Editing Time travel (section)

==== 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" />