A Tipler cylinder, also called a Tipler time machine, is a hypothetical object theorized to be a potential mode of time travel—although results have shown that a Tipler cylinder could only allow time travel if its length were infinite or with the existence of negative energy.

Discovery

The Tipler cylinder was discovered as a solution to the equations of general relativity by Willem Jacob van Stockum in 1936 and Kornel Lanczos in 1924, but not recognized as allowing closed timelike curves until an analysis by Frank Tipler in 1974. In the article "Rotating Cylinders and the Possibility of Global Causality Violation", Tipler showed that in a spacetime containing a "sufficiently large rotating cylinder" spinning around its axis, the cylinder should create a frame-dragging effect. This frame-dragging effect warps spacetime in such a way that the light cones of objects in the cylinder's proximity become tilted, so that part of the light cone then points backwards along the time axis on a spacetime diagram. Therefore, a spacecraft accelerating sufficiently in the appropriate direction can travel backwards through time along a closed timelike curve. 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." 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."

References

;Notes

;Bibliography

  1. Frank Jennings Tipler, Causality Violation in General Relativity, Ph.D. thesis at the University of Maryland, College Park (1976). Source: Dissertation Abstracts International, Vol. 37–06, Section B, p. 2923. Also available as Dissertation 76–29,018 from Xerox University Microfilms, Ann Arbor, MI.
  2. Penrose, Roger. "The Question of Cosmic Censorship". Journal of Astrophysics and Astronomy Vol. 20 (September 1999): 233.
  3. Wald, Robert (ed.). Black Holes and Relativistic Stars. University of Chicago Press, 1998. .
  • Rotating cylinders and the possibility of global causality violation -- Full text of original paper by Frank Tipler.