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.

The Tipler cylinder was discovered as a solution to the equations of general relativity by Willem Jacob van Stockum ^{ [1] } in 1936 and Kornel Lanczos ^{ [2] } in 1924, but not recognized as allowing closed timelike curves ^{ [3] } until an analysis by Frank Tipler ^{ [4] } in 1974. Tipler showed in his 1974 paper, "Rotating Cylinders and the Possibility of Global Causality Violation" that in a spacetime containing a "...sufficiently large rotating cylinder...^{ [5] }" 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 spacetime diagram. Therefore, a spacecraft accelerating sufficiently in the appropriate direction can travel backwards through time along a closed timelike curve.^{ [4] }

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).

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,^{ [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 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 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 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."^{ [8] }

This article appears to contain trivial, minor, or unrelated references to popular culture .(July 2023) |

*Steins;Gate*is a visual novel which mentions Tipler cylinders with the topic of time travel and John Titor.- John DeChancie's
*Starrigger*series uses vertically-aligned Tipler cylinders (called Kerr–Tipler objects) to create spacetime gateways along an intergalactic highway. - Larry Niven's short story, "Rotating Cylinders and the Possibility of Global Causality Violation", borrows its title from Tipler's paper.
^{ [9] } - Poul Anderson includes it in his novel
*The Avatar*.^{ [10] } - Vernor Vinge in the novel
*Marooned in Realtime*(although the object is described as being a naked black hole).^{ [11] } - Kris Straub's
*Starslip*comic includes a Tipler cylinder created as a work of art, which also causes time travel.^{ [12] } - Ian Douglas has a Tipler cylinder created by aliens of unknown origin in
*Singularity*, the third book of the*Star Carrier*series. *Star Trek Online*uses a device by the same name which enables the player to reverse time several (up to 7~13 secs.) seconds within a localised field.^{ [13] }(The specificity of thirteen seconds of time reversal, along with the device having a beryllium core, are references to the science fiction comedy*Galaxy Quest*.)- In his
*Warstrider*series of novels, William H. Keith uses a Tipler cylinder with a length-to-width ratio of 512 that allows travel to and from the core of the Milky Way galaxy. - In Terry Pratchett's
*Discworld*series, the "procrastinators" used by the History Monks are considered to be a type of Tipler cylinder. - The
*Greens*, a race of parasite aliens, tried to build a Tipler cylinder in the*Lifeline*mobile game series. This is explained in the*Halfway To Infinity*game. - A Tipler cylinder is used as a plot device in Chuck Grossart's story "The Phoenix Descent".
- Episode 9 of the webseries
*Ask Weathersby*^{ [14] }mentions the Tipler cylinder, discussing time travel.^{ [15] } - In "The Miracle of Christmas", Episode 2.11 of the American TV series
*Timeless*, a Tipler cylinder is mentioned as being added to an upgraded time machine. - In season 2 episode 14 of "Gabby Duran & the Unsittables - Zeke to the Future" a Tipler's Infinity Cylinder is mentioned as a possible time travel device.
- SCP-2540: an entry on the collaborative fiction writing website, SCP Foundation (Wikidot site) describing the efforts of Foundation researchers trying to understand a 4D Tipler's cylinder that is perceived as an ordinary key lime (
*Citrus aurantiifolia*).

The weak and the strong **cosmic censorship hypotheses** are two mathematical conjectures about the structure of gravitational singularities arising in general relativity.

**Time travel** is the hypothetical activity of traveling into the past or future. Time travel is a widely recognized concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a hypothetical device known as a **time machine**. The idea of a time machine was popularized by H. G. Wells' 1895 novel *The Time Machine*.

A **wormhole ** is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.

The **Novikov self-consistency principle**, also known as the **Novikov self-consistency conjecture** and Larry Niven's **law of conservation of history**, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s. Novikov intended it to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves. The principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever, then the probability of that event is zero. It would thus be impossible to create time paradoxes.

A **gravitational singularity**, **spacetime singularity** or simply **singularity** is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.

Physical **causality** is a physical relationship between causes and effects. It is considered to be fundamental to all natural sciences and behavioural sciences, especially physics. Causality is also a topic studied from the perspectives of philosophy, statistics and logic. Causality means that an effect can not occur from a cause that is not in the back (past) light cone of that event. Similarly, a cause can not have an effect outside its front (future) light cone.

In mathematical physics, a **closed timelike curve** (**CTC**) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given space-time passes through an event horizon, a property which can be called chronological censorship, then that space-time with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.

The **Penrose–Hawking singularity theorems** are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The **Penrose singularity theorem** is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The **Hawking singularity theorem** is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose was awarded the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity", which he shared with Reinhard Genzel and Andrea Ghez.

The **chronology protection conjecture** is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales - even when the latter theory states that it should be possible. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the **causal violation**.

