Total+History+on+Speed+of+Light

=**Speed** of **light**=

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Jump to: [|navigation], [|search]"**Light** barrier" redirects here. For the device, see [|Photoelectric sensor].For other uses, see [|**Speed** of **light** (disambiguation)] and [|Lightspeed (disambiguation)].[|Sunlight] takes about 8 minutes, 19 seconds to reach Earth.
 * Speed** of **light** in different units|| [|metres per second] || 299,792,458 ||
 * [|kilometres per second] || 299,792.458 ||
 * [|kilometres per hour] || 1,079 million ||
 * [|miles per second] || 186,282.4 ||
 * [|miles per hour] || 671 million ||
 * [|astronomical units] per day || 173 ||
 * [|Planck units] || 1 (exact) ||

Travel times at the **speed** of **light**||~ Distance ||~ Time || All values are approximate unless noted otherwise. The ****speed** of **light**** (usually denoted //**c**//) is a [|physical constant]. It is the [|**speed**] at which [|electromagnetic radiation] (such as **light**) travels in [|vacuum], the **speed** of [|massless particles], and the fastest **speed** at which energy or [|information] can travel. Its value is exactly 299,792,458 [|metres per second],[|[1]][|[2]] often approximated as 300,000 kilometres per second or 186,000 miles per second (see the table on the right for more units). For much of human history, it was not known whether **light** was transmitted instantaneously or merely very quickly. In the 17th century, [|Ole Rømer] first demonstrated that it traveled at a finite **speed** by studying the apparent motion of [|Jupiter]'s moon [|Io]. After centuries of increasingly precise measurements, in 1975 the **speed** of **light** was known to be 299,792,458 m/s with a relative [|measurement uncertainty] of 4 parts per billion. In 1983, the [|meter] was redefined in the [|International System of Units] (SI) as the distance traveled by **light** in vacuum in 1 ⁄ 299,792,458 of a [|second]. As a result, the numerical value of //c// in meters per second is now fixed exactly by the definition of the meter.[|[1]][|[2]] According to the theory of [|special relativity], //c// connects space and time in the unified structure of [|spacetime], and its square is the [|constant of proportionality] between [|mass and energy] (//E// = //mc//2).[|[3]] In any [|inertial frame of reference], independently of the relative velocity of the emitter and the observer, //c// is the **speed** of all [|massless particles] and associated [|fields], including all electromagnetic radiation in [|free space],[|[4]] and it is believed to be the [|**speed** of gravity] and of [|gravitational waves].[|[5]][|[6]] It is an upper bound on the **speed** at which energy, matter, and [|information] can travel,[|[7]][|[8]] as surpassing it "would lead to the destruction of the essential relation between cause and effect."[|[9]] Its finite value is a limiting factor in the operational **speed** of electronic devices.[|[10]] The **speed** at which **light** propagates through [|transparent materials], such as glass or air, is less 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 ≈ 200,000 km/s ; the [|refractive index of air] for visible **light** is about 1.0003, so the **speed** of **light** in air is very close to //c//. hide] * [|1] [|Numerical value, notation and units]
 * one foot || 1.0 [|ns] ||
 * one metre || 3.3 ns ||
 * one kilometre || 3.3 [|μs] ||
 * one [|statute mile] || 5.4 μs ||
 * from the [|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 [|parsec] || 3.26 years ||
 * from [|Alpha Centauri] to Earth || 4.4 years ||
 * across the [|Milky Way] || 100,000 years ||
 * from [|Andromeda Galaxy] to Earth || 2.5 million years ||
 * ==Contents==
 * [|2] [|Fundamental role in physics]
 * [|2.1] [|Upper limit on speeds]
 * [|2.1.1] [|Faster-than-**light** observations and experiments]
 * [|2.1.1.1] [|Galaxies moving faster than **light**]
 * [|3] [|Propagation of **light**]
 * [|3.1] [|In a medium]
 * [|4] [|Practical effects of finiteness]
 * [|4.1] [|Distance measurement]
 * [|4.2] [|Astronomy]
 * [|5] [|Measurement]
 * [|5.1] [|Astronomical measurements]
 * [|5.2] [|Time of flight techniques]
 * [|5.3] [|Permittivity]
 * [|5.4] [|Cavity resonance]
 * [|5.5] [|Laser interferometry]
 * [|6] [|History]
 * [|6.1] [|First measurement attempts]
 * [|6.2] [|19th and early 20th century]
 * [|6.3] [|Increased accuracy and redefinition of the metre]
 * [|7] [|See also]
 * [|8] [|Notes]
 * [|9] [|References]
 * [|9.1] [|Citations]
 * [|9.2] [|Historical references]
 * [|9.3] [|Modern references]
 * [|10] [|External links] ||

