Editing Closed timelike curve (section)

== Consequences ==
One feature of a CTC is that it opens the possibility of a worldline which is not connected to earlier times, and so the existence of events that cannot be traced to an earlier cause. Ordinarily, [[causality]] demands that each event in spacetime is preceded by its cause in every rest frame. This principle is critical in [[determinism]], which in the language of [[general relativity]] states complete knowledge of the universe on a spacelike [[Cauchy surface]] can be used to calculate the complete state of the rest of spacetime. However, in a CTC, causality breaks down, because an event can be "simultaneous" with its cause—in some sense an event may be able to cause itself. It is impossible to determine based only on knowledge of the past whether or not something exists in the CTC that can interfere with other objects in spacetime. A CTC therefore results in a [[Cauchy horizon]], and a region of spacetime that cannot be predicted from perfect knowledge of some past time.

No CTC can be continuously deformed as a CTC to a point (that is, a CTC and a point are not [[timelike homotopic]]), as the manifold would not be causally well behaved at that point. The topological feature which prevents the CTC from being deformed to a point is known as a [[timelike topological feature]].

The existence of CTCs would arguably place restrictions on physically allowable states of matter-energy fields in the universe. Propagating a field configuration along the family of closed timelike [[World line|worldlines]] must, according to such arguments, eventually result in the state that is identical to the original one. This idea has been explored by some scientists{{Who|date=November 2022}} as a possible approach towards disproving the existence of CTCs.

While [[Quantum mechanics of time travel|quantum formulations of CTCs]] have been proposed,<ref>{{Cite journal|last=Deutsch|first=David|date=1991-11-15|title=Quantum mechanics near closed timelike lines|journal=Physical Review D|language=en-US|volume=44|issue=10|pages=3197–3217|doi=10.1103/physrevd.44.3197|issn=0556-2821|bibcode=1991PhRvD..44.3197D|pmid=10013776}}</ref><ref>{{Cite journal|last1=Lloyd|first1=Seth|last2=Maccone|first2=Lorenzo|last3=Garcia-Patron|first3=Raul|last4=Giovannetti|first4=Vittorio|last5=Shikano|first5=Yutaka|date=2011-07-13|title=Quantum mechanics of time travel through post-selected teleportation|journal=Physical Review D|volume=84|issue=2|pages=025007|doi=10.1103/physrevd.84.025007|issn=1550-7998|arxiv=1007.2615|bibcode=2011PhRvD..84b5007L|s2cid=15972766}}</ref> a strong challenge to them is their ability to freely create [[Quantum entanglement|entanglement]],<ref>{{Cite journal|last1=Moulick|first1=Subhayan Roy|last2=Panigrahi|first2=Prasanta K.|date=2016-11-29|title=Timelike curves can increase entanglement with LOCC|journal=Scientific Reports|volume=6|issue=1|pages=37958|doi=10.1038/srep37958|pmid=27897219|pmc=5126586|arxiv=1511.00538 |bibcode=2016NatSR...637958M|issn=2045-2322}}</ref> which quantum theory predicts is impossible. If Deutsch's prescription holds, the existence of these CTCs implies also equivalence of quantum and classical computation (both in [[PSPACE]]).<ref name=aaronson>{{cite journal | doi=10.1098/rspa.2008.0350|bibcode = 2009RSPSA.465..631A | title=Closed timelike curves make quantum and classical computing equivalent | year=2009 | last1=Watrous | first1=John | last2=Aaronson | first2=Scott | journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | volume=465 | issue=2102 | pages=631 |arxiv = 0808.2669 |s2cid = 745646 }}</ref> If Lloyd's prescription holds, quantum computations would be PP-complete.