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, according to Coleman and Korte, p.199 of ‘Hermann Weyl’s Raum – Zeit – Materie and a General Introduction to His Scientific Work’, Hermann Weyl invented the idea of wormholes in 1921 in connection with his analysis of mass in terms of electromagnetic field energy.

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.

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 , and if the topology of is of the form ~ R x , where is a three-manifold of nontrivial topology, whose boundary has topology of the form d ~ S, and if, furthermore, the hypersurfaces are all spacelike, then the region 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

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 are 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.

It is known that (Lorentzian) wormholes are possible 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 analyzes using semiclassical gravity have suggested they might do in the case of traversable 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).

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 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, such as a type held open by cosmic strings which was put forward in a 1989 paper by Matt Visser.

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.

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.

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(sqr)=-c(sqr)dt(sqr)+dl(sqr)+[k(sqr)+l(sqr)][d0(sqr)+sin(sqr)0do(sqr)]

Wormholes=time travel….it’s as simple as that folks!

Thank-you