[[|edit]] Numerical value, notation and units
The **speed** of **light** is a [|dimensional physical constant], so its numerical value depends on the system of units used. In the [|International System of Units] (SI), the metre is defined as the distance **light** travels in vacuum in 1 ⁄ 299,792,458 of a second (see "[|Redefinition of the metre]", below). The effect of this definition is to fix the **speed** of **light** in vacuum at exactly 299,792,458 m/s .[|[Note 1]][|[12]][|[13]][|[14]] The **speed** of **light** in vacuum is usually denoted by //c//, for "constant" or the Latin //[|celeritas]// (meaning "swiftness"). Originally, the symbol //V// was used, introduced by [|Maxwell] in 1865. In 1856, [|Weber] and [|Kohlrausch] had used //c// for a constant later shown to equal √ 2 times the **speed** of **light** in vacuum. In 1894, [|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.[|[15]][|[16]] Some authors use //c// for the **speed** of waves in //any// material medium, and //c//0 for the **speed** of **light** in vacuum.[|[17]] This subscripted notation, which is endorsed in official SI literature,[|[1]] has the same form as other related constants: namely, //μ//0 for the [|vacuum permeability] or magnetic constant, //ε//0 for the [|vacuum permittivity] or electric constant, and //Z//0 for the [|impedance of free space]. This article uses //c// exclusively for the **speed** of **light** in vacuum. In branches of physics in which the **speed** of **light** plays an important part, such as in relativity, it is common to use systems of [|natural units] of measurement in which //c// = 1 .[|[18]][|[19]] When such a system of measurement is used, the **speed** of **light** drops out of the equations of physics, because multiplication or division by 1 does not affect the result.

[[|edit]] Fundamental role in physics
See also: [|Introduction to special relativity] and [|Special relativity] The **speed** at which **light** propagates in vacuum is independent both of the motion of the **light** source and of the [|inertial frame of reference] of the observer.[|[Note 2]] The constancy of the **speed** of **light** was postulated by Albert Einstein in 1905, motivated by [|Maxwell's theory of electromagnetism] and the lack of evidence for the [|luminiferous ether];[|[20]] it has since been consistently confirmed by many experiments.[|[Note 3]][|[19]][|[21]] The theory of [|special relativity] explores the consequences of such an invariant **speed** //c// and the assumption that the laws of physics are the same in all inertial frames of reference.[|[22]][|[23]] One consequence is that //c// is the **speed** at which all massless particles and waves, including **light**, must travel. The Lorentz factor //γ// as a function of velocity. It starts at 1 and approaches infinity as //v// approaches //c//. Special relativity has many counter-intuitive implications, which have been verified in many experiments.[|[24]] These include the [|equivalence of mass and energy] (//E// = //mc//2), [|length contraction] (moving objects shorten),[|[Note 4]] and [|time dilation] (moving clocks run slower). The factor //γ// by which lengths contract and times dilate, known as the [|Lorentz factor], is given by //γ// = (1 − //v//2///c//2)−1/2, where //v// is the **speed** of the object; its difference 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//. Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame. Another counter-intuitive consequence of special relativity is 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; neither event can be the [|cause] of the other. 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//.[|[27]] Lorentz invariance has become 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 may seem to be unrelated to **light**. For example, general relativity predicts that //c// is also the [|**speed** of gravity] and of [|gravitational waves].[|[28]] In [|non-inertial frames] of reference (gravitationally curved space 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 in physics 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, various theories have suggested that the [|**speed** of **light** has changed over time].[|[30]][|[31]] Although no conclusive evidence for such theories has been found, they remain the subject of ongoing research.[|[32]][|[33]][|[34]]

