NASA heliophysicist Alex Young explains how this simple sound connects us with the Sun and all the other stars in the universe.
The Sound of the Sun. The sound of the sun. Scientists measure the changing light waves given off by the sun
using an instrument called a dopplergraph that is mounted on a
spacecraft called the Solar and Heliospheric Observatory (SOHO). ...
SOHO is a project of international cooperation between ESA and NASA.
MØLLER ENERGY AND WORMHOLES Department of Mathematics ...
citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.178.1741&rep=rep1...pdf
by J SCHETTLER - Related articles
two asymptotically flat spacetimes (parallel universes) via an Einstein-Rosen bridge (worm- hole throat). The Kruskal extension of Schwarzschild geometry ...Einstein - Rosen Bridge
u2.lege.net/cetinbal/pdfdosya/EinsteinRosenBridge.pdf
by SJ George - Cited by 2 - Related articles
The Einstein-Rosen Bridge is based on generally relativity and work ... published by the French mathematician and philosopher Pierre Simon Laplace in two.
by T OKAMOTO - Cited by 1 - Related articles
3. 2.1. Topology of Einstein-Rosen Bridge. 3. 2.2. Dynamics of the Schwarzschild Throat. 4. 2.3. Causality Preserved. 5. 2.4. Crossing Bridges. 6. 3. Traversable ...
by E Guendelman - 2016 - Cited by 3 - Related articles
Nov 24, 2016 - 3rd National Congress on Physical Sciences, 29 Sept. – 2 Oct. 2016, Sofia. Section: Mathematical Physics. Einstein-Rosen “Bridge” Revisited ...
by MO Katanaev - 2013 - Cited by 5 - Related articles
Oct 28, 2013 - Passing the Einstein–Rosen bridge. M. O. Katanaev ∗. Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991, Russia. October 29 ...
Nov 30, 2015 - Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable ... We can start with a mathematical definition of a wormhole,. Definition ...
by AA Maknickas - 2014 - Related articles
Aug 23, 2014 - which has mathematical singularities both at zero and at the so-called ... ”bridge” that today has the formal name ”Einstein-Rosen bridge”.Wormhole
Jump to navigation
Jump to search
A wormhole (or Einstein–Rosen bridge) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant.
A wormhole can be visualized as a tunnel with two ends, each at
separate points in spacetime (i.e., different locations or different
points of time). More precisely it is a transcendental bijection of the
spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in Anti-de Sitter space.
Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.
A wormhole could connect extremely long distances such as a billion light years or more, short distances such as a few meters, different universes, or different points in time.[1]
Part of a series of articles about |
General relativity |
---|
Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.
A wormhole could connect extremely long distances such as a billion light years or more, short distances such as a few meters, different universes, or different points in time.[1]
Contents
Visualization
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, however theoretically a wormhole could connect these two points by folding that plane so the points are touching. In this way it would be much easier to traverse the distance since the two points are now touching.
Terminology
In 1928, Hermann Weyl proposed a wormhole hypothesis of matter in connection with mass analysis of electromagnetic field energy;[2][3] however, he did not use the term "wormhole" (he spoke of "one-dimensional tubes" instead).[4]American theoretical physicist John Archibald Wheeler (inspired by Weyl's work)[4] coined the term "wormhole" in a 1957 paper co-authored by Charles Misner:[5]
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 geometrically and topologically.[further explanation needed] From a topological point of view, an intra-universe wormhole (a wormhole between two points in the same universe) 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 (1996).[6][page needed]If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form ∂Σ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent 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).
Development
Schwarzschild wormholes
The equations of the theory of general relativity have valid solutions that contain wormholes. The first type of wormhole solution discovered was the Schwarzschild wormhole,[7] which would be present in the Schwarzschild metric describing an eternal black hole, but it was found that it would collapse too quickly for anything to cross from one end to the other. Wormholes that could be crossed in both directions, known as traversable wormholes, would only be possible if exotic matter with negative energy density could be used to stabilize them.[8]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. 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 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 coordinate systems such that if a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') is picked and an "embedding diagram" drawn depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein–Rosen bridge". Note that the Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region, along with the part of the diagram corresponding to the other universe.[10]
The Einstein–Rosen bridge was discovered by Ludwig Flamm in 1916,[11] 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.[9][12] However, in 1962, John Archibald Wheeler and Robert W. Fuller published a paper[13] 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 dynamical 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.[14]
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).
