{"id":6,"date":"2019-05-06T21:04:47","date_gmt":"2019-05-06T18:04:47","guid":{"rendered":"http:\/\/siteblog.tuc.gr\/adimas1\/?page_id=6"},"modified":"2019-05-06T21:24:59","modified_gmt":"2019-05-06T18:24:59","slug":"wormholes","status":"publish","type":"page","link":"https:\/\/siteblog.tuc.gr\/adimas1\/wormholes\/","title":{"rendered":"Astronomy"},"content":{"rendered":"

WORMHOLES<\/strong><\/p>\n

A\u00a0wormhole<\/b>\u00a0(or\u00a0Einstein\u2013Rosen bridge<\/b>) is a speculative structure linking disparate points in\u00a0spacetime<\/a>, and is based on a special\u00a0solution of the Einstein field equations<\/a>\u00a0solved using a\u00a0Jacobian matrix and determinant<\/a>. 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\u00a0Calabi\u2013Yau<\/a>\u00a0manifold manifesting itself in\u00a0Anti-de Sitter space<\/a>.<\/p>\n

Wormholes are consistent with the\u00a0general theory of relativity<\/a>, but whether wormholes actually exist remains to be seen.<\/p>\n

A wormhole could connect extremely long distances such as a billion\u00a0light years<\/a>\u00a0or more, short distances such as a few\u00a0meters<\/a>, different\u00a0universes<\/a>, or different points in time.[1]<\/a><\/sup><\/p>\n

The equations of the theory of\u00a0general relativity<\/a>\u00a0have valid solutions that contain wormholes. The first type of wormhole solution discovered was the\u00a0Schwarzschild wormhole<\/i>,[7]<\/a><\/sup>\u00a0which would be present in the\u00a0Schwarzschild metric<\/a>describing an\u00a0eternal black hole<\/i>, 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\u00a0traversable wormholes<\/a>, would only be possible if\u00a0exotic matter<\/a>\u00a0with negative\u00a0energy density<\/a>\u00a0could be used to stabilize them.[8]<\/a><\/sup><\/p>\n

Dane Solis wormholes, also known as\u00a0Einstein\u2013Rosen bridges<\/i>[7]<\/a><\/sup>\u00a0(named after\u00a0Albert Einstein<\/a>\u00a0and\u00a0Nathan Rosen<\/a>),[9]<\/a><\/sup>\u00a0are connections between areas of space that can be modeled as\u00a0vacuum solutions<\/a>\u00a0to the\u00a0Einstein field equations<\/a>, and that are now understood to be intrinsic parts of the\u00a0maximally extended<\/a>\u00a0version of the\u00a0Schwarzschild metric<\/a>\u00a0describing an eternal black hole with no charge and no rotation. Here, “maximally extended” refers to the idea that the\u00a0spacetime<\/a>\u00a0should not have any “edges”: it should be possible to continue this path arbitrarily far into the particle’s future or past for any possible trajectory of a free-falling particle (following a\u00a0geodesic<\/a>\u00a0in the spacetime).<\/p>\n

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\u00a0event horizon<\/a>\u00a0from the outside, there must be a separate\u00a0white hole<\/a>\u00a0interior region that allows us to extrapolate the trajectories of particles that an outside observer sees rising up\u00a0away<\/i>\u00a0from 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\u00a0Kruskal\u2013Szekeres coordinates<\/a>.<\/p>\n

In this spacetime, it is possible to come up with\u00a0coordinate systems<\/a>\u00a0such that if a\u00a0hypersurface<\/a>\u00a0of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a\u00a0space-like<\/a>\u00a0separation, 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\u2013Rosen 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]<\/a><\/sup><\/p>\n

The Einstein\u2013Rosen bridge was discovered by\u00a0Ludwig Flamm<\/a>\u00a0in 1916,[11]<\/a><\/sup>\u00a0a 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]<\/a><\/sup>[12]<\/a><\/sup>\u00a0However, in 1962,\u00a0John Archibald Wheeler<\/a>\u00a0and\u00a0Robert W. Fuller<\/a>\u00a0published a paper[13]<\/a><\/sup>\u00a0showing 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.<\/p>\n

According to general relativity, the\u00a0gravitational collapse<\/a>\u00a0of a sufficiently compact mass forms a singular Schwarzschild black hole. In the\u00a0Einstein\u2013Cartan<\/a>\u2013Sciama\u2013Kibble theory of gravity, however, it forms a regular Einstein\u2013Rosen bridge. This theory extends general relativity by removing a constraint of the symmetry of the\u00a0affine connection<\/a>\u00a0and regarding its antisymmetric part, the\u00a0torsion tensor<\/a>, as a dynamical variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin<\/a>) of matter. The minimal coupling between torsion and\u00a0Dirac spinors<\/a>\u00a0generates a repulsive spin\u2013spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity.[clarification needed<\/span><\/a><\/i>]<\/sup>\u00a0Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.[14]<\/a><\/sup><\/p>\n

Although Schwarzschild wormholes are not traversable in both directions, their existence inspired\u00a0Kip Thorne<\/a>\u00a0to imagine traversable wormholes created by holding the “throat” of a Schwarzschild wormhole open with\u00a0exotic matter<\/a>\u00a0(material that has negative mass\/energy).<\/p>\n

Other non-traversable wormholes include\u00a0Lorentzian wormholes<\/i>\u00a0(first proposed by John Archibald Wheeler in 1957), wormholes creating a\u00a0spacetime foam<\/a>\u00a0in a general relativistic spacetime manifold depicted by a\u00a0Lorentzian manifold<\/a>,[15]<\/a><\/sup>\u00a0and\u00a0Euclidean wormholes<\/i>\u00a0(named after\u00a0Euclidean manifold<\/a>, a structure of\u00a0Riemannian manifold<\/a>).[16]<\/a><\/sup><\/p>\n

