Physics:Speed of light

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Short description: Speed at which all massless particles and associated fields travel in vacuum

Speed of light
The distance from the Sun to Earth is shown as 150 million kilometres, an approximate average. Sizes to scale.
Sunlight takes about 8 minutes and 17 seconds to travel from the Sun to Earth (using the average distance).
Exact values
metres per second299792458
Approximate values (to three significant digits)
kilometres per hour1080000000
miles per second186000
miles per hour[1]671000000
astronomical units per day173[Note 1]
parsecs per year0.307[Note 2]
Approximate light signal travel times
one foot1.0 ns
one metre3.3 ns
from geostationary orbit to Earth119 ms
the length of Earth's equator134 ms
from Moon to Earth1.3 s
from Sun to Earth (1 AU)8.3 min
one light-year1.0 year
one parsec3.26 years
from the nearest star to Sun (1.3 pc)4.2 years
from the nearest galaxy to Earth25000 years
across the Milky Way100000 years
from the Andromeda Galaxy to Earth2.5 million years

The speed of light in vacuum, commonly denoted c, is a universal physical constant that is important in many areas of physics. Its exact value is defined as 299792458 metres per second (approximately 300000 km/s or 186000 mi/s).[Note 3] According to the special theory of relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space.

All forms of electromagnetic radiation — not just 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. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also ultimately limits the data transfer between the CPU and memory chips in computers. The speed of light can be used with time of flight measurements to measure large distances to high precision.

Ole Rømer first demonstrated in 1676 that light travels at a finite speed (non-instantaneously) by studying the apparent motion of Jupiter's moon Io. Progressively more accurate measurements of its speed came over the following centuries. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism.[4] In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source.[5] 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 the 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 approach c, but can never actually reach it, regardless of the frame of reference in which their speed is measured. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence, E = mc2.[6] 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 = 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.

Numerical value, notation, and units

The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal 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 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.[7][8]


Since 1983, the metre has been defined in the International System of Units (SI) as the distance light travels in vacuum in ​1299792458 of a second. This definition fixes the speed of light in vacuum at exactly 299792458 m/s.[11] As a dimensional physical constant, the numerical value of c is different for different unit systems. For example, in imperial units, the speed of light is approximately 186282 miles per second,[Note 4] or roughly 1 foot per nanosecond.[12][13] In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1.[14][15] Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result. Its unit of lightsecond/second is still relevant, even if omitted.

Fundamental role in physics



Special relativity has many counterintuitive and experimentally verified implications.[23] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 8] and time dilation (moving clocks run more slowly). The factor γ by which lengths contract and times dilate is known as the Lorentz factor and is given by γ = (1 − v2/c2)−1/2, where v is the speed of the object. The difference of γ from 1 is negligible for speeds much slower than c, such as most everyday speeds—in which case special relativity is closely approximated by Galilean relativity—but it increases at relativistic speeds and diverges to infinity as v approaches c. For example, a time dilation factor of γ = 2 occurs at a relative velocity of 86.6% of the speed of light (v = 0.866 c). Similarly, a time dilation factor of γ = 10 occurs at v = 99.5% c.

The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with c relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c.[26] Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. As such, the parameter c is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that c is also the speed of gravity and of gravitational waves,[27] and observations of gravitational waves have been consistent with this prediction.[28] In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.[29]

It is generally assumed that fundamental constants such as c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that the speed of light may have changed over time.[30][31] No conclusive evidence for such changes has been found, but they remain the subject of ongoing research.[32][33]


Upper limit on speeds



More generally, it is impossible for signals or energy to travel faster than c. One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated.[Note 9][40] In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,[18] and would lead to paradoxes such as the tachyonic antitelephone.[41]

Faster-than-light observations and experiments

There are situations in which it may seem that matter, energy, or information-carrying signal travels at speeds greater than c, but they do not. For example, as is discussed in the propagation of light in a medium section below, many wave velocities can exceed c. The phase velocity of X-rays through most glasses can routinely exceed c,[42] but phase velocity does not determine the velocity at which waves convey information.[43]




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 tunnel through a barrier is constant, regardless of the thickness of the barrier.[47][48] This could result in a virtual particle crossing a large gap faster-than-light. However, no information can be sent using this effect.[49]


A 2011 report of neutrinos appearing to travel faster than light turned out to be due to experimental error.[52][53]


Propagation of light

In classical physics, light is described as a type of electromagnetic wave. The classical behaviour of the electromagnetic field is described by Maxwell's equations, which predict that the speed c with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant ε0 and the magnetic constant μ0, by the equation[55]

