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The basic notion of an intra-universe wormhole is that it is a [[Compact space|compact]] region of [[spacetime]] whose boundary is topologically trivial but whose interior is not [[simply connected]]. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's ''Lorentzian Wormholes'':
The basic notion of an intra-universe wormhole is that it is a [[Compact space|compact]] region of [[spacetime]] whose boundary is topologically trivial but whose interior is not [[simply connected]]. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's ''Lorentzian Wormholes'':


:If a Lorentzian spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of nontrivial topology, whose boundary has topology of the form dΣ ~ S<sup>2</sup>, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.
:If a Lorentzian [[spacetime]] contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of nontrivial topology, whose boundary has topology of the form dΣ ~ S<sup>2</sup>, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.


Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the spacetime is simply connected.
Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the spacetime is simply connected.

Revision as of 23:43, 27 December 2007

For other uses, see Wormhole (disambiguation).
File:Worm3.jpg
Analogy to a wormhole in a curved 2D space (see Embedding Diagram)
Artist's impression of a wormhole as seen by an observer crossing the event horizon of a Schwarzschild wormhole, which is similar to a Schwarzschild black hole but with the singularity replaced by an unstable path to a white hole in another universe. The observer originates from the right, and another universe becomes visible in the center of the wormhole shadow once the horizon is crossed. This new region is, however, unreachable in the case of a Schwarzschild wormhole, as the bridge between the black hole and white hole will always collapse before the observer has time to cross it. See White Holes and Wormholes for a more technical discussion and an animation of what an observer sees when falling into a Schwarzschild wormhole.

In physics, a wormhole is a hypothetical topological feature of spacetime that is essentially a 'shortcut' through space and time. A wormhole has at least two mouths which are connected to a single throat or tube. If the wormhole is traversable, matter can 'travel' from one mouth to the other by passing through the throat. While there is no observational evidence for wormholes, spacetimes containing wormholes are known to be valid solutions in general relativity.

The term wormhole was coined by the American theoretical physicist John Wheeler in 1957. However, the idea of wormholes was invented already in 1921 by the German mathematician Hermann Weyl in connection with his analysis of mass in terms of electromagnetic field energy.[1]

This analysis forces one to consider situations...where there is a net flux of lines of force through what topologists would call a handle of the multiply-connected space and what physicists might perhaps be excused for more vividly terming a ‘wormhole’.

— John Wheeler in Annals of Physics

The name "wormhole" comes from an analogy used to explain the phenomenon. If a worm is travelling over the skin of an apple, then the worm could take a shortcut to the opposite side of the apple's skin by burrowing through its center, rather than travelling the entire distance around, just as a wormhole traveler could take a shortcut to the opposite side of the universe through a topologically nontrivial tunnel.

Definition

The basic notion of an intra-universe wormhole is that it is a compact region of spacetime whose boundary is topologically trivial but whose interior is not simply connected. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's Lorentzian Wormholes:

If a Lorentzian spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of nontrivial topology, whose boundary has topology of the form dΣ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.

Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the spacetime is simply connected.

Wormhole types

Intra-universe wormholes connect one location of a universe to another location of the same universe (in the same present time or unpresent). A wormhole should be able to connect distant locations in the universe by creating a shortcut through spacetime, allowing travel between them that is faster than it would take light to make the journey through normal space. See the image above. Inter-universe wormholes connect one universe with another [1], [2]. This gives rise to the speculation that such wormholes could be used to travel from one parallel universe to another. A wormhole which connects (usually closed) universes is often called a Schwarzschild wormhole. Another application of a wormhole might be time travel. In that case, it is a shortcut from one point in space and time to another. In string theory, a wormhole has been envisioned to connect two D-branes, where the mouths are attached to the branes and are connected by a flux tube [3]. Finally, wormholes are believed to be a part of spacetime foam [4]. There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes. Lorentzian wormholes are mainly studied in general relativity and semiclassical gravity, while Euclidean wormholes are studied in particle physics. Traversable wormholes are a special kind of Lorentzian wormholes which would allow a human to travel from one side of the wormhole to the other. Serguei Krasnikov suggested the term spacetime shortcut as a more general term for (traversable) wormholes and propulsion systems like the Alcubierre drive and the Krasnikov tube to indicate hyperfast interstellar travel.

