View source for Physics:Causal loop

{{Short description|Sequence of events which cause each other}}
[[File:Causal loop billiard ball.svg|thumb|right|Top: original billiard ball [[Physics:Trajectory|trajectory]].{{clear}}Middle: the ball emerges from the future at a different trajectory from the original, and collides with its past self, changing its trajectory.{{clear}}Bottom: the changed trajectory causes the ball to enter and exit the time machine in exactly the same way that changed its trajectory. The changed trajectory is its own cause, without an origin.]]

A '''causal loop''', also known as  a '''bootstrap paradox''', '''information loop''', '''ontological paradox''', and a '''predestination paradox''', is a theoretical proposition, wherein by means of either [[Physics:Retrocausality|retrocausality]] or [[Physics:Time travel|time travel]], an event (an action, information, object, or person)<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">{{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> is among the causes of another event, which is in turn among the causes of the first-mentioned event.<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> Such causally looped events then exist in [[Physics:Spacetime|spacetime]], but their origin cannot be determined.<ref name="Smith" /><ref name="Lobo" /> A hypothetical example of a causality loop is given of a [[Engineering:Billiard ball|billiard ball]] striking its past self: the billiard ball moves in a path towards a time machine, and the future self of the billiard ball emerges from the time machine ''before'' its past self enters it, giving its past self a glancing blow, altering the past ball's path and causing it to enter the time machine at an angle that would cause its future self to strike its past self the very glancing blow that altered its path. In this sequence of events, the change in the ball's path is its own cause, which might appear paradoxical.<ref name="Thorne">{{cite book | last = Thorne | first = Kip S. |  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>

==Terminology in physics, philosophy, and fiction==
{{anchor|terminology}}
Backwards time travel would allow for causal loops involving events, information, people or objects whose histories form a closed loop, and thus seem to "come from nowhere."<ref name="Smith" /> The notion of objects or information that are "self-existing" in this way is often viewed as paradoxical,<ref name="Lobo" /> with several authors referring to a causal loop involving information or objects without origin as a  ''bootstrap paradox'',<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}} "A second class of logical paradoxes associated with time travel are the bootstrap paradoxes related to information (or objects, or even people?) being created from nothing."</ref><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 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|343}} an ''information paradox'',<ref name="Everett" /> or 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> The use of "bootstrap" in this context refers to the expression "pulling yourself up by your bootstraps" and to [[Biography:Robert A. Heinlein|Robert A. Heinlein]]'s time travel story "By His Bootstraps".<ref name="Klosterman"/><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> 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>

An example of a causal loop paradox involving information is given by Allan Everett: suppose a time traveler copies a mathematical proof from a textbook, then travels back in time to meet the mathematician who first published the proof, at a date prior to publication, and allows the mathematician to simply copy the proof. In this case, the information in the proof has no origin.<ref name="Everett"/> A similar example is given in the television series ''Doctor Who'' of a hypothetical time-traveler who copies Beethoven's music from the future and publishes it in Beethoven's time in Beethoven's name.<ref>{{cite web|last=Holmes|first=Jonathan|work=Radio Times|url=http://www.radiotimes.com/news/2015-10-10/doctor-who-what-is-the-bootstrap-paradox|title=Doctor Who: what is the Bootstrap Paradox?|date=October 10, 2015}}</ref> 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.<ref name="Everett" />

[[Biography:Sergey Krasnikov|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 this 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}}

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">{{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 [[Religion:Jinn|Jinn]] of the [[Religion:Quran|Quran]], which are described as leaving no trace when they disappear.<ref name="Toomey2012" />{{Rp|200–203}} Lossev and Novikov allowed the term "Jinn" to cover both objects and information with 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 [[Physics:Second law of thermodynamics|second law of thermodynamics]] seems to require that the object tends to a lower energy state over the course of 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}}

The term ''predestination paradox'' is used in the ''Star Trek'' franchise to mean "a time loop in which a time traveler who has gone into the past causes an event that ultimately causes the original future version of the person to go back into the past."<ref>{{cite book|last1=Okuda|first1=Michael|last2=Okuda|first2=Denise|title=The Star Trek Encyclopedia|date=1999|publisher=Pocket Books|isbn=0-671-53609-5|page=384}}</ref> This use of the phrase was created for a sequence in a 1996 episode of ''Star Trek: Deep Space Nine'' titled "Trials and Tribble-ations",<ref>{{cite book|last1=Erdmann|first1=Terry J.|last2=Hutzel|first2=Gary|title=Star Trek: The Magic of Tribbles|date=2001|publisher=Pocket Books|isbn=0-7434-4623-2|page=[https://books.google.com/books?id=W6bvoGUg7G8C&lpg=PP1&pg=PA31 31]}}</ref> although the phrase had been used previously to refer to belief systems such as [[Religion:Calvinism|Calvinism]] and some forms of [[Philosophy:Marxism|Marxism]] that encourage followers to strive to produce certain outcomes while at the same time teaching that the outcomes are predetermined.<ref>{{cite journal |last=Daniels|first=Robert V.|date=May–June 1960|title=Soviet Power and Marxist Determinism|journal=Problems of Communism|volume=9|page=[http://babel.hathitrust.org/cgi/pt?id=mdp.39015059418874;view=1up;seq=159 17]}}</ref> Smeenk and Morgenstern use 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, but ends up helping to cause that same event.<ref name="smeenk" /><ref name="Morgenstern">{{citation|url=http://cs.nyu.edu/web/Research/TechReports/TR2013-950/TR2013-950.pdf |title=Foundations of a Formal Theory of Time Travel |last=Morgenstern|first=Leora|year=2010|page=6}}</ref>

