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## Tipler Cylinder

An Overview and Comparison by Dr. David Lewis Anderson

A Tipler Cylinder uses a massive and long cylinder spinning around its longitudinal axis. The rotation creates a frame-dragging effect and fields of closed time-like curves traversable in a way to achieve subluminal time travel to the past.

Civilizations with the technology to harness black holes might be better advised to leave wormholes alone and try the time-warp method suggested by U.S. astronomer Frank Tipler. He has a simple recipe for a time machine: First take a piece of material 10 time the mass of the Sun, squeeze it together and roll it into a long, thin, super-dense cylinder – a bit like a black hole that has passed through a spaghetti factory. Then spin the cylinder up to a few billion revolutions per minute and see what happens.

Tipler predicts that a ship following a carefully plotted spiral course around the cylinder would immediately find itself on a "closed, time-like curve." It would emerge thousands, even billions, of years from its starting point and possibly several galaxies away. There are problems, though. For the mathematics to work properly, Tipler’s cylinder has to be infinitely long. Also, odd things happen near the ends and you need to steer well clear of them in your timeship. However, if you make the device as long as you can, and stick to paths close to the middle of the cylinder, you should survive the trip!

The 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 would appear infinite.

The key characteristics of the application of Tipler Cylinders for time control and time travel are presented in the picture below. This is followed by more detail describing the approach below.

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. 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.

 Closed timelike curve formation using rotating cylinder model
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, 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." Hawking's proof appears in his 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 "there 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."