Tipler cylinder

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A Tipler cylinder, also called a Tipler time machine, is a hypothetical object theorized to be a potential mode of time travel—an approach that is conceivably functional within humanity's current understanding of physics, specifically the theory of general relativity, although later results have shown that a Tipler cylinder could only allow time travel if its length were infinite (see the discussion of Hawking's conjecture below).

Frank J. Tipler showed in his 1974 paper, "Rotating Cylinders and the Possibility of Global Causality Violation" that in a spacetime containing a massive, infinitely long cylinder which was spinning along its longitudinal 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 space time diagram. Therefore a spacecraft accelerating sufficiently in the appropriate direction can travel backwards through time along a closed timelike curve or CTC.^[1]

CTC's are associated, in Lorentzian manifolds which are interpreted physically as spacetimes, with the possibility of causal anomalies such as going back in time and potentially shooting your own grandfather, although paradoxes might be avoided using some constraint such as the Novikov self-consistency principle. They have an unnerving habit of appearing in some of the most important exact solutions in general relativity, including the Kerr vacuum (which models a rotating black hole) and the van Stockum dust (which models a cylindrically symmetrical configuration of rotating pressureless fluid or dust).

An objection to the practicality of building a Tipler cylinder was discovered by Stephen Hawking, who posited a conjecture showing 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,^[2] he did not prove this. But Hawking argues that because of his conjecture, "it can't be done with positive energy density everywhere! I can prove that to build a finite time machine, you need negative energy."^[3] This argument comes from Hawking's 1992 paper on the chronology protection conjecture, where 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."^[4]

[edit] Tipler cylinders in fiction

• John DeChancie's Starrigger series uses vertically-aligned Tipler cylinders (officially called Kerr-Tipler objects) to create spacetime gateways along an intergalactic highway.
• Larry Niven wrote a short story, Rotating Cylinders and the Possibility of Global Causality Violation that borrowed its title from Tipler's paper.^[5]
• Poul Anderson in The Avatar.^[6]

[edit] References