Information about 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 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 hole in higher-dimensional space.

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 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 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 series.

In the novel Contact by Carl Sagan and subsequent 1997 film starring Jodie Foster and Matthew McConaughey, Jodie's character Ellie travels 24 light years to the star Vega, through a series of wormholes. The entire trip, which lasted 18 hours to Ellie, passed by in a fraction of a second on Earth, making it seem as though she didn't go anywhere. In her defense, Foster references an Einstein-Rosen bridge and 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 the Stargate is described as generating a wormhole where objects are deconstructed and the energy in the form of electromagnetic waves is sent through to be reconstructed 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 , 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.

Worm holes in popular culture

• 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.
• The entire premise of the 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 .
• 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 spacetime a new wormhole all right, but it's clenching tight fast."—Prof. Farnsworth in the Futurama episode "Roswell that ends well".
• In Déjà Vu (film) have some scientists 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

See also

• Black hole
• Supermassive black hole
• Micro black hole
• Intermediate-mass black hole
• Rotating black hole
• White hole
• Gravastar
• Compact stars
• Faster-than-light
• Chronology protection conjecture
• Alcubierre drive
• Neutron star
• Self-consistency principle
• Roman ring
• Schwarzschild metric
• Schwarzschild radius
• String theory
• Theory of relativity
• Time travel
• Timeline of black hole physics
• Spacecraft propulsion

References

• DeBenedictis, Andrew and Das, A.. On a General Class of Wormhole Geometries. arXiv eprint server. Retrieved on August 12, 2005.
• Dzhunushaliev, Vladimir. Strings in the Einstein's paradigm of matter. arXiv eprint server. Retrieved on August 12, 2005.
• Einstein, Albert and Rosen, Nathan. The Particle Problem in the General Theory of Relativity. Physical Review 48, 73 (1935).
• Fuller, Robert W. and Wheeler, John A.. Causality and Multiply-Connected Space-Time. Physical Review 128, 919 (1962).
• Garattini, Remo. How Spacetime Foam modifies the brick wall. arXiv eprint server. Retrieved on August 12, 2005.
• González-Díaz, Pedro F.. Quantum time machine. arXiv eprint server. Retrieved on August 12, 2005.
• González-Díaz, Pedro F.. Ringholes and closed timelike curves. arXiv eprint server. Retrieved on August 12, 2005.
• Khatsymosky, Vladimir M.. Towards possibility of self-maintained vacuum traversable wormhole. arXiv eprint server. Retrieved on August 12, 2005.
• Krasnikov, Serguei. Counter example to a quantum inequality. arXiv eprint server. Retrieved on August 12, 2005.
• Krasnikov, Serguei. The quantum inequalities do not forbid spacetime shortcuts. arXiv eprint server. Retrieved on August 12, 2005.
• Li, Li-Xin. Two Open Universes Connected by a Wormhole: Exact Solutions. arXiv eprint server. Retrieved on August 12, 2005.
• Morris, Michael S., Thorne, Kip S., and Yurtsever, Ulvi. Wormholes, Time Machines, and the Weak Energy Condition. Physical Review Letters 61, 1446–1449 (1988).
• Morris, Michael S. and Thorne, Kip S.. Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. American Journal of Physics 56, 395-412 (1988).
• Nandi, Kamal K. and Zhang, Yuan-Zhong. A Quantum Constraint for the Physical Viability of Classical Traversable Lorentzian Wormholes. arXiv eprint server. Retrieved on August 12, 2005.
• Ori, Amos. A new time-machine model with compact vacuum core. arXiv eprint server. Retrieved on August 12, 2005.
• Roman, Thomas, A.. Some Thoughts on Energy Conditions and Wormholes. arXiv eprint server. Retrieved on August 12, 2005.
• Teo, Edward. Rotating traversable wormholes. arXiv eprint server. Retrieved on August 12, 2005.
• Visser, Matt. The quantum physics of chronology protection by Matt Visser.. arXiv eprint server. Retrieved on August 12, 2005. An excellent and more concise review.
• Visser, Matt. Traversable wormholes: Some simple examples. Physical Review D 39, 3182–3184 (1989).

External links

• Creating a Traversable Wormhole by Mohammad Mansouryar
• 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.
• New Improved Wormholes by John G. Cramer
• White holes and Wormholes provides a very good description of Schwarzschild wormholes with graphics and animations, by Andrew J. S. Hamilton.
• Questions and Answers about Wormholes a comprehensive wormhole FAQ.
• Wormhole on arxiv.org