Editing Temporal paradox

{{Short description|Theoretical paradox resulting from time travel}}
{{About|apparent contradictions in the concept of time travel|the controversy over the origin of birds|Temporal paradox (paleontology)}}
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.

==Types==
{{anchor|Causal loop}}
{{redirect|Causal loop|the cause and effect diagram|causal loop diagram|the plot device|time loop}}
Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox.<ref name="Stanford backward">{{citation|url=https://plato.stanford.edu/entries/causation-backwards/|title=Backward Causation|author=Jan Faye|date=November 18, 2015|access-date=May 25, 2019|encyclopedia=Stanford Encyclopedia of Philosophy}}</ref> Bootstrap paradoxes violate causality by allowing future events to influence the past and cause themselves, or "[[bootstrapping]]", which derives from the idiom "{{linktext|pull oneself up by one's bootstraps}}."<ref name="Klosterman">{{cite book |last1=Klosterman |first1=Chuck |title=Eating the Dinosaur |date=2009 |publisher=Scribner |location=New York |isbn=9781439168486|edition=1st Scribner hardcover|pages=[https://books.google.com/books?id=lZurDFJtAWwC&lpg=PA60&pg=PA60 60–62]}}</ref><ref>{{cite web|last=Ross |first=Kelley L. |title=Time Travel Paradoxes |date=1997 |url=http://www.friesian.com/paradox.htm |url-status=dead |archive-url=https://web.archive.org/web/19980118212457/http://www.friesian.com/paradox.htm |archive-date=January 18, 1998 }}</ref> 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 prevent the conception of one of their ancestors, thus eliminating all the ancestor's descendants.<ref name="Nato" /> [[Newcomb's paradox]] stems from the apparent contradictions that stem from the assumptions of both [[free will]] and foreknowledge of future events. All of these are sometimes referred to individually as "causal loops." The term "[[time loop]]" is sometimes referred to as a causal loop,<ref name="Klosterman" /> but although they appear similar, causal loops are unchanging and self-originating, whereas time loops are constantly resetting.<ref>{{cite book|title=Time Travel in Popular Media|last1=Jones|first1=Matthew|last2=Ormrod|first2=Joan|year=2015|publisher=[[McFarland & Company]]|isbn=9780786478071|page=207}}</ref>

===Bootstrap paradox===
A bootstrap paradox, also known as an '''information loop''', an ''information paradox'',<ref name="Everett" /> an ''ontological paradox'',<ref name="smeenk">{{Citation |last1=Smeenk|first1=Chris|last2=Wüthrich|first2=Christian|editor-last=Callender|editor-first=Craig|contribution=Time Travel and Time Machines|title=The Oxford Handbook of Philosophy of Time|year=2011|publisher=Oxford University Press|isbn = 978-0-19-929820-4|page=[https://books.google.com/books?id=PrapBAAAQBAJ&lpg=PP1&pg=PT720 581]}}</ref> 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]].<ref name="Smith">{{cite web |url=http://plato.stanford.edu/entries/time-travel/index.html#CauLoo |last=Smith|first=Nicholas J.J.|date=2013 |title=Time Travel |website=Stanford Encyclopedia of Philosophy |access-date=June 13, 2015}}</ref><ref name="Lobo" /><ref>{{cite book|last=Rea|first=Michael|title=Metaphysics: The Basics|date=2014|publisher=Routledge|location=New York|isbn=978-0-415-57441-9|edition=1. publ.|page=[https://books.google.com/books?id=v1IsAwAAQBAJ&lpg=PP1&pg=PA78 78]}}</ref><ref>{{cite book|last1=Rea|first1=Michael C.|title=Arguing about Metaphysics|date=2009|publisher=Routledge|location=New York [u.a.]|isbn=978-0-415-95826-4|page=204}}</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">{{cite book|last1=Everett|first1=Allen|last2=Roman|first2=Thomas|title=Time Travel and Warp Drives|date=2012|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-22498-5|pages=[https://books.google.com/books?id=Dm5xt_XbFyoC&lpg=PP1&pg=PA136 136–139]}}</ref><ref>{{cite book|last=Visser|first=Matt|title=Lorentzian Wormholes: From Einstein to Hawking|date=1996|publisher=Springer-Verlag|location=New York|isbn=1-56396-653-0|page=213}}</ref> A notable 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 (film)|Predestination]]'' is based on the story. Allen Everett gives the movie ''[[Somewhere in Time (film)|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" /> An example of information which "came from nowhere" is in the movie ''[[Star Trek IV: The Voyage Home]]'', in which a 23rd-century engineer travels back in time, and gives the formula for [[list of Star Trek materials#Transparent aluminum|transparent aluminum]] to the 20th-century engineer who supposedly invented it.

