ATipler cylinder, also called aTipler time machine, is ahypothetical objecttheorized to be a potential mode oftime travel—although results have shown that a Tipler cylinder could only allow time travel if its length were infinite or with the existence ofnegative energy.
The Tipler cylinder was discovered as a solution to the equations of general relativity byWillem Jacob van Stockum[1] in 1936 andKornel Lanczos[2] in 1924, but not recognized as allowingclosed timelike curves[3] until an analysis byFrank Tipler[4] in 1974. Tipler showed in his 1974 article "Rotating Cylinders and the Possibility of Global Causality Violation"[5] that in aspacetime containing a "sufficiently large rotatingcylinder" spinning around its axis, the cylinder should create aframe-dragging effect. This frame-dragging effect warps spacetime in such a way that thelight 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 aspacetime diagram. Therefore, aspacecraft accelerating sufficiently in the appropriate direction can travel backwards through time along aclosed timelike curve.[4]
CTCs are associated, inLorentzian manifolds which are interpreted physically as spacetimes, with the possibility of causal anomalies such as a person going back in time andpotentially shooting their own grandfather, although paradoxes might be avoided using some constraint such as theNovikov self-consistency principle. They appear in some of the most important exact solutions in general relativity, including theKerr vacuum (which models arotating black hole) and thevan Stockum dust (which models a cylindrically symmetrical configuration of rotating pressureless fluid ordust).
An objection to the practicality of building a Tipler cylinder was discovered byStephen Hawking, who argued that according to general relativity it is impossible to build a time machine in any finite region that satisfies theweak energy condition, meaning that the region contains noexotic 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,[6] 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."[7] Hawking's argument appears in his 1992 paper on thechronology 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 ofquantum 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 aCauchy 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."[8]
