Editing Closed timelike curve (section)

{{Short description|World line of a particle in spacetime which returns to its starting point}}
{{Refimprove|date=November 2014}}

In [[mathematical physics]], a '''closed timelike curve''' ('''CTC''') is a [[world line]] in a [[Lorentzian manifold]], of a material particle in [[spacetime]], that is "closed", returning to its starting point. This possibility was first discovered by [[Willem Jacob van Stockum]] in 1937<ref>Stockum, W. J. van (1937). "The gravitational field of a distribution of particles rotating around an axis of symmetry.". Proc. Roy. Soc. Edinburgh. 57.</ref> and later confirmed by [[Kurt Gödel]] in 1949,<ref name="Hawking2013">Stephen Hawking, ''[[My Brief History]]'', chapter 11</ref> who discovered a solution to the equations of [[general relativity]] (GR) allowing CTCs known as the [[Gödel metric]]; and since then other GR solutions containing CTCs have been found, such as the [[Tipler cylinder]] and [[Wormhole#Traversable wormholes|traversable wormholes]]. If CTCs exist, their existence would seem to imply at least the theoretical possibility of [[time travel]] backwards in time, raising the spectre of the [[grandfather paradox]], although the [[Novikov self-consistency principle]] seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of [[quantum gravity]] which would replace GR, an idea which [[Stephen Hawking]] labeled the [[chronology protection conjecture]]. Others note that if every closed timelike curve in a given spacetime passes through an [[event horizon]], a property which can be called chronological censorship, then that spacetime with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.<ref name=monroe>{{cite journal | doi= 10.1007/s10701-008-9254-9 | author= H. Monroe | title = Are Causality Violations Undesirable? | year = 2008 | journal = Foundations of Physics | volume = 38 | pages = 1065&ndash;1069 |arxiv = gr-qc/0609054 | issue= 11 |bibcode = 2008FoPh...38.1065M | s2cid= 119707350 }}</ref>