Editing Tipler cylinder (section)

== Practicality ==
An objection to the practicality of building a Tipler cylinder was discovered by [[Stephen Hawking]], who argued that according to general relativity it is impossible to build a time machine in any finite region that satisfies the [[weak energy condition]], meaning that the region contains no [[exotic matter]] with negative energy. The Tipler cylinder, on the other hand, does not involve any negative energy. Tipler's original solution involved a cylinder of infinite length, which is 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="Earman2">{{cite book | last = Earman | first = John | title = Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes | publisher = Oxford University Press |date= 1995 | pages = 169 | isbn = 0-19-509591-X}}</ref> he did not prove this. But Hawking comments: "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">{{cite book | last = Hawking | first = Stephen | title = The Future of Spacetime | publisher = W. W. Norton | date = 2002 | pages = [https://archive.org/details/futureofspacetim0000unse/page/96 96] | isbn = 0-393-02022-3 | url-access = registration | url = https://archive.org/details/futureofspacetim0000unse/page/96 }}</ref> Hawking's argument appears in his 1992 paper on the [[chronology protection conjecture]] (though the argument is distinct from the conjecture itself, since the argument asserts that classical general relativity predicts a finite region containing closed timelike curves can only be created if there is a violation of the weak energy condition in that region, whereas the conjecture predicts that closed timelike curves will prove to be impossible in a future theory of [[quantum gravity]] which replaces general relativity). In the paper, he examines "the case that the causality violations appear in a finite region of spacetime without curvature singularities" and proves that "[t]here will be a [[Cauchy horizon]] that is compactly generated and that in general contains one or more closed null geodesics which will be incomplete. One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics. If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon."<ref name="chronology protection">{{cite journal | first=Stephen | last=Hawking | author-link = Stephen Hawking | url=http://link.aps.org/abstract/PRD/v46/p603 | title=Chronology protection conjecture | journal = Physical Review D | volume = 46 | year=1992 | pages = 603–611 | doi=10.1103/PhysRevD.46.603 |bibcode = 1992PhRvD..46..603H | issue=2 | pmid=10014972 | url-access=subscription }}</ref>