==Self-fulfilling prophecy==
A [[Self-fulfilling prophecy|self-fulfilling prophecy]] may be a form of causality loop. [[Philosophy:Predestination|Predestination]] does not necessarily involve a [[Philosophy:Supernatural|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}}</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> A notable fictional example of a self-fulfilling prophecy occurs in the classical play ''Oedipus Rex'', in which Oedipus becomes the king of Thebes and in the process unwittingly fulfills a prophecy that he would kill his father and marry his mother. The prophecy itself serves as the impetus for his actions, and thus it is self-fulfilling.<ref>{{citation|last=Dodds|first=E.R.|year=1966|title=Greece & Rome}} 2nd Ser., Vol. 13, No. 1, pp. 37–49</ref><ref>{{cite book|last1=Popper|first1=Karl|title=Unended Quest: An Intellectual Autobiography|date=1985|publisher=Open Court|location=La Salle, Ill.|isbn=978-0-87548-343-6|edition=Rev.|page=139}}</ref> The movie ''12&nbsp;Monkeys'' heavily deals with themes of predestination and the Cassandra complex, where the protagonist who travels back in time explains that he can't change the past.<ref name="Klosterman" />

==Novikov self-consistency principle==
{{main|Novikov self-consistency principle}}
[[Physics:General relativity|General relativity]] permits some [[Physics:Exact solutions in general relativity|exact solutions]] that allow for [[Physics:Time travel|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> Some of these exact solutions describe universes that contain closed timelike curves, or [[World line|world line]]s that lead back to the same point in spacetime.<ref>{{cite book |last=Carroll|first=Sean | title=Spacetime and Geometry | publisher=Addison Wesley | year=2004 | isbn=0-8053-8732-3}}</ref><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><ref>{{cite journal | doi= 10.1007/s10714-005-0163-3 | last1=Bonnor|first1=W. |last2=Steadman|first2=B.R. | title = Exact solutions of the Einstein-Maxwell equations with closed timelike curves | year = 2005 | journal = Gen. Rel. Grav. | volume = 37 | pages = 1833 | issue= 11 |bibcode = 2005GReGr..37.1833B | s2cid=121204248}}</ref> Physicist Igor Dmitriyevich Novikov discussed the possibility of closed timelike curves in his books in 1975 and 1983,<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}}</ref>{{Rp|at=p. 42 note 10}} offering the opinion that only self-consistent trips back in time would be permitted.<ref>Novikov, Igor (1983). ''Evolution of the Universe'', p. 169: "The close of time curves does not necessarily imply a violation of causality, since the events along such a closed line may be all 'self-adjusted'—they all affect one another through the closed cycle and follow one another in a self-consistent way."</ref> In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves",<ref name="Friedman1990" /> the authors suggested the ''principle of self-consistency,'' which states that ''the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent.'' The authors later 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 [[Biography:Joseph Polchinski|Joseph Polchinski]] argued that one could avoid questions of [[Philosophy:Free will|free will]] by considering a potentially paradoxical situation involving a [[Engineering:Billiard ball|billiard ball]] sent back in time. In this situation, the ball is fired into a [[Physics:Wormhole|wormhole]] at an angle such that, if it continues along its course, it will exit in the past at just the right angle to hit its earlier self, knocking it off course, which would stop it from entering the wormhole in the first place. [[Biography:Kip Thorne|Kip Thorne]] referred to this problem as "Polchinski's paradox".<ref name="Thorne" /> Two students at Caltech, Fernando Echeverria and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies. In the revised scenario, the ball would emerge from the future at a different angle from the one that had generated the paradox, and delivers its past self a glancing blow instead of knocking it completely away from the wormhole. This blow changes its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary glancing blow. Echeverria and Klinkhammer actually 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 actually be an infinite number of self-consistent solutions.<ref name="Thorne" />

