Speed of light
28736
226140491
2008-07-17T00:21:03Z
Vsmith
84417
Reverted edits by [[Special:Contributions/98.165.126.153|98.165.126.153]] ([[User talk:98.165.126.153|talk]]) to last version by Martin Hogbin
{{redirect|Lightspeed}}
{{otheruses}}
[[Image:Usaf-laser.jpg|right|thumb|200px|Light traveling through a medium such as air (for example, this [[laser]]) travels slower than light through a vacuum.]]
The '''speed of light''' in the [[vacuum of free space]] is an important [[physical constant]] usually denoted by the letter ''c''.<ref>[[NIST]] and [[BIPM]] practice is to use ''c''<sub><small>0</small></sub> for the speed of light in vacuum in accord with international standard [[ISO 31-5]]. See [http://physics.nist.gov/Pubs/SP330/sp330.pdf NIST ''Special Publication 330'', Appendix 2, p. 45 ]: "Current practice is to use ''c''<sub><small>0</small></sub> to denote the speed of light in vacuum (ISO 31)." However older publications use just ''c'' and many physicists may continue to do this in cases where there is no ambiguity. </ref> It is the speed of all [[electromagnetic radiation]], including visible [[light]], in free space. It is the speed of anything having zero [[rest mass]].<ref name=Chow>
{{cite book
|author=Tai L. Chow
|title=Electromagnetic theory
|year= 2006
|page =391-392
|publisher=Jones and Bartlett
|location=Sudbury MA
|isbn=0-7637-3827-1
|url=http://books.google.com/books?id=dpnpMhw1zo8C&pg=PA153&dq=isbn:0763738271&sig=PgEEBA6TQEZ5fD_AhJQ8dd7MGHo#PPR6,M1}}
</ref>
The SI [[metre]] is defined such that the speed of light in a vacuum is exactly [[Orders of magnitude (speed)|299,792,458]] [[metres per second]]<ref name=si-meter>{{cite web |url=http://www.bipm.org/en/si/si_brochure/chapter2/2-1/metre.html |title= Unit of length (metre) |accessdate=2007-11-28 |author=[[BIPM]] |work=SI brochure, Section 2.1.1.1 |publisher=[[BIPM]] }}</ref> (1,079,252,848.8 km/h or 299,792.458 km/s). The speed of light can be assigned a definite numerical value because the fundamental [[SI]] unit of length, the [[metre]], has been defined since [[October 21]], [[1983]], as the distance light travels in a vacuum in 1/299,792,458 of a second; in other words, any increase in the measurement precision of the speed of light would refine the definition of the metre, but not alter the numerical value of ''c''. The approximate value of 3{{e|8}} m/s is commonly used in rough estimates (the error is 0.07%). In [[imperial unit]]s, the speed of light is about 670,616,629.4 miles per hour or 983,571,056.4 [[feet per second]] (roughly one [[Foot (unit of length)|foot]] per [[nanosecond]]), which is about 186,282.397 [[mile]]s per second.
The speed of light when it passes through a [[transparency (optics)|transparent or translucent]] material medium, like glass or air, is less than its speed in a vacuum. The ratio of the speed of light in the vacuum to the observed [[phase velocity]] is called the [[refractive index]] of the medium. See [[dispersion (optics)]]. In [[general relativity]] ''c'' remains an important constant of [[spacetime]], however the concepts of 'distance', 'time', and therefore 'speed' are not always unambiguously defined due to the curvature of spacetime caused by [[gravitation]]. When measured [[locally]], light in a vacuum always passes an observer at ''c''.
== Overview ==
The speed of light in vacuum is now viewed as a fundamental physical constant. This postulate, together with the principle of relativity that all inertial frames are equivalent, forms the basis of Einstein's theory of [[special relativity]].
Experimental evidence has shown that the speed of light is independent of the motion of the source. It has also been confirmed experimentally that the two-way speed of light (for example from a source, to a mirror, and back again) is constant. It is not, however, possible to measure the one-way speed of light (for example from a source to a distant detector) without some convention as to how clocks at the source and receiver should be synchronized.<ref>{{cite book |title=Special Relativity and its Experimental Foundations |last=Zhang|first=Yuan Zhong |publisher=World Scientific |pages=p171 }}</ref> Einstein (who was aware of this fact) postulated that the speed of light should be taken as constant in all cases, one-way and two-way.
It is worth noting that it is the constant speed ''c'', rather than light itself, that is fundamental to special relativity; thus if light is somehow manipulated to travel at less than ''c'', this manipulation will not directly affect the theory of special relativity.
An observer moving with respect to a collection of light sources would find that light from the sources ahead would be [[Blue shift|blueshifted]] while light from those behind was [[redshift]]ed.
===Use of the symbol 'c' for the speed of light===
The symbol 'c' for 'constant' or the [[Latin]] ''[[celeritas]]'' ("swiftness")<ref>{{cite web | url = http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html | title = Why is c the symbol for the speed of light? | accessdate = 2007-06-05}}</ref> is generally used for the speed of light. [[NIST]] and [[BIPM]] practice is to use ''c''<sub><small>0</small></sub> for the speed of light in vacuum. Occasionally, some writers use ''c'' for the speed of light in media other than vacuum. Throughout this article ''c'' is used exclusively to denote the speed of light in a vacuum.
In branches of physics in which the speed of light plays an important part, for example relativity, it is common to use a system of units in which ''c'' is 1, thus no symbol for the speed of light is required.
===Causality and information transfer===
If information could travel faster than ''c'' in one reference frame, [[causality (physics)|causality]] would be violated: in some other reference frames, the information would be received before it had been sent, so the "effect" could be observed before the "cause". Such a violation of causality has never been recorded.<ref>{{cite book |title=Special Relativity and its Experimental Foundations |last=Zhang|first=Yuan Zhong |publisher=World Scientific |pages=p31 }}</ref>
[[Image:Light cone.svg|thumb|A [[light cone]] defines locations that are in [[causality (physics)|causal contact]] and those that are not.]]
