Temporal paradox
Template:Short description Template:About 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.<ref name="stanford backward2" />
Causal loop
Template:Redirect A causal loop, also known as a bootstrap paradox, information loop, information paradox,<ref name="Everett" /> or ontological paradox,<ref name="smeenk">Template:Citation</ref> 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.<ref name="Smith">Template:Cite web</ref><ref name="Lobo">Template:Cite book</ref><ref>Template:Cite book</ref><ref>Template:Cite book</ref> 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 "Template:Linktext."<ref name="Klosterman">Template:Cite book</ref><ref>Template:Cite web</ref>
Backward time travel would allow information, people, or objects whose histories seem to "come from nowhere".<ref name="Smith" /> Such causally looped events then exist in spacetime, but their origin cannot be determined.<ref name="Smith" /><ref name="Lobo" /> The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical.<ref name="Lobo" /><ref name="Everett">Template:Cite book</ref><ref>Template:Cite book</ref> 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.<ref name="Krasnikov2001">Template:Citation</ref>Template:Rp He does not find these paradoxical and attributes problems regarding the validity of time travel to other factors in the interpretation of general relativity.<ref name="Krasnikov2001" />Template:Rp
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.<ref name="Everett" /> 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.<ref name="smeenk" />
Consistency paradox
The consistency paradox, commonly known as the grandfather paradox, occurs when the past is changed in any way.<ref name="Smith" /> The paradox of changing the past stems from modal 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.<ref name="Norman" /> Consistency paradoxes occur whenever any change to the past is possible.<ref name="Lobo" />
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.<ref name="Smith" /> 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.<ref name="Smith" /> Another proposed resolution is simply that time travel is impossible.<ref name="Swartz" />
Variants
Template:AnchorTemplate:Anchor The grandfather paradox encompasses any change to the past,<ref name="NicholasSmith2">Template:Cite encyclopedia</ref> and it is presented in many variations, including killing one's past self.<ref name="horwich">Template:Cite book</ref><ref name="stanford backward2">Template:Citation</ref> Both the "retro-suicide paradox" and the "grandfather paradox" appeared in letters written into Amazing Stories in the 1920s.<ref name="Nahin 1999">Template:Cite book</ref> 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 rise to power in Germany, thus preventing 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.<ref>Template:Cite book</ref>
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.<ref>Template:Cite journal</ref><ref>Template:Cite book</ref>
Free will and causality
Template:Main Newcomb's paradox is a thought experiment showing an apparent contradiction between the expected utility principle and the strategic dominance principle.<ref name="Wolpert">Template:Cite journal</ref> The thought experiment is often extended to explore causality and free will.
Predestination sometimes involves a supernatural power, though it could be the result of other "infallible foreknowledge" mechanisms.<ref>Template:Cite journal</ref> 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.<ref name="divine">Template:Cite journal</ref><ref>Template:Cite journal</ref> Problems arising from infallibility and influence from the future are explored in the infallible predictor version of Newcomb's paradox.<ref>Template:Cite book</ref>
Proposed resolutions
Logical impossibility of time travel
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.<ref name="Norman">Template:Citation</ref><ref>Template:Cite book</ref>
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,<ref name="NicholasSmith2"/> 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.<ref name="Swartz">Template:Cite web</ref>
Emergent time
If time is not an inherent property of the universe but is instead emergent from the laws of entropy, as some modern theories suggest,<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> 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 present state of the 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 irreversible 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.<ref>Template:Cite web</ref> It has been argued that since the traveler arrives in a different history and not their own history, this is not "genuine" time travel.<ref name="Stanford time travel" />
Illusory time
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.<ref name="Yourgrau">Template:Cite book</ref><ref name="holt">Template:Cite magazine</ref> 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".Template:Citation needed
Novikov self-consistency principle
Template:Main A 1992 paper by physicists Andrei Lossev and Igor Novikov labeled such items without origin as Jinn, with the singular term Jinnee.<ref name="Lossev1992">Template:Cite journal</ref>Template:Rp This terminology was inspired by the Jinn of the Quran, which are described as leaving no trace when they disappear.<ref name="Toomey2012">Template:Cite book</ref>Template:Rp 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".<ref name="Everett" /><ref name="Lossev1992" />Template:Rp<ref name="Toomey2012" />Template:Rp 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; the second 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 in closed systems, a Jinnee could interact with its environment in such a way as to regain "lost" entropy.<ref name="Everett" /><ref name="Toomey2012" />Template:Rp They emphasize that there is no "strict difference" between Jinn of the first and second kind.<ref name="Lossev1992" />Template:Rp 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."<ref name="Krasnikov2001" />Template:Rp
The self-consistency principle developed by Igor Dmitriyevich Novikov<ref name="Friedman1990">Template:Cite journal</ref>Template:Rp 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<ref>Template:Citation</ref> that contain closed timelike curves that lead back to the same point in spacetime,<ref>Template:Cite journal</ref> 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.<ref name="Thorne" />
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".<ref name="Thorne">Template:Cite book</ref> 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.<ref>Template:Cite journal</ref> 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.<ref name="Thorne" /> It is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.<ref name="Earman1995187188">Template:Cite book</ref>Template:Rp 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.<ref name="Earman1995187188" />Template:Rp
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.<ref>Template:Cite book</ref> Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity.<ref name="Krasnikov2001" />Template:Rp 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.<ref>Template:Cite journal</ref>
Parallel universes
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.<ref name="Stanford time travel">Template:Citation</ref> 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.<ref name="Hawking warp">Template:Cite web</ref>
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.<ref name="Deutsch">Template:Cite journal</ref> 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.<ref>Template:Cite journal</ref> 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.<ref name="Everett MWI">Template:Cite journal</ref>
See also
- Quantum mechanics of time travel
- Fermi paradox
- Cosmic censorship hypothesis
- Retrocausality
- Wormhole
- Causality
- Causal structure
- Chronology protection conjecture
- Münchhausen trilemma
- Time loop
- Time travel in fiction
- Time travel