Editing Speed of light (section)

{{Short description|Speed of electromagnetic waves in vacuum}}
{{Redirect|Lightspeed|other uses|Speed of light (disambiguation)|and|Lightspeed (disambiguation)}}
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{{Use Oxford spelling|date=August 2022}}
{{Use dmy dates|date=August 2022|cs1-dates=l}}
{{Infobox
| title            = Speed of light
| image            = [[File:Earth to Sun - en.png|frameless|upright=1.35|alt=The distance from the Sun to Earth is shown as 150 million kilometres, an approximate average. Sizes to scale.]]
| caption          = On average, [[sunlight]] takes 8{{nbsp}}minutes and 17{{nbsp}}seconds to travel from the [[Sun]] to [[Earth]].<!-- (1 AU − 1 solar radius − 1 earth radius)/c = (149597871 − 695500 − 6371)/299792.458 = 496.66 s = 8 min 17 s -->
| header1          = Exact value
| labelstyle       = font-weight:normal
| label2           = [[metre per second|metres per second]]
| data2            = {{val|299792458}}
| header4          = Approximate values (to three significant digits)<!-- This section lists various values for c, to three significant digits. Please do not change to more exact values! -->
| label5           = [[kilometres per hour]]
| data5            = {{val|1080000000}}
| label6           = [[miles per hour|miles per second]]
| data6            = {{val|186000}}
| label7           = [[miles per hour]]<ref>{{Cite book |title=Elementary and Intermediate Algebra: A Combined Course, Student Support Edition |edition=4th illustrated |first1=Ron |last1=Larson |first2=Robert P. |last2=Hostetler |publisher=Cengage Learning |year=2007 |isbn=978-0-618-75354-3 |page=197 |url=https://books.google.com/books?id=qe-YvKoeiasC&pg=PA179}}</ref>
| data7            = {{val|671000000}}
| label8           = [[astronomical unit]]s per day
| data8            = 173{{#tag:ref|Exact value: {{nowrap|({{val|299792458}} × {{val|86400}}<!--60 × 60 × 24--> / {{val|149597870700}}) AU/day}}.|group="Note"}}
| label9           = [[parsec]]s per year
| data9            = 0.307{{#tag:ref|Exact value: {{nowrap|({{val|999992651|end=&nbsp;π}} / {{val|10246429500}}) pc/y}}.|group="Note"}}
| header10         = Approximate light signal travel times
| label11          = '''Distance'''
| data11           = '''Time'''
| label12          = one [[foot (unit)|foot]]
| data12           = 1.0 [[Nanosecond|ns]]
| label13          = one [[metre]]
| data13           = 3.3 ns
| label15          = from [[geostationary orbit]] to Earth
| data15           = 119 [[millisecond|ms]]
| label16          = the length of Earth's [[equator]]
| data16           = 134 ms
| label17          = from [[Moon]] to Earth
| data17           = 1.3 [[second|s]]
| label18          = from [[Sun]] to Earth (1&nbsp;[[astronomical unit|AU]])
| data18           = 8.3 [[minute|min]]
| label20          = one [[light-year]]
| data20           = 1.0 [[year]]
| label21          = one parsec
| data21           = 3.26 years
| label22          = from the [[Proxima Centauri|nearest star]] to Sun ({{val|1.3|u={{abbr|pc|parsec}}}})
| data22           = 4.2 years
| label23          = from the [[Sagittarius Dwarf Spheroidal Galaxy|nearest galaxy]] to Earth
| data23           = {{val|70,000|u=years}}
| label24          = across the [[Milky Way]]
| data24           = {{val|87,400|u=years}}
| label25          = from the [[Andromeda Galaxy]] to Earth
| data25           = 2.5 million years
}}
{{Special relativity sidebar}}

The '''speed of light''' in [[vacuum]], commonly denoted {{mvar|'''c'''}}, is a universal [[physical constant]] exactly equal to {{convert|299792458|m/s|km/s mi/s e6mph|abbr=off|sigfig=3|disp=x| (approximately }}). It is exact because, by international agreement, a [[Metre#Speed of light definition|metre]] is defined as the length of the path travelled by [[light]] in vacuum during a time interval of {{frac|1|{{val|299792458}}}} [[second]]. The speed of light is [[invariant (physics)|the same for all observers]], no matter their relative velocity. It is the upper limit for the speed at which [[Information#Physics_and_determinacy|information]], [[matter]], or [[energy]] can travel through [[Space#Relativity|space]].<ref>{{cite book |title=Special Relativity and How it Works |author1=Moses Fayngold |edition=illustrated |publisher=John Wiley & Sons |year=2008 |isbn=978-3-527-40607-4 |page=497 |url=https://books.google.com/books?id=Q3egk8Ds6ogC}} [https://books.google.com/books?id=Q3egk8Ds6ogC&pg=PA497 Extract of page 497].</ref><ref>{{cite book |title=Special Relativity |author1=Albert Shadowitz |edition=revised |publisher=Courier Corporation |year=1988 |isbn=978-0-486-65743-1 |page=79 |url=https://books.google.com/books?id=1axfJqUT6R0C}} [https://books.google.com/books?id=1axfJqUT6R0C&pg=PA79 Extract of page 79].</ref><ref>{{Cite journal |last1=Peres |first1=Asher |author-link=Asher Peres |last2=Terno |first2=Daniel R. |date=2004-01-06 |title=Quantum information and relativity theory |url=https://link.aps.org/doi/10.1103/RevModPhys.76.93 |journal=Reviews of Modern Physics |language=en |volume=76 |issue=1 |pages=93–123 |doi=10.1103/RevModPhys.76.93 |arxiv=quant-ph/0212023 |bibcode=2004RvMP...76...93P |s2cid=7481797 |issn=0034-6861}}</ref> 