To put it another way, information propagates to and from a point from regions defined by a [[light cone]]. The [[Spacetime#Space-time intervals|interval]] AB in the diagram to the right is "[[time-like]]" (that is, there is a frame of reference in which event A and event B occur at the same location in space, separated only by their occurring at different times, and if A precedes B in that frame then A precedes B in all frames: there is no frame of reference in which event A and event B occur simultaneously). Thus, it is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the "cause" and B the "effect").
On the other hand, the interval AC in the diagram to the right is "[[space-like]]" (that is, there is a frame of reference in which event A and event C occur simultaneously, separated only in space; see [[Relativity of simultaneity|simultaneity]]). However, there are also frames in which A precedes C (as shown) or in which C precedes A. Barring some way of traveling [[faster than light]], it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C.
===Light years===
[[astronomy|Astronomical]] distances are sometimes measured in [[light year]]s (the distance that light would travel in one Earth year, roughly [[1 E15 m|9.46{{e|12}}]] kilometres or about 5.88{{e|12}} miles). Because light travels at a large but finite speed, it takes time for light to cover large distances. Thus, the light we observe from distant objects in the universe was emitted from them long ago: in effect, we see their distant past. Even in terms of our own star we see into the past as well. Light from the sun takes around eight and one-third minutes to reach the earth. If the sun were destroyed this instant, we would have no way of knowing until its light reached us.
==Communications and GPS==
The speed of light is of relevance to [[telecommunication|communications]]. For example, given the equatorial circumference of the [[Earth]] is about 40,075 km and ''c'' about 300,000 km/s, the theoretical shortest time for a piece of information to travel half the globe along the surface is {{#expr: 0.066838 round 4}} s.
The actual transit time is longer, in part because the speed of light is slower by about 35% in an [[optical fiber]]<ref name=Midwinter>For multimode and single mode step index fibers operating at wavelengths near 850 nm a typical cladding would have a refractive index of 1.518 and the doped core would have a refractive index of 1.538 which is 1.3% greater. {{cite book | author=John E. Midwinter | title=Optical Fibers for Transmission | year=1979 | publisher=John Wiley & Sons | location=New York}}</ref> depending on its [[refractive index]] ''n'', <math>v = c/n </math> and straight lines rarely occur in global communications situations, but also because delays are created when the signal passes through an electronic switch or signal regenerator. A typical <!-- round trip? --> time as of 2004 for a [[United States|U.S.]] to [[Australia]] or [[Japan]] computer-to-computer [[ping]] is 0.18 s. The speed of light additionally affects [[wireless communication]]s design.
Another consequence of the finite speed of light is that communications with spacecraft are not instantaneous, and the gap becomes more noticeable as distances increase. This delay was significant for communications between [[Houston]] [[Mission Control Center|ground control]] and [[Apollo 8]] when it became the first spacecraft to orbit the [[Moon]]: for every question, Houston had to wait nearly 3 [[second]]s for the answer to arrive, even when the astronauts replied immediately. On the [[Mars Pathfinder]] expedition, the robot would not respond to communications for almost 10 minutes. Only then would the operators know the fate of their maneuvers.
This effect forms the basis of the [[Global Positioning System]] (GPS) and similar [[navigation]] systems. One's position can be determined by means of the delays in radio signals received from a number of satellites, each carrying a very accurate [[atomic clock]], and very carefully [[Synchronization|synchronized]]. It is remarkable that, to work properly, this method requires that (among many other effects) the relative motion of satellite and receiver be taken into effect, which was how (on an interplanetary scale) the finite speed of light was originally discovered (see the following section).
Similarly, instantaneous remote control of interplanetary spacecraft is impossible because it takes time for the Earth-based controllers to receive information from the craft, and an equal time for instructions to be received by the craft. It can take hours for controllers to become aware of a problem, respond with instructions, and have the spacecraft receive the instructions.
The speed of light can also be of concern on very short distances. In [[supercomputer]]s, the speed of light imposes a limit on how quickly data can be sent between [[central processing unit|processor]]s. If a processor operates at 1 [[GHz]], a signal can only travel a maximum of 300 mm in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single [[integrated circuit|chips]].
== Physics ==
===Constant velocity from all inertial reference frames===
Most individuals are accustomed to the addition rule of velocities: if two cars approach each other from opposite directions, each traveling at a speed of 50 [[kilometres per hour|km/h]], relative to the road surface, one expects that each car will measure the other as approaching at a combined speed of 50 + 50 = 100 km/h to a very high degree of accuracy.
However, as speeds increase this rule becomes less accurate. Two spaceships approaching each other, each traveling at 90% the speed of light relative to some third observer between them, do not measure each other as approaching at 90% + 90% = 180% the speed of light; instead they each measure the other as approaching at slightly less than 99.5% the speed of light. This last result is given by the [[Albert Einstein|Einstein]] [[velocity-addition formula]]:<ref>Current practice is to use ''c''<sub><small>0</small></sub> to denote the speed of light in vacuum [[ISO 31]]. In the original Recommendation of 1983, the symbol ''c'' was used for this purpose.</ref>
: <math>u = {v + w \over 1 + v w / {c}^2} \,\!</math>
where <math>v</math> and <math>w</math> are the (positive) velocities of the spaceships as measured by the third observer, and <math>u</math> is the measured velocity of either space ship as observed by the other.<ref>Francis Weston Sears, ''Introduction to the Theory of Relativity'', p. 24, footnote: <blockquote>Except in giving a name to [this equation], the term "velocity" is used in this book to mean the speed and direction of motion. Velocity is a vector quantity, whereas speed refers only to the magnitude of the velocity. Since we have restricted motion to a single dimension (along the x-axis), we have not needed to introduce the concept of velocity here.</ref> This reduces to <math>u = v + w</math> for sufficiently small values of <math>v</math> and <math>w</math> (such as those typically encountered in common daily experiences), as the term <math> v w / {c}^2</math> approaches zero, reducing the denominator to 1.
If one of the velocities for the above formula (or both) are ''c'', the final result is ''c'', as is expected if the speed of light is the same in all reference frames. Another important result is that this formula always returns a value which is less than ''c'' whenever ''v'' and ''w'' are less than ''c'': this shows that no acceleration in any frame of reference can cause one to exceed the speed of light with respect to another observer. Thus ''c'' acts as a speed limit for all objects with respect to all other objects in special relativity.
