Editing Speed of light (section)

== Faster-than-light observations and experiments ==
{{See also|Faster-than-light|Superluminal motion}}

There are situations in which it may seem that matter, energy, or information-carrying signal travels at speeds greater than&nbsp;''c'', but they do not. For example, as is discussed in the [[#In a medium|propagation of light in a medium]] section below, many wave velocities can exceed&nbsp;''c''. The [[phase velocity]] of [[X-ray]]s through most glasses can routinely exceed ''c'',<ref>
{{Cite book
 |last=Hecht |first=E.
 |year=1987
 |title=Optics
 |page=62
 |edition=2
 |publisher=Addison-Wesley
 |isbn=978-0-201-11609-0
}}</ref> but phase velocity does not determine the velocity at which waves convey information.<ref>
{{Cite book
 |last=Quimby |first=R. S.
 |title=Photonics and lasers: an introduction
 |publisher=John Wiley and Sons
 |year=2006
 |page=9
 |isbn=978-0-471-71974-8
 |url=https://books.google.com/books?id=yWeDVfaVGxsC&pg=PA9
}}</ref>

If a laser beam is swept quickly across a distant object, the spot of light can move faster than&nbsp;''c'', although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed&nbsp;''c''. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed&nbsp;''c'' from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than&nbsp;''c'', after a delay in time.<ref>
{{Cite news
 |last=Wertheim |first=M.
 |title=The Shadow Goes
 |url=https://www.nytimes.com/2007/06/20/opinion/20wertheim.html?_r=1&scp=1&sq=%27the%20shadow%20goes%27&st=cse&oref=slogin
 |work=The New York Times
 |access-date=21 August 2009
 |date=20 June 2007
}}</ref> In neither case does any matter, energy, or information travel faster than light.<ref name=Gibbs>
{{Cite web
 |last=Gibbs
 |first=P.
 |year=1997
 |title=Is Faster-Than-Light Travel or Communication Possible?
 |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
 |publisher=[[University of California, Riverside]]
 |work=Usenet Physics FAQ
 |access-date=20 August 2008
 |archive-date=10 March 2010
 |archive-url=https://web.archive.org/web/20100310205556/http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
 |url-status=dead
}}</ref>

The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their [[Faster-than-light#Closing speeds|closing speed]]) may have a value in excess of&nbsp;''c''. However, this does not represent the speed of any single object as measured in a single inertial frame.<ref name="Gibbs" />

Certain quantum effects appear to be transmitted instantaneously and therefore faster than ''c'', as in the [[EPR paradox]]. An example involves the [[quantum state]]s of two particles that can be [[quantum entanglement|entangled]]. Until either of the particles is observed, they exist in a [[quantum superposition|superposition]] of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously. However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.<ref name=Gibbs /><ref>See, for example:
* {{Cite book
 |last=Sakurai |first=J. J. |author-link=J. J. Sakurai
 |year=1994
 |editor-last=Tuan |editor-first=S. F.
 |title=[[Modern Quantum Mechanics]] |edition=Revised |pages=[https://archive.org/details/modernquantummec00saku_488/page/n243 231]–232
 |publisher=Addison-Wesley
 |isbn=978-0-201-53929-5
}}
* {{Cite book|last=Peres|first=Asher|title=Quantum Theory: Concepts and Methods|title-link=Quantum Theory: Concepts and Methods|publisher=[[Kluwer]]|year=1993|isbn=0-7923-2549-4|pages=170|oclc=28854083|author-link=Asher Peres}}
* {{Cite book
 |first=Carlton M.
 |last=Caves
 |author-link=Carlton Caves
 |chapter=Quantum Information Science: Emerging No More
 |title=OSA Century of Optics
 |pages=320–326
 |arxiv=1302.1864
 |publisher=[[Optica (society)|Optica]]
 |year=2015
 |isbn=978-1-943-58004-0
 |quote=[I]t was natural to dream that quantum correlations could be used for faster-than-light communication, but this speculation was quickly shot down, and the shooting established the principle that quantum states cannot be copied.
}}</ref>