[math]\displaystyle{ c =\frac {1}{\sqrt{\varepsilon_0 \mu_0}} \ . }[/math]


Extensions of QED in which the photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed c of special relativity would then be the upper limit of the speed of light in vacuum.[29] No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon.[56] The limit obtained depends on the model used: if the massive photon is described by Proca theory,[57] the experimental upper bound for its mass is about 10−57 grams;[58] if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m10−14 eV/c2  (roughly 2 × 10−47 g).[57]

Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of gamma-ray burst GRB 090510 found no evidence for a dependence of photon speed on energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching the Planck scale.[59]

In a medium

In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity vp. A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocity vg, and its earliest part travels at the front velocity vf.[60]


The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a refractive index. The refractive index of a material is defined as the ratio of c to the phase velocity vp in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air is approximately 1.0003.[61] Denser media, such as water,[62] glass,[63] and diamond,[64] have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than-c speeds in material substances. As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a Bose–Einstein condensate of the element rubidium. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped", it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light.[65]

In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than c. In other materials, it is possible for the refractive index to become smaller than 1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative.[66] The requirement that causality is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient, are linked by the Kramers–Kronig relations.Cite error: Closing </ref> missing for <ref> tag The opposite, group velocities exceeding c, was proposed theoretically in 1993 and achieved experimentally in 2000.[67] It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.[60]



Practical effects of finiteness


Small scales

In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 gigahertz, a signal can travel only a maximum of about 30 centimetres (1 ft) in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips.[69][70]

Large distances on Earth

Given that the equatorial circumference of the Earth is about 40075 km and that c is about 300000 km/s, the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is travelling around the globe in an optical fibre, the actual transit time is longer, in part because the speed of light is slower by about 35% in an optical fibre, depending on its refractive index n.[Note 10] Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.[72]

Spaceflights and astronomy



Receiving light and other signals from distant astronomical sources can even take much longer. For example, it has taken 13 billion (13×109) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images.[75][76] Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when the universe was less than a billion years old.[75] The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the evolution of stars, of galaxies, and of the universe itself.[77]

Astronomical distances are sometimes expressed in light-years, especially in popular science publications and media.[78] A light-year is the distance light travels in one Julian year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs. In round figures, a light year is nearly 10 trillion kilometres or nearly 6 trillion miles. Proxima Centauri, the closest star to Earth after the Sun, is around 4.2 light-years away.[79]

Distance measurement


High-frequency trading

The speed of light has become important in high-frequency trading, where traders seek to gain minute advantages by delivering their trades to exchanges fractions of a second ahead of other traders. For example, traders have been switching to microwave communications between trading hubs, because of the advantage which microwaves travelling at near to the speed of light in air have over fibre optic signals, which travel 30–40% slower.[83][84]


There are different ways to determine the value of c. One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and Earth-based setups. However, it is also possible to determine c from other physical laws where it appears, for example, by determining the values of the electromagnetic constants ε0 and μ0 and using their relation to c. Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling c. This is described in more detail in the "Interferometry" section below.

In 1983 the metre was defined as "the length of the path travelled by light in vacuum during a time interval of ​1299792458 of a second",[85] fixing the value of the speed of light at 299792458 m/s by definition, as described below. Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of c.

Astronomical measurements


Outer space is a convenient setting for measuring the speed of light because of its large scale and nearly perfect vacuum. Typically, one measures the time needed for light to traverse some reference distance in the Solar System, such as the radius of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units.

Ole Christensen Rømer used an astronomical measurement to make the first quantitative estimate of the speed of light in the year 1676.[86][87] When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the diameter of the Earth's orbit around the Sun. The observed change in the moon's orbital period is caused by the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for Jupiter's innermost moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.[86]


Another method is to use the aberration of light, discovered and explained by James Bradley in the 18th century.[88] This effect results from the vector addition of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 arcseconds)[89] it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled 10210 times faster than the Earth in its orbit (the modern figure is 10066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.[88]

Astronomical unit

An astronomical unit (AU) is approximately the average distance between the Earth and Sun. It was redefined in 2012 as exactly 149597870700 m.[90][91] Previously the AU was not based on the International System of Units but in terms of the gravitational force exerted by the Sun in the framework of classical mechanics.[Note 11] The current definition uses the recommended value in metres for the previous definition of the astronomical unit, which was determined by measurement.[90] This redefinition is analogous to that of the metre and likewise has the effect of fixing the speed of light to an exact value in astronomical units per second (via the exact speed of light in metres per second).[93]


light time for unit distance: tau = 499.004783836(10) s


Time of flight techniques

Diagram of the Fizeau apparatus

A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the Fizeau–Foucault apparatus developed by Hippolyte Fizeau and Léon Foucault, based on a suggestion by François Arago.[97]




Electromagnetic constants


Cavity resonance

Electromagnetic standing waves in a cavity


The Essen–Gordon-Smith result, 299792±9 km/s, was substantially more precise than those found by optical techniques.[101] By 1950, repeated measurements by Essen established a result of 299792.5±3.0 km/s.[104]



Schematic of the working of a Michelson interferometer.