All forms of [[electromagnetic radiation]], including [[visible light]], travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. Much [[starlight]] viewed on [[Earth]] is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When [[Data communication|communicating]] with distant [[space probe]]s, it can take hours for signals to travel. In [[computing]], the speed of light fixes the ultimate minimum [[Latency (engineering)|communication delay]]. The speed of light can be used in [[time of flight]] measurements to measure large distances to extremely high precision.

[[Ole Rømer]] first [[Rømer's determination of the speed of light|demonstrated]] that light does not travel instantaneously by studying the apparent motion of [[Jupiter]]'s moon [[Io (moon)|Io]]. In an 1865 [[A Dynamical Theory of the Electromagnetic Field|paper]], [[James Clerk Maxwell]] proposed that light was an [[Electromagnetic radiation|electromagnetic wave]] and, therefore, travelled at speed {{Mvar|c}}.<ref>{{Cite web |title=How is the speed of light measured? |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html |url-status=dead |website=The Physics and Relativity FAQ |first=Philip |last=Gibbs |date=1997 |archive-url=https://web.archive.org/web/20150821181850/http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html |archive-date=21 August 2015 }}</ref> [[Albert Einstein]] postulated that the speed of light {{Mvar|c}} with respect to any [[inertial frame of reference]] is a constant and is independent of the motion of the light source.<ref name="stachel">{{Cite book |title=Einstein from "B" to "Z" – Volume 9 of Einstein studies |first1=J. J. |last1=Stachel |publisher=Springer |year=2002 |isbn=978-0-8176-4143-6 |page=226 |url=https://books.google.com/books?id=OAsQ_hFjhrAC&pg=PA226}}</ref> He explored the consequences of that postulate by deriving the [[theory of relativity]] and, so showed that the parameter {{Mvar|c}} had relevance outside of the context of light and electromagnetism.

[[Massless particle]]s and [[field (physics)|field]] perturbations, such as [[gravitational wave]]s, also travel at speed {{Mvar|c}} in vacuum. Such particles and waves travel at {{Mvar|c}} regardless of the motion of the source or the inertial reference frame of the [[observer (special relativity)|observer]]. Particles with nonzero [[rest mass]] can be accelerated to approach {{Mvar|c}} but can never reach it, regardless of the frame of reference in which their speed is measured. In the [[theory of relativity]], {{Mvar|c}} interrelates [[spacetime|space and time]] and appears in the famous [[mass–energy equivalence]], {{math|1=''E'' = ''mc''{{i sup|2}}}}.<ref>See, for example:
* {{Cite journal|last1=Feigenbaum|first1=Mitchell J.|author-link=Mitchell Feigenbaum|last2=Mermin|first2=N. David|author-link2=N. David Mermin|date=January 1988|title=E = mc<sup>2</sup>|url=http://aapt.scitation.org/doi/10.1119/1.15422|journal=[[American Journal of Physics]]|language=en|volume=56|issue=1|pages=18–21|doi=10.1119/1.15422|bibcode=1988AmJPh..56...18F|issn=0002-9505|url-access=subscription}}
* {{Cite book |last1=Uzan |first1=J-P |last2=Leclercq |first2=B |year=2008 |title=The Natural Laws of the Universe: Understanding Fundamental Constants |url=https://books.google.com/books?id=dSAWX8TNpScC&pg=PA43 |pages=43–44 |publisher=Springer |isbn=978-0-387-73454-5 }}</ref>

In some cases, objects or waves may appear to travel [[#Faster-than-light observations and experiments|faster than light]]. The [[expansion of the universe]] is understood to exceed the speed of light beyond [[Hubble volume|a certain boundary]]. The speed at which light propagates through [[Transparency and translucency|transparent materials]], such as glass or air, is less than {{Mvar|c}}; similarly, the speed of [[electromagnetic waves]] in wire cables is slower than {{Mvar|c}}. The ratio between {{Mvar|c}} and the speed {{Mvar|v}} at which light travels in a material is called the [[refractive index]] {{mvar|n}} of the material ({{math|1={{Mvar|n}} = {{sfrac|{{Mvar|c}}|{{Mvar|v}}}}}}). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at {{nowrap|{{sfrac|{{Mvar|c}}|1.5}} ≈ {{cvt|200000|km/s|mi/s|comma=gaps|sigfig=3}}}}; the [[refractive index of air]] for visible light is about 1.0003, so the speed of light in air is about {{cvt|{{#expr:299792.458*(1-1/1.0003) round 0}}|km/s|mi/s|comma=gaps|sigfig=2}} slower than {{Mvar|c}}.

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