Editing Time travel (section)

=== General relativity ===
Time travel to the past is theoretically possible in certain general relativity spacetime geometries that permit traveling [[faster-than-light|faster than the speed of light]], such as [[cosmic string]]s, traversable [[wormhole]]s, and [[Alcubierre drive]]s.<ref>{{cite web|url=http://ccrg.rit.edu/files/FasterThanLight.pdf|title=Warp Drives, Wormholes, and Black Holes|author=Miguel Alcubierre|date=June 29, 2012|access-date=January 25, 2017|archive-date=March 18, 2016|archive-url=https://web.archive.org/web/20160318223348/http://ccrg.rit.edu/files/FasterThanLight.pdf|url-status=dead}}</ref><ref name="Gott">{{cite book|author=J. Richard Gott|title=Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time|url=https://books.google.com/books?id=3QBgCgAAQBAJ&pg=PT45|date=25 August 2015|publisher=HMH|isbn=978-0-547-52657-7|page=33|access-date=3 February 2018|archive-date=24 March 2023|archive-url=https://web.archive.org/web/20230324181808/https://books.google.com/books?id=3QBgCgAAQBAJ&pg=PT45|url-status=live}}</ref>{{rp|33–130}} The theory of [[general relativity]] does suggest a scientific basis for the possibility of backward time travel in certain unusual scenarios, although arguments from [[semiclassical gravity]] suggest that when [[quantum mechanics|quantum]] effects are incorporated into general relativity, these loopholes may be closed.<ref>{{cite book|arxiv=gr-qc/0204022|last=Visser|first=Matt|title=The quantum physics of chronology protection|url=https://archive.org/details/arxiv-gr-qc0204022|year=2002|bibcode=2003ftpc.book..161V}}</ref> These semiclassical arguments led [[Stephen Hawking]] to formulate the [[chronology protection conjecture]], suggesting that the fundamental laws of nature prevent time travel,<ref name="chronology protection">{{cite journal|first=Stephen|last=Hawking|author-link=Stephen Hawking|title=Chronology protection conjecture|journal=Physical Review D|volume=46|year=1992|issue=2|pages=603–611|doi=10.1103/PhysRevD.46.603|pmid=10014972|bibcode=1992PhRvD..46..603H|url=http://thelifeofpsi.com/wp-content/uploads/2014/09/Hawking-1992.pdf|archive-url=https://web.archive.org/web/20150227141021/http://thelifeofpsi.com/wp-content/uploads/2014/09/Hawking-1992.pdf|archive-date=2015-02-27}}</ref> but physicists cannot come to a definitive judgment on the issue without a theory of [[quantum gravity]] to join quantum mechanics and general relativity into a completely unified theory.<ref name="sagan-nova">{{cite web|url=https://www.pbs.org/wgbh/nova/time/sagan.html|title=Carl Sagan Ponders Time Travel|work=NOVA|date=December 10, 1999|publisher=[[PBS]]|access-date=April 26, 2017|archive-date=July 15, 2019|archive-url=https://web.archive.org/web/20190715000440/https://www.pbs.org/wgbh/nova/time/sagan.html|url-status=live}}</ref><ref name="futureofspacetime">{{cite book|last1=Hawking|first1=Stephen|author-link=Stephen Hawking|last2=Thorne|first2=Kip|author-link2=Kip Thorne|last3=Novikov|first3=Igor|author-link3=Igor Dmitriyevich Novikov|last4=Ferris|first4=Timothy|author-link4=Timothy Ferris|last5=Lightman|first5=Alan|author-link5=Alan Lightman|title=The Future of Spacetime|publisher=W. W. Norton|year=2002|isbn=978-0-393-02022-9|url=https://books.google.com/books?id=LlVcB7rz4mkC&pg=PA750}}</ref>{{rp|150}}

