Editing Wormhole (section)

=== Traversable wormholes<!--linked from 'Joseph Polchinski'--> ===
The [[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 energy|negative]] at a given point.<ref>{{cite book |last1=Everett |first1=Allen |last2=Roman |first2=Thomas |title=Time Travel and Warp Drives |publisher=[[University of Chicago Press]] |year=2012 |page=[https://archive.org/details/isbn_9780226224985/page/n182 167] |isbn=978-0-226-22498-5 |url-access=registration |url = https://archive.org/details/isbn_9780226224985 }}</ref> Many physicists, such as [[Stephen Hawking]],<ref>{{cite web |url=http://www.hawking.org.uk/space-and-time-warps.html |title=Space and Time Warps |website=Hawking.org.uk |access-date=2010-11-11 |archive-date=2012-02-10 |archive-url=https://web.archive.org/web/20120210233225/http://www.hawking.org.uk/space-and-time-warps.html |url-status=dead }}</ref> [[Kip Thorne]],<ref name="time travel" /> and others,<ref>{{cite journal |author1=Sopova |author2=Ford |doi=10.1103/PhysRevD.66.045026 |title=The Energy Density in the Casimir Effect |date=2002 |volume=66 |issue=4 |page=045026 |journal=[[Physical Review D]] |arxiv=quant-ph/0204125 |bibcode=2002PhRvD..66d5026S |citeseerx=10.1.1.251.7471 |s2cid=10649139 }}</ref><ref>{{cite journal |author1=Ford |author2=Roman |doi=10.1103/PhysRevD.51.4277 |year=1995 |title=Averaged Energy Conditions and Quantum Inequalities |pages=4277–4286 |issue=8 |volume=51 |journal=[[Physical Review D]] |arxiv=gr-qc/9410043 |bibcode=1995PhRvD..51.4277F |pmid=10018903 |s2cid=7413835 }}</ref><ref>{{cite journal |doi=10.1103/PhysRevLett.81.3567 |author1=Olum |title=Superluminal travel requires negative energies |date=1998 |volume=81 |issue=17 |pages=3567–3570 |journal=[[Physical Review Letters]] |arxiv=gr-qc/9805003 |bibcode=1998PhRvL..81.3567O |s2cid=14513456 }}</ref> argued that such effects might make it possible to stabilize a traversable wormhole.<ref>{{cite web |url = https://www.quantamagazine.org/newfound-wormhole-allows-information-to-escape-black-holes-20171023/|title=Newfound Wormhole Allows Information to Escape Black Holes |website = Quanta Magazine |date=23 October 2017 }}</ref> The only known natural process that is theoretically predicted to form a wormhole in the context of general relativity and quantum mechanics was put forth by [[Juan Maldacena]] and [[Leonard Susskind]] in their [[ER = EPR]] conjecture. The [[quantum foam]] hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the [[Planck scale]],<ref name="Thorne1994" />{{rp|494–496}}<ref name="quantumdynamics">{{cite journal |first=Redmount |last=Ian H. |author2=Wai-Mo Suen |title=Quantum Dynamics of Lorentzian Spacetime Foam |journal=[[Physical Review D]] |volume=49 |year=1994 |issue=10 |pages=5199–5210 |doi=10.1103/PhysRevD.49.5199 |pmid=10016836 |arxiv=gr-qc/9309017 |bibcode=1994PhRvD..49.5199R |s2cid=39296197 }}</ref> and stable versions of such wormholes have been suggested as [[dark matter]] candidates.<ref>{{cite journal |last1=Kirillov |first1=A. A. |first2=E. |last2=P. Savelova |title=Dark Matter from a gas of wormholes |journal=[[Physics Letters B]] |volume=660 |issue=3 |pages=93–99 |year=2008 |arxiv=0707.1081 |doi=10.1016/j.physletb.2007.12.034 |bibcode=2008PhLB..660...93K|s2cid=12150385 }}</ref><ref>{{cite journal |last=Rodrigo |first=Enrico |title=Denouement of a Wormhole-Brane Encounter |journal=[[International Journal of Modern Physics D]] |volume=18 |issue=12 |pages=1809–1819 |year=2009 |arxiv=0908.2651 |doi=10.1142/S0218271809015333 |bibcode=2009IJMPD..18.1809R |s2cid=119239038 }}</ref> 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 scale|macroscopic]] size by [[Inflation (cosmology)|cosmic inflation]].<ref name="naturalwormholes">{{cite journal |author=John G. Cramer |author2=Robert L. Forward |author3=Michael S. Morris|author4=Matt Visser |author5=Gregory Benford |author6=Geoffrey A. Landis |name-list-style=amp |date=1995 |title=Natural Wormholes as Gravitational Lenses |journal=[[Physical Review D]] |volume=51 |issue=6 |pages=3117–3120 |arxiv=astro-ph/9409051 |doi=10.1103/PhysRevD.51.3117 |pmid=10018782 |bibcode=1995PhRvD..51.3117C |s2cid=42837620 |url = https://cds.cern.ch/record/268926 }}</ref>

