Editing Faster-than-light (section)

==Justifications==

===Casimir vacuum and quantum tunnelling===
[[Special relativity]] postulates that the speed of light in vacuum is invariant in [[inertial frame]]s. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the [[International System of Units|SI]] unit of length (the [[meter]]) has been defined using the [[speed of light]].

The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called simply the [[vacuum energy]], which could perhaps be altered in certain cases.<ref>{{cite magazine |title=What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy? |url=https://www.scientificamerican.com/article/follow-up-what-is-the-zer/ |magazine=Scientific American |date=1997-08-18 |access-date=2009-05-27}}</ref> When vacuum energy is lowered, light itself has been predicted to go faster than the standard value ''c''. This is known as the [[Scharnhorst effect]]. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a [[Casimir effect#Vacuum energy|Casimir vacuum]]. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 10<sup>36</sup>.<ref>{{Cite web |last=Scharnhorst |first=Klaus |date=1990-05-12 |title=Secret of the vacuum: Speedier light |url=http://www.nat.vu.nl/~scharnh/m16scine.htm |access-date=2009-05-27 |website=[[Vrije Universiteit Amsterdam]]}}</ref> Accordingly, there has as yet been no experimental verification of the prediction. A recent analysis<ref name="lib">{{Cite journal |last1=Liberati |first1=Stefano |last2=Sonego |first2=Sebastiano |last3=Visser |first3=Matt |year=2002 |title=Faster-than-c Signals, Special Relativity, and Causality |journal=[[Annals of Physics]] |language=en |volume=298 |issue=1 |pages=167–185 |arxiv=gr-qc/0107091 |bibcode=2002AnPhy.298..167L |doi=10.1006/aphy.2002.6233 |s2cid=48166}}</ref> argued that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "[[preferred frame]]" for FTL signaling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative [[chronology protection conjecture]] which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze. Other authors argue that Scharnhorst's original analysis, which seemed to show the possibility of faster-than-''c'' signals, involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.<ref>{{Cite journal |last=Fearn |first=H. |year=2007 |title=Can light signals travel faster than ''c'' in nontrivial vacua in flat space-time? Relativistic causality II |journal=Laser Physics |language=en |volume=17 |issue=5 |pages=695–699 |arxiv=0706.0553 |bibcode=2007LaPhy..17..695F |doi=10.1134/S1054660X07050155 |issn=1054-660X |s2cid=61962}}</ref>

It was later claimed by Eckle ''et al.'' that particle tunneling does indeed occur in zero real time.<ref name="Eckle">{{cite journal |last1=Eckle |first1=P. |last2=Pfeiffer |first2=A. N. |last3=Cirelli |first3=C. |last4=Staudte |first4=A. |last5=Dorner |first5=R. |last6=Muller |first6=H. G. |last7=Buttiker |first7=M. |last8=Keller |first8=U. |title=Attosecond Ionization and Tunneling Delay Time Measurements in Helium |journal=Science |date=5 December 2008 |volume=322 |issue=5907 |pages=1525–1529 |doi=10.1126/science.1163439|pmid=19056981 |bibcode=2008Sci...322.1525E|s2cid=206515239 }}</ref> Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500–600 attoseconds (an [[attosecond]] is one quintillionth (10<sup>&minus;18</sup>) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.<ref name="WinfulHartman">{{cite journal |last=Winful |first=Herbert G. |title=Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox |journal=Physics Reports |volume=436 |issue=1–2 |pages=1–69 |date=December 2006 |url=http://sitemaker.umich.edu/herbert.winful/files/physics_reports_review_article__2006_.pdf |doi=10.1016/j.physrep.2006.09.002 |bibcode=2006PhR...436....1W |access-date=2010-06-08 |archive-url=https://web.archive.org/web/20111218061131/http://sitemaker.umich.edu/herbert.winful/files/physics_reports_review_article__2006_.pdf |archive-date=2011-12-18 |url-status=dead }}</ref><ref name="WinfulArticle">For a summary of Herbert G. Winful's explanation for apparently superluminal tunneling time which does not involve reshaping, see {{cite journal|last1=Winful|first1=Herbert|title=New paradigm resolves old paradox of faster-than-light tunneling|journal=SPIE Newsroom|date=2007|doi=10.1117/2.1200711.0927}}</ref><ref name="Sokolovski">{{cite journal |last=Sokolovski |first=D. |title=Why does relativity allow quantum tunneling to 'take no time'? |journal=Proceedings of the Royal Society A |volume=460 |issue=2042 |pages=499–506 |date=8 February 2004 |doi=10.1098/rspa.2003.1222 |bibcode=2004RSPSA.460..499S|s2cid=122620657 }}</ref>