Other non-traversable wormholes include Lorentzian wormholes (first proposed by John Archibald Wheeler in 1957), wormholes creating a spacetime foam in a general relativistic spacetime manifold depicted by a Lorentzian manifold,[15] and Euclidean wormholes (named after Euclidean manifold, a structure of Riemannian manifold).[16]
Traversable wormholes
This Casimir effect shows that quantum field theory allows the energy density in certain regions of space to be negative relative to the ordinary matter vacuum energy, and it has been shown theoretically that quantum field theory allows states where energy can be arbitrarily negative at a given point.[17] Many physicists, such as Stephen Hawking,[18] Kip Thorne,[19] and others,[20][21][22] argue that such effects might make it possible to stabilize a traversable wormhole.[23][24] Physicists have not found any natural process that would be predicted to form a wormhole naturally in the context of general relativity, although the quantum foam hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the Planck scale,[25]:494–496[26] and stable versions of such wormholes have been suggested as dark matter candidates.[27][28] It has also been proposed that, if a tiny wormhole held open by a negative mass cosmic string had appeared around the time of the Big Bang, it could have been inflated to macroscopic size by cosmic inflation.[29]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.[19] 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.[25]:504
Raychaudhuri's theorem and exotic matter
To see why exotic matter is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side. The expansion goes from negative to positive. As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck. According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition. Quantum effects such as the Casimir effect cannot violate the averaged null energy condition in any neighborhood of space with zero curvature,[34] but calculations in semiclassical gravity suggest that quantum effects may be able to violate this condition in curved spacetime.[35] Although it was hoped recently that quantum effects could not violate an achronal version of the averaged null energy condition,[36] violations have nevertheless been found,[37] so it remains an open possibility that quantum effects might be used to support a wormhole.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.[38]Faster-than-light travel
Time travel
If traversable wormholes exist, they could allow time travel.[19] A proposed time-travel machine using a traversable wormhole would hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced propulsion system, and then brought back to the point of origin. Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance. For both of these methods, time dilation causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently through the wormhole than outside it, so that synchronized clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.[25]:502 This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside. One significant limitation of such a time machine is that it is only possible to go as far back in time as the initial creation of the machine;[25]:503 It is more of a path through time rather than it is a device that itself moves through time, and it would not allow the technology itself to be moved backward in time.[39][40]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,[6]:101 and many physicists believe that the required negative energy may actually be possible due to the Casimir effect in quantum physics.[41] 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.[42]
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,[43] or otherwise prevent information from passing through the wormhole.[44] 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.[45]
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.[46] However, later it was shown that such model of closed timelike curve can have internal inconsistencies as it will lead to strange phenomena like distinguishing non-orthogonal quantum states and distinguishing proper and improper mixture.[47][48] 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.[49]
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[50] (named after Hugh Everett) in Steven Weinberg's formulation of nonlinear quantum mechanics.[51]
The possibility of communication between parallel universes has been dubbed interuniversal travel.[52]
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:[53]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.[54][55]
For the Schwarzschild spherically symmetric static solution
( = proper time, = 1)
If one replaces with according to
The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to > 0 and < 0, which are joined by a hyperplane or = 0 in which vanishes. We call such a connection between the two sheets a "bridge".For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution
— A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity"
( = electrical charge)
The field equations without denominators in the case when = 0 can be written
In order to eliminate singularities, if one replaces by according to the equation:
and with = 0 one obtains[56][57]
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.Movies like Interstellar have mentioned wormhole. Einstein - Rosen bridge is mentioned in Thor: Ragnarok.
See also
Notes
References
- DeBenedictis, Andrew & Das, A. (2001). "On a General Class of Wormhole Geometries". Classical and Quantum Gravity. 18 (7): 1187–1204. arXiv:gr-qc/0009072. Bibcode:2001CQGra..18.1187D. CiteSeerX 10.1.1.339.8662. doi:10.1088/0264-9381/18/7/304.
- Dzhunushaliev, Vladimir (2002). "Strings in the Einstein's paradigm of matter". Classical and Quantum Gravity. 19 (19): 4817–4824. arXiv:gr-qc/0205055. Bibcode:2002CQGra..19.4817D. CiteSeerX 10.1.1.339.1518. doi:10.1088/0264-9381/19/19/302.
- Einstein, Albert & Rosen, Nathan (1935). "The Particle Problem in the General Theory of Relativity". Physical Review. 48: 73. Bibcode:1935PhRv...48...73E. doi:10.1103/PhysRev.48.73.