Before the advent of laser technology, coherent radio sources were used for interferometry measurements of the speed of light.[108] However interferometric determination of wavelength becomes less precise with wavelength and the experiments were thus limited in precision by the long wavelength (~4 mm (0.16 in)) of the radiowaves. The precision can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure the frequency of the light. One way around this problem is to start with a low frequency signal of which the frequency can be precisely measured, and from this signal progressively synthesize higher frequency signals whose frequency can then be linked to the original signal. A laser can then be locked to the frequency, and its wavelength can be determined using interferometry.[109] This technique was due to a group at the National Bureau of Standards (which later became the National Institute of Standards and Technology). They used it in 1972 to measure the speed of light in vacuum with a fractional uncertainty of 3.5×10−9.[109][110]


History of measurements of c (in km/s)
<1638 Galileo, covered lanterns inconclusive[111][112][113]:1252[Note 14]
<1667 Accademia del Cimento, covered lanterns inconclusive[113]:1253[114]
1675 Rømer and Huygens, moons of Jupiter 220000[87][115] ‒27% error
1729 James Bradley, aberration of light 301000[98] +0.40% error
1849 Hippolyte Fizeau, toothed wheel 315000[98] +5.1% error
1862 Léon Foucault, rotating mirror 298000±500[98] ‒0.60% error
1907 Rosa and Dorsey, EM constants 299710±30[101][102] ‒280 ppm error
1926 Albert A. Michelson, rotating mirror 299796±4[116] +12 ppm error
1950 Essen and Gordon-Smith, cavity resonator 299792.5±3.0[104] +0.14 ppm error
1958 K.D. Froome, radio interferometry 299792.50±0.10[108] +0.14 ppm error
1972 Evenson et al., laser interferometry 299792.4562±0.0011[110] ‒0.006 ppm error
1983 17th CGPM, definition of the metre 299792.458 (exact)[85] exact, as defined

Until the early modern period, it was not known whether light travelled instantaneously or at a very fast finite speed. The first extant recorded examination of this subject was in Ancient Greece . The ancient Greeks, Muslim scholars, and classical European scientists long debated this until Rømer provided the first calculation of the speed of light. Einstein's Theory of Special Relativity concluded that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.

Early history

Empedocles (c. 490–430 BC) was the first to propose a theory of light[117] and claimed that light has a finite speed.[118] He maintained that light was something in motion, and therefore must take some time to travel. Aristotle argued, to the contrary, that "light is due to the presence of something, but it is not a movement".[119] Euclid and Ptolemy advanced Empedocles' emission theory of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria argued that the speed of light must be infinite because distant objects such as stars appear immediately upon opening the eyes.[120] Early Islamic philosophers initially agreed with the Aristotelian view that light had no speed of travel. In 1021, Alhazen (Ibn al-Haytham) published the Book of Optics, in which he presented a series of arguments dismissing the emission theory of vision in favour of the now accepted intromission theory, in which light moves from an object into the eye.[121] This led Alhazen to propose that light must have a finite speed,[119][122][123] and that the speed of light is variable, decreasing in denser bodies.[123][124] He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from our senses.[125] Also in the 11th century, Abū Rayhān al-Bīrūnī agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.[126]

In the 13th century, Roger Bacon argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle.[127][128] In the 1270s, Witelo considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.[129]

In the early 17th century, Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it. René Descartes argued that if the speed of light were to be 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 were found to be finite, his whole system of philosophy might be demolished.[119] In Descartes' derivation of Snell's law, he assumed that even though the speed of light was instantaneous, the denser the medium, the faster was light's speed.[130] Pierre de Fermat derived Snell's law using the opposing assumption, the denser the medium the slower light travelled. Fermat also argued in support of a finite speed of light.[131]

First measurement attempts

In 1629, Isaac Beeckman proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile (1.6 km) away. In 1638, Galileo Galilei proposed an experiment, 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. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid.[111][112] In 1667, the Accademia del Cimento of Florence reported that it had performed Galileo's experiment, with the lanterns separated by about one mile, but no delay was observed.[132] The actual delay in this experiment would have been about 11 microseconds.