===Predestination paradox===
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" />

The "predestination paradox" is a concept in time travel and temporal mechanics, often explored in science fiction. It occurs when a future event is the cause of a past event, which in turn becomes the cause of the future event, forming a self-sustaining loop in time. This paradox challenges conventional understandings of cause and effect, as the events involved are both the origin and the result of each other. A notable example is found in the TV series ''[[Doctor Who]]'', where a [[Father's Day (Doctor Who)|character saves her father in the past]], fulfilling a memory he had shared with her as a child about a strange woman having saved his life. The predestination paradox raises philosophical questions about free will, determinism, and the nature of time itself. It is commonly used as a narrative device in fiction to highlight the interconnectedness of events and the inevitability of certain outcomes.

===Consistency paradox===
The consistency paradox or grandfather paradox occurs when the past is changed in any way that directly negates the conditions required for the time travel to occur in the first place, thus creating a contradiction. A common example given is traveling to the past and preventing the conception of one's ancestors (such as causing the death of the ancestor's parent beforehand), thus preventing the conception of oneself. If the traveler were not born, then it would not be possible to undertake such an act in the first place; therefore, the ancestor proceeds to beget the traveler's next-generation ancestor and secure the line to the traveler. There is no predicted outcome to this scenario.<ref name="Smith" /> Consistency paradoxes occur whenever changing the past is possible.<ref name="Lobo" /> A possible resolution is that a time traveller ''can'' do anything that ''did'' happen, but ''cannot'' do anything that ''did not'' happen. Doing something that did not happen results in a contradiction.<ref name="Smith" /> This is referred to as the [[Novikov self-consistency principle]].

==== Variants ====
{{anchor|Retro-suicide paradox}}{{Anchor|Hitler's murder paradox}}
The grandfather paradox encompasses any change to the past,<ref name="NicholasSmith2">{{cite encyclopedia |title=Time Travel |encyclopedia=Stanford Encyclopedia of Philosophy |url=http://plato.stanford.edu/entries/time-travel/index.html#CauLoo |access-date=November 2, 2015 |date=2013 |author=Nicholas J.J. Smith}}</ref> and it is presented in many variations, including killing one's past self.<ref name="horwich">{{cite book |last1=Horwich |first1=Paul |title=Asymmetries in Time: Problems in the Philosophy of Science |date=1987 |publisher=MIT Press |isbn=0262580888 |edition=2nd |location=Cambridge, Massachusetts |page=116}}</ref><ref name="stanford backward2">{{citation |author=Jan Faye |title=Backward Causation |date=November 18, 2015 |url=https://plato.stanford.edu/entries/causation-backwards/ |encyclopedia=Stanford Encyclopedia of Philosophy |access-date=May 25, 2019}}</ref> Both the "retro-suicide paradox" and the "grandfather paradox" appeared in letters written into ''[[Amazing Stories]]'' in the 1920s.<ref name="Nahin 1999">{{cite book |last=Nahin |first=Paul J. |url=https://archive.org/details/timemachinestime0000nahi_m8y6 |title=Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction |date=1999 |publisher=Springer-Verlag |isbn=0-387-98571-9 |edition=2nd |location=New York |access-date=2022-02-19 |url-access=registration}}</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>{{cite book |last1=Brennan |first1=J.H. |url=https://books.google.com/books?id=UBf_HjZHUxkC |title=Time Travel: A New Perspective |date=1997 |publisher=Llewellyn Publications |isbn=9781567180855 |edition=1st |location=Minnesota |page=23}}</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>{{cite journal |last1=Garrison |first1=J.C. |last2=Mitchell |first2=M.W. |last3=Chiao |first3=R.Y. |last4=Bolda |first4=E.L. |date=August 1998 |title=Superluminal Signals: Causal Loop Paradoxes Revisited |journal=Physics Letters A |volume=245 |issue=1–2 |pages=19–25 |arxiv=quant-ph/9810031 |bibcode=1998PhLA..245...19G |doi=10.1016/S0375-9601(98)00381-8 |s2cid=51796022}}</ref><ref>{{cite book |last1=Nahin |first1=Paul J. |title=Time Machine Tales |date=2016 |publisher=Springer International Publishing |isbn=9783319488622 |pages=335–336}}</ref>