=== Luminiferous aether (discredited) ===
[[Image:Michelson Interferometer Green Laser Interference.jpg|thumb|right|Interference pattern produced with a Michelson interferometer]]
Before the advent of special relativity, it was believed that light travels through a medium called the [[luminiferous aether]]. Maxwell’s equations predict a given speed of light, in much the same way as is the [[speed of sound]] in [[air]]. The speed of sound in air is relative to the movement of the air itself, and the speed of sound in air with respect to an observer may be changed if the observer is moving with respect to the air (or [[wind|vice versa]]). The speed of light was believed to be relative to a medium of transmission for light that acted as air does for the transmission of sound—the luminiferous aether.
The [[Michelson-Morley experiment|Michelson–Morley experiment]], arguably the most famous and useful failed experiment in the history of physics, was designed to detect the motion of the Earth through the luminiferous aether. It could not find any trace of this kind of motion, suggesting, as a result, that it is impossible to detect one's presumed absolute motion, that is, motion with respect to the hypothesized luminiferous aether. The Michelson–Morley experiment said little about the speed of light relative to the light’s source and observer’s velocity, as both the source and observer in this experiment were traveling at the same velocity together in space.
===Interaction with transparent materials===
[[Image:PrismAndLight.jpg|right|thumb|300px|The [[refractive index]] of a material indicates how much slower the speed of light is in that medium than in a vacuum. The slower speed of light in materials can cause [[refraction]], as demonstrated by this [[triangular prism (optics)|prism]] (in the case of a prism splitting white light into a [[visible spectrum|spectrum]] of colours, the refraction is known as [[dispersion (optics)|dispersion]]).]]
In passing through materials, the observed speed of light can differ from ''c''. The ratio of ''c'' to the [[phase velocity]] of light in the material is called the [[refractive index]]. The speed of light in [[Earth's atmosphere|air]] is only slightly less than ''c''. Denser media, such as [[water]] and [[glass]], can slow light much more, to fractions such as <math>\tfrac{1}{2}</math> and <math>\tfrac{2}{3}</math> of ''c''. Through diamond, light is much slower—only about 124,000 kilometres per second, less than <math>\tfrac{1}{2}</math> of ''c''.<ref>{{cite web | url = http://physics.bu.edu/py106/notes/Refraction.html | title = Refraction, Snell's law, and total internal reflection |publisher=Boston University Physics | accessdate = 2007-01-24}}</ref> This reduction in speed is also responsible for bending of light at an interface between two materials with different indices, a phenomenon known as [[refraction]].
Since the speed of light in a material depends on the refractive index, and the refractive index may depend on the frequency of the light, light at different frequencies can travel at different speeds through the same material. This effect is called dispersion.
Classically, considering electromagnetic radiation to be a wave, the charges of each atom (primarily the [[electron]]s) interact with the electric and magnetic fields of the radiation, slowing its progress.
A more complete description of the passage of light through a medium is given by [[quantum electrodynamics]].
==Faster-than-light observations and experiments==
{{main|Faster-than-light}}
[[Image:TrigaReactorCore.jpeg|thumb|230px|The blue glow in this "swimming pool" [[nuclear reactor]] is [[Čerenkov radiation]], emitted as a result of [[electron]]s traveling faster than the speed of light in water.]]
It is generally considered that it is impossible for any [[information]] or [[matter]] to travel faster than ''c''. The equations of relativity show that, for an object travelling faster than ''c'', some physical quantities would be not represented by [[real numbers]]. However, there are many physical situations in which speeds greater than ''c'' are encountered.
===Things that can travel faster than ''c''===
=====Wave velocities and synchronized events=====
It has long been known theoretically that it is possible for the "[[group velocity]]" of light to exceed ''c''.<ref>{{cite web| url = http://gregegan.customer.netspace.net.au/APPLETS/20/20.html| title = Applets Gallery / Subluminal| first = Greg| last = Egan| authorlink = Greg Egan| date = 2000-08-17| accessdate = 2007-02-06}}<br />
References {{cite journal| author = LJ Wang| coauthors = A Kuzmich & A Dogariu| title = Gain-assisted superluminal light propagation| journal = Nature| issue = 406| pages = p277| year = 2000 |doi=10.1038/35018520| volume = 406 }}''</ref> One recent experiment made the group velocity of [[laser]] beams travel for extremely short distances through [[caesium]] atoms at 300 times ''c''. In 2002, at the [[Université de Moncton]], physicist [[Alain Haché]] made history by sending pulses at a group velocity of three times light speed over a long distance for the first time, transmitted through a 120-metre cable made from a coaxial [[photonic crystal]].<ref>[http://physicsweb.org/articles/news/6/1/13 Electrical pulses break light speed record], physicsweb, [[22 January]] [[2002]]; see also {{cite journal |last=Haché |first=Alain |authorlink= |coauthors=Poirier, Louis |year=2002 |month= |title=Long-range superluminal pulse propagation in a coaxial photonic crystal |journal=Appl. Phys. Lett. |volume=80 |issue= |pages=518 |doi=10.1063/1.1432760 |url= |accessdate= |quote= }}</ref>
However, it is not possible to use this technique to transfer [[information]] faster than ''c'': the velocity of information transfer depends on the [[front velocity]] (the speed at which the first rise of a pulse above zero moves forward) and the product of the group velocity and the front velocity is equal to the square of the normal speed of light in the material.
Exceeding the group velocity of light in this manner is comparable to exceeding the speed of sound by arranging people distantly spaced in a line, and asking them all to shout "I'm here!", one after another with short intervals, each one timing it by looking at their own wristwatch so they don't have to wait until they hear the previous person shouting. Another example can be seen when watching ocean waves washing up on shore. With a narrow enough angle between the wave and the shoreline, the breakers travel along the waves' length much faster than the waves' movement inland.
=====Light spots and shadows=====
If a laser is swept across a distant object, the spot of light can easily be made to move at a speed greater than ''c''.<ref>{{cite web | url = http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html | title = Shadows and Light Spots | accessdate = 2008-03-02}}</ref> Similarly, a shadow projected onto a distant object can be made to move faster than ''c''. In neither case does any matter or information travel faster than light.