Echeverria, Klinkhammer and Thorne published a paper discussing these results in 1991;<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 }}</ref> in addition, they reported that they had tried to see if they could find ''any'' initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus 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}}

==Quantum computation with negative delay==
Physicist [[Biography:David Deutsch|David Deutsch]] shows in a 1991 paper that quantum computation with a negative delay&mdash;backwards time travel&mdash;could solve NP problems in [[Time complexity#Polynomial time|polynomial time]],<ref name="Deutsch1991">{{cite journal | first=David | last=Deutsch | title= Quantum mechanics near closed timelike lines | journal = Physical Review D | volume = 44 | issue = 10 | year=1991 | doi= 10.1103/PhysRevD.44.3197 | pmid=10013776 | pages=3197–3217 | bibcode=1991PhRvD..44.3197D}}</ref> and [[Biography:Scott Aaronson|Scott Aaronson]] later extended this result to show that the model could also be used to solve [[PSPACE]] problems in polynomial time.<ref>{{cite journal|journal=Scientific American|volume=298|issue=3|date=March 2008|title=The Limits of Quantum Computers|pages=68–69|url=http://www.scottaaronson.com/writings/limitsqc-draft.pdf|bibcode=2008SciAm.298c..62A|last1=Aaronson|first1=Scott|doi=10.1038/scientificamerican0308-62|pmid=18357822}}</ref><ref>{{cite journal | first=Scott | last=Aaronson |author2=John Watrous | url=http://www.scottaaronson.com/papers/ctc.pdf | title=Closed Timelike Curves Make Quantum and Classical Computing Equivalent | journal = Proceedings of the Royal Society A | volume = 465 | year=2009 | issue = 2102 | doi=10.1098/rspa.2008.0350 | pages=631–647 | bibcode=2009RSPSA.465..631A|arxiv = 0808.2669 | s2cid=745646 }}</ref> Deutsch shows that quantum computation with a negative delay produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning.<ref name="Deutsch1991" /> Researchers published in 2014 a simulation validating Deutsch's model with photons.<ref name=RingbauerEtAl2014>{{cite journal|author1=Martin Ringbauer|author2=Matthew A. Broome|author3=Casey R. Myers|author4=Andrew G. White|author5=Timothy C. Ralph|title=Experimental simulation of closed timelike curves|journal=Nature Communications|date=19 Jun 2014|volume=5|doi=10.1038/ncomms5145|arxiv = 1501.05014 |bibcode = 2014NatCo...5.4145R|pmid=24942489|page=4145|s2cid=12779043}}</ref> However, it was shown in an article by Tolksdorf and Verch that Deutsch's CTC (closed timelike curve, or a causal loop) fixed point condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic [[Physics:Quantum field theory|quantum field theory]] on spacetimes where CTCs are excluded, casting doubts on whether Deutsch's condition is really characteristic of quantum processes mimicking CTCs in the sense of [[Physics:General relativity|general relativity]].<ref>{{cite journal
| last1        = Tolksdorf
| first1       = Juergen
| last2        = Verch
| first2       = Rainer
|date=2018
| title        = Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
| journal      = Communications in Mathematical Physics
| volume       = 357
| issue        = 1
| pages        = 319–351
| arxiv        = 1609.01496
| bibcode      =2018CMaPh.357..319T 
| doi          =  10.1007/s00220-017-2943-5
| s2cid = 55346710
}}</ref>
In a later article,<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
| volume       = 51
| issue        = 93
| series       = 
| page = 93
| arxiv        = 1912.02301
| bibcode      = 2021FoPh...51...93T
| doi          =  10.1007/s10701-021-00496-z
| s2cid = 208637445
}}</ref>
the same authors have shown that  Deutsch's CTC fixed point condition can also be fulfilled in any system
subject to the laws of classical [[Physics:Statistical mechanics|statistical mechanics]], even if it is not built up by quantum systems. The authors conclude that hence, 
Deutsch's condition is not specific to quantum physics, nor does it depend on the quantum nature of a physical system so that it can be fulfilled.
In consequence, Tolksdorf and Verch further conclude that Deutsch's condition is not sufficiently specific to allow statements about time travel scenarios or their hypothetical realization by quantum physics, and that Deutsch's attempt to explain the possibility of his proposed time-travel scenario using the many-world interpretation of quantum mechanics is misleading.

==See also==
{{div col}}
* {{annotated link|Causality}}
* {{annotated link|Physics:Causal structure}}
* {{annotated link|Chronology protection conjecture}}
* {{annotated link|Philosophy:Münchhausen trilemma}}
* {{annotated link|Physics:Grandfather paradox}}
* {{annotated link|Newcomb's paradox}}
{{div col end}}

==References==
{{reflist|30em}}

{{Time travel}}

[[Category:Causality]]
[[Category:Temporal paradoxes]]

{{Sourceattribution|Causal loop|1}}