===Newcomb's paradox===
{{main|Newcomb's paradox}}
Newcomb's paradox is a [[thought experiment]] showing an apparent contradiction between the [[expected utility hypothesis|expected utility]] principle and the [[strategic dominance]] principle.<ref name="Wolpert">{{cite journal |first1=D. H. |last1=Wolpert |first2=G. |last2=Benford |title=The lesson of Newcomb's paradox |journal=[[Synthese]]|date=June 2013 |volume=190 |issue=9 |pages=1637–1646 |doi=10.1007/s11229-011-9899-3 |jstor=41931515|s2cid=113227 }}</ref> 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{{how?|date=September 2024}}, then perfect predictions appear to contradict free will because decisions apparently made with free will are already known to the perfect predictor{{what?|date=September 2024}}.<ref>{{cite journal |author=Craig |year=1987 |url=http://www.leaderu.com/offices/billcraig/docs/newcomb.html |title=Divine Foreknowledge and Newcomb's Paradox |journal=Philosophia |volume=17 |issue=3 |pages=331–350 |doi=10.1007/BF02455055|s2cid=143485859 |url-access=subscription }}</ref><ref>{{cite journal |last=Craig |first=William Lane |author-link=William Lane Craig |year=1988 |title=Tachyons, Time Travel, and Divine Omniscience |journal=[[The Journal of Philosophy]] |volume=85 |issue=3 |pages=135–150 |jstor=2027068|doi=10.2307/2027068 }}</ref> [[Predestination]] does not necessarily involve a [[supernatural]] power, and could be the result of other "infallible foreknowledge" mechanisms.<ref>{{cite journal |last=Craig|first=William Lane|year=1987 |url=http://www.leaderu.com/offices/billcraig/docs/newcomb.html |title=Divine Foreknowledge and Newcomb's Paradox |journal=Philosophia |volume=17 |issue=3 |pages=331–350 |doi=10.1007/BF02455055|s2cid=143485859|url-access=subscription }}</ref> Problems arising from infallibility and influencing the future are explored in Newcomb's paradox.<ref>{{cite book|last=Dummett|first=Michael|title=The Seas of Language|isbn=9780198240112|year=1996|publisher=Oxford University Press|pages=356, 370–375}}</ref>

== Proposed resolutions ==
=== Logical impossibility ===
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">{{citation |author=Norman Swartz |title=Beyond Experience: Metaphysical Theories and Philosophical Constraints |date=2001 |url=https://www.sfu.ca/~swartz/beyond_experience/chap08.htm |pages=226–227 |publisher=University of Toronto Press}}</ref><ref>{{cite book |last1=Dummett |first1=Michael |title=The Seas of Language |date=1996 |publisher=Oxford University Press |isbn=0198236212 |edition=New |location=Oxford |pages=368–369}}</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">{{cite web |author=Norman Swartz |year=1993 |title=Time Travel - Visiting the Past |url=https://www.sfu.ca/~swartz/time_travel1.htm |access-date=2016-04-21 |publisher=SFU.ca}}</ref>

=== Emergent time and entropic reconfiguration ===
A recent proposed resolution argues that if time is not an inherent property of the universe but is instead [[emergent phenomena|emergent]] from the laws of [[entropy]], as some modern theories suggest,<ref>{{cite journal |last=Rovelli |first=Carlo |date=2009 |title=Forget time |journal=Foundations of Physics |volume=41 |issue=9 |pages=1475–1490 |arxiv=0903.3832 |bibcode=2011FoPh...41.1475R |doi=10.1007/s10701-011-9561-4 |s2cid=9891985}}</ref><ref>{{cite journal |last=Verlinde |first=Erik |date=2011 |title=On the Origin of Gravity and the Laws of Newton |journal=Journal of High Energy Physics |volume=2011 |issue=4 |page=29 |arxiv=1001.0785 |bibcode=2011JHEP...04..029V |doi=10.1007/JHEP04(2011)029 |s2cid=118622227}}</ref> then it presents a natural solution to the Grandfather Paradox.<ref>{{cite web |title=Resolving the Grandfather Paradox through Emergent Time |url=https://filmboards.com/t/Science/Resolving-the-Grandfather-Paradox-3561233/ |website=Filmboards |access-date=14 March 2025}}</ref> 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.