=====Quantum mechanics=====
The speed of light may also appear to be exceeded in some phenomena involving [[evanescent wave]]s, such as [[quantum tunnelling|tunnelling]]. Experiments indicate that the [[phase velocity]] and the group velocity of evanescent waves may exceed ''c''; however, it would appear that the front velocity does not exceed ''c'', so, again, it is not possible for information to be transmitted faster than ''c''.
In [[quantum mechanics]], certain quantum effects may be transmitted at speeds greater than ''c'' (indeed, [[action at a distance (physics)|action at a distance]] has long been perceived by some as a problem with quantum mechanics: see [[EPR paradox]], [[interpretations of quantum mechanics]]). For example, the [[quantum state]]s of two particles can be [[quantum entanglement|entangled]], so the state of one particle fixes the state of the other particle (say, one must have [[spin (physics)|spin]] +½ and the other must have spin −½). Until the particles are observed, they exist in a [[quantum superposition|superposition]] of two quantum states, (+½, −½) and (−½, +½). If the particles are separated and one of them is observed to determine its quantum state then the quantum state of the second particle is determined automatically. If, as in some interpretations of quantum mechanics, one presumes that the information about the quantum state is local to one particle, then one must conclude that second particle takes up its quantum state instantaneously, as soon as the first observation is carried out. However, it is impossible to control which quantum state the first particle will take on when it is observed, so no information can be transmitted in this manner. The laws of physics also appear to prevent information from being transferred through more clever ways and this has led to the formulation of rules such as the [[no-cloning theorem]] and the [[no-communication theorem]].
===Closing speeds===
If two objects are travelling towards one another, each at 0.8''c'' as measured in a particular inertial frame of reference, then they are getting closer together at 1.6''c'' as measured in that frame.<ref>{{cite web | url = http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html | title = Third Party Observers | accessdate = 2008-03-02}}</ref> This is called a closing speed. Note that a closing speed does not represent the speed of any object in an inertial frame.
===Proper Speeds===
If a spaceship travels to a planet one light year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance travelled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a [[proper velocity]]. There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. Note that a light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller.
===Things which only appear to travel faster than ''c''===
So-called [[superluminal motion]] is seen in certain astronomical objects<ref>{{cite journal |author=M. Rees|title=The Appearance of Relativistically Expanding Radio Sources|journal=Nature |volume=211 |pages=468|year=1966}}</ref>, such as the [[relativistic jet|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 [[projection]] effect caused by objects moving near the speed of light and at a small [[angle]] to the line of sight.
===Travel faster than the speed of light in a medium===
Although it may sound paradoxical, it is possible for [[shock wave]]s to be formed with electromagnetic radiation<ref>Cerenkov, P.A., "Visible Emission of Clean Liquids by Action of γ Radiation", ''Doklady Akad. Nauk SSSR'' 2 (1934) 451. Reprinted in
Selected Papers of Soviet Physicists, ''Usp. Fiz. Nauk'' 93 (1967) 385. V sbornike: Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie pod redaktsiej A. N. Gorbunova i E. P. Čerenkovoj, M.,"Nauka,'' 1999, s. 149-153. ([http://dbserv.ihep.su/hist/owa/hw.move?s_c=VAVILOV+1934&m=1 ref])</ref>. As a charged particle travels through an [[Electrical insulation|insulating]] medium, it disrupts the local electromagnetic field in the medium. Electrons in the atoms of the medium will be displaced and [[polarization|polarised]] by the passing field of the charged particle, and photons are emitted as the electrons in the medium restore themselves to equilibrium after the disruption has passed. (In a [[conductor (material)|conductor]], the equilibrium can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves travel, as when a charged particle exceeds the speed of light '''in that medium''', the photons constructively interfere and intensify the observed radiation. The result (analogous to a [[sonic boom]]) is known as [[Čerenkov radiation]].
===General relativity===
Some topics (such as the expansion of the universe, and wormholes) require the application of [[general relativity]] and are covered in the main [[faster-than-light|faster than light]] article.
===Other theories concerning the speed of light===
Particles that travel faster than light, dubbed [[tachyon]]s, have been proposed by [[particle physics|particle physicists]] but have yet to be observed, and would potentially violate [[causality]] if they were.
Some physicists, notably [[João Magueijo]] and [[John Moffat]], have proposed that in the past light traveled much faster than the current speed of light. This theory is called [[variable speed of light]] (VSL) and its supporters claim that it has the ability to explain many [[physical cosmology|cosmological]] puzzles better than its rival, the [[Cosmic inflation|inflation]] model of the [[universe]]{{Fact|date=June 2008}}. However, it has not gained wide acceptance.
== Slow light ==
{{main|Slow light}}
[[Image:Supernumerary rainbow 03 contrast.jpg|right|thumb|[[Refraction|Refractive]] phenomena, such as this [[rainbow]], are due to the slower speed of light in a medium (water, in this case).]]
Light traveling through a medium other than a vacuum travels below ''c'' as a result of the time lag between the [[Polarization density|polarization]] response of the medium and the incident light. However, certain materials have an exceptionally high group index and a correspondingly low [[group velocity]]. In 1999, a team of scientists led by [[Lene Hau]] were able to slow the speed of a light pulse to about 17 metres per second;<ref>{{cite journal |author=L.V. Hau, S.E. Harris, Z. Dutton, and C.H. Behroozi |title=Light speed reduction to 17 metres per second in an ultracold atomic gas |journal=Nature |volume=397 |date=1999-02-18 |pages=594–598 |url=http://www.nature.com/nature/journal/v397/n6720/full/397594a0.html |format=HTML | doi = 10.1038/17561 <!--Retrieved from CrossRef by DOI bot-->}}</ref> in 2001, they were able to momentarily stop a beam.<ref>{{cite journal |author=C. Liu, Z. Dutton, C.H. Behroozi, and L.V. Hau |title=Observation of coherent optical information storage in an atomic medium using halted light pulses |journal=Nature |volume=409 |date=2001-01-25 |pages=490–493 |url=http://www.nature.com/nature/journal/v409/n6819/pdf/409490a0.pdf|format=PDF | doi = 10.1038/35054017 <!--Retrieved from CrossRef by DOI bot-->}}</ref>
In 2003, [[Mikhail Lukin]], with scientists at [[Harvard University]] and the [[Lebedev Physical Institute|Lebedev Institute]] in [[Moscow]], succeeded in completely halting light by directing it into a [[Bose–Einstein condensate]] of the element [[rubidium]], the atoms of which, in Lukin's words, behaved "like tiny mirrors" due to an interference pattern in two "control" beams.<ref>{{cite journal |author=M. Bajcsy1, A.S. Zibrov, and M.D. Lukin|title=Stationary pulses of light in an atomic medium |journal=Nature |doi= 10.1038/nature02176 |volume=426 |pages=638–641 |date=2003-12-11 }}</ref>
== History ==
Until relatively recent times, the speed of light was largely a matter of conjecture. [[Empedocles]] maintained that light was something in motion, and therefore there had to be some time elapsed in travelling. [[Aristotle]] said that, on the contrary, "light is due to the presence of something, but it is not a movement". Furthermore, if light had a finite speed, it would have to be very great; Aristotle asserted "the strain upon our powers of belief is too great" to believe this.