- Fuller, Robert W. & Wheeler, John A. (1962). "Causality and Multiply-Connected Space-Time". Physical Review. 128 (2): 919. Bibcode:1962PhRv..128..919F. doi:10.1103/PhysRev.128.919.
- Garattini, Remo (2004). "How Spacetime Foam modifies the brick wall". Modern Physics Letters A. 19 (36): 2673–2682. arXiv:gr-qc/0409015. Bibcode:2004MPLA...19.2673G. doi:10.1142/S0217732304015658.
- González-Díaz, Pedro F. (1998). "Quantum time machine". Physical Review D. 58 (12): 124011. arXiv:gr-qc/9712033. Bibcode:1998PhRvD..58l4011G. doi:10.1103/PhysRevD.58.124011. hdl:10261/100644.
- González-Díaz, Pedro F. (1996). "Ringholes and closed timelike curves". Physical Review D. 54 (10): 6122–6131. arXiv:gr-qc/9608059. Bibcode:1996PhRvD..54.6122G. doi:10.1103/PhysRevD.54.6122.
- Khatsymosky, Vladimir M. (1997). "Towards possibility of self-maintained vacuum traversable wormhole". Physics Letters B. 399 (3–4): 215–222. arXiv:gr-qc/9612013. Bibcode:1997PhLB..399..215K. doi:10.1016/S0370-2693(97)00290-6.
- Krasnikov, Serguei (2006). "Counter example to a quantum inequality". Gravity and Cosmology. 46 (2006): 195. arXiv:gr-qc/0409007. Bibcode:2006GrCo...12..195K.
- Krasnikov, Serguei (2003). "The quantum inequalities do not forbid spacetime shortcuts". Physical Review D. 67 (10): 104013. arXiv:gr-qc/0207057. Bibcode:2003PhRvD..67j4013K. doi:10.1103/PhysRevD.67.104013.
- Li, Li-Xin (2001). "Two Open Universes Connected by a Wormhole: Exact Solutions". Journal of Geometry and Physics. 40 (2): 154–160. arXiv:hep-th/0102143. Bibcode:2001JGP....40..154L. CiteSeerX 10.1.1.267.8664. doi:10.1016/S0393-0440(01)00028-6.
- Morris, Michael S.; Thorne, Kip S. & Yurtsever, Ulvi (1988). "Wormholes, Time Machines, and the Weak Energy Condition". Physical Review Letters. 61 (13): 1446–1449. Bibcode:1988PhRvL..61.1446M. doi:10.1103/PhysRevLett.61.1446. PMID 10038800.
- Morris, Michael S. & Thorne, Kip S. (1988). "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity". American Journal of Physics. 56 (5): 395–412. Bibcode:1988AmJPh..56..395M. doi:10.1119/1.15620.
- Nandi, Kamal K. & Zhang, Yuan-Zhong (2006). "A Quantum Constraint for the Physical Viability of Classical Traversable Lorentzian Wormholes". Journal of Nonlinear Phenomena in Complex Systems. 9 (2006): 61–67. arXiv:gr-qc/0409053. Bibcode:2004gr.qc.....9053N.
- Ori, Amos (2005). "A new time-machine model with compact vacuum core". Physical Review Letters. 95 (2): 021101. arXiv:gr-qc/0503077. Bibcode:2005PhRvL..95b1101O. doi:10.1103/PhysRevLett.95.021101. PMID 16090670.
- Roman, Thomas A. (2004). Some Thoughts on Energy Conditions and Wormholes. The Tenth Marcel Grossmann Meeting. pp. 1909–1924. arXiv:gr-qc/0409090. doi:10.1142/9789812704030_0236. ISBN 978-981-256-667-6.
- Teo, Edward (1998). "Rotating traversable wormholes". Physical Review D. 58 (2): 024014. arXiv:gr-qc/9803098. Bibcode:1998PhRvD..58b4014T. CiteSeerX 10.1.1.339.966. doi:10.1103/PhysRevD.58.024014.
- Visser, Matt (2002). "The quantum physics of chronology protection by Matt Visser". arXiv:gr-qc/0204022. An excellent and more concise review.
- Visser, Matt (1989). "Traversable wormholes: Some simple examples". Physical Review D. 39 (10): 3182–3184. arXiv:0809.0907. Bibcode:1989PhRvD..39.3182V. doi:10.1103/PhysRevD.39.3182.
External links
Wikimedia Commons has media related to Wormholes. |
- 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 at the Wayback Machine (archived February 22, 2012)
- 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 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
- N.A.S.A's current theory on wormhole creation
No comments:
Post a Comment