===Give up (absolute) relativity===
Because of the strong empirical support for [[special relativity]], any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is [[doubly special relativity]], which posits that the [[Planck length]] is also the same in all reference frames, and is associated with the work of [[Giovanni Amelino-Camelia]] and [[João Magueijo]].<ref>{{cite book|first=Giovanni|last=Amelino-Camelia|date=1 November 2009|arxiv=1003.3942|volume=9|pages=123–170|doi=10.1142/9789814287333_0006|chapter=Doubly-Special Relativity: Facts, Myths and Some Key Open Issues|title = Recent Developments in Theoretical Physics|series = Statistical Science and Interdisciplinary Research|isbn = 978-981-4287-32-6|s2cid=118855372}}</ref><ref>{{cite journal|title=Doubly Special Relativity|first=Giovanni|last=Amelino-Camelia|date=1 July 2002|journal=Nature|volume=418|issue=6893|pages=34–35|doi=10.1038/418034a|arxiv=gr-qc/0207049|bibcode=2002Natur.418...34A|pmid=12097897|s2cid=16844423}}</ref>
There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., [[Mach's principle]]), which implies that the rest frame of the universe might be ''preferred'' by conventional measurements of natural law. If confirmed, this would imply [[special relativity]] is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the [[observable universe]], it is difficult to imagine (much less construct) experiments to test this hypothesis. Despite this difficulty, such experiments have been proposed.<ref>{{cite journal|last=Chang|first=Donald C.|title=Is there a resting frame in the universe? A proposed experimental test based on a precise measurement of particle mass|journal=The European Physical Journal Plus|doi=10.1140/epjp/i2017-11402-4|date=March 22, 2017|volume=132|issue=3|page=140|arxiv=1706.05252|bibcode=2017EPJP..132..140C|doi-access=free}}</ref>

===Spacetime distortion===
Although the theory of [[special relativity]] forbids objects to have a relative velocity greater than light speed, and [[general relativity]] reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "[[recession velocity]]" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.<ref name="ly93" /> [[Miguel Alcubierre]] theorized that it would be possible to create a [[Alcubierre drive|warp drive]], in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally traveling faster than light.<ref>{{cite journal |last1=Alcubierre |first1=Miguel |title=The warp drive: hyper-fast travel within general relativity |journal=Classical and Quantum Gravity |date=1 May 1994 |volume=11 |issue=5 |pages=L73–L77 |doi=10.1088/0264-9381/11/5/001|arxiv=gr-qc/0009013 |citeseerx=10.1.1.338.8690 |bibcode=1994CQGra..11L..73A|s2cid=4797900 }}</ref> However, [[Alcubierre drive#Difficulties|several objections]] raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the [[wormhole#Traversable wormholes|traversable wormhole]], which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not ''locally'' move faster than light travelling through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.

