Wormhole
General relativity |
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A wormhole is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.[1]
A wormhole can be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different points in time, or both).
Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen. Many scientists postulate that wormholes are merely projections of a fourth spatial dimension, analogous to how a two-dimensional (2D) being could experience only part of a three-dimensional (3D) object.[2] A well-known analogy of such constructs is provided by the Klein bottle, displaying a hole when rendered in three dimensions but not in four or higher dimensions.
Theoretically, a wormhole might connect extremely long distances such as a billion
In 1995, Matt Visser suggested there may be many wormholes in the universe if cosmic strings with negative mass were generated in the early universe.[4][5] Some physicists, such as Kip Thorne, have suggested how to make wormholes artificially.[6]
Visualization
For a simplified notion of a wormhole,
Another way to imagine wormholes is to take a sheet of paper and draw two somewhat distant points on one side of the paper. The sheet of paper represents a plane in the spacetime continuum, and the two points represent a distance to be traveled, but theoretically, a wormhole could connect these two points by folding that plane (i.e. the paper) so the points are touching. In this way, it would be much easier to traverse the distance since the two points are now touching. [citation needed]
Terminology
In 1928, German mathematician, philosopher and theoretical physicist Hermann Weyl proposed a wormhole hypothesis of matter in connection with mass analysis of electromagnetic field energy;[7][8] however, he did not use the term "wormhole" (he spoke of "one-dimensional tubes" instead).[9]
American
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".— Charles Misner and John Wheeler in Annals of Physics
Modern definitions
Wormholes have been defined both
If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ S × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has the topology of the form ∂Σ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasi-permanent intrauniverse wormhole.
Geometrically, wormholes can be described as regions of spacetime that constrain the incremental deformation of closed surfaces. For example, in Enrico Rodrigo's The Physics of Stargates, a wormhole is defined informally as:
a region of spacetime containing a "
world tube" (the time evolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line(the time evolution of a point or observer).
Development
Schwarzschild wormholes
The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the
Einstein–Rosen bridges
Einstein–Rosen bridges, also known as EPR=KOI bridges
In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region that allows us to extrapolate the trajectories of particles that an outside observer sees rising up away from the event horizon.[19] And just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see the light that fell in from the other one), and likewise particles from the interior white hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates.
In this spacetime, it is possible to come up with
The Einstein–Rosen bridge was discovered by Ludwig Flamm in 1916,[21] a few months after Schwarzschild published his solution, and was rediscovered by Albert Einstein and his colleague Nathan Rosen, who published their result in 1935.[18][22] However, in 1962, John Archibald Wheeler and Robert W. Fuller published a paper[23] showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region.
According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole. In the Einstein–Cartan–Sciama–Kibble theory of gravity, however, it forms a regular Einstein–Rosen bridge. This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamic variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin) of matter. The minimal coupling between torsion and Dirac spinors generates a repulsive spin–spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity.[clarification needed] Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.[24]
Although Schwarzschild wormholes are not traversable in both directions, 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).[25]
Other non-traversable wormholes include Lorentzian wormholes (first proposed by John Archibald Wheeler in 1957), wormholes creating a
Traversable wormholes
The
Lorentzian traversable wormholes would allow travel in both directions 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 in a 1973 paper by Homer Ellis
Kip Thorne and his graduate student Mike Morris independently discovered in 1988 the Ellis wormhole and argued for its use as a tool for teaching general relativity.[42] For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is also known 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 where the traversing path does not pass through a region of exotic matter. However, in the pure Gauss–Bonnet gravity (a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology) exotic matter is not needed in order for wormholes to exist—they can exist even with no matter.[43] A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al.,[39] 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 how to convert a wormhole traversing space into one traversing time by accelerating one of its two mouths.[30] However, according to general relativity, it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time "machine". Until this time it could not have been noticed or have been used.[35]: 504
Raychaudhuri's theorem and exotic matter
To see why
Modified general relativity
In some hypotheses where general relativity is modified, it is possible to have a wormhole that does not collapse without having to resort to exotic matter. For example, this is possible with R2 gravity, a form of f(R) gravity.[48]
Faster-than-light travel
The impossibility of faster-than-light relative speed applies only locally. Wormholes might allow effective 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 whose length is shorter than the distance between them outside the wormhole, the time taken to traverse it could 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 same wormhole would beat the traveler.