One of the ancient theories of vision was that light was emitted from the eye, instead of entering the eye from another source. Using this theory, [[Heron of Alexandria]] advanced the argument that the speed of light must be [[infinite]], since distant objects such as stars appear immediately upon opening the eyes.
===Medieval and early modern theories===
[[Early Islamic philosophy|Early Muslim philosophers]] initially agreed with the [[Aristotelian physics|Aristotelian]] and Ptolemaic theories on the speed of light being infinite. This changed in 1021, however, when the [[Islamic physics|Iraqi physicist]], [[Ibn al-Haytham]] (Alhazen), published the ''[[Book of Optics]]'', which provided [[experiment]]al proof of the intromission theory of [[Visual perception|vision]], where light moves from an object into the eye, making use of instruments such as the [[camera obscura]] to demonstrate this. This led to Alhazen proposing that light must therefore have a finite speed.<ref name=Hamarneh>Sami Hamarneh (March 1972), "Review: Hakim Mohammed Said, ''Ibn al-Haitham''", ''[[Isis (journal)|Isis]]'' '''63''' (1): 119</ref><ref>{{citation|title=Scientific Method, Statistical Method and the Speed of Light|first1=R. J.|last1=MacKay|first2=R. W.|last2=Oldford|journal=Statistical Science|volume=15|issue=3|date=August 2000|pages=254–78}}</ref> He further proposed that the speed of light was variable, with its speed decreasing in denser bodies.<ref>{{MacTutor|id=Al-Haytham|title=Abu Ali al-Hasan ibn al-Haytham}}</ref>
Some of Alhazen's contemporaries, notably the [[Islamic science|Persian scientists]], [[Avicenna]] (Ibn Sina) and [[Abū Rayhān al-Bīrūnī]], also agreed that light had a finite speed. Avicenna theorized that, if the perception of light was due to the emission of some sort of particles by a luminous source, the speed of light must be finite.<ref>[[George Sarton]], ''Introduction to the History of Science'', Vol. 1, p. 710.</ref> Al-Biruni further observed that the speed of light is much faster than the [[speed of sound]].<ref>{{MacTutor|id=Al-Biruni|title=Abu Arrayhan Muhammad ibn Ahmad al-Biruni}}</ref> In 1574, the [[Islamic astronomer|Ottoman astronomer]] and physicist [[Taqi al-Din]] agreed with Alhazen that the speed of light was constant, <ref name=Topdemir>{{citation|first=Hüseyin Gazi|last=Topdemir|title=Takîyüddîn'in Optik Kitabi|publisher=Ministery of Culture Press, [[Ankara]]|year=1999}} ([[cf.]] {{cite web|author=Dr. Hüseyin Gazi Topdemir|title=Taqi al-Din ibn Ma‘ruf and the Science of Optics: The Nature of Light and the Mechanism of Vision|publisher=FSTC Limited|url=http://muslimheritage.com/topics/default.cfm?ArticleID=951|date=30 June 2008|accessdate=2008-07-04}})</ref>
A comment on a verse in the [[Rigveda]] by the 14th century [[India]]n scholar [[Sayana]]
<ref>Sayana-commentary on Rigveda 1.50, see: Müller, Max (ed.): Rig-Veda-Samhita, together with the Commentary of Sayana. Oxford University Press, London (1890).</ref> may be interpreted as suggesting a value for the speed of light that is in good agreement with its actual speed.
In the early 17th century, [[Johannes Kepler]] believed that the speed of light was infinite since empty space presents no obstacle to it. [[Francis Bacon]] argued that the speed of light was not necessarily infinite, since something can travel too fast to be perceived. [[René Descartes]] argued that if the speed of light were finite, the [[Sun]], [[Earth]], and [[Moon]] would be noticeably out of alignment during a [[lunar eclipse]]. Since such misalignment had not been observed, Descartes concluded the speed of light was infinite. Descartes speculated that if the speed of light was found to be finite, his whole system of philosophy might be demolished.<ref>{{cite web |title=Historical Background, footnote 5 |publisher=Statistics and Actuarial Science, University of Waterloo |url=http://www.stats.uwaterloo.ca/~rwoldfor/papers/sci-method/paperrev/node2.html |accessdate=2007-08-03}}</ref>
===Measurement of the speed of light===
====Early attempts====
[[Isaac Beeckman]] proposed an experiment (1629) in which a person would observe the flash of a [[cannon]] reflecting off a [[mirror]] about one mile away. [[Galileo Galilei|Galileo]] proposed an experiment (1638), with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a [[lantern]] and its perception some distance away. This experiment was carried out by the [[Accademia del Cimento]] of [[Florence]] in 1667, with the lanterns separated by about one mile. No delay was observed. [[Robert Hooke]] explained the negative results as Galileo had by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great.
[[Image:Roemer.jpg|thumb|right|Rømer's observations of the occultations of Io from Earth.]]