[[|edit]] Upper limit on speeds
See also: [|Chronology protection conjecture] According to special relativity, the energy of an object with [|rest mass] //m// and **speed** //v// is given by //γmc//2, where //γ// is the Lorentz factor defined above. When //v// is zero, //γ// is equal to one, giving rise to the famous //E// = //mc//2 formula for [|mass-energy equivalence]. Since the //γ// factor approaches infinity as //v// approaches //c//, it would take an infinite amount of energy to accelerate an object with mass to the **speed** of **light**. The **speed** of **light** is the upper limit for the speeds of objects with positive rest mass.[//[|citation needed]//] More generally, it is normally impossible for any information or energy to travel faster than //c//. One reason is that according to the theory of special relativity, 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,[|[Note 5]] and [|causality] would be violated.[|[Note 6]][|[9]] In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,[|[21]] and would lead to [|paradoxes].[|[Note 7]][|[36]]

[[|edit]] Faster-than-**light** observations and experiments
Main article: [|Faster-than-**light**]See also: [|Scharnhorst effect] and [|Hartman effect] There are situations in which it may seem that matter, energy, or information travels at speeds greater than //c//, but they do not. For example, if a laser beam is swept quickly across a distant object, the spot of **light** can move faster than //c//, but the only physical entities that are moving are the laser and its emitted **light**, which travels at the **speed** //c// from the laser to the various positions of the spot. The movement of the spot will be delayed after the laser is moved because of the time it takes **light** to get to the distant object from the laser. Similarly, a shadow projected onto a distant object can be made to move faster than //c//.[|[37]] In neither case does any matter or information travel faster than **light**.[|[38]] In some [|interpretations of quantum mechanics], certain quantum effects may seem to be transmitted faster than //c//—and thus instantaneously in some frame—as in the [|EPR paradox]. An example involves the [|quantum states] of two particles that can be [|entangled]. Until either of the particles is observed, they exist in a [|superposition] of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously (i.e., faster than **light** could travel from one particle to the other). However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.[|[38]][|[39]] Another prediction of faster-than-**light** speeds occurs for [|quantum tunnelling] and is called the [|Hartman effect].[|[40]][|[41]] However, no information can be sent using this effect.[|[42]] The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their [|closing **speed**]) may have a value in excess of //c//. However, this does not represent the **speed** of any single object as measured in a single inertial frame. So-called [|superluminal motion] is seen in certain astronomical objects,[|[43]] such as the [|relativistic jets] of [|radio galaxies] and [|quasars]. 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 approaching Earth at a small angle to the line of sight: since the **light** which was emitted when the jet was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the **light** rays were emitted.[|[44]]

[[|edit]] Galaxies moving faster than **light**
See also: [|Metric expansion of space] and [|Hubble's law] In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion //through// space, but rather to the [|expansion of space] itself.[|[38]] For example, galaxies far away from Earth appear to be moving away from the Earth with a **speed** proportional to their distances. Beyond a boundary called the [|Hubble sphere], this apparent recessional velocity becomes greater than the **speed** of **light**.[|[45]]

[[|edit]] 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 through the vacuum is related to the [|electric constant] //ε//0 and the [|magnetic constant] //μ//0 by the equation //c// = 1/ √ //ε//0//μ//0  .[|[46]] In modern [|quantum physics], the electromagnetic field is described by the theory of [|quantum electrodynamics] (QED). In this theory, **light** is described by the fundamental excitations (or quanta) of the electromagnetic field, called [|photons]. In QED, photons are massless particles and thus, according to special relativity, they must travel at the **speed** of **light**. 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]] To date no such effects have been observed,[|[47]][|[48]][|[49]] putting stringent limits on the mass of the photon. The limit obtained depends on the used model: if the massive photon is described by [|Proca theory],[|[50]] the experimental upper bound for its mass is about 10−57 [|grams];[|[51]] if photon mass is generated by a [|Higgs mechanism], the experimental upper limit is less sharp, //m// ≤ 10−14 [|eV/c2] [|[50]] (roughly 2 × 10−47 g). 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 the spectrum of [|gamma-ray burst] [|GRB 090510] did not find any difference in the speeds of photons of different energies, confirming that Lorentz invariance is verified at least down to the scale of the [|Planck length] (//l//P = √ [|//ħ//][|//G//]///c//3 ≈ 1.6163 × 10−35 m ) divided by 1.2.[|[52]]

