Editing Speed of light (section)

== Numerical value, notation, and units ==
The speed of light in vacuum is usually denoted by a lowercase {{math|''c''}}. The origin of the letter choice is unclear, with guesses including "c" for "constant" or the Latin {{lang|la|[[:wikt:celeritas|celeritas]]}} (meaning 'swiftness, celerity').<ref name=Mendelson-2006/> The "c" was used for "celerity" meaning a velocity in books by [[Leonhard Euler]] and others, but this velocity was not specifically for light; [[Isaac Asimov]] wrote a popular science article, "C for Celeritas", but did not explain the origin.<ref>{{Cite journal |last1=Pelosi |first1=G. |last2=Selleri |first2=S. |date=December 2010 |title="c" Utrum est ut Celeritas an Constantia? (Does "c" Stand for Speed or Constancy?) |url=https://ieeexplore.ieee.org/document/5723273 |journal=IEEE Antennas and Propagation Magazine |volume=52 |issue=6 |pages=207–219 |doi=10.1109/MAP.2010.5723273 |bibcode=2010IAPM...52..207P |issn=1045-9243}}</ref>  In 1856, [[Wilhelm Eduard Weber]] and [[Rudolf Kohlrausch]] had used {{math|''c''}} for a different constant that was later shown to equal {{radic|2}} times the speed of light in vacuum. Historically, the symbol ''V'' was used as an alternative symbol for the speed of light, introduced by [[James Clerk Maxwell]] in 1865. In 1903, [[Max Abraham]] used  {{math|''c''}} with its modern meaning in a widely read textbook on electromagnetism. [[Albert Einstein|Einstein]] used ''V'' in his [[Annus Mirabilis papers|original German-language papers]] on special relativity in 1905<!--, the 1923 English translation of them by Perrett and Jeffery using {{math|''c''}}-->, but in 1907 he switched to {{math|''c''}}, which by then had become the standard symbol for the speed of light.<ref name=Yc>
{{Cite web
 |last=Gibbs
 |first=P.
 |year=2004
 |orig-year=1997
 |title=Why is ''c'' the symbol for the speed of light?
 |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html
 |work=Usenet Physics FAQ
 |publisher=[[University of California, Riverside]]
 |access-date=16 November 2009
 |archive-url=https://web.archive.org/web/20100325220247/http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html
 |archive-date=25 March 2010
 |url-status=dead
}}
"The origins of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch [...] Weber apparently meant c to stand for 'constant' in his force law, but there is evidence that physicists such as Lorentz and Einstein were accustomed to a common convention that c could be used as a variable for velocity. This usage can be traced back to the classic Latin texts in which c stood for 'celeritas', meaning 'speed'."
</ref><ref name=Mendelson-2006>
{{Cite journal
 |last=Mendelson |first=K. S.
 |year=2006
 |title=The story of ''c''
 |journal=[[American Journal of Physics]]
 |volume=74 |issue=11 |pages=995–997
 |doi=10.1119/1.2238887
|bibcode = 2006AmJPh..74..995M  | issn=0002-9505}}</ref>

Sometimes {{math|''c''}} is used for the speed of waves in any material medium, and {{math|''c''}}<sub>0</sub> for the speed of light in vacuum.<ref name=handbook>See, for example:
* {{Cite book
 |last=Lide |first=D. R.
 |year=2004
 |title=CRC Handbook of Chemistry and Physics
 |url=https://books.google.com/books?id=WDll8hA006AC&q=speed+of+light+%22c0+OR+%22&pg=PT76
 |pages=2–9
 |publisher=[[CRC Press]]
 |isbn=978-0-8493-0485-9
}}
* {{Cite book
 |last=Harris |first=J. W. |year=2002
 |title=Handbook of Physics
 |url=https://books.google.com/books?id=c60mCxGRMR8C&q=speed+of+light+%22c0+OR+%22+date:2000-2009&pg=PA499
 |page=499
 |publisher=Springer
 |isbn=978-0-387-95269-7
|display-authors=etal}}
* {{Cite book
 |last=Whitaker |first=J. C.
 |year=2005
 |title=The Electronics Handbook
 |url=https://books.google.com/books?id=FdSQSAC3_EwC&q=speed+of+light+c0+handbook&pg=PA235
 |page=235
 |publisher=CRC Press
 |isbn=978-0-8493-1889-4
}}
* {{Cite book
 |last=Cohen |first=E. R. |year=2007
 |title=Quantities, Units and Symbols in Physical Chemistry
 |url=https://books.google.com/books?id=TElmhULQoeIC&q=speed+of+light+c0+handbook&pg=PA143
 |page=184
 |edition=3
 |publisher=[[Royal Society of Chemistry]]
 |isbn=978-0-85404-433-7
 |display-authors=etal
}}</ref> This subscripted notation, which is endorsed in official SI literature,<ref name=BIPM_SI_units>{{SIbrochure8th|page=112}}</ref> has the same form as related electromagnetic constants: namely, ''μ''<sub>0</sub> for the [[vacuum permeability]] or magnetic constant, ''ε''<sub>0</sub> for the [[vacuum permittivity]] or electric constant, and ''Z''<sub>0</sub> for the [[impedance of free space]]. This article uses {{math|''c''}} exclusively for the speed of light in vacuum.