====Astronomical techniques====
The first quantitative estimate of the speed of light was made in 1676 by [[Ole Christensen Rømer]], who was studying the [[motion (physics)|motions]] of [[Jupiter (planet)|Jupiter's]] moon, [[Io (moon)|Io]], with a [[telescope]]. It is possible to time the [[orbital revolution]] of Io because it enters and exits Jupiter's shadow at regular [[interval (time)|interval]]s (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5 [[hour]]s when [[Earth]] was closest to Jupiter (at H). He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. This was as a result of the extra time it took for light to cross the extra distance between the planets, time which had accumulated in the interval between one signal and the next. The opposite is the case when they are approaching (as from F to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the [[astronomical unit]]); the modern estimate is about 16 minutes and 40 seconds.
Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by [[Christiaan Huygens]], who estimated the speed of light to be 1,000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), 26% lower than the currently accepted value, but still very much faster than any physical phenomenon then known.
[[Isaac Newton]] also accepted the finite speed. In his 1704 book ''[[Opticks]]'' he reports the value of 16.6 Earth diameters per second (210,000 kilometres per second, 30% less than the actual value), which it seems he inferred for himself (whether from Rømer's data, or otherwise, is not known). The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. And later observations also showed the effect with the three other Galilean moons, where it was more difficult to observe, thus laying to rest some further objections that had been raised.
Even if, by these observations, the finite speed of light may not have been established to everyone's satisfaction (notably [[Giovanni Domenico Cassini|Jean-Dominique Cassini]]'s), after the observations of [[James Bradley]] (1728), the hypothesis of infinite speed was considered discredited. Bradley deduced that starlight falling on the Earth should appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit to the speed of light. This "[[aberration of light]]", as it is called, was observed to be about 1/200 of a degree. Bradley calculated the speed of light as about 298,000 kilometres per second (185,000 miles per second). This is only slightly less than the currently accepted value (less than one percent). The aberration effect has been studied extensively over the succeeding centuries, notably by [[Friedrich Georg Wilhelm Struve]] and [[:de:Magnus Nyrén]].
[[Image:Speed of light (Fizeau).PNG|thumb|right|Diagram of the [[Fizeau–Foucault apparatus]].]]
====Earth-bound techniques====
The first successful measurement of the speed of light using an earthbound apparatus was carried out by [[Hippolyte Fizeau]] in 1849. (This measures the speed of light in air, which is slower than the speed of light in vacuum by a factor of the refractive index of air, about 1.0003.) Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror several thousand metres away. On the way from the source to the mirror, the beam passed through a rotating cog wheel. At a certain rate of rotation, the beam could pass through one gap on the way out and another on the way back. If <math>\alpha</math> is the angle between two consecutive openings and <math>L</math> the distance between the toothed wheel and the mirror, then the tooth wheel must rotate with the angular speed:
:<math> \omega=\frac{\alpha c}{2L} </math>
in order for the light to pass through.
But at slightly higher or lower rates, the beam would strike a tooth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 kilometres per second. Fizeau's method was later refined by [[Marie Alfred Cornu]] (1872) and [[Henri Joseph Anastase Perrotin|Joseph Perrotin]] (1900).
[[Leon Foucault]] improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estimate, published in 1862, was 298,000 kilometres per second. Foucault's method was also used by [[Simon Newcomb]] and [[Albert A. Michelson]]. Michelson began his lengthy career by replicating and improving on Foucault's method.
In 1926, Michelson used a rotating [[Prism (optics)|prism]] to measure the time it took light to make a round trip from [[Mount Wilson (California)|Mount Wilson]] to [[Mount San Antonio]] in [[California]], a distance of about 22 miles (36 km). The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second).
====Laboratory-based methods====
During [[World War II]], the development of the [[cavity resonance wavemeter]] for use in [[radar]], together with precision timing methods, opened the way to laboratory-based measurements of the speed of light. In 1946, [[Louis Essen]] in collaboration with [[A.C. Gordon-Smith]]
used a [[microwave]] cavity of precisely known dimensions to establish the [[frequency]] for a variety of [[normal mode]]s of microwaves—which, in common with all electromagnetic radiation, travels at the speed of light in vacuum. As the [[wavelength]] of the modes was known from the geometry of the cavity and from [[electromagnetic theory]], knowledge of the associated frequencies enabled a calculation of the speed of light. Their result, 299,792±3 km/s, was substantially greater than those found by optical techniques, and prompted much controversy. However, by 1950 repeated measurements by Essen established a result of 299,792.5±1 km/s; this became the value adopted by the 12th General Assembly of the [[Radio-Scientific Union]] in 1957. Most subsequent measurements have been consistent with this value.
With modern electronics (and most particularly the availability of [[oscilloscopes]] with time resolutions in the sub-nanosecond regime) the speed of light can now be directly measured by timing the delay of a light pulse from a laser or a LED in reflecting from a mirror, and this kind of experiment is now routine in undergraduate physics laboratories.<ref>J. Cooke, M. Martin, . McCartney and H. Wilf, “Direct determination of the speed of light as a general physics laboratory experiment”, ''American Journal of Physics,'' Volume 36, p. 847 (1968). See also Ulabe and Hauk, [http://ieeexplore.ieee.org/iel5/5/17614/00811601.pdf?arnumber=811601 Proc. of the IEEE]</ref><ref>Kenichiro Aoki� and Takahisa Mitsui, "A small tabletop experiment for a direct measurement of the speed of light," available from [http://arxiv.org/pdf/0705.3996 ArXiv] (3/20/2008) </ref><ref>Mary B. James, Robert B. Ormond, and Aric J. Stasch, "Speed of light measurement for the myriad," ''American Journal of Physics,'' Volume 67, Issue 8, August 1999 pp. 681-684, doi:10.1119/1.19352 Available from [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000067000008000681000001&idtype=cvips&gifs=yes AIP] (3/20/2008)</ref>
====Speed of light set by definition====