[[|edit]] In a medium
See also: [|Refractive index] and [|Dispersion (optics)] When **light** enters materials, its energy is absorbed. In the case of [|transparent materials], this energy is quickly re-radiated. However, this absorption and re-radiation introduces a delay. As **light** propagates through dielectric material it undergoes continuous absorption and re-radiation. Therefore the **speed** of **light** in a medium is said to be less than //c//, which should be read as the **speed** of energy propagation at the macroscopic level. At an atomic level, electromagnetic waves always travel at //c// in the empty space between atoms. Two factors influence this slowing: stronger absorption leading to shorter path length between each re-radiation cycle, and longer delays. The slowing is therefore the result of these two factors.[|[53]] The refractive index of a transparent material is defined as the ratio of //c// to the **speed** of **light** //v// in the material. Larger indices of refraction indicate smaller 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.[|[54]] Denser media, such as [|water] and glass, have refractive indexes of around 1.3 and 1.5 respectively for visible **light**.[|[55]][|Diamond] has a refractive index of about 2.4.[|[56]] The **light** passing through a [|dispersive prism] demonstrates refraction and, by the splitting of [|white] **light** into a [|spectrum] of colors, dispersion. If the refractive index of a material depends on the frequency of the **light** passing through the medium, there exist two notions of the **speed** of **light** in the medium. One is the **speed** of a wave of a [|single frequency] //f//. This is called the [|phase velocity] //v//p(//f//), and is related to the frequency-dependent refractive index //n//(//f//) by //v//p(//f//) = //c/////n//(//f//). The other is the average velocity of a pulse of **light** consisting of different frequencies of **light**. This is called the [|group velocity] and not only depends on the properties of the medium but also the distribution of frequencies in the pulse. A pulse with different group and phase velocities is said to undergo [|dispersion]. Certain materials have an exceptionally low group velocity for **light** waves, a phenomenon called [|slow **light**]. 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 (61 km/h; 38 mph);[|[57]] in 2001, they were able to momentarily stop a beam.[|[58]] In 2003, scientists at [|Harvard University] and the [|Lebedev Physical 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.[|[59]][|[60]] It is also possible for the group velocity of **light** pulses to exceed //c//.[|[61]] In an experiment in 2000, [|laser] beams travelled for extremely short distances through [|caesium] atoms with a group velocity of 300 times //c//.[|[62]] It is not possible to transmit information faster than //c// by this means because the **speed** of information transfer cannot exceed the [|front velocity] of the wave pulse, which is always less than //c//.[|[63]] 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].[|[64]]

[[|edit]] Practical effects of finiteness
The finiteness of the **speed** of **light** has implications for various sciences and technologies. For some it creates challenges or limits: for example, //c//, being the upper limit of the **speed** with which signals can be sent, provides a theoretical upper limit for the operating **speed** of microprocessors. For others it creates opportunities, for example to measure distances. The **speed** of **light** is of relevance to [|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 about 67 milliseconds. When **light** is traveling around the globe in an [|optical fiber], the actual transit time is longer, in part because the **speed** of **light** is slower by about 35% in an optical fiber, depending on its refractive index //n//,[|[65]] //v// = //c/////n//. Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator. A typical time as of 2004 for a U.S. to Australia or Japan computer-to-computer [|ping] is 0.18 s .[//[|citation needed]//] The **speed** of **light** additionally affects [|wireless communications] design.[//[|clarification needed]//] A beam of **light** is depicted travelling between the Earth and the Moon in the same time it takes **light** to scale the distance between them: 1.255 seconds at its mean orbital (surface to surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale. Another consequence of the finite **speed** of **light** is that communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between [|ground control] and [|Apollo 8] when it became the first manned spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three seconds for the answer to arrive.[|[66]] The communications delay between Earth and [|Mars] is almost ten minutes. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until ten minutes later; it would then take at least a further ten minutes for instructions to travel from Earth to Mars. The **speed** of **light** can also be of concern over very short distances. 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 only travel 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, which 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].[|[67]]

