Tipler cylinder

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.

CTCs are associated, in Lorentzian manifolds which are interpreted physically as spacetimes, with the possibility of causal anomalies such as a person going back in time and potentially shooting their own grandfather, although paradoxes might be avoided using some constraint such as the Novikov self-consistency principle. They appear 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).

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, he did not prove this.