Wormhole

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Wormholes

In physics, a wormhole (also known as Abbreviated Space) is a hypothetical topological feature of spacetime that is essentially a "shortcut" or "abbreviation" through space and time. A wormhole has at least two mouths which are connected to a single throat. If the wormhole is traversable, matter can 'travel' from one mouth to the other by passing through the throat.

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 traveller could take a shortcut to the opposite side of the universe through a hole in higher-dimensional space.

Definition

There 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). A wormhole should be able to connect distant locations in the universe by bending 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 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 ^*." target="_blank" >Finally, wormholes are believed to be a part of spacetime foam [http://arxiv.org/abs/gr-qc/0409015. There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes. Lorentzian wormholes are mainly studied in semiclassical gravity and 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. Sergey Krasnikov tossed 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 unknown whether (Lorentzian) wormholes are possible or not within the framework of general relativity. Most known solutions of general relativity which allow for 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 wormholes, nor has it been established that exotic matter cannot exist.

Recently Amos Ori envisioned a wormhole which allowed time travel, did not require any exotic matter, and satisfied the weak, dominant, and strong energy conditions ^*. Since there is no established theory of quantum gravity, it is impossible to say with any certainty whether wormholes are possible or not within that theoretical framework.

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 universe. Wormholes connect two points in spacetime, which means that they would allow travel in time as well as in space.

Wormholes and faster-than-light space travel

Often there is confusion about the idea that wormholes allow superluminal (faster-than-light) space travel. In fact there is no real superluminal travel involved. Assume that the wormhole connects two remote locations. While traveling through a wormhole, subluminal (slower-than-light) speeds can be used. The time in which the distance was traveled would appear faster (due to the fact that it goes through a line(a-b) in a curved space instead of going through space outside of the wormhole, which is like going through the center of an apple rather than going around it on the outside, hence the name wormhole) than it would take light to make the journey through normal space. In other words, while you might need to run to get around a mountain in a certain time, you can walk comfortably if there is a tunnel through the center; no additional speed is needed, because the subjective distance is shorter.

Wormholes and time travel

A wormhole could allow time travel. This could be accomplished by accelerating one end of the wormhole relative to the other, and then sometime later bringing it back; relativistic time dilation would result in less time having passed for the accelerated wormhole mouth compared with the stationary one, meaning that anything which entered the stationary wormhole mouth would exit the accelerated one at a point in time prior to its entry. The path through such a wormhole is called a closed timelike curve, and a wormhole with this property is sometimes referred to as a "timehole."

It is thought that it may not be possible to convert a wormhole into a time machine in this manner, some mathematical models indicate that a feedback loop of virtual particles would circulate through the timehole with ever-increasing intensity, destroying it before any information could be passed through it. This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. There is also the Roman ring, which is a very stable configuration of more than one wormhole. This ring allows a closed time loop with stable wormholes. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Censorship Hypothesis.

Schwarzschild wormholes

Wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modelled as vacuum solutions to the Einstein field equations by sticking a model of a black hole and a model of a white hole together. However, this type of wormhole is unstable enough to pinch off instantly as soon as it forms.

While the equations of General Relativity suggest that a Schwarzschild wormhole could be stabilized by holding its "throat" open with exotic matter (material that has negative mass), it would still be impossible for a traveller to go through this type of wormhole because they can only go through an event horizon in one direction, and both ends of the hole have an event horizon. This leaves the traveller trapped in the middle of the wormhole.

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.

Wormhole metrics

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

ds^2= - c^2 dt^2 + dl^2 + (k^2 + l^2)(d \theta^2 + sin^2 \theta  d\phi^2)

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

ds^2= - (1 - \frac{2GM}{rc^2})dt^2 + \frac{dr^2}{1 - \frac{2GM}{rc^2}} + r^2(d \theta^2 + sin^2 \theta  d\phi^2)

Wormholes in fiction

Wormholes are a popular feature of science fiction as they allow interstellar 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 techology does not yet exist, but to use wormholes as a means of allowing humans to travel long distances in short time periods. Military science fiction (such as Babylon 5) often use a "jump drive" to propel a spacecraft between two fixed "jump points" connecting solar systems. Connecting solar 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 postulated by Larry Niven and Jerry Pournelle in Mote in God's Eye and related novels is an especially well thought out example. The development process is described by Niven in N-Space, a volume of collected works. David Weber has also used the device in the Honorverse and other books such as those based upon the Starfire universe, and has described a 'history' of development and exploitation in several essays in collections of related short stories. Naturally occuring wormholes form the basis for interstellar travel in Lois McMaster Bujold's Vorkosigan Saga; the world of Barrayar was isolated from the rest of human civilization for centuries after the connecting wormhole collapsed, until a new route was discovered, and they are the frequent subject of political plots and military campaigns.They are also used to create an Interstellar Commonwealth in Peter F. Hamilton's Commonwealth Saga.

Wormholes feature prominently in the television series Farscape. They are the cause of John Crichton's presence in the alien universe, as well as the reason for many of the events that subsequently take place. In Stargate SG-1 and Stargate Atlantis, a wormhole is created by a Stargate, and as opposed to other science fiction programs, many of the technical issues facing wormhole travel are addressed.

References

An excellent and more concise review.

External links

What exactly is a 'wormhole'? answered by Richard F. Holman, William A. Hiscock and Matt Visser.
Why wormholes? by Matt Visser.
Wormholes in General Relativity by Soshichi Uchii.
Time, Time Travel & Traversable Wormholes includes a discussion forum.
White holes and Wormholes provides a very good description of Schwarzschild wormholes with graphics and animations, by Andrew J. S. Hamilton.
Wormhole on arxiv.org
Scientific American Magazine (December 2005 Issue) Wormhole A game about wormholes.
Wormhole MUD - A Sci-Fi Multi-User_Dungeon

Wormhole theory | Lorentzian manifolds | Black holes

General relativity

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