[[|edit]] Distance measurement
[|Radar] systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip [|transit time] multiplied by the **speed** of **light**. A [|Global Positioning System] (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because **light** travels about 300,000 kilometres (186,000 miles) in one second, these measurements of small fractions of a second must be very precise. The [|Lunar Laser Ranging Experiment], [|radar astronomy] and the [|Deep Space Network] determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times.

[[|edit]] Astronomy
The finite **speed** of **light** is important in astronomy. Due to the vast distances involved, it can take a very long time for **light** to travel from its source to Earth. 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.[|[68]][|[69]] 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.[|[68]] The fact that farther-away objects appear younger (due to the finite **speed** of **light**) allows astronomers to infer the [|evolution of stars], [|of galaxies], and [|of the universe] itself. Astronomical distances are sometimes expressed in [|**light**-years], especially in [|popular science] publications.[|[70]] A **light**‑year is the distance **light** travels in one year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 [|parsecs]. [|Proxima Centauri], the closest star to Earth after the Sun, is around 4.2 **light**‑years away.[|[71]]

[[|edit]] Measurement
To measure the **speed** of **light**, various methods can be used which involve observation of astronomical phenomena or experimental setups on Earth. The setups could use mechanical devices (e.g. toothed wheels), [|optics] (e.g. [|beam splitters], [|lenses] and [|mirrors]), [|electro-optics] (e.g. [|lasers]), or electronics in conjunction with a [|cavity resonator].

[[|edit]] Astronomical measurements
Due to the large scale and the vacuum of space observations in the [|solar system] and in astronomy in general provide a natural setting for measuring the **speed** of **light**. The result of such a measurement usually appears as the time needed for **light** to transverse 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 accurate the length of the reference distance is known in Earth-based units. As such, it is customary to express the results in [|astronomical units] per day. An astronomical unit is approximately equal to the average distance between the Earth and the Sun.[|[Note 8]] Since the most used reference length scale in modern experiments (the SI metre) is determined by the **speed** of **light**, the value of //c// is fixed when measured in metres per second. Measurements of //c// in astronomical units provides an independent alternative to measure //c//. One such method was used by [|Ole Christensen Rømer] to provide [|the first quantitative estimate of the **speed** of **light**].[|[73]][|[74]] When observing the periods of moons orbiting a distant planet these periods appear to be shorter when the Earth is approaching that planet than when the Earth is receding from it. This effect occurs because the Earth's movement causes the path travelled by **light** from the planet to Earth to shorten (or lengthen respectively). The observed change in period is the time needed by **light** to cover the difference in path length. Rømer observed this effect for [|Jupiter]'s innermost moon [|Io] and deduced from it that **light** takes 22 minutes to cross the diameter of the Earth's orbit. Aberration of **light**: **light** from a distant source will appear to a different location for a moving telescope due to the finite **speed** of **light**. Another method is to use the [|aberration of **light**], discovered and explained by [|James Bradley] in the 18th century.[|[75]] 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 left). 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])[|[76]] 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 easily converted in the time needed to travel from the Sun to Earth. In 1729, Bradley used this method to derive that **light** travelled 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take **light** 8 minutes 12 seconds to travel from the Sun to the Earth.[|[75]] Nowadays, the "**light** time for unit distance"—the inverse of //c//, expressed in seconds per astronomical unit—is measured by comparing the time for radio signals to reach different spacecraft in the Solar System, with their position calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a [|best fit] value for the **light** time per unit distance is obtained. As of 2009[|[update]], the best estimate, as approved by the [|International Astronomical Union] (IAU), is:[|[77]][|[78]][|[79]] The relative uncertainty in these measurements is 0.02 parts per billion (2 × 10−11), equivalent to the uncertainty in Earth-based measurements of length by interferometry.[|[80]][|[81]] Since the meter is defined to be the length travelled by **light** in a certain time interval, the measurement of the **light** time for unit distance can also be interpreted as measuring the length of an AU in meters.
 * light** time for unit distance: 499.004 7 83 8 36(10) s //c// = 0.002 0 03 9 88 8 04 1 0(4) AU/s = 173.144 6 32 6 74(3) AU/day