==== Different spacetime geometries ====
The theory of [[general relativity]] describes the universe under a system of [[Einstein field equations|field equations]] that determine the [[Metric (general relativity)|metric]], or distance function, of spacetime. There exist exact solutions to these equations that include [[closed time-like curve]]s, which are [[world line]]s that intersect themselves; some point in the causal future of the world line is also in its causal past, a situation that can be described as time travel. Such a solution was first proposed by [[Kurt Gödel]], a solution known as the [[Gödel metric]], but his (and others') solution requires the universe to have physical characteristics that it does not appear to have,<ref name="Thorne1994"/>{{rp|499}} such as [[Mach's principle|rotation]] and lack of [[Hubble expansion]]. Whether general relativity forbids closed time-like curves for all realistic conditions is still being researched.<ref name="Hawking">S. W. Hawking, ''Introductory note to 1949 and 1952'' in Kurt Gödel, ''Collected works'', Volume II (S. Feferman et al., eds).</ref>

==== Wormholes ====
{{main|Wormhole}}
Wormholes are a hypothetical warped spacetime permitted by the [[Einstein field equations]] of general relativity.<ref name="Visser1996">{{cite book|last=Visser|first=Matt|author-link=Matt Visser|title=Lorentzian Wormholes|publisher=Springer-Verlag|year=1996|isbn=978-1-56396-653-8}}</ref>{{rp|100}} A proposed time-travel machine using a [[Wormhole#Traversable wormholes|traversable wormhole]] would hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced [[Vehicle propulsion|propulsion system]], and then brought back to the point of origin. Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance. For both these methods, [[time dilation]] causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently ''through'' the wormhole than ''outside'' it, so that [[Synchronization|synchronized]] clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.<ref name="Thorne1994" />{{rp|502}} This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside. One significant limitation of such a time machine is that it is only possible to go as far back in time as the initial creation of the machine;<ref name="Thorne1994" />{{rp|503}} in essence, it is more of a path through time than it is a device that itself moves through time, and it would not allow the technology itself to be moved backward in time.

According to current theories on the nature of wormholes, construction of a traversable wormhole would require the existence of a substance with [[negative energy]], often referred to as "[[exotic matter]]". More technically, the wormhole spacetime requires a distribution of energy that violates various [[energy condition]]s, such as the null energy condition along with the weak, strong, and dominant energy conditions. However, it is known that quantum effects can lead to small measurable violations of the null energy condition,<ref name="Visser1996" />{{rp|101}} and many physicists believe that the required negative energy may actually be possible due to the [[Casimir effect]] in quantum physics.<ref name="casimir">{{cite web|url=http://www.npl.washington.edu/av/altvw69.html|title=NASA Goes FTL Part 1: Wormhole Physics|work=Analog Science Fiction & Fact Magazine|year=1994|access-date=December 2, 2006|last1=Cramer|first1=John G.|author-link=John G. Cramer|archive-url=https://web.archive.org/web/20060627211046/http://www.npl.washington.edu/av/altvw69.html <!-- Bot retrieved archive -->|archive-date=June 27, 2006}}</ref> Although early calculations suggested that a very large amount of negative energy would be required, later calculations showed that the amount of negative energy can be made arbitrarily small.<ref name="negative energy">{{cite journal|first=Matt|last=Visser|author-link=Matt Visser|author2=Sayan Kar|author3=Naresh Dadhich|title=Traversable wormholes with arbitrarily small energy condition violations|journal=[[Physical Review Letters]]|volume=90|year=2003|issue=20|pages=201102.1–201102.4|doi=10.1103/PhysRevLett.90.201102|arxiv=gr-qc/0301003|bibcode=2003PhRvL..90t1102V|pmid=12785880|s2cid=8813962}}</ref>