Gerald Cleaver and Richard Obousy, a professor and student of [[Baylor University]], theorized that manipulating the extra spatial dimensions of [[string theory]] around a spaceship with an extremely large amount of energy would create a "bubble" that could cause the ship to travel faster than the speed of light. To create this bubble, the physicists believe manipulating the 10th spatial dimension would alter the [[dark energy]] in three large spatial dimensions: height, width and length. Cleaver said positive dark energy is currently responsible for speeding up the expansion rate of our universe as time moves on.<ref>{{Cite web |title=Traveling Faster Than the Speed of Light: A New Idea That Could Make It Happen |url=https://www.newswise.com/articles/traveling-faster-than-the-speed-of-light-a-new-idea-that-could-make-it-happen |access-date=2023-08-24 |website=www.newswise.com |language=en}}</ref>

===Lorentz symmetry violation===
{{Main|Modern searches for Lorentz violation|Standard-Model Extension}}

The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called [[Standard-Model Extension]].<ref>{{cite journal |arxiv=hep-ph/9703464 |bibcode=1997PhRvD..55.6760C |doi=10.1103/PhysRevD.55.6760 |title=CPT violation and the standard model |year=1997 |last1=Colladay |first1=Don |last2=Kostelecký |first2=V. Alan |journal=Physical Review D |volume=55 |issue=11 |pages=6760–6774|s2cid=7651433 }}</ref><ref>{{cite journal |arxiv=hep-ph/9809521 |bibcode=1998PhRvD..58k6002C |doi=10.1103/PhysRevD.58.116002 |title=Lorentz-violating extension of the standard model |year=1998 |last1=Colladay |first1=Don |last2=Kostelecký |first2=V. Alan |journal=Physical Review D |volume=58 |issue=11 |pages=116002|s2cid=4013391 }}</ref><ref>{{cite journal |arxiv=hep-th/0312310 |bibcode=2004PhRvD..69j5009K |doi=10.1103/PhysRevD.69.105009 |title=Gravity, Lorentz violation, and the standard model |year=2004 |last1=Kostelecký |first1=V. Alan |journal=Physical Review D |volume=69 |issue=10 |pages=105009|s2cid=55185765 }}</ref> This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments<ref name="Gonzalez-Mestres2009b">{{Cite journal |last=Gonzalez-Mestres |first=Luis |year=2009 |title=AUGER-HiRes results and models of Lorentz symmetry violation |journal=Nuclear Physics B - Proceedings Supplements |language=en |volume=190 |pages=191–197 |arxiv=0902.0994 |bibcode=2009NuPhS.190..191G |doi=10.1016/j.nuclphysbps.2009.03.088 |s2cid=14848782}}</ref> and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.<ref name="autogenerated1">{{cite journal |arxiv=0801.0287 |bibcode=2011RvMP...83...11K |doi=10.1103/RevModPhys.83.11 |title=Data tables for Lorentz and CPT violation |year=2011 |last1=Kostelecký |first1=V. Alan |last2=Russell |first2=Neil |journal=Reviews of Modern Physics |volume=83 |issue=1 |pages=11–31|s2cid=3236027 }}</ref>
The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including [[Lorentz-violating neutrino oscillations]] and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.

In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that [[spontaneous symmetry breaking]] of Lorentz invariance<ref>{{cite journal |last1=Kostelecký |first1=V. A. |last2=Samuel |first2=S. |title=Spontaneous breaking of Lorentz symmetry in string theory |journal=Physical Review D |date=15 January 1989 |volume=39 |issue=2 |pages=683–685 |doi=10.1103/PhysRevD.39.683|pmid=9959689 |bibcode=1989PhRvD..39..683K|hdl=2022/18649 |url=https://scholarworks.iu.edu/dspace/bitstream/handle/2022/18649/PhysRevD.39.683.pdf |archive-url=https://web.archive.org/web/20210713090335/https://scholarworks.iu.edu/dspace/bitstream/handle/2022/18649/PhysRevD.39.683.pdf |archive-date=2021-07-13 |url-status=live | hdl-access=free }}</ref> shortly after the [[Big Bang]] could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field;<ref>{{cite web |date=2004-04-05 |title=PhysicsWeb – Breaking Lorentz symmetry |url=http://physicsweb.org/article/world/17/3/7 |archive-url=https://web.archive.org/web/20040405031103/http://physicsweb.org/article/world/17/3/7 |archive-date=2004-04-05 |access-date=2011-09-26 |publisher=PhysicsWeb}}</ref> however, there are also some models where Lorentz symmetry is broken in a more fundamental way. If Lorentz symmetry can cease to be a fundamental symmetry at the Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.

