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A Tipler cylinder, also called a Tipler time machine, is a
hypothetical A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or tho ...
object theorized to be a potential mode of
time travel Time travel is the hypothetical activity of traveling into the past or future. Time travel is a concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a device known a ...
—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 Negative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects. Gravitational energy Gravitational energy, or gravitational potential energy, is the po ...
.


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 Available in
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in 1974. Tipler showed in his 1974 article "Rotating Cylinders and the Possibility of Global Causality Violation" that in a
spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
containing a "sufficiently large rotating
cylinder A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite ...
" spinning around its axis, the cylinder should create a
frame-dragging Frame-dragging is an effect on spacetime, predicted by Albert Einstein's General relativity, general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary Field (physics), field is one that is ...
effect. This frame-dragging effect warps spacetime in such a way that the
light cone In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single Event (relativity), event (localized to a single point in space and a single moment in time) and traveling in all direct ...
s 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 A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction witho ...
. Therefore, a
spacecraft A spacecraft is a vehicle that is designed spaceflight, to fly and operate in outer space. Spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth observation, Weather s ...
accelerating sufficiently in the appropriate direction can travel backwards through time along a closed timelike curve. CTCs are associated, in
Lorentzian manifolds Lorentzian may refer to * Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution * Lorentz lineshape (spectroscopy) * Lorentz transformation * Lorentzian manifold In mathematical phys ...
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 A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All currently known celestial objects, including planets, stars (Sun), galaxies, and black holes, spin about one ...
) and the van Stockum dust (which models a cylindrically symmetrical configuration of rotating pressureless fluid or
dust Dust is made of particle size, fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian processes, aeolian process), Types of volcan ...
).


Practicality

An objection to the practicality of building a Tipler cylinder was discovered by
Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
, 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 There are several proposed types of exotic matter: * Hypothetical particles and states of matter that have not yet been encountered, but whose properties would be within the realm of mainstream physics if found to exist. * Several particles who ...
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 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 Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...
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 " ere 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 # Frank Jennings Tipler
''Causality Violation in General Relativity''
Ph.D. thesis at the
University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...
(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. # Penrose, Roger. "The Question of Cosmic Censorship". '' Journal of Astrophysics and Astronomy'' Vol. 20 (September 1999): 233. # Wald, Robert (ed.). ''Black Holes and Relativistic Stars''.
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
Press, 1998. . {{Time travel Megastructures Fiction about physics Time travel devices