Traversable wormholes<\/span><\/h3>\n

The\u00a0Casimir effect<\/a>\u00a0shows that\u00a0quantum field theory<\/a>\u00a0allows the energy density in certain regions of space to be negative relative to the ordinary matter\u00a0vacuum energy<\/a>, and it has been shown theoretically that quantum field theory allows states where energy can be\u00a0arbitrarily<\/i>\u00a0negative<\/a>\u00a0at a given point.[17]<\/a><\/sup>\u00a0Many physicists, such as\u00a0Stephen Hawking<\/a>,[18]<\/a><\/sup>\u00a0Kip Thorne<\/a>,[19]<\/a><\/sup>\u00a0and others,[20]<\/a><\/sup>[21]<\/a><\/sup>[22]<\/a><\/sup>\u00a0argue that such effects might make it possible to stabilize a traversable wormhole.[23]<\/a><\/sup>[24]<\/a><\/sup>\u00a0Physicists have not found any natural process that would be predicted to form a wormhole naturally in the context of general relativity, although the\u00a0quantum foam<\/a>\u00a0hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the\u00a0Planck scale<\/a>,[25]<\/a><\/sup>:494\u2013496<\/sup>[26]<\/a><\/sup>\u00a0and stable versions of such wormholes have been suggested as\u00a0dark matter<\/a>\u00a0candidates.[27]<\/a><\/sup>[28]<\/a><\/sup>\u00a0It has also been proposed that, if a tiny wormhole held open by a\u00a0negative mass<\/a>\u00a0cosmic string<\/a>\u00a0had appeared around the time of the\u00a0Big Bang<\/a>, it could have been inflated to\u00a0macroscopic<\/a>\u00a0size by\u00a0cosmic inflation<\/a>.[29]<\/a><\/sup><\/p>\n

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Image of a simulated traversable wormhole that connects the square in front of the physical institutes of\u00a0University of T\u00fcbingen<\/a>\u00a0with the sand dunes near Boulogne sur Mer in the north of France. The image is calculated with 4D\u00a0raytracing<\/a>\u00a0in a Morris\u2013Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.[30]<\/a><\/sup><\/p>\n<\/div>\n<\/div>\n<\/div>\n

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.\u00a0<\/span>The possibility of traversable wormholes in general relativity was first demonstrated in a 1973 paper by Homer Ellis[31]<\/a><\/sup>\u00a0and independently in a 1973 paper by K. A. Bronnikov.[32]<\/a><\/sup>\u00a0Ellis analyzed the topology and the\u00a0geodesics<\/a>\u00a0of the\u00a0Ellis drainhole<\/a>, showing it to be geodesically complete, horizonless, singularity-free, and fully traversable in both directions. The drainhole is a solution manifold of Einstein’s field equations for a vacuum space-time, modified by inclusion of a scalar field minimally coupled to the\u00a0Ricci tensor<\/a>\u00a0with antiorthodox polarity (negative instead of positive). (Ellis specifically rejected referring to the scalar field as ‘exotic’ because of the antiorthodox coupling, finding arguments for doing so unpersuasive.) The solution depends on two parameters:\u00a0m<\/var>, which fixes the strength of its gravitational field, and\u00a0n<\/var>, which determines the curvature of its spatial cross sections. When\u00a0m<\/var>\u00a0is set equal to 0, the drainhole’s gravitational field vanishes. What is left is the\u00a0Ellis wormhole<\/a>, a nongravitating, purely geometric, traversable wormhole.\u00a0Kip Thorne<\/a>\u00a0and his graduate student\u00a0Mike Morris<\/a>, unaware of the 1973 papers by Ellis and Bronnikov, manufactured, and in 1988 published, a duplicate of the Ellis wormhole for use as a tool for teaching general relativity. For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of\u00a0exotic matter<\/a>, was from 1988 to 2015 referred to in the literature as a\u00a0Morris\u2013Thorne wormhole<\/i>. 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\u00a0Matt Visser<\/a>, 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\u00a0Gauss\u2013Bonnet gravity<\/a>\u00a0(a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of\u00a0brane cosmology<\/a>) exotic matter is not needed in order for wormholes to exist\u2014they can exist even with no matter.[33]<\/a><\/sup>\u00a0A type held open by negative mass\u00a0cosmic strings<\/a>\u00a0was put forth by Visser in collaboration with\u00a0Cramer<\/a>\u00a0et al.<\/i>,[29]<\/a><\/sup>\u00a0in which it was proposed that such wormholes could have been naturally created in the early universe.<\/p>\n

Wormholes connect two points in spacetime, which means that they would in principle allow\u00a0travel in time<\/a>, 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]<\/a><\/sup>\u00a0However, 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]<\/a><\/sup>:504<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"

WORMHOLES A\u00a0wormhole\u00a0(or\u00a0Einstein\u2013Rosen bridge) is a speculative structure linking disparate points in\u00a0spacetime, and is based on a special\u00a0solution of the Einstein field equations\u00a0solved using a\u00a0Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":307,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/pages\/6","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/users\/307"}],"replies":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/comments?post=6"}],"version-history":[{"count":6,"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/pages\/6\/revisions"}],"predecessor-version":[{"id":36,"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/pages\/6\/revisions\/36"}],"wp:attachment":[{"href":"https:\/\/siteblog.tuc.gr\/adimas1\/wp-json\/wp\/v2\/media?parent=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}