Speed of light

Speed of light
	On average, sunlight takes 8 minutes and 17 seconds to travel from the Sun to Earth.
Exact value
metres per second	299792458
Approximate values (to three significant digits)
kilometres per hour	1080000000
miles per second	186000
miles per hour	671000000
astronomical units per day	173
parsecs per year	0.307
Approximate light signal travel times
Distance	Time
one foot	1.0 ns
one metre	3.3 ns
from geostationary orbit to Earth	119 ms
the length of Earth's equator	134 ms
from Moon to Earth	1.3 s
from Sun to Earth (1 AU)	8.3 min
one light-year	1.0 year
one parsec	3.26 years
from the nearest star to Sun (1.3 pc)	4.2 years
from the nearest galaxy to Earth	70000 years
across the Milky Way	87400 years
from the Andromeda Galaxy to Earth	2.5 million years

The speed of light in vacuum, commonly denoted $c$ , is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour).^{[Note 3]} According to the special theory of relativity, $c$ is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.^[4]^[5]^[6]

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 very 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 communicating with distant space probes, it can take minutes to hours for signals to travel. In computing, the speed of light fixes the ultimate minimum 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 demonstrated in 1676 that light does not travel instantaneously by studying the apparent motion of Jupiter's moon Io. Progressively more accurate measurements of its speed came over the following centuries. In a paper published in 1865, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed $c$ .^[7] In 1905, Albert Einstein postulated that the speed of light $c$ with respect to any inertial frame of reference is a constant and is independent of the motion of the light source.^[8] He explored the consequences of that postulate by deriving the theory of relativity and, in doing so, showed that the parameter $c$ had relevance outside of the context of light and electromagnetism.

Massless particles and field perturbations, such as gravitational waves, also travel at speed $c$ in vacuum. Such particles and waves travel at $c$ regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can be accelerated to approach $c$ but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity, $c$ interrelates space and time and appears in the famous mass–energy equivalence, $E = mc 2$ .^[9]

In some cases, objects or waves may appear to travel faster than light (e.g., phase velocities of waves, the appearance of certain high-speed astronomical objects, and particular quantum effects). The expansion of the universe is understood to exceed the speed of light beyond a certain boundary.

The speed at which light propagates through transparent materials, such as glass or air, is less than $c$ ; similarly, the speed of electromagnetic waves in wire cables is slower than $c$ . The ratio between $c$ and the speed $v$ at which light travels in a material is called the refractive index $n$ of the material ( $n = .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠c/v⁠$ ). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ⁠ $c$ /1.5⁠ ≈ 200000 km/s (124000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than $c$ .

^ Larson, Ron; Hostetler, Robert P. (2007). Elementary and Intermediate Algebra: A Combined Course, Student Support Edition (4th illustrated ed.). Cengage Learning. p. 197. ISBN 978-0-618-75354-3.
^ ^a ^b "Definitions of the SI base units". physics.nist.gov. 29 May 2019. Retrieved 8 February 2022.
^ Penrose, R (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books. pp. 410–411. ISBN 978-0-679-77631-4. ... the most accurate standard for the metre is conveniently defined so that there are exactly 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 standard metre rule in Paris.
^ Moses Fayngold (2008). Special Relativity and How it Works (illustrated ed.). John Wiley & Sons. p. 497. ISBN 978-3-527-40607-4. Extract of page 497.
^ Albert Shadowitz (1988). Special Relativity (revised ed.). Courier Corporation. p. 79. ISBN 978-0-486-65743-1. Extract of page 79.
^ Peres, Asher; Terno, Daniel R. (6 January 2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797.
^ Gibbs, Philip (1997). "How is the speed of light measured?". The Physics and Relativity FAQ. Archived from the original on 21 August 2015.
^ Stachel, J. J. (2002). Einstein from "B" to "Z" – Volume 9 of Einstein studies. Springer. p. 226. ISBN 978-0-8176-4143-6.
^
See, for example:
- Feigenbaum, Mitchell J.; Mermin, N. David (January 1988). "E = mc²". American Journal of Physics. 56 (1): 18–21. Bibcode:1988AmJPh..56...18F. doi:10.1119/1.15422. ISSN 0002-9505.
- Uzan, J-P; Leclercq, B (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Springer. pp. 43–44. ISBN 978-0-387-73454-5.

Cite error: There are <ref group=Note> tags on this page, but the references will not show without a {{reflist|group=Note}} template (see the help page).

[1] Larson, Ron; Hostetler, Robert P. (2007). Elementary and Intermediate Algebra: A Combined Course, Student Support Edition (4th illustrated ed.). Cengage Learning. p. 197. ISBN 978-0-618-75354-3.

[nist-definitions-4] "Definitions of the SI base units". physics.nist.gov. 29 May 2019. Retrieved 8 February 2022.

[penrose-5] Penrose, R (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books. pp. 410–411. ISBN 978-0-679-77631-4. ... the most accurate standard for the metre is conveniently defined so that there are exactly 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 standard metre rule in Paris.

[7] Moses Fayngold (2008). Special Relativity and How it Works (illustrated ed.). John Wiley & Sons. p. 497. ISBN 978-3-527-40607-4. Extract of page 497.

[8] Albert Shadowitz (1988). Special Relativity (revised ed.). Courier Corporation. p. 79. ISBN 978-0-486-65743-1. Extract of page 79.

[9] Peres, Asher; Terno, Daniel R. (6 January 2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797.

[10] Gibbs, Philip (1997). "How is the speed of light measured?". The Physics and Relativity FAQ. Archived from the original on 21 August 2015.

[stachel-11] Stachel, J. J. (2002). Einstein from "B" to "Z" – Volume 9 of Einstein studies. Springer. p. 226. ISBN 978-0-8176-4143-6.

[12] See, for example:
Feigenbaum, Mitchell J.; Mermin, N. David (January 1988). "E = mc²". American Journal of Physics. 56 (1): 18–21. Bibcode:1988AmJPh..56...18F. doi:10.1119/1.15422. ISSN 0002-9505.

Uzan, J-P; Leclercq, B (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Springer. pp. 43–44. ISBN 978-0-387-73454-5.

[10] Feigenbaum, Mitchell J.; Mermin, N. David (January 1988). "E = mc²". American Journal of Physics. 56 (1): 18–21. Bibcode:1988AmJPh..56...18F. doi:10.1119/1.15422. ISSN 0002-9505.

[11] Uzan, J-P; Leclercq, B (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Springer. pp. 43–44. ISBN 978-0-387-73454-5.

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