In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,<ref name="CERNCourrier">{{cite web|last=Mavromatos |first=Nick E. |title=Testing models for quantum gravity |work=CERN Courier |url=http://cerncourier.com/cws/article/cern/28696 |date=15 August 2002}}</ref><ref name="NYT">{{Cite news |last=Overbye |first=Dennis |date=2002-12-31 |title=Interpreting the Cosmic Rays |language=en-US |work=The New York Times |url=https://www.nytimes.com/2002/12/31/science/interpreting-the-cosmic-rays.html |access-date=2023-08-24 |issn=0362-4331}}</ref> existing low-energy bounds cannot be applied to high-energy phenomena; however, many searches for Lorentz violation at high energies have been carried out using the [[Standard-Model Extension]].<ref name="autogenerated1"/>
Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.

===Superfluid theories of physical vacuum===
{{Main|Superfluid vacuum theory}}

In this approach, the physical [[vacuum]] is viewed as a quantum [[superfluid]] which is essentially non-relativistic, whereas [[Lorentz symmetry]] is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.<ref name="volovik03">{{cite journal |last1=Volovik |first1=G. E. |year=2003 |title=The Universe in a helium droplet |journal=International Series of Monographs on Physics |volume=117 |pages=1–507}}</ref> Within the framework of the approach, a theory was proposed in which the physical vacuum is conjectured to be a [[Bose–Einstein condensate|quantum Bose liquid]] whose ground-state [[wave function|wavefunction]] is described by the [[logarithmic Schrödinger equation]]. It was shown that the [[general relativity|relativistic gravitational interaction]] arises as the small-amplitude [[collective excitation]] mode<ref>{{cite journal |title=Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory |last1=Zloshchastiev |first1=Konstantin G. |year=2011 |doi=10.5506/APhysPolB.42.261 |journal=Acta Physica Polonica B |volume=42 |issue=2 |pages=261–292 |arxiv=0912.4139 |bibcode= 2011AcPPB..42..261Z|s2cid=118152708 }}</ref> whereas relativistic [[elementary particle]]s can be described by the [[quasiparticle|particle-like modes]] in the limit of low momenta.<ref>{{cite journal |arxiv=1108.0847 |bibcode=2011JPhB...44s5303A |doi=10.1088/0953-4075/44/19/195303 |title=Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent |year=2011 |last1=Avdeenkov |first1=Alexander V. |last2=Zloshchastiev |first2=Konstantin G. |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=44 |issue=19 |page=195303|s2cid=119248001 }}</ref> The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the [[theory of relativity|relativistic]] one – they can reach the [[speed of light#Upper limit on speeds|speed of light limit]] at finite energy; also, faster-than-light propagation is possible without requiring moving objects to have [[imaginary mass]].<ref>{{cite journal |arxiv=0906.4282 |bibcode=2010AIPC.1206..112Z |doi=10.1063/1.3292518 |title=Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences |journal=American Institute of Physics Conference Series |volume=1206 |pages=288–297 |series=AIP Conference Proceedings |year=2010 |last1=Zloshchastiev |first1=Konstantin G. |last2=Chakrabarti |first2=Sandip K. |last3=Zhuk |first3=Alexander I. |last4=Bisnovatyi-Kogan |first4=Gennady S.}}</ref><ref>{{cite journal |arxiv=1003.0657 |bibcode=2011PhLA..375.2305Z |doi=10.1016/j.physleta.2011.05.012 |title=Vacuum Cherenkov effect in logarithmic nonlinear quantum theory |year=2011 |last1=Zloshchastiev |first1=Konstantin G. |journal=Physics Letters A |volume=375 |issue=24 |pages=2305–2308|s2cid=118152360 }}</ref>