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 traversible, matter can 'travel' from one mouth to the other by passing through the throat.

The name "wormhole" comes from the following analogy used to explain the phenomenon: imagine that the universe is the skin of an apple, and a worm is traveling over its surface. The distance from one side of the apple to the other is equal to half the apple's circumference if the worm stays on the apple's surface, but if it instead burrows a wormhole directly through the apple the distance it has to travel is considerably less.

Definition

Giving a precise definition of a wormhole is slightly tricky. The idea which one wishes to capture is that 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. 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 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. Serguei V. 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 [5]. 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 than it would take light to make the journey through normal space.

Wormholes and time travel

A wormhole could potentially 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 to 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, however; 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 Time Warps [6], and will likely require a theory of quantum gravity to resolve.

Many physicists, including Stephen Hawking (see Hawking's Chronology Protection Conjecture), believe that due to the problems a wormhole would theoretically create, including allowing time travel, that something fundamental in the laws of physics would prohibit them. However, this remains speculation, and the notion that nature would censor inconvenient objects has already failed in the case of the cosmic censorship principle.

Schwarzschild wormholes

Wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are theoretical bridges between areas of space that are thought to be found in the center of a black hole and white hole, joining two universes. They exist in solutions to Einstein's equations, and are thought to be extremely unstable, and would instantly fall apart once created. Some speculation exists that quasars are actually white holes instead of supermassive black holes.

It is impossible for a traveller to go through this type of wormhole because they can only go through a horizon in one direction. If the traveler is formed of non-exotic matter once they reach the center of the Schwarzschild wormhole then, they can't leave the other side, and they can't leave through where they came since the side they came in though was a black hole, meaning nothing can escape it once inside the Schwarzschild radius.

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 θ 2 + sin 2 θ d φ 2)

another type of a theory is the schwarzchild metrics,

Wormholes in fiction

---The Bajoran wormhole From Star Trek: Deep Space Nine--

Wormholes are also a popular feature of science fiction as they allow interstellar travel within human timescales.

They are a centerpiece of Carl Sagan's novel Contact, for which Kip Thorne advised Sagan on the possibilities of wormholes.

The setting of the television series Star Trek: Deep Space Nine is a space station, Deep Space Nine, located near the Bajoran wormhole. This wormhole is unique in the Star Trek universe because of its stability.

Wormholes are also the principal means of space travel in the Stargate movie and the spin-off television series, Stargate SG-1 and Stargate Atlantis. The central plot device of the programs is a transportation network consisting of the ring-shaped devices known as Stargates, which generate wormholes that allow one-way matter transmission between gates when the correct spatial coordinates are "dialed".

In 2005 wormholes were used to support the plot of the television miniseries The Triangle.

The television series Farscape features an American astronaut who accidentally gets shot through a wormhole and ends up in a distant part of the universe, and also features the use of wormholes to reach other universes (or "unrealized realities") and as weapons of mass destruction.

An open Stargate from Stargate SG-1:

In the FOX/Sci-Fi series Sliders, a method is found to create a wormhole that allows travel not between distant points but between different universes; objects or people that travel through the wormhole begin and end in the same location geographically (e.g. if one leaves San Francisco, one will arrive in an alternate San Francisco) and chronologically (if it is 1999 at the origin point, so it is at the destination, at least by the currently-accepted calendar on our Earth.) Early in the series the wormhole is referred to by the name Einstein-Rosen-Podolsky bridge. This series presumes that we exist as part of a multiverse and asks what might have resulted had major or minor events in history occurred differently; it is these choices that give rise to the alternate universes in which the series is set. The same premise is used in the Star Trek: The Next Generation episode Parallels and the Star Trek: The Original Series episode The Alternative Factor which premiered in 1967.

In Star Trek: The Motion Picture, Willard Decker recalls that "Voyager 6" (aka V'ger) disappeared into what they used to call a "black hole". At one time, black holes in science fiction were often incorrectly endowed with the traits of wormholes. This has for the most part disappeared as a black hole isn't really a hole in space but a dense mass and the visible vortex effect often associated with black holes is merely the accretion disk of visible matter being drawn toward it. Decker's line is most likely to inform that it was probably a wormhole that Voyager 6 entered.

In 2000, Arthur C. Clarke and Stephen Baxter co-wrote a science fiction novel, The Light of Other Days, which discusses the problems which arise when a wormhole is used for faster than light communication.

A related method of faster-than-light travel that often arises in science fiction, especially military science fiction, is a "jump drive" that can 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 and has described a 'history' of development and exploitation in several essays in collections of related short stories.

The Commonwealth Saga by Peter F. Hamilton describes how wormhole technology could be used to explore, colonize and connect to other worlds without having to resort to traditional travel via starships. This technology is the basis of the formation of the titular Intersolar Commonwealth, and is used so extensively that it is possible to ride trains between the planets of the Commonwealth.

Richard Kelly's science-fiction movie, Donnie Darko, also explores the possibility of the existence of wormholes in the universe. While in the original theatrical release, the relevance of wormholes to the plot is unclear, in the Director's Cut, the 'book' "The Philosophy of Time Travel" is presented in more depth. In this version, the wormhole is the path connecting the real universe, and the parallel universe, which in the movie lasts from the jet engine crashing into the Darko family home until Halloween when the actual jet loses its engine to the wormhole, at which point the parallel universe collapses.

Lois McMaster Bujold uses wormholes as a major transportation system in the Miles Vorkosigan novels. Control over wormhole routes and jumps even become the basis for war.