Theoretical basis

It is known that (Lorentzian) wormholes are not excluded within the framework of general relativity, but the physical plausibility of these solutions is uncertain. It is also unknown whether a theory of quantum gravity, merging general relativity with quantum mechanics, would still allow them. Most known solutions of general relativity which allow for traversable wormholes require the existence of exotic matter, a theoretical substance which has negative energy density. However, it has not been mathematically proven that this is an absolute requirement for traversable wormholes, nor has it been established that exotic matter cannot exist.

In March 2005, Amos Ori envisioned a wormhole which allows time travel, does not require any exotic matter and satisfies the weak, dominant, and strong energy conditions [5]. The stability of this solution is uncertain, so it is unclear whether infinite precision would be required for it to form in a way that allows time travel and also whether quantum effects would uphold chronology protection in this case, as analyses using semiclassical gravity have suggested they might do in the case of traversable wormholes.

Schwarzschild wormholes

Lorentzian wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modeled as vacuum solutions to the Einstein field equations by sticking a model of a black hole and a model of a white hole together. This solution was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through.

Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.

While Schwarzschild wormholes are not traversable, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the 'throat' of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).

Traversable wormholes

Lorentzian traversable wormholes would allow travel from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris in a 1988 paper; for this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is referred to as a Morris-Thorne wormhole. Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in which a path through the wormhole can be made in which the traversing path does not pass through a region of exotic matter. A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al., [2], in which it was proposed that such wormholes could have been naturally created in the early universe.

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time as well as in space. In a 1988 paper, Morris, Thorne and Yurtsever[3] worked out explicitly how to convert a wormhole traversing space into one traversing time.

Wormholes and faster-than-light travel

Special relativity only applies locally. Wormholes allow superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole. However, a light beam traveling through the wormhole would always beat the traveler. As an analogy, running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it. You can walk slowly while reaching your destination more quickly because the length of your path is shorter.

Wormholes and time travel

A wormhole could allow time travel. This could be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry. For example, if clocks at both mouths both showed the date as 2000 before one mouth was accelerated, and after being taken on a trip at relativistic velocities the accelerated mouth was brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010, then a traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve.

It is thought that it may not be possible to convert a wormhole into a time machine in this manner: some analyses using the semiclassical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture. This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps. There is also the Roman ring, which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.

Wormhole metrics

Theories of wormhole metrics describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole metric is the following:

One type of non-traversable wormhole metric is the Schwarzschild solution:

Wormholes in fiction

Main article: Wormholes in fiction

Wormholes are a popular feature of science fiction as they allow interstellar (and sometimes interuniversal) travel within human timescales. It is common for the creators of a fictional universe to decide that faster-than-light travel is either impossible or that the technology does not yet exist, but to use wormholes as a means of allowing humans to travel long distances in short periods. Military science fiction (such as the Wing Commander games) often use a "jump drive" to propel a spacecraft between two fixed "jump points" connecting stellar systems. Connecting systems in a network like this results in a fixed "terrain" with choke points that can be useful for constructing plots related to military campaigns. The Alderson points used by Larry Niven and Jerry Pournelle in The Mote in God's Eye and related novels are an example, although the mechanism does not seem to describe actual wormhole physics. David Weber has also used the device in the Honorverse and other books such as those based upon the Starfire universe. Naturally occurring wormholes form the basis for interstellar travel in Lois McMaster Bujold's Vorkosigan Saga. They are also used to create an Interstellar Commonwealth in Peter F. Hamilton's Commonwealth Saga.

Wormholes also play pivotal roles in science fiction where faster-than-light travel is possible though limited, allowing connections between regions that would be otherwise unreachable within conventional timelines. Several examples appear in the Star Trek franchise, including the Bajoran wormhole in the Deep Space Nine series.

