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Theoretical paradox resulting from time travel
apparent contradictions in the concept of time travel
A temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with the current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility.

Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox. Bootstrap paradoxes violate causality by allowing future events to influence the past and cause themselves, or "bootstrapping", which derives from the idiom "pull oneself up by one's bootstraps." Consistency paradoxes, on the other hand, are those where future events influence the past to cause an apparent contradiction, exemplified by the grandfather paradox, where a person travels to the past to kill their grandfather.

A boot strap paradox, also known as an information loop, an information paradox, or a "predestination paradox" is a paradox of time travel that occurs when any event, such as an action, information, an object, or a person, ultimately causes itself, as a consequence of either retrocausality or time travel. Backward time travel would allow information, people, or objects whose histories seem to "come from nowhere". Everett gives the movie Somewhere in Time as an example involving an object with no origin: an old woman gives a watch to a playwright who later travels back in time and meets the same woman when she was young, and gives her the same watch that she will later give to him. and it is presented in many variations, including killing one's past self. Both the "retro suicide paradox" and the "grandfather paradox" appeared in letters written into Amazing Stories in the 1920s. Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", in which the protagonist travels back in time to murder Adolf Hitler before he can instigate World War II and the Holocaust. Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed. Physicist John Garrison et al. give a variation of the paradox of an electronic circuit that sends a signal through a time machine to shut itself off, and receives the signal before it sends it.

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. Predestination does not necessarily involve a supernatural power, and could be the result of other "infallible foreknowledge" mechanisms. Problems arising from infallibility and influencing the future are explored in Newcomb's paradox.

Even without knowing whether time travel to the past is physically possible, it is possible to show using modal logic that changing the past results in a logical contradiction. If it is necessarily true that the past happened in a certain way, then it is false and impossible for the past to have occurred in any other way. A time traveler would not be able to change the past from the way it is, but would only act in a way that is already consistent with what necessarily happened. Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, arguing that the possibility of creating a contradiction rules out time travel to the past entirely. However, some philosophers and scientists believe that time travel into the past need not be logically impossible provided that there is no possibility of changing the past,

Consideration of the possibility of backward time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion. He suggests something along the lines of the block time view, in which time is just another dimension like space, with all events at all times being fixed within this four dimensional "block".

Sergey Krasnikov writes that these bootstrap paradoxes – information or an object looping through time – are the same; the primary apparent paradox is a physical system evolving into a state in a way that is not governed by its laws. He does not find these paradoxical and attributes problems regarding the validity of time travel to other factors in the interpretation of general relativity. This terminology was inspired by the Jinn of the Quran, which are described as leaving no trace when they disappear. Lossev and Novikov allowed the term "Jinn" to cover both objects and information with the reflexive origin; they called the former "Jinn of the first kind", and the latter "Jinn of the second kind". expresses one view as to how backward time travel would be possible without the generation of paradoxes. According to this hypothesis, even though general relativity permits some exact solutions that allow for time travel that contain closed timelike curves that lead back to the same point in spacetime, physics in or near closed timelike curves (time machines) can only be consistent with the universal laws of physics, and thus only self consistent events can occur. 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. The authors concluded that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent to the past. Thorne and two of his students at Caltech, Fernando Echeverria and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies, and found that there was more than one self consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could be an infinite number of self consistent solutions. The lack of constraints on initial conditions only applies to spacetime outside of the chronology violating region of spacetime; the constraints on the chronology violating region might prove to be paradoxical, but this is not yet known. Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity.

The interacting multiple universes approach is a variation of the many worlds interpretation of quantum mechanics that involves time travelers arriving in a different universe than the one from which they came; it has been argued that, since travelers arrive in a different universe's history and not their history, this is not "genuine" time travel. Stephen Hawking has argued for the chronology protection conjecture, that even if the MWI is correct, we should expect each time traveler to experience a single self consistent history so that time travelers remain within their world rather than traveling to a different one. David Deutsch has proposed that quantum computation with a negative delay—backward time travel—produces only self consistent solutions, and the chronology violating region imposes constraints that are not apparent through classical reasoning. However Deutsch's self consistency condition has been demonstrated as capable of being fulfilled to arbitrary precision by any system subject to the laws of classical statistical mechanics, even if it is not built up by quantum systems. Allen Everett has also argued that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time, with different particles emerging in different worlds.