In 1983, the 17th [[Conférence Générale des Poids et Mesures]] defined the [[metre]] in terms of the distance traveled by light in a given amount of time, which amounts to adopting a '''standard value''' for the speed of light in vacuum:<ref>This definition raises an interesting question: What really is a ''vacuum''? For a discussion, see the article [[free space]].</ref>
<blockquote>The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.<ref name=si-meter /></blockquote>
Here, the term ''vacuum'' is meant in the technical sense of [[free space]]. This definition of the metre relies on the definition of the [[second]], which is:
<blockquote>The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.<ref>{{cite web |url=http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html |title= Unit of time (second) |accessdate=2008-01-30 |author=[[BIPM]] |work=SI brochure, Section 2.1.1.1 |publisher=BIPM }}</ref><ref>This definition is subject to a note: ''This definition refers to a caesium atom at rest at a temperature of 0 K.'' This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K.</ref></blockquote>
The consequence of this definition is that further refinements in the current experimental value of the speed of light would only adjust the length of a metre.<ref>"The new definition of the meter, accepted by the 17th
Conférence Générale des Poids et Mesures in 1983, was
quite simple and elegant: [See definition in text]. A consequence of this
definition is that the speed of light is now a '''defined'''
constant, '''not to be measured again'''." [http://nvl.nist.gov/pub/nistpubs/sp958-lide/191-193.pdf NIST]</ref> This point is made explicit by [[nondimensionalization]] in the article on [[Maxwell's equations#Nondimensionalization and unobservability of the_speed of light|Maxwell's equations]]. The value of ''c'', or ''c''<sub><small>0</small></sub>,<ref>International standards agencies now use ''c''<sub><small>0</small></sub> to denote the speed of light in vacuum, following standard [[ISO 31-5]]. See, for example, the [http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf BIPM SI Units brochure, 8<sup>th</sup> Edition].</ref> namely:
:<math> c = c_0 \ \stackrel{\mathrm{def}}{=}\ 299\;792\;458 \ \mathrm {m/s} \ ,</math>
combined with the definition of [[magnetic constant]] μ<sub><small>0</small></sub>, also defines the [[electric constant]] ε<sub><small>0</small></sub> in [[SI]] units. The [[magnetic constant]] <math>\mu_0</math> is not dependent on ''c'' and as a result of the definition of the [[ampere]], has a standard value in [[SI]] units of:<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?mu0|search_for=magnetic+constant NIST magnetic constant]</ref>
:<math> \mu_0 \ \stackrel{\mathrm{def}}{=}\ 4\,\pi\,\times\ 10^{-7} \quad \mathrm{(in~ kg\, m\, s^{-2}\, A^{-2}, \, or \, N \, A^{-2})} \ .</math>.
The electric constant has then the '''exact''' value<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?ep0 NIST electric constant]</ref>
:<math> \varepsilon_0 \ \stackrel{\mathrm{def}}{=}\ \frac {1}{\mu_0 {c}^2} \approx 8.854187817 \ldots \times 10^{-12} \quad \mathrm{(in~ A^2\, s^4\, kg^{-1}\, m^{-3}, \, or \, F \, m^{-1})} \ .</math>
The periods of ellipsis (…) indicates a non-terminating decimal due to the irrationality of π, not an experimental uncertainty. These constants appear in [[Maxwell's equations]].
…
===Special relativity===
After the work of [[James Clerk Maxwell]], it was believed that light travelled at a constant speed relative to the "[[luminiferous aether]]", the medium that was then thought to be necessary for the transmission of light. This speed was determined by the ([[permittivity]] and [[permeability (electromagnetism)|permeability]]) of the aether.
[[Image:interferometer.svg|thumb|right|A schematic representation of a [[Albert Michelson|Michelson]] [[interferometer]], as used for the Michelson-Morley experiment.]]
In 1887, the physicists [[Albert Michelson]] and [[Edward Morley]] performed the influential [[Michelson-Morley experiment]] to measure the velocity of the [[Earth]] through the aether. As shown in the diagram of a Michelson [[interferometer]], a [[beam splitter|half-silvered mirror]] was used to split a beam of [[monochromatic]] light into two beams traveling at [[right angle]]s to one another. After leaving the splitter, each beam was reflected back and forth between [[mirror]]s several times (the same number for each beam to give a long but equal path length; the actual Michelson-Morley experiment used more [[mirror]]s than shown) then recombined to produce a pattern of constructive and destructive [[interference]]. Any slight change in speed of light along one arm of the interferometer compared with its speed along the other arm (because the apparatus was moving with the Earth through the proposed "aether") would then be observed as a change in the pattern of interference. In the event, the experiment gave a [[null result]].
[[Ernst Mach]] was among the first physicists to suggest that the experiment amounted to a disproof of the aether theory. Developments in theoretical physics had already begun to provide an alternative theory, [[Lorentz-FitzGerald contraction hypothesis|Fitzgerald-Lorentz contraction]], which explained the null result of the experiment.
It is uncertain whether [[Albert Einstein]] knew the results of the Michelson-Morley experiment, but the null result of the experiment greatly assisted the acceptance of his [[theory of relativity]]. The constant speed of light is one of the fundamental Postulates (together with [[causality (physics)|causality]] and the [[equivalence of inertial frames]]) of special relativity.
==See also==
* [[Čerenkov radiation]]
* [[Electromagnetic wave equation]]
* [[Faster-than-light]]
* [[Free space]]
* [[Fundamental Speed]]
* [[Mathematical descriptions of the electromagnetic field]]
* [[Maxwell's equations]]
* [[Meter]]
* [[SI units]]
* [[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]
* [[Speed of sound]]
* [[Vacuum state|Vacuum]]
==References==
===Footnotes===
{{reflist}}
===Historical references===
{{refbegin}}
* Ole Rømer. "Démonstration touchant le mouvement de la lumière", ''[[Journal des sçavans]]'', 7 Décembre 1676, pp. 223–236. Translated as "A Demonstration concerning the Motion of Light", ''Philosophical Transactions of the [[Royal Society]]'' no. 136, pp. 893–894; [[June 25]], [[1677]]. ''(Rømer's 1676 paper, in English and French, as [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Roemer-1677/Roemer-1677.html bitmap images], and [http://astro.campus.ecp.fr/histoire/roemer.html in French as plain text])''
* Edmund Halley. "Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London", ''Philosophical Transactions'' XVIII, No. 214, pp 237–256, Nov.–Dec., 1694.
* H.L. Fizeau. "Sur une expérience relative à la vitesse de propagation de la lumière", ''Comptes Rendus'' 29, 90–92, 132, 1849.
* J.L. Foucault. "Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil", ''Comptes Rendus'' 55, 501–503, 792–796, 1862.
