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A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past. They are often employed to demonstrate the impossibility of time travel. Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and free will causality paradoxes exemplified by the Newcomb paradox.
Backward time travel would allow information, people, or objects whose histories seem to "come from nowhere". Such causally looped events then exist in spacetime, but their origin cannot be determined. The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical. (2026). 9780226224985, University of Chicago Press. ISBN 9780226224985 Sergey Krasnikov writes that both paradoxes, either 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.
An example occurs in the 1958 science fiction short story "—All You Zombies—", by Robert A. Heinlein, wherein the main character, an intersex individual, becomes both their own mother and father; the 2014 film Predestination is based on the story. Allen 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 shows her the watch that she will later give to him. Smeenk uses the term "predestination paradox" to refer specifically to situations in which a time traveler goes back in time to try to prevent some event in the past.
A common example given is a time traveler killing their grandfather so he can't father one of their parents, thus preventing their own conception. If the traveler were not born, they could not kill their grandfather; therefore, the grandfather proceeds to beget the traveler's parent who begets the traveler. This scenario is self-contradictory. One proposed resolution for this paradox is that a time traveller can do anything that did happen, but cannot do anything that did not happen. Another proposed resolution is simply that time travel is impossible.
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. (2026). 9783319488622, Springer International Publishing. ISBN 9783319488622
Predestination sometimes involves a supernatural power, though it could be the result of other "infallible foreknowledge" mechanisms. By allowing for "perfect predictors", for example if time travel exists as a mechanism for making perfect predictions by allowing true knowledge of the future, then perfect predictions appear to contradict free will because decisions apparently made with free will are already known to the perfect predictor, meaning the choice apparently made with free will was already made. Problems arising from infallibility and influence from the future are explored in the infallible predictor version of Newcomb's paradox.
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, as suggested, for example, by the Novikov self-consistency principle. Dowden revised his view after being convinced of this in an exchange with the philosopher Norman Swartz.
The self-consistency principle developed by Igor Dmitriyevich Novikov 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.
Physicist Joseph Polchinski considered a potentially paradoxical situation involving a billiard ball that is fired into a wormhole at just the right angle such that it will be sent back in time and collides with its earlier self, knocking it off course, which would stop it from entering the wormhole in the first place. Kip Thorne referred to this problem as "Polchinski's paradox". 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. It is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.John Earman (1995). 019509591X, Oxford University Press. 019509591X 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.
Novikov's views are not widely accepted. Visser views causal loops and Novikov's self-consistency principle as an ad hoc solution, and supposes that there are far more damaging implications of time travel. Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity. Another conjecture, the cosmic censorship hypothesis, suggests that every closed timelike curve passes through an event horizon, which prevents such causal loops from being observed.
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. 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 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.
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