In 1993, [[Matt Visser]] argued that the two mouths of a wormhole with such an induced clock difference could not be brought together without inducing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other.<ref name="visser_1">{{cite journal|first=Matt|last=Visser|author-link=Matt Visser|title=From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture|journal=Physical Review D|volume=47|year=1993|issue=2|pages=554–565|doi=10.1103/PhysRevD.47.554|pmid=10015609|arxiv=hep-th/9202090|bibcode=1993PhRvD..47..554V|s2cid=16830951}}</ref> Because of this, the two mouths could not be brought close enough for [[Causality (physics)|causality]] violation to take place. However, in a 1997 paper, Visser hypothesized that a complex "[[Roman ring]]" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.<ref name="visser_2">{{cite journal|first=Matt|last=Visser|author-link=Matt Visser|title=Traversable wormholes: the Roman ring|journal=Physical Review D|volume=55|year=1997|issue=8|pages=5212–5214|doi=10.1103/PhysRevD.55.5212|arxiv=gr-qc/9702043|bibcode=1997PhRvD..55.5212V|s2cid=2869291}}</ref>

==== Other approaches based on general relativity ====
Another approach involves a dense spinning cylinder usually referred to as a [[Tipler cylinder]], a GR solution discovered by [[Willem Jacob van Stockum]]<ref name="stockum">{{cite journal|first=Willem Jacob|last=van Stockum|author-link=Willem Jacob van Stockum|url=http://www-lorentz.leidenuniv.nl/history/stockum/Proc_R_Soc_Edinb_57_135_1937.jpg|title=The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry|year=1936|journal=Proceedings of the Royal Society of Edinburgh|url-status=dead|archive-url=https://web.archive.org/web/20080819215608/http://www-lorentz.leidenuniv.nl/history/stockum/Proc_R_Soc_Edinb_57_135_1937.jpg|archive-date=2008-08-19}}</ref> in 1936 and [[Kornel Lanczos]]<ref name="lanczos">{{cite journal|first=Kornel|last=Lanczos|author-link=Kornel Lanczos|doi=10.1023/A:1010277120072|title=On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation|year=1924 <!--republished in 1997-->|journal=General Relativity and Gravitation|publisher=Springland Netherlands|volume=29|issue=3|pages=363–399|s2cid=116891680}}</ref> in 1924, but not recognized as allowing closed timelike curves<ref name="Earman">{{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=978-0-19-509591-3|bibcode=1995bcws.book.....E}}</ref>{{rp|21}} until an analysis by [[Frank Tipler]] in 1974.<ref name="tipler">{{cite journal|first=Frank J|last=Tipler|author-link=Frank J. Tipler|title=Rotating Cylinders and the Possibility of Global Causality Violation|journal=Physical Review D|volume=9|year=1974|issue=8|page=2203|doi=10.1103/PhysRevD.9.2203|bibcode=1974PhRvD...9.2203T|s2cid=17524515}}</ref> If a cylinder is infinitely long and spins fast enough about its long axis, then a spaceship flying around the cylinder on a spiral path could travel back in time (or forward, depending on the direction of its spiral). However, the density and speed required is so great that ordinary matter is not strong enough to construct it. 

A more fundamental objection to time travel schemes based on rotating cylinders or cosmic strings has been put forward by Stephen Hawking, who proved a theorem showing that according to general relativity it is impossible to build a time machine of a special type (a "time machine with the compactly generated Cauchy horizon") in a region where the [[weak energy condition]] is satisfied, meaning that the region contains no matter with negative energy density ([[exotic matter]]). Solutions such as Tipler's assume cylinders of infinite length, which are easier to analyze mathematically, and although Tipler suggested that a finite cylinder might produce closed timelike curves if the rotation rate were fast enough,<ref name="Earman" />{{rp|169}} he did not prove this. But Hawking points out that because of his theorem, "it can't be done with positive energy density everywhere! I can prove that to build a finite time machine, you need negative energy."<ref name="futureofspacetime" />{{rp|96}} This result comes from Hawking's 1992 paper on the [[chronology protection conjecture]], which Hawking states as "The laws of physics do not allow the appearance of closed timelike curves."<ref name="chronology protection" />