Atemporal paradox,time paradox, ortime travel paradox, is an apparent or actual contradiction associated with the idea oftime 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.[1]
A causal loop, also known as a bootstrap paradox, information loop, information paradox,[3] or ontological paradox,[4] occurs when any event, such as an action, information, an object, or a person, ultimately causes itself, as a consequence of eitherretrocausality ortime travel.[5][6][7][8] A causal loop appears to violate causality by allowing future events to influence the past and cause themselves. This is sometimes called "bootstrapping", which derives from the idiom "pull oneself up by one's bootstraps."[9][10]
Backward time travel would allow information, people, or objects whose histories seem to "come from nowhere".[5] Such causally looped events then exist inspacetime, but their origin cannot be determined.[5][6] The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical.[6][3][11]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.[12]: 4 He does not find these paradoxical and attributes problems regarding the validity of time travel to other factors in the interpretation of general relativity.[12]: 14–16
An example occurs in the 1958science fictionshort story "—All You Zombies—", byRobert A. Heinlein, wherein the main character, anintersex individual, becomes both their own mother and father; the 2014 filmPredestination is based on the story. Allen Everett gives the movieSomewhere 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.[3] 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.[4]
The consistency paradox, commonly known as the grandfather paradox, occurs when the past is changed in any way.[5] The paradox of changing the past stems frommodal logic: 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, so any change to the past would be a paradox.[13] Consistency paradoxes occur whenever any change to the past is possible.[6]
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.[5]One proposed resolution for this paradox is that a time travellercan do anything thatdid happen, butcannot do anything thatdid not happen.[5] Another proposed resolution is simply that time travel is impossible.[14]
The grandfather paradox encompasses any change to the past,[15] and it is presented in many variations, including killing one's past self.[16][1] Both the "retro-suicide paradox" and the "grandfather paradox" appeared in letters written intoAmazing Stories in the 1920s.[17] Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", in which the protagonist travels back in time to murderAdolf Hitler before he can rise to power in Germany, thus preventingWorld War II and theHolocaust. Rather than necessarily physically preventing time travel, the action removes anyreason for the travel, along with any knowledge that the reason ever existed.[18]
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.[19][20]
Newcomb's paradox is athought experiment showing an apparent contradiction between theexpected utility principle and thestrategic dominance principle.[21] The thought experiment is often extended to explorecausality and free will.
Predestination sometimes involves asupernatural power, though it could be the result of other "infallible foreknowledge" mechanisms.[22] 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.[23][24] Problems arising from infallibility and influence from the future are explored in the infallible predictor version of Newcomb's paradox.[25]
Even without knowing whether time travel to the past is physically possible, it is possible to show usingmodal 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 itis, but would only act in a way that is already consistent with whatnecessarily happened.[13][26]
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 philosopherBradley Dowden made this sort of argument in the textbookLogical 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,[15] as suggested, for example, by theNovikov self-consistency principle. Dowden revised his view after being convinced of this in an exchange with the philosopherNorman Swartz.[14]
If time is not an inherent property of the universe but is insteademergent from the laws ofentropy, as some modern theories suggest,[27][28] then it presents a natural solution to the Grandfather Paradox. In this framework, "time travel" is reinterpreted not as movement along a linear continuum but as a reconfiguration of the local space or the entire universe to match a prior entropic configuration. Because the original chronological sequence—including events like the time traveler's birth—remains preserved in the universe's entropic progression, actions within the reconfigured state cannot alter the causal history that produced the traveler. This avoids paradoxes by treating time as a thermodynamic artifact rather than a mutable dimension.[29] It has been argued that since the traveler arrives in a different history and not their own history, this is not "genuine" time travel.[30]
LogicianKurt Gödel speculated, through considerations of the possibility of backward time travel in a hypothetical universe described by aGödel metric, that time might itself be a sort of illusion.[31][32] He suggested something along the lines of theblock time view, in which time is just another dimension like space, with all events at all times being fixed within this four-dimensional "block".[citation needed]
A 1992 paper by physicists Andrei Lossev andIgor Novikov labeled items without origin (items that seem to "come from nowhere," as mentioned above) asJinn, with the singular termJinnee.[33]: 2311–2312 This terminology was inspired by theJinn of theQuran, which are described as leaving no trace when they disappear.[34]: 200–203 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".[3][33]: 2315–2317 [34]: 208 They point out that an object making circular passage through time must be identical whenever it is brought back to the past, otherwise it would create an inconsistency; thesecond law of thermodynamics seems to require that the object tends to a lower energy state throughout its history, and such objects that are identical in repeating points in their history seem to contradict this, but Lossev and Novikov argued that since the second law only requires entropy to increase inclosed systems, a Jinnee could interact with its environment in such a way as to regain "lost" entropy.[3][34]: 200–203 They emphasize that there is no "strict difference" between Jinn of the first and second kind.[33]: 2320 Krasnikov equivocates between "Jinn", "self-sufficient loops", and "self-existing objects", calling them "lions" or "looping or intruding objects", and asserts that they are no less physical than conventional objects, "which, after all, also could appear only from either infinity or a singularity."[12]: 8–9
The self-consistency principle developed byIgor Dmitriyevich Novikov[35]: p. 42 note 10 expresses one view as to how backwardtime travel would be possible without the generation of paradoxes. According to this hypothesis, even thoughgeneral relativity permits someexact solutions that allow fortime travel[36] that containclosed timelike curves that lead back to the same point in spacetime,[37] physics in or nearclosed 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.[38]
PhysicistJoseph Polchinski considered a potentially paradoxical situation involving abilliard ball that is fired into awormhole 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".[38] 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.[39] Later analysis by Thorne andRobert Forward showed that for certain initial trajectories of the billiard ball, there could be an infinite number of self-consistent solutions.[38] It is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.[40]: 184 The lack of constraints on initial conditions only applies to spacetime outside of thechronology-violating region of spacetime; the constraints on the chronology-violating region might prove to be paradoxical, but this is not yet known.[40]: 187–188
Novikov's views are not widely accepted. Visser views causal loops and Novikov's self-consistency principle as anad hoc solution, and supposes that there are far more damaging implications of time travel.[41] Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity.[12]: 14–16 Another conjecture, thecosmic censorship hypothesis, suggests that every closed timelike curve passes through anevent horizon, which prevents such causal loops from being observed.[42]
Themany-worlds interpretation of quantum physics poses that all possible quantum events can occur in mutually exclusive histories.[43] A variation of this interpretation, calledinteracting many-worlds, may involve time travelers arriving in a different universe than the one they came from. It's been argued that since the traveler arrives in a different universe's history and not their own history, this is not "genuine" time travel.[30] Stephen Hawking has argued 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.[44]
David Deutsch has proposed thatquantum 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.[45] Deutsch's self-consistency condition has been demonstrated as capable of being fulfilled to arbitrary precision by any system subject to the laws of classicalstatistical mechanics, even if it is not built up by quantum systems.[46] 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.[47]
Polchinski's paradox.