=== 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">{{cite book |last1=Yourgrau |first1=Palle |url=https://books.google.com/books?id=GtY907BlhxYC&q=2005+A+World+Without+Time:+The+Forgotten+Legacy+of+G%C3%B6del+and+Einstein&pg=PA134 |title=A World Without Time: The Forgotten Legacy of Godel and Einstein |date=4 March 2009 |publisher=Basic Books |isbn=9780786737000 |location=New York |page=134 |access-date=December 18, 2017}}</ref><ref name="holt">{{cite magazine |last=Holt |first=Jim |date=2005-02-21 |title=Time Bandits |url=https://www.newyorker.com/magazine/2005/02/28/time-bandits-2 |magazine=The New Yorker |access-date=2017-12-13}}</ref> He suggests something along the lines of the [[Eternalism (philosophy of time)|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".{{Citation needed|date=September 2016}}

=== Physical impossibility ===
[[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.<ref name="Krasnikov2001">{{citation|last=Krasnikov|first=S.|year=2001|title=The time travel paradox|journal=Phys. Rev. D|volume=65|issue=6|page=06401 |arxiv=gr-qc/0109029|bibcode = 2002PhRvD..65f4013K |doi = 10.1103/PhysRevD.65.064013 |s2cid=18460829}}</ref>{{Rp|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.<ref name="Krasnikov2001" />{{Rp|14–16}}

==== Self-sufficient loops ====
A 1992 paper by physicists Andrei Lossev and [[Igor Dmitriyevich Novikov|Igor Novikov]] labeled such items without origin as ''Jinn'', with the singular term ''Jinnee''.<ref name="Lossev1992">{{cite journal|last1=Lossev|first1=Andrei|last2=Novikov|first2=Igor|date=15 May 1992|title=The Jinn of the time machine: non-trivial self-consistent solutions|journal=Class. Quantum Gravity|volume=9|issue=10|pages=2309–2321|url=http://thelifeofpsi.com/wp-content/uploads/2015/01/Lossev-Novikov-1992.pdf|doi=10.1088/0264-9381/9/10/014|bibcode=1992CQGra...9.2309L|s2cid=250912686 |access-date=16 November 2015|archive-url=https://web.archive.org/web/20151117014658/http://thelifeofpsi.com/wp-content/uploads/2015/01/Lossev-Novikov-1992.pdf|archive-date=17 November 2015|url-status=dead}}</ref>{{Rp|2311–2312}} This terminology was inspired by the [[Jinn]] of the [[Quran]], which are described as leaving no trace when they disappear.<ref name="Toomey2012">{{cite book|last=Toomey|first=David|title=The New Time Travelers|date=2012|publisher=W. W. Norton & Company|location=New York, New York|isbn=978-0-393-06013-3|url=https://archive.org/details/newtimetravelers00toom}}</ref>{{Rp|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".<ref name="Everett" /><ref name="Lossev1992" />{{Rp|2315–2317}}<ref name="Toomey2012" />{{Rp|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; 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" />{{Rp|200–203}} They emphasize that there is no "strict difference" between Jinn of the first and second kind.<ref name="Lossev1992" />{{Rp|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."<ref name="Krasnikov2001" />{{Rp|8–9}}

==== Novikov self-consistency principle ====
{{main|Novikov self-consistency principle}}
The self-consistency principle developed by [[Igor Dmitriyevich Novikov]]<ref name="Friedman1990">{{cite journal |ref={{harvid|Friedman|1990}}|last1=Friedman|first1=John |last2=Morris|first2=Michael S.|last3=Novikov|first3=Igor D.|last4=Echeverria|first4=Fernando |last5=Klinkhammer|first5=Gunnar |last6=Thorne|first6=Kip S.|last7=Yurtsever|first7=Ulvi| url=http://authors.library.caltech.edu/3737/ | title=Cauchy problem in spacetimes with closed timelike curves | journal = Physical Review D | volume = 42 | year=1990 | issue=6 | doi=10.1103/PhysRevD.42.1915 | pages=1915–1930 | bibcode=1990PhRvD..42.1915F | pmid=10013039|url-access=subscription}}</ref>{{Rp|at=p. 42 note 10}} 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 in general relativity|exact solutions]] that allow for [[time travel]]<ref>{{citation|last=Krasnikov|first=S.|year=2002|title=No time machines in classical general relativity|journal=Classical and Quantum Gravity|volume=19|issue=15|page=4109|arxiv = gr-qc/0111054 |bibcode = 2002CQGra..19.4109K |doi = 10.1088/0264-9381/19/15/316 |s2cid=16517920}}</ref> that contain [[closed timelike curves]] that lead back to the same point in spacetime,<ref>{{cite journal |last=Gödel|first=Kurt| title=An Example of a New Type of Cosmological Solution of Einstein's Field Equations of Gravitation | journal=Rev. Mod. Phys. | year=1949 | volume=21 | pages=447–450 | doi=10.1103/RevModPhys.21.447 | issue=3|bibcode = 1949RvMP...21..447G | doi-access=free }}</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" />

