In physics, a wormhole is a hypothetical topologicalfeature of spacetime that is, fundamentally, a 'shortcut' through space and time. Simply,spacetime is a two-dimensional (2-D) surface that, when 'folded' over, allows the formation of a wormhole bridge. A wormhole has at least two mouths that are connected via a throat or tube. If the wormhole is traversable, then matter can 'travel' from one mouth to the other via the throat. There is no observational evidence for wormholes, and, although wormholes are valid solutions in general relativity, this is only true if exotic matter can be used to stabilize them. Even if the wormhole is stabilized, even a slight fluctuation in space would collapse it. If such exotic matter — that is, matter with negative mass — does not exist, all wormhole-containing solutions to Einstein’s field equations are vacuum solutions, which require an impossible vacuum, free of all matter and energy.
The American theoretical physicist John Archibald Wheeler coined the term wormhole in 1957; however, in 1921, the German mathematicianHermann Weyl already had proposed the wormhole theory, in connection with mass analysis ofelectromagnetic 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
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[edit]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 Minkowski 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 the 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]Schwarzschild wormholes
Lorentzian wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modeled asvacuum solutions to the Einstein field equations by combining models of a black hole and a white hole. 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]Traversability
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. However in the pure Gauss-Bonnet theory exotic matter is not needed in order for wormholes to exist- they can exist even with no matter.[2] A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al.,[3] 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 1988, Morris, Thorne and Yurtsever worked out explicitly how to convert a wormhole traversing space into one traversing time.[4] However, it has been said a time traversing wormhole cannot take a person back to before it was made[citation needed] but this is disputed[by whom?].
[edit]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. A person can walk slowly while reaching his or her destination more quickly because the distance is smaller.
[edit]Time travel
A wormhole could allow time travel.[4] 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, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is 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. A traveller 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 aclosed 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 theRoman 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.
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