In Carl Sagan's novel Contact and subsequent 1997 film starring Jodie Foster and Matthew McConaughey, Foster's character Ellie travels 26 light years through a series of wormholes to the star Vega. The round trip, which to Ellie lasts 18 hours, passes by in a fraction of a second on Earth, making it seem that she didn't go anywhere. In her defense, Foster mentions an Einstein-Rosen bridge and tells how she was able to travel faster than light and time. Analysis of the situation by Kip Thorne, on the request of Sagan, is quoted by Thorne as being his original impetus for analyzing the physics of wormholes.

Wormholes play major roles in the television series Farscape, where they are the cause of John Crichton's presence in the alien universe, and in the Stargate series, where stargates create a stable artificial wormhole where matter is disintegrated, converted into energy, and is sent through to be reintegrated at the other side. In the science fiction series Sliders, a wormhole (or vortex, as it is usually called in the show) is used to travel between parallel worlds, and one is seen at least once or twice in every episode. In the pilot episode it was referred to as an "Einstein-Rosen-Podolsky bridge".

In the video game sequel TimeSplitters: Future Perfect, the main character Cortez jumps through a series of wormholes.

Wormholes are used in a large number of other works of fiction; a longer discussion is available in the Wormholes in fiction article.

  • In the South Park episode "Starvin Marvin in Space", Marvin, Kyle, Cartman, Stan, and Kenny fly into a worm hole.
  • In the Lloyd in Space episode "Caution: Wormhole!", Lloyd falls in a worm hole and Eddy jumps into the same worm hole.
  • One of the storylines in Farscape involves controlling wormholes and what different species would do with the ability.
  • One of the theories concerning Desmond of Lost is his ability to time travel through wormholes relating to the Casimir effect.

TV shows Stargate SG-1 and Stargate Atlantis is the ability to activate wormholes on command and use them to traverse the Milky Way Galaxy and beyond to the Pegasus Galaxy.

  • The Star Trek franchise mentions wormholes on several occasions, including a stable wormhole as a major plot device throughout the series Star Trek: Deep Space Nine.
  • In Team Galaxy, the team went into a wormhole and went forward in time by one year.
  • Sliders is a 1995 science fiction series based on four travelers that move between parallel universes in each episode via wormholes.
  • "We tore the universe a new spacehole all right, but it's clenching shut fast."—Prof. Farnsworth in the Futurama episode "Roswell That Ends Well".
  • In Déjà Vu (film) some scientists have made a wormhole to watch and even change the past.
  • In Donnie Darko the film's protagonist of the same name receives revelations of future events from a "gigantic bunny rabbit," possibly through a wormhole.
  • In Justice League the league uses a wormhole to remove dark matter that is extingushing the sun.
  • In Timeline a wormhole is used to transport people back to 14th century France.
  • In an episode of Invader Zim titled A Room with a Moose, Zim sends his classmates into a wormhole as they ride a bus.
  • In issue 40 of the webcomic Dresden Codak, Kim Ross discusses the use of the Casimir Effect to stabilize a wormhole and go back in time
  • In the Mystery Science Theater 3000 episode "Prince of Space," the Satellite of Love, The Widowmaker, and all their occupants are sucked into a wormhole, which has various effects. Eventually, everyone is deposited in ancient Rome.
  • In the MMORPG EVE Online, a wormhole is the device through which humanity comes to inhabit the region of space explored in the game.

See also

References

  1. ^ Coleman, Korte, Hermann Weyl's Raum - Zeit - Materie and a General Introduction to His Scientific Work, p. 199
  2. ^ John G. Cramer, Robert L. Forward, Michael S. Morris, Matt Visser, Gregory Benford, and Geoffrey A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51 (1995) 3117-3120
  3. ^ M. Morris, K. Thorne, and U. Yurtsever, Wormholes, Time Machines, and the Weak Energy Condition, Physical Review, 61, 13, September 1988, pp. 1446 - 1449
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