[[File:Grandfather_paradox_billiard_ball.svg|right|thumb|Top: original billiard ball trajectory. Middle: the billiard ball emerges from the future, and delivers its past self a strike that averts the past ball from entering the time machine. Bottom: The billiard ball never enters the time machine, giving rise to the paradox, putting into question how its older self could ever emerge from the time machine and divert its course.]]
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">{{cite book | last = Thorne | first = Kip S. | author-link = Kip Thorne | title = Black Holes and Time Warps | publisher = W. W. Norton | year= 1994 | isbn = 0-393-31276-3|pages=509–513| title-link = Black Holes and Time Warps }}</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>{{cite journal |ref={{harvid|Echeverria|1991}}| first=Fernando | last=Echeverria |author2=Gunnar Klinkhammer |author3=Kip Thorne | url=http://authors.library.caltech.edu/6469/ | title=Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory | journal = Physical Review D | volume = 44 | year=1991 | issue=4 | doi=10.1103/PhysRevD.44.1077 | pages=1077–1099| pmid=10013968 |bibcode = 1991PhRvD..44.1077E | url-access=subscription }}</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">{{cite book | last = Earman | first = John | title = Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes | publisher = Oxford University Press |year= 1995 | isbn = 0-19-509591-X}}</ref>{{Rp|184}} The lack of constraints on initial conditions only applies to spacetime outside of the [[Chronology protection conjecture|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" />{{Rp|187–188}}

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>{{cite book | last = Nahin | first =Paul J. | title = Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction | publisher =American Institute of Physics |year= 1999 | isbn = 0-387-98571-9|pages=345–352}}</ref> Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity.<ref name="Krasnikov2001" />{{Rp|14–16}} 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>{{cite journal |last1=Visser |first1=Matt |date=15 April 1997 |title=Traversable wormholes: The Roman ring |journal=Physical Review D |volume=55 |issue=8 |pages=5212–5214 |arxiv=gr-qc/9702043 |bibcode=1997PhRvD..55.5212V |doi=10.1103/PhysRevD.55.5212 |s2cid=2869291}}</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">{{citation |author1=Frank Arntzenius |title=Time Travel and Modern Physics |date=December 23, 2009 |url=http://plato.stanford.edu/entries/time-travel-phys/ |encyclopedia=Stanford Encyclopedia of Philosophy |access-date=May 25, 2019 |author2=Tim Maudlin}}</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">{{cite web |last1=Hawking |first1=Stephen |year=1999 |title=Space and Time Warps |url=http://www.hawking.org.uk/space-and-time-warps.html |access-date=February 25, 2012 |archive-date=February 10, 2012 |archive-url=https://web.archive.org/web/20120210233225/http://www.hawking.org.uk/space-and-time-warps.html |url-status=dead }}</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">{{cite journal |last1=Deutsch |first1=David |author-link=David Deutsch |date=15 November 1991 |title=Quantum mechanics near closed timelike lines |journal=Physical Review D |volume=44 |issue=10 |pages=3197–3217 |bibcode=1991PhRvD..44.3197D |doi=10.1103/PhysRevD.44.3197 |pmid=10013776}}</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>{{cite journal |last1=Tolksdorf |first1=Juergen |last2=Verch |first2=Rainer |date=2021 |title=The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems |journal=Foundations of Physics |series= |volume=51 |issue=93 |page=93 |arxiv=1912.02301 |bibcode=2021FoPh...51...93T |doi=10.1007/s10701-021-00496-z |authorlink2= |authorlink1= |s2cid=208637445}}</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">{{cite journal |last=Everett |first=Allen |year=2004 |title=Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics |journal=Physical Review D |volume=69 |issue=124023 |pages=124023 |arxiv=gr-qc/0410035 |bibcode=2004PhRvD..69l4023E |doi=10.1103/PhysRevD.69.124023 |s2cid=18597824}}</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]]

==References==
{{reflist|30em|refs=

<ref name="Lobo">{{cite book |arxiv=gr-qc/0206078 |bibcode=2003ntgp.conf..289L |chapter=Time, Closed Timelike Curves and Causality |title=The Nature of Time: Geometry, Physics and Perception |volume=95 |pages=289–296 |series=NATO Science Series II |last=Lobo |first=Francisco|year=2003 |isbn=1-4020-1200-4}}</ref>

<ref name="Nato">{{cite journal |title=Time, Closed Timelike Curves and Causality |author=Francisco Lobo |journal=Nato Science Series II |year=2003 |volume=95 |pages=289–296 |arxiv=gr-qc/0206078 |bibcode=2003ntgp.conf..289L}}</ref>

}}

{{Time travel}}

[[Category:Causality]]
[[Category:Physical paradoxes]]
[[Category:Temporal paradoxes| ]]
[[Category:Thought experiments in physics]]
[[Category:Time travel]]