Another quantum effect that predicts the occurrence of faster-than-light speeds is called the [[Hartman effect]]: under certain conditions the time needed for a [[virtual particle]] to [[quantum tunnelling|tunnel]] through a barrier is constant, regardless of the thickness of the barrier.<ref name=Muga>
{{Cite book
 |editor-last=Muga |editor-first=J. G. |editor-last2=Mayato |editor-first2=R. S. |editor-last3=Egusquiza |editor-first3=I. L.
 |year=2007
 |title=Time in Quantum Mechanics
 |url=https://books.google.com/books?id=InKru6zHQWgC&pg=PA48
 |page=48
 |publisher=Springer
 |isbn=978-3-540-73472-7
}}</ref><ref name=Recami>
{{Cite book
 |last1=Hernández-Figueroa |first1=H. E. |last2=Zamboni-Rached |first2=M. |last3=Recami |first3=E.
 |year=2007
 |title=Localized Waves
 |url=https://books.google.com/books?id=xxbXgL967PwC&pg=PA26
 |page=26
 |publisher=[[Wiley Interscience]]
 |isbn=978-0-470-10885-7
}}</ref> This could result in a virtual particle crossing a large gap faster than light. However, no information can be sent using this effect.<ref name=Wynne>
{{Cite journal
 |last=Wynne
 |first=K.
 |year=2002
 |title=Causality and the nature of information
 |journal=[[Optics Communications]]
 |volume=209
 |issue=1–3
 |pages=84–100
 |doi=10.1016/S0030-4018(02)01638-3
 |bibcode=2002OptCo.209...85W
 |url=http://bcp.phys.strath.ac.uk/the_group/r/uf/2002-OC-causality.pdf
 |archive-url=https://web.archive.org/web/20090325093856/http://bcp.phys.strath.ac.uk/the_group/r/uf/2002-OC-causality.pdf
 |archive-date=2009-03-25
}}</ref>

So-called [[superluminal motion]] is seen in certain astronomical objects,<ref>
{{Cite journal
 |last=Rees |first=M. |author-link=Martin Rees
 |year=1966
 |title=The Appearance of Relativistically Expanding Radio Sources
 |journal=[[Nature (journal)|Nature]]
 |volume=211
 |issue=5048 |page=468
 |doi=10.1038/211468a0
 |bibcode = 1966Natur.211..468R |s2cid=41065207
}}</ref> such as the [[relativistic jet]]s of [[radio galaxy|radio galaxies]] and [[quasar]]s. However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a [[graphical projection|projection]] effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted.<ref>
{{Cite web
 |last=Chase |first=I. P.
 |title=Apparent Superluminal Velocity of Galaxies
 |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/Superluminal/superluminal.html
 |publisher=[[University of California, Riverside]]
 |work=Usenet Physics FAQ
 |access-date=26 November 2009
}}</ref>

A 2011 experiment where [[Faster-than-light neutrino anomaly|neutrinos were observed to travel faster than light]] turned out to be due to experimental error.<ref name=nature1204>{{Cite journal |title=Embattled neutrino project leaders step down |journal=[[Nature News]] |first=Eugenie Samuel |last=Reich |date=2 April 2012 |access-date=11 February 2022 |doi=10.1038/nature.2012.10371 |s2cid=211730430 |url=http://www.nature.com/news/embattled-neutrino-project-leaders-step-down-1.10371}}</ref><ref>{{Cite journal |author=OPERA Collaboration |author-link=OPERA experiment |title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam |date=12 July 2012 |arxiv=1109.4897 |doi=10.1007/JHEP10(2012)093 |volume=2012 |issue=10 |page=93 |journal=[[Journal of High Energy Physics]] |bibcode=2012JHEP...10..093A |s2cid=17652398 }}</ref>

In models of the [[expansion of the universe|expanding universe]], the farther galaxies are from each other, the faster they drift apart. For example, galaxies far away from Earth are inferred to be moving away from the Earth with speeds proportional to their distances. Beyond a boundary called the [[Hubble sphere]], the rate at which their distance from Earth increases becomes greater than the speed of light.<ref name=Harrison>
{{Cite book
 |last= Harrison |first=E. R.
 |year=2003
 |title=Masks of the Universe
 |url=https://books.google.com/books?id=tSowGCP0kMIC&pg=PA206
 |page=206
 |publisher=Cambridge University Press
 |isbn=978-0-521-77351-5
}}</ref>
These recession rates, defined as the increase in [[comoving and proper distances|proper distance]] per [[cosmological time]], are not velocities in a relativistic sense. Faster-than-light cosmological recession speeds are only a [[coordinate conditions|coordinate]] artifact.