[[|edit]] Time of flight techniques
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]. Diagram of the [|Fizeau apparatus] The setup as used by Fizeau consists of a beam of **light** directed at a mirror 8 kilometres (5 mi) away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the **speed** of **light** can be calculated.[|[82]] The method of Foucault replaces the cogwheel by a rotating mirror. Because the mirror keeps rotating while the **light** travels to the distant mirror and back, the **light** is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known **speed** of rotation and the distance to the distant mirror the **speed** of **light** may be calculated.[|[83]] Nowadays, using [|oscilloscopes] with time resolutions of less than one nanosecond, the **speed** of **light** can be directly measured by timing the delay of a **light** pulse from a laser or an LED reflected from a mirror. This method is less precise (with errors of the order of 1%) than other modern techniques, but it is sometimes used as a laboratory experiment in college physics classes.[|[84]][|[85]][|[86]]

[[|edit]] Permittivity
An option for measuring //c// that does not directly depend on the propagation of electromagnetic waves is to use relation between //c// and the [|vacuum permittivity] //ε//0 [|vacuum permeability] //μ//0 established by Maxwell theory, //c//2 = 1///ε//0//μ//0. The vacuum permittivity may be determined by measuring the [|capacitance] and dimensions of a [|capacitor], whereas the value of the [|vacuum permeability] is fixed at exactly 4π × 10−7 H·m−1 though the definition of the [|ampere]. Rosa and Dorsey used this method in 1907 to find a value of 299,710 ± 22 km/s .[|[87]][|[88]]

[[|edit]] Cavity resonance
Electromagnetic [|standing waves] in a cavity. Another way to measure the **speed** of **light** is to independently measure the frequency //f// and wavelength //λ// of an electromagnetic wave in vacuum. The value of //c// can then be found by using the relation //c// = //fλ//. One option is to measure the resonance frequency of a [|cavity resonator]. If the dimensions of the resonance cavity are also known, these can be used determine the wavelength of the wave. In 1946, [|Louis Essen] and A.C. Gordon-Smith establish the frequency for a variety of [|normal modes] of microwaves of a [|microwave cavity] of precisely known dimensions. 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**.[|[87]][|[89]] The Essen–Gordon-Smith result, 299,792 ± 9 km/s, was substantially more precise than those found by optical techniques.[|[87]] By 1950, repeated measurements by Essen established a result of 299,792.5 ± 3.0 km/s .[|[90]] A household demonstration of this technique is possible, using a microwave oven and food such as marshmallows or margarine: if the turntable is removed so that the food does not move, it will cook the fastest at the [|antinodes] (the points at which the wave amplitude is the greatest), where it will begin to melt. The distance between two such spots is half the wavelength of the microwaves; by measuring this distance and multiplying the wavelength by the microwave frequency (usually displayed on the back of the oven, typically 2450 MHz), the value of //c// can be calculated, "often with less than 5% error".[|[91]][|[92]]

[[|edit]] Laser interferometry
An alternative to the cavity resonator method to find the wavelength for determining the **speed** of **light** is to use a form of [|interferometer].[|[93]] A [|coherent **light**] beam with a known frequency (//f//), as from a [|laser], is split to follow two paths and then recombined. By carefully changing the path length and observing the [|interference pattern], the wavelength of the **light** (//λ//) can be determined, which is related to the **speed** of **light** by the equation //c// = //λf//. The main difficulty in measuring //c// through interferometry is to measure the frequency of **light** in or near the optical region; such frequencies are too high to be measured with conventional methods. This was first overcome by a group at the US [|National Institute of Standards and Technology] (NIST) laboratories in [|Boulder, Colorado], in 1972.[|[94]] By a series of [|photodiodes] and specially constructed metal–insulator–metal [|diodes], they succeeded in linking the frequency of a [|methane]-stabilized [|infrared] laser to the frequency of the [|caesium] transition used in [|atomic clocks] (nearly 10,000 times lower, in the [|microwave] region).[|[95]] Their results for the frequency and wavelength of the infrared laser, and the resulting value for //c//, were: //f// = 88.376 1 81 6 27 ± 0.000 0 00 0 50 THz ; //λ// = 3.392 2 31 3 76 ± 0.000 0 00 0 12 µm ; //c// = 299,792,456.2 ± 1.1 m/s ; nearly a hundred times more precise than previous measurements of the **speed** of **light**.[|[94]][|[95]]