=== Use in unit systems ===
{{Further information|Metre#Speed of light definition}}
Since 1983, the constant {{math|''c''}} has been defined in the [[International System of Units]] (SI) as ''exactly'' {{val|299792458|u=m/s}}; this relationship is used to define the metre as exactly the distance that light travels in vacuum in {{frac|1|{{val|299792458}}}} of a second. The second is, in turn, defined to be the length of time occupied by {{val|9192631770|u=cycles}} of the radiation emitted by a [[caesium]]-133 [[atom]] in a transition between two specified [[energy level|energy states]].<ref name="nist-definitions">{{Cite web |url=https://physics.nist.gov/cuu/Units/current.html |title=Definitions of the SI base units |website=physics.nist.gov |date=29 May 2019 |access-date=8 February 2022}}</ref> By using the value of {{math|''c''}}, as well as an accurate measurement of the second, one can  establish a standard for the metre.<ref name="fixes">See, for example:
* {{Cite book
 |last=Sydenham |first=P. H.
 |year=2003
 |chapter=Measurement of length
 |chapter-url=https://books.google.com/books?id=sarHIbCVOUAC&pg=PA56
 |editor=Boyes, W
 |title=Instrumentation Reference Book
 |edition=3
 |page=56
 |publisher=[[Butterworth–Heinemann]]
 |isbn=978-0-7506-7123-1
 |quote=...{{nbsp}}if the speed of light is defined as a fixed number then, in principle, the time standard will serve as the length standard{{nbsp}}...
}}
* {{Cite web
 |title=CODATA value: Speed of Light in Vacuum
 |url=http://physics.nist.gov/cgi-bin/cuu/Value?c
 |work=The NIST reference on Constants, Units, and Uncertainty
 |publisher=[[National Institute of Standards and Technology|NIST]]
 |access-date=21 August 2009
}}
* {{Cite book
 |last1=Jespersen |first1=J. |last2=Fitz-Randolph |first2=J. |last3=Robb |first3=J.
 |year=1999
 |title=From Sundials to Atomic Clocks: Understanding Time and Frequency
 |url=https://books.google.com/books?id=Z7chuo4ebUAC&pg=PA280
 |page=280
 |edition=Reprint of National Bureau of Standards 1977, 2nd
 |publisher=[[Courier Dover]]
 |isbn=978-0-486-40913-9
}}</ref> 

The particular value chosen for the speed of light provided  a more accurate definition of the metre that still agreed as much as possible with the definition used before 1983.<ref name="nist-definitions"/><ref name="penrose">{{Cite book |last=Penrose |first=R | author-link=Roger Penrose |year=2004 |title=The Road to Reality: A Complete Guide to the Laws of the Universe |pages=[https://archive.org/details/roadtoreality00penr_319/page/n438 410]–411 |publisher=Vintage Books |isbn=978-0-679-77631-4 |quote=...{{nbsp}}the most accurate standard for the metre is conveniently ''defined'' so that there are exactly {{val|299792458}} of them to the distance travelled by light in a standard second, giving a value for the metre that very accurately matches the now inadequately precise [[History of the metre#International prototype metre|standard metre rule]] in Paris. |title-link=The Road to Reality: A Complete Guide to the Laws of the Universe }}</ref>

As a [[Physical constant#Dimensional and dimensionless physical constants|dimensional physical constant]], the numerical value of {{math|''c''}} is different for different unit systems. For example, in [[imperial units]], the speed of light is approximately {{val|186,282}} miles per second,{{#tag:ref|The speed of light in imperial is exactly
: {{val|186,282|u=miles}}, {{val|698|u=yards}}, {{val|2|u=feet}}, and {{sfrac|5|21|127}}{{nbsp}}inches per second.|group="Note"|name="imperial"}} or roughly 1 [[Foot (unit)|foot]] per nanosecond.{{#tag:ref|The exact value is {{sfrac|{{val|149,896,229}}|{{val|152,400,000}}}}{{nbsp}}{{sfrac|ft|ns}} ≈ 0.98{{nbsp}}{{sfrac|ft|ns}}.|group="Note"|name="nanosecond"}}<ref>{{Cite book|last=Mermin |first=N. David |url=https://www.worldcat.org/oclc/57283944 |title=It's About Time: Understanding Einstein's Relativity |date=2005 |publisher=Princeton University Press |isbn=0-691-12201-6 |location=Princeton |oclc=57283944 |author-link=N. David Mermin |page=22}}</ref><ref>{{Cite web|url=https://americanhistory.si.edu/collections/search/object/nmah_692464 |title=Nanoseconds Associated with Grace Hopper |website=[[National Museum of American History]] |quote=[[Grace Hopper|Grace Murray Hopper]] (1906–1992), a mathematician who became a naval officer and computer scientist during World War II, started distributing these wire "nanoseconds" in the late 1960s in order to demonstrate how designing smaller components would produce faster computers. |access-date=1 March 2022}}</ref>

In branches of physics in which {{math|''c''}} appears often, such as in relativity, it is common to use systems of [[natural units]] of measurement or the [[geometrized unit system]] where {{nowrap|{{math|''c''}} {{=}} 1}}.<ref name="Lawrie">
{{Cite book
 |last=Lawrie |first=I. D.
 |year=2002
 |chapter=Appendix C: Natural units
 |chapter-url=https://books.google.com/books?id=9HZStxmfi3UC&pg=PA540
 |title=A Unified Grand Tour of Theoretical Physics
 |page=540
 |edition=2
 |publisher=CRC Press
 |isbn=978-0-7503-0604-1
}}</ref><ref name="Hsu1">
{{Cite book
 |last=Hsu |first=L.
 |year=2006
 |chapter=Appendix A: Systems of units and the development of relativity theories
 |chapter-url=https://books.google.com/books?id=amLqckyrvUwC&pg=PA428
 |title=A Broader View of Relativity: General Implications of Lorentz and Poincaré Invariance
 |pages=427–428
 |edition=2
 |publisher=[[World Scientific]]
 |isbn=978-981-256-651-5
}}</ref> Using these units, {{math|''c''}} does not appear explicitly because multiplication or division by{{nbsp}}1 does not affect the result. Its unit of [[light-second]] per second is still relevant, even if omitted.