannot be determined. A causal loop may involve an event, a person or object, or information. The terms boot-strap paradox, predestination paradox or ontological paradox are sometimes used in fiction to refer to a causal loop.
The consistency paradox or grandfather paradox occurs when the past is changed in any way, thus creating a contradiction. If a time traveler were ever to go back in time and kill their grandfather in his childhood, it would result in one of the time traveler's parents, and ergo the time traveler, not being born. If the time traveler were not born, then it would not be possible for them to kill the grandfather in the first place. Therefore, the grandfather lives to offspring the time traveler's parents, and therefore the time traveler. There is, thus no predicted outcome to this. Consistency paradoxes occur whenever changing the past is possible.
A possible resolution is that a time traveler can do anything that did happen, but cannot do anything that did not happen. Doing something that did not happen results in a contradiction.
The Fermi paradox can be adapted for time travel, and phrased "if time travel were possible, where are all the visitors from the future?" Answers vary, from time travel not being possible, to the possibility that visitors from the future cannot reach any arbitrary point in the past, or that they disguise themselves to avoid detection.
Newcomb's paradox is a thought experiment showing an apparent contradiction between the expected utility principle and the strategic dominance principle. The thought experiment is often extended to explore causality and free will by allowing for "perfect predictors": if perfect predictors of the future exist, for example if time travel exists as a mechanism for making perfect predictions, then perfect predictions appear to contradict free will because decisions apparently made with free will are already known to the perfect predictor.
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