Rømer's observations of the occultations of Io from Earth


In his 1704 book Opticks, Isaac Newton reported Rømer's calculations of the finite speed of light and gave a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8 minutes 19 seconds).[133] Newton queried whether Rømer's eclipse shadows were coloured; hearing that they were not, he concluded the different colours travelled at the same speed. In 1729, James Bradley discovered stellar aberration.[88] From this effect he determined that light must travel 10210 times faster than the Earth in its orbit (the modern figure is 10066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.[88]

Connections with electromagnetism

In the 19th century Hippolyte Fizeau developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of 315000 km/s.[134] His method was improved upon by Léon Foucault who obtained a value of 298000 km/s in 1862.[98] In the year 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge, 1/ε0μ0, by discharging a Leyden jar, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff calculated that an electric signal in a resistanceless wire travels along the wire at this speed.[135] In the early 1860s, Maxwell showed that, according to the theory of electromagnetism he was working on, electromagnetic waves propagate in empty space[136] at a speed equal to the above Weber/Kohlrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.[137]

"Luminiferous aether"

Hendrik Lorentz (right) with Albert Einstein


Special relativity


Increased accuracy of c and redefinition of the metre and second

In the second half of the 20th century, much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. These were aided by new, more precise, definitions of the metre and second. In 1950, Louis Essen determined the speed as 299792.5±3.0 km/s, using cavity resonance.[104] This value was adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. In 1960, the metre was redefined in terms of the wavelength of a particular spectral line of krypton-86, and, in 1967, the second was redefined in terms of the hyperfine transition frequency of the ground state of caesium-133.[145]


Defined as an explicit constant

In 1983 the 17th meeting of the General Conference on Weights and Measures (CGPM) found that wavelengths from frequency measurements and a given value for the speed of light are more reproducible than the previous standard. They kept the 1967 definition of second, so the caesium hyperfine frequency would now determine both the second and the metre. To do this, they redefined the metre as "the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second."[85] As a result of this definition, the value of the speed of light in vacuum is exactly 299792458 m/s[149][150] and has become a defined constant in the SI system of units.[11] Improved experimental techniques that, prior to 1983, would have measured the speed of light no longer affect the known value of the speed of light in SI units, but instead allow a more precise realization of the metre by more accurately measuring the wavelength of krypton-86 and other light sources.[151][152]

In 2011, the CGPM stated its intention to redefine all seven SI base units using what it calls "the explicit-constant formulation", where each "unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant", as was done for the speed of light. It proposed a new, but completely equivalent, wording of the metre's definition: "The metre, symbol m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299792458 when it is expressed in the SI unit m s−1."[153] This was one of the changes that was incorporated in the 2019 redefinition of the SI base units, also termed the New SI.[154]

See also


  1. Exact value: (299792458 × 60 × 60 × 24 / 149597870700) AU/day
  2. Exact value: (999992651π / 10246429500) pc/y
  3. It is exact because, by a 1983 international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of ​1299792458 second. This particular value was chosen in order to provide a more accurate definition of the metre that still agreed as much as possible with the definition used before. See, for example, the NIST website[2] or the explanation by Penrose.[3] The second is in turn defined to be the length of time occupied by 9192631770 cycles of the radiation emitted by a caesium-133 atom in a transition between two specified energy states.[2]
  4. The speed of light in imperial and United States customary units is based on an inch of exactly 2.54 cm and is exactly
    299792458 m/s × 100 cm/m × 1/2.54 in/cm
    which is approximately 186282 miles, 698 yards, 2 feet, and 5 inches per second.
  6. See Michelson–Morley experiment and Kennedy–Thorndike experiment, for example.
  7. Because neutrinos have a small but non-zero mass, they travel through empty space very slightly more slowly than light. However, because they pass through matter much more easily than light does, there are in theory occasions when the neutrino signal from an astronomical event might reach Earth before an optical signal can, like supernovae.[22]
  9. It has been speculated that the Scharnhorst effect does allow signals to travel slightly faster than c, but the validity of those calculations has been questioned,[38] and it appears the special conditions in which this effect might occur would prevent one from using it to violate causality.[39]
  10. A typical value for the refractive index of optical fibre is between 1.518 and 1.538.[71]
  11. The astronomical unit was defined as the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians (approximately ​1365.256898 of a revolution) per day.[92]
  13. A detailed discussion of the interferometer and its use for determining the speed of light can be found in Vaughan (1989).[107]
  15. Between 1960 and 1983 the metre was defined as "the length equal to 1650763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom."[146] It was discovered in the 1970s that this spectral line was not symmetric, which put a limit on the precision with which the definition could be realized in interferometry experiments.[147]


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Further reading

Historical references

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