In theoretical physics, a **Penrose diagram** is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity. It is an extension of the Minkowski diagram of special relativity where the vertical dimension represents time, and the horizontal dimension represents a space dimension. Using this design, all light rays take a 45° path.. Locally, the metric on a Penrose diagram is conformally equivalent to the metric of the spacetime depicted. The conformal factor is chosen such that the entire infinite spacetime is transformed into a Penrose diagram of finite size, with infinity on the boundary of the diagram. For spherically symmetric spacetimes, every point in the Penrose diagram corresponds to a 2-dimensional sphere .

A **temporal paradox**, **time paradox**, or **time travel paradox**, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with the current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility. Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox.

A **Krasnikov tube** is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive with the endpoints displaced in time as well as space. The idea was proposed by Sergey Krasnikov in 1995.

**Ronald Lawrence Mallett** is an American theoretical physicist, academic and author. He has been a faculty member of the University of Connecticut since 1975 and is best known for his position on the possibility of time travel.

The **Gödel metric**, also known as the **Gödel solution** or **Gödel universe**, is an exact solution, found in 1949 by Kurt Gödel, of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second associated with a negative cosmological constant.

In general relativity, the **van Stockum dust** is an exact solution of the Einstein field equations in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is *increasing* with distance from this axis, the solution is rather artificial, but as one of the simplest known solutions in general relativity, it stands as a pedagogically important example.

A **Malament–Hogarth (M-H) spacetime**, named after David B. Malament and Mark Hogarth, is a relativistic spacetime that possesses the following property: there exists a worldline and an event *p* such that all events along are a finite interval in the past of *p*, but the proper time along is infinite. The event *p* is known as an M-H event.

**Misner space** is an abstract mathematical spacetime, first described by Charles W. Misner. It is also known as the Lorentzian orbifold . It is a simplified, two-dimensional version of the Taub–NUT spacetime. It contains a non-curvature singularity and is an important counterexample to various hypotheses in general relativity.

In mathematical physics, the **causal structure** of a Lorentzian manifold describes the causal relationships between points in the manifold.

- Notes

- ↑ van Stockum, Willem Jacob (1936). "The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry".
*Proceedings of the Royal Society of Edinburgh*. - ↑ Lanczos, Kornel (1997) [1924]. "On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation".
*General Relativity and Gravitation*. Springland Netherlands.**29**(3): 363–399. doi:10.1023/A:1010277120072. S2CID 116891680. - ↑ Earman, John (1995).
*Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes*. Oxford University Press. p. 21. ISBN 0-19-509591-X. - 1 2 Tipler, Frank (1974). "Rotating Cylinders and the Possibility of Global Causality Violation".
*Physical Review D*.**9**(8): 2203–2206. Bibcode:1974PhRvD...9.2203T. doi:10.1103/PhysRevD.9.2203. Archived from the original (PDF) on 2009-10-25. Available in GIF format here: pages 1, 2, 3 and 4. See also here. - ↑ Tipler, Frank J. (1974). "Rotating cylinders and the possibility of global causality violation*".
*Physical Review D*.**9**(8): 2203–2206. Bibcode:1974PhRvD...9.2203T. doi:10.1103/PhysRevD.9.2203. - ↑ Earman, John (1995).
*Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes*. Oxford University Press. p. 169. ISBN 0-19-509591-X. - ↑ Hawking, Stephen (2002).
*The Future of Spacetime*. W. W. Norton. pp. 96. ISBN 0-393-02022-3. - ↑ Hawking, Stephen (1992). "Chronology protection conjecture".
*Physical Review D*.**46**(2): 603–611. Bibcode:1992PhRvD..46..603H. doi:10.1103/PhysRevD.46.603. PMID 10014972. - ↑ "Larry Niven Bibliography".
*larryniven.net*. Retrieved 2013-04-22. - ↑ Nahin, Paul J. (20 April 2001).
*Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction*. p. 95. ISBN 9780387985718. - ↑ Vinge, Vernor (2004).
*Marooned in Realtime*. Macmillan. p. 174. ISBN 1429915129 . Retrieved 2014-03-05. - ↑ Straub, Kris (2007-07-23). "Starslip".
*starslip.krisstraub.com*. Retrieved 2023-05-13. - ↑ "Universal Consoles".
*Star Trek Online Wiki*. Curse, Inc. Retrieved 2014-03-05. - ↑ "Ask Mister Weathersby (Season 1) - YouTube".
*www.youtube.com*. - ↑ "Ask Weathersby, Episode 9". Archived from the original on 2021-12-21 – via YouTube.

- Bibliography

- Frank Jennings Tipler,
*Causality Violation in General Relativity*, Ph.D. thesis at the University of Maryland, College Park (1976). Source: Dissertation Abstracts International, Vol. 37–06, Section B, pg. 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 Press, 1998. ISBN 0-226-87034-0

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