Time travel
If
According to current theories on the nature of wormholes, construction of a traversable wormhole would require the existence of a substance with negative energy, often referred to as "exotic matter". More technically, the wormhole spacetime requires a distribution of energy that violates various energy conditions, such as the null energy condition along with the weak, strong, and dominant energy conditions. However, it is known that quantum effects can lead to small measurable violations of the null energy condition,[11]: 101 and many physicists believe that the required negative energy may actually be possible due to the Casimir effect in quantum physics.[51] Although early calculations suggested a very large amount of negative energy would be required, later calculations showed that the amount of negative energy can be made arbitrarily small.[52]
In 1993, Matt Visser argued that the two mouths of a wormhole with such an induced clock difference could not be brought together without inducing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other,[53] or otherwise prevent information from passing through the wormhole.[54] Because of this, the two mouths could not be brought close enough for causality violation to take place. However, in a 1997 paper, Visser hypothesized that a complex "Roman ring" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.[55]
Interuniversal travel
A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the many-worlds interpretation of quantum mechanics.
In 1991 David Deutsch showed that quantum theory is fully consistent (in the sense that the so-called density matrix can be made free of discontinuities) in spacetimes with closed timelike curves.[56] However, later it was shown that such a model of closed timelike curves can have internal inconsistencies as it will lead to strange phenomena like distinguishing non-orthogonal quantum states and distinguishing proper and improper mixture.[57][58] Accordingly, the destructive positive feedback loop of virtual particles circulating through a wormhole time machine, a result indicated by semi-classical calculations, is averted. A particle returning from the future does not return to its universe of origination but to a parallel universe. This suggests that a wormhole time machine with an exceedingly short time jump is a theoretical bridge between contemporaneous parallel universes.[12]
Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski's proposal of an Everett phone[59] (named after Hugh Everett) in Steven Weinberg's formulation of nonlinear quantum mechanics.[60]
The possibility of communication between parallel universes has been dubbed interuniversal travel.[61]
Wormhole can also be depicted in a
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:[62]
first presented by Ellis (see Ellis wormhole) as a special case of the Ellis drainhole.
One type of non-traversable wormhole metric is the Schwarzschild solution (see the first diagram):
The original Einstein–Rosen bridge was described in an article published in July 1935.[63][64]
For the Schwarzschild spherically symmetric static solution
where is the proper time and .
If one replaces with according to
The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to and , which are joined by a hyperplane or in which vanishes. We call such a connection between the two sheets a "bridge".
— A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity"
For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution
where is the electric charge.
The field equations without denominators in the case when can be written
In order to eliminate singularities, if one replaces by according to the equation:
The solution is free from singularities for all finite points in the space of the two sheets
— A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity"
In fiction
Wormholes are a common element in science fiction because they allow interstellar, intergalactic, and sometimes even interuniversal travel within human lifetime scales. In fiction, wormholes have also served as a method for time travel.
See also
Notes
References
Citations
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External links
- "What exactly is a 'wormhole'? Have wormholes been proven to exist or are they still theoretical??" answered by Richard F. Holman, William A. Hiscock and Matt Visser
- "Why wormholes?" by Matt Visser (October 1996)
- Wormholes in General Relativity by Soshichi Uchii at the Wayback Machine (archived February 22, 2012)
- Questions and Answers about Wormholes – A comprehensive wormhole FAQ by Enrico Rodrigo
- Large Hadron Collider – Theory on how the collider could create a small wormhole, possibly allowing time travel into the past
- animation that simulates traversing a wormhole
- Renderings and animations of a Morris-Thorne wormhole
- NASA's current theory on wormhole creation