* A.A. Michelson. "Experimental Determination of the Velocity of Light", ''Proceedings of the American Association for the Advancement of Science'' 27, 71–77, 1878. ([http://www.gutenberg.org/etext/11753 Project Gutenberg Etext version])
* Simon Newcomb. "The Velocity of Light", ''Nature'', pp 29–32, [[May 13]], [[1886]].
* Joseph Perrotin. "Sur la vitesse de la lumière", ''Comptes Rendus'' 131, 731–734, 1900.
* A.A. Michelson, F.G. Pease, and F. Pearson. "Measurement Of The Velocity Of Light In A Partial Vacuum", ''Astrophysical Journal'' 82, 26–61, 1935.
{{refend}}
===Modern references===
{{refbegin}}
* Léon Brillouin. ''Wave propagation and group velocity''. Academic Press Inc., 1960.
* John David Jackson. ''Classical electrodynamics''. John Wiley & Sons, 2nd edition, 1975; 3rd edition, 1998. ISBN 0-471-30932-X
* R.J. MacKay and R.W. Oldford. [http://www.stats.uwaterloo.ca/~rwoldfor/papers/sci-method/paperrev "Scientific Method, Statistical Method and the Speed of Light"], ''Statistical Science'' 15(3):254–278, 2000.
* Gerd Keiser. ''Optical Fiber Communications'', pp 32.Mcgraw-Hill, 3rd edition, 2000. ISBN 0072321016.
* Subhash Kak, {{PDFlink|[http://arxiv.org/pdf/physics/9804020 "The Speed of light and Puranic cosmology"]|107 [[Kibibyte|KiB]]<!-- application/pdf, 110111 bytes -->}}, ''Annals of the Bhandarkar Oriental Research Institute'' '''80''' (1999) 113–123.
* Subhash C. Kak, {{PDFlink|[http://www.ece.lsu.edu/kak/sayana.pdf "Sayana's astronomy"]|83.4 [[Kibibyte|KiB]]<!-- application/pdf, 85472 bytes -->}}, ''Indian Journal of the History of Science'' '''33''' (1998).
{{refend}}
== External links ==
{{Wikibooks|Special Relativity}}
{{wikinews|Two German scientists claim to have broken the speed of light}}
*[http://physics.nist.gov/cgi-bin/cuu/Value?c Speed of light in vacuum] ''(at [[NIST]])''
*[http://www.bipm.org/en/si/si_brochure/chapter2/2-1/metre.html Definition of the metre] ''(BIPM)''
*[http://www.itl.nist.gov/div898/bayesian/datagall/michelso.htm Data Gallery: Michelson Speed of Light (Univariate Location Estimation)] ''(download data gathered by [[Albert Abraham Michelson|A.A. Michelson]])''
*[http://physicsweb.org/article/news/7/12/5 Switching light on and off] ''(news article on stopping light)''
*[http://news.bbc.co.uk/hi/english/sci/tech/newsid_841000/841690.stm Beam smashes light barrier] ''(news article on group velocity experiment)''
*[http://www.netspace.net.au/~gregegan/APPLETS/20/20.html Subluminal] ''(Java applet demonstrating group velocity information limits)''
*[http://www.mathpages.com/rr/s3-03/3-03.htm De Mora Luminis] at MathPages
*[http://www.ertin.com/sloan_on_speed_of_light.html Light discussion on adding velocities]
*[http://www.colorado.edu/physics/2000/waves_particles/lightspeed-1.html Speed of Light] (University of Colorado Department of Physics)
*[http://www.npl.co.uk/server.php?show=ConWebDoc.1144 How would we know if the speed of light was varying with time?]
*[http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html How is the speed of light measured?]
<!-- en-GB, -ise -->
{{featured article}}
{{extreme motion}}
[[Category:Light]]
[[Category:Units of velocity]]
[[Category:Special relativity]]
[[Category:Fundamental physics concepts]]
{{Link FA|de}}
{{Link FA|es}}
{{Link FA|sk}}
[[als:Lichtgeschwindigkeit]]
[[ar:سرعة الضوء]]
[[az:İşığın sürəti]]
[[bn:আলোর দ্রুতি]]
[[zh-min-nan:Kng-sok]]
[[be-x-old:Хуткасьць сьвятла]]
[[bs:Brzina svjetlosti]]
[[br:Tizh ar gouloù]]
[[bg:Скорост на светлината]]
[[ca:Velocitat de la llum]]
[[cs:Rychlost světla]]
[[da:Lysets hastighed]]
[[de:Lichtgeschwindigkeit]]
[[et:Valguse kiirus]]
[[el:Ταχύτητα του φωτός]]
[[es:Velocidad de la luz]]
[[eo:Lumrapideco]]
[[eu:Argiaren abiadura]]
[[fa:سرعت نور]]
[[fr:Vitesse de la lumière]]
[[fur:Velocitât de lûs]]
[[gl:Velocidade da luz]]
[[zh-classical:光速]]
[[ko:빛의 속도]]
[[hr:Brzina svjetlosti]]
[[id:Kecepatan cahaya]]
[[is:Ljóshraði]]
[[it:Velocità della luce]]
[[he:מהירות האור]]
[[sw:Kasi ya nuru]]
[[la:Celeritas luminis]]
[[lv:Gaismas ātrums]]
[[lb:Liichtgeschwëndegkeet]]
[[lt:Šviesos greitis]]
[[jbo:nilsutra lo gusni]]
[[hu:Fénysebesség]]
[[ml:പ്രകാശവേഗം]]
[[ms:Kelajuan cahaya]]
[[nl:Lichtsnelheid]]
[[ja:光速]]
[[no:Lysets hastighet]]
[[pl:Prędkość światła]]
[[pt:Velocidade da luz]]
[[ro:Viteza luminii]]
[[ru:Скорость света]]
[[sq:Shpejtësia e dritës]]
[[simple:Speed of light]]
[[sk:Rýchlosť svetla]]
[[sl:Hitrost svetlobe]]
[[sr:Брзина светлости]]
[[sh:Brzina svjetlosti]]
[[fi:Valonnopeus]]
[[sv:Ljusets hastighet]]
[[th:อัตราเร็วของแสง]]
[[vi:Tốc độ ánh sáng]]
[[tr:Işık hızı]]
[[uk:Швидкість світла]]
[[zh:光速]]