Wormhole

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For other uses, see Wormhole (disambiguation).
analogy to a wormhole in a curved 2D space (see Embedding Diagram)
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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 animation of what an observer sees when falling into a Schwarzschild wormhole.
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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 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. 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 introduced by the American theoretical physicist John Wheeler in 1957.

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

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[edit] 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.

[edit] 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 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 [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. 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.

[edit] Theoretical basis

It is known that (Lorentzian) wormholes are possible within the framework of general relativity, but the physical plausibility of these solutions is uncertain, and it is also unknown whether a theory of quantum gravity which merged 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 allowed time travel, did not require any exotic matter, and satisfied 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 allowed 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.

[edit] Schwarzschild wormholes

Lorentzian 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. 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).

[edit] 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. Wormholes connect two points in spacetime, which means that they would allow travel in time as well as in space. 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 discovered, 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 solutions in general relativity, such as a type held open by cosmic strings which was put forward in a 1989 paper by Matt Visser.

[edit] 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.

[edit] 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.

[edit] 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)

[edit] Wormholes in fiction

Main article: 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 technology 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 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 postulated by Larry Niven and Jerry Pournelle in The 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 occurring 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.

The book Diaspora and the short story The Planck Dive by Greg Egan feature scientifically well-founded depictions of wormholes. Java applets illustrating the ideas can be found on his homepage.

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", a term which may have arisen from a confusion between "Einstein-Rosen bridges" (a genuine term for Schwarzschild wormholes) and the Einstein-Podolsky-Rosen paradox (a famous thought-experiment in quantum mechanics which is unrelated to wormholes) or as a suggestion that the Earth featured in the pilot is not our own.

Wormholes are a common feature in the computer game Elite in which they are short-lived constructs created on-demand by the hyper-drive as a means of interstellar transport.

Wormholes are also seen in the computer game Freelancer, commonly referred as jump holes. They are supposed to be black hole-like formations with ultra-high gravity amounts, that work like 'portals' for players to travel instantly between different star systems.

Diagram to illustrate the concept of how a Stargate creates a passage to the Moon, seen in "Stargate SG-1: True Science".
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Diagram to illustrate the concept of how a Stargate creates a passage to the Moon, seen in "Stargate SG-1: True Science".

A wormhole plays a pivotal role in many episodes and the Dominion story arc in the Star Trek series Deep Space Nine. The Bajoran wormhole (pictured above) connects points in the Alpha and Gamma Quadrants, allowing ships to traverse a distance of 70,000 light years in just a few minutes. One of the main points of use during the series involved the invasion of the Alpha Quadrant by the Dominion. This story arc dominated the final seasons of the series.

In the series Stargate, the Stargate generates a wormhole between itself and the gate at the destination, by being supplied with a threshold amount of electricity. Objects in transit between gates are broken down into their individual elemental components, and then into energy, and it is this "wormhole" they travel through before being reconstructed on the other side. Nevertheless, unlike some other science fiction series, many of the technical issues facing wormhole travel are addressed.

In the film Event Horizon, the experimental ship uses a top secret prototype stardrive. The drive folds space-time and creates an artificial wormhole extending to any point in the universe, allowing the ship to traverse great distances instantaneously.

In the Dune universe of Frank Herbert, ships called Heighliners use the Holtzman effect to fold space and allow instantaneous travel, but the process is risky, requiring a Guild Navigator to foresee the proper safe path (though they are later replaced by technological devices).

In the 2006 movie Deja Vu, a top secret government project can monitor the past at a running time frame of four and a half days in the past using an Einstein-Rosen bridge. The protagonist (played by Denzel Washington) is sent back in time to try and prevent an event from occurring.

[edit] See also

[edit] More on wormholes in fiction

[edit] References

[edit] External links

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