[[File:Wurmloch.jpg|thumb|right|Image of a simulated traversable wormhole that connects the square in front of the physical institutes of [[University of Tübingen]] with the sand dunes near [[Boulogne-sur-Mer]] in the north of France. The image is calculated with 4D [[Ray tracing (graphics)|raytracing]] in a Morris–Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.{{NoteTag|Other computer-rendered images and animations of traversable wormholes can be seen on [http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html this page] by the creator of the image in the article, and [https://web.archive.org/web/20151228145356/https://www.vis.uni-stuttgart.de/~muelleta/MTvis/ this page] has additional renderings.}}]]

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. {{anchor|Ellis–Bronnikov precedence}}<!--'Ellis wormhole' redirects here-->The possibility of traversable wormholes in general relativity was first demonstrated in a 1973 paper by Homer Ellis<ref name="ellis1">{{cite journal |author = H. G. Ellis |year = 1973 |title = Ether flow through a drainhole: A particle model in general relativity |journal = Journal of Mathematical Physics |volume = 14 |issue = 1 |pages = 104–118 |bibcode = 1973JMP....14..104E |doi = 10.1063/1.1666161}}</ref> and independently in a 1973 paper by K. A. Bronnikov.<ref name="bron">{{cite journal |author = K. A. Bronnikov |year = 1973 |title = Scalar-tensor theory and scalar charge |journal = Acta Physica Polonica |volume = B4 |pages = 251–266}}</ref> Ellis analyzed the topology and the [[geodesic]]s of the [[Ellis drainhole]], 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 spacetime, modified by inclusion of a scalar field minimally coupled to the [[Ricci tensor]] with 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: {{var|m}}, which fixes the strength of its gravitational field, and {{var|n}}, which determines the curvature of its spatial cross sections. When {{var|m}} is set equal to 0, the drainhole's gravitational field vanishes. What is left is the [[Ellis wormhole]], a nongravitating, purely geometric, traversable wormhole.

[[Kip Thorne]] and his graduate student [[Mike Morris (physicist)|Mike Morris]] independently discovered in 1988 the Ellis wormhole and argued for its use as a tool for teaching general relativity.<ref>{{cite journal |author1=Morris, Michael S. |author2=Thorne, Kip S. |name-list-style=amp |year=1988 |title=Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity |journal=[[American Journal of Physics]] |volume=56 |issue=5 |pages=395–412 |doi=10.1119/1.15620 |bibcode=1988AmJPh..56..395M |doi-access=free }}</ref> 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. In the pure [[Gauss–Bonnet gravity]] (a modification to general relativity involving extra spatial dimensions that is sometimes studied in the context of [[brane cosmology]]), however, exotic matter is not needed in order for wormholes to exist—they can exist even with no matter.<ref>{{cite journal |author1=Elias Gravanis |author2=Steven Willison |doi=10.1103/PhysRevD.75.084025 |year=2007 |title = 'Mass without mass' from thin shells in Gauss-Bonnet gravity |issue=8 |page=084025 |volume=75 |journal=Phys. Rev. D |arxiv=gr-qc/0701152 |bibcode=2007PhRvD..75h4025G |s2cid=53529713 }}</ref> A type held open by negative mass [[cosmic string]]s was put forth by Visser in collaboration with [[John G. Cramer|Cramer]] ''et al.'',<ref name="naturalwormholes" /> 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 [[time travel|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.<ref name="time travel">{{cite journal |title=Wormholes, Time Machines, and the Weak Energy Condition |year=1988 |last1=Morris|first1=Michael|last2=Thorne|first2=Kip|last3=Yurtsever|first3=Ulvi |journal=Physical Review Letters |volume=61|issue=13|pages=1446–1449 |url = http://authors.library.caltech.edu/9262/1/MORprl88.pdf |doi=10.1103/PhysRevLett.61.1446 |pmid=10038800 |bibcode=1988PhRvL..61.1446M }}</ref> According to general relativity, however, 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.<ref name="Thorne1994" />{{Rp|504}}