Quantum foam
Quantum foam, also referred to as spacetime foam, is a concept in quantum mechanics, derived by John Wheeler in 1955. It is sometimes likened to the old concept of the ether/aether.

The foam is a qualitative description of the turbulence that the phenomenon creates at extremely small distances of the order of the Planck length. At such small scales of time and space the uncertainty principle allows particles and energy to briefly come into existence, and then annihilate, without violating conservation laws. As the scale of time and space being discussed shrinks, the energy of the virtual particles increases. At sufficiently small scale space is not smooth as would be expected from observations at larger scales.

Foaming through the universe
Quantum foam is theorized to create masses of virtual particles. They are particle-antiparticle pairs, and prior to their annihilation, exist for a short period of time, on the order of the Planck time. They are created randomly from photons; the higher the energy of the photon from which they are created, the longer the time they will exist prior to annihilation.

These virtual particles make their existence known by the Casimir effect. It is thought that there are constant quantum fluctuations in "empty" space, even at the energetic homogeneity referred to as absolute zero. Due to this, quantum fluctuations are often described using the term "zero-point energy".

The "foamy" spacetime would look like a complex turbulent storm-tossed sea. Some physicists theorize the formation of wormholes therein; speculation arising from this includes the possibility of hyperspatial links to other universes. As far as realistic phenomena are concerned, it's thought that the hyperspatial nature of the quantum foam may account for such diverse physical principles as inertia, propagation of light, and time flow.

Reginald Cahill has developed a theory called Process physics, which describes space as a quantum foam system in which gravity is an inhomogeneous flow of the quantum foam into matter. According to this theory, the so-called spiral galaxy rotation-velocity anomaly may be explained without the need for dark matter.

Various scientists have theorized that quantum foam is an incredibly powerful source of zero-point energy. It has been estimated that one cubic centimeter of space contains enough zero point energy to boil all the world's oceans. However, estimates of this energy vary widely due to the huge disparity in the calculations of the quantum foam density, which vary more than 1:10100. Physicist Michio Kaku thinks that this enormous uncertainty in the estimation of quantum-foam density would represent the largest disparity for any quantity in all of physics.

Wormhole...

Professor Kip Thorne, of the California Institute of Technology, was stimulated, in the summer of 1985, to search for alternate wormhole solutions that would allow safe passage for interstellar travelers. His motivation was a request for help from his friend and colleague, Carl Sagan. Professor Sagan was writing a science fiction story (The novel was entitled Contact which has been made into a motion picture staring Jodi Foster as the heroine) in which his heroine needed to cross a great interstellar distance in a very short time, namely the distance between Earth and the star Vega.. Professor Thorne was only too happy to oblige. He found a solution which was so simple that he was surprised no one had found it before. The solution has the following metric equation.

Where b(r) determines the spatial shape of the wormhole, and Phi(r) determines the gravitational redshift. This solution has the property of having no horizons or excessive tidal forces to deal with which makes it safe for humans to travel through. But it does have one unfortunate drawback. In order to hold the throat open there has to be a negative energy density inside. There is no no known material that has this property. Though electro-magnetic vacuum fluctuations are sometimes measured to have negative energy densities and are correspondingly called ``exotic''. In order to keep the wormhole open it needs to be threaded with exotic matter that will create a tension to push the walls apart. This exotic matter would have the curious effect of defocusing light as it passed through.

References

Visser, Matt. The quantum physics of chronology protection by Matt Visser.. arXiv eprint server. URL accessed on August 12, 2005. An excellent and more concise review.
Khatsymosky, Vladimir M.. Towards possibility of self-maintained vacuum traversable wormhole. arXiv eprint server. URL accessed on August 12, 2005.
Roman, Thomas, A.. Some Thoughts on Energy Conditions and Wormholes. arXiv eprint server. URL accessed on August 12, 2005.
Krasnikov, Serguei. The quantum inequalities do not forbid spacetime shortcuts. arXiv eprint server. URL accessed on August 12, 2005.
Krasnikov, Serguei. Counter example to a quantum inequality. arXiv eprint server. URL accessed on August 12, 2005.
Teo, Edward. Rotating traversable wormholes. arXiv eprint server. URL accessed on August 12, 2005.
González-Díaz, Pedro F.. Ringholes and closed timelike curves. arXiv eprint server. URL accessed on August 12, 2005.
González-Díaz, Pedro F.. Quantum time machine. arXiv eprint server. URL accessed on August 12, 2005.
DeBenedictis, Andrew and Das, A.. On a General Class of Wormhole Geometries. arXiv eprint server. URL accessed on August 12, 2005.
Li, Li-Xin. Two Open Universes Connected by a Wormhole: Exact Solutions. arXiv eprint server. URL accessed on August 12, 2005.
Nandi, Kamal K. and Zhang, Yuan-Zhong. A Quantum Constraint for the Physical Viability of Classical Traversable Lorentzian Wormholes. arXiv eprint server. URL accessed on August 12, 2005.
Dzhunushaliev, Vladimir. Strings in the Einstein's paradigm of matter. arXiv eprint server. URL accessed on August 12, 2005.
Garattini, Remo. How Spacetime Foam modifies the brick wall. arXiv eprint server. URL accessed on August 12, 2005.
Ori, Amos. A new time-machine model with compact vacuum core. arXiv eprint server. URL accessed on August 12, 2005.
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