[[|edit]] History
Until the [|early modern period], it was not known whether **light** travelled instantaneously or at a finite **speed**. The first extant recorded examination of this subject was in [|ancient Greece]. [|Empedocles] 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".[|[96]] [|Euclid] and [|Ptolemy] advanced the [|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. [|Early Islamic philosophers] initially agreed with the [|Aristotelian view] that **light** had no **speed** of travel. In 1021, [|Islamic physicist] [|Alhazen] (Ibn al-Haytham) published the //[|Book of Optics]//, in which he used experiments related to the [|camera obscura] to support the now accepted intromission theory of [|vision], in which **light** moves from an object into the eye.[|[97]] This led Alhazen to propose that **light** must therefore have a finite **speed**,[|[96]][|[98]][|[99]] and that the **speed** of **light** is variable, decreasing in denser bodies.[|[99]][|[100]] He argued that **light** is a "substantial matter", the propagation of which requires time "even if this is hidden to our senses".[|[101]] 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.[|[102]] [|Roger Bacon] argued that the **speed** of **light** in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle.[|[103]][|[104]] In the 1270s, [|Witelo] considered the possibility of **light** travelling at infinite **speed** in a vacuum, but slowing down in denser bodies.[|[105]] A comment on a verse in the //[|Rigveda]// by the 14th century [|Indian] scholar [|Sayana] mentioned a **speed** of **light** equivalent to about 186,400 miles per second, which was apparently chosen so that **light** would encircle the [|Puranic] universe in one day.[|[106]][|[107]] In 1574, the [|Ottoman astronomer] and physicist [|Taqi al-Din] concluded that the **speed** of **light** is finite, correctly explained [|refraction] as the result of **light** traveling more slowly in denser bodies, and suggested that it would take a long time for **light** from distant stars to reach the Earth.[|[108]][|[109]] 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 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.[|[96]]

[[|edit]] First measurement attempts
In 1629, [|Isaac Beeckman] proposed an experiment in which a person would observe 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 weren't, it must nevertheless be extraordinarily rapid.[|[110]][|[111]] Galileo's experiment was carried out by the [|Accademia del Cimento] of Florence, Italy, in 1667, with the lanterns separated by about one mile, but no delay was observed. Based on the modern value of the **speed** of **light**, the actual delay in this experiment would be about 11 [|microseconds]. [|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. Rømer's observations of the occultations of Io from Earth The first quantitative estimate of the **speed** of **light** was made in 1676 by [|Ole Christensen Rømer] (see [|Rømer's determination of the **speed** of **light**]).[|[73]][|[74]] From the observation that the periods of Jupiter's innermost moon [|Io] appeared to be shorter when the earth was approaching Jupiter than when receding from it, he concluded that **light** travels at a finite **speed**, and was able to estimate that would take **light** 22 minutes to cross the diameter of Earth's orbit. [|Christiaan Huygens] combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of **speed** of **light** of 220,000 km/s, 26% lower than the actual value.[|[112]] 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).[|[113]] Newton queried whether Rømer's eclipse shadows were coloured; hearing that they weren't, he concluded the different colours travelled at the same **speed**. In 1729, [|James Bradley] discovered the [|aberration of **light**].[|[75]] From this effect he determined that **light** must travel 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take **light** 8 minutes 12 seconds to travel from the Sun to the Earth.[|[75]]

[[|edit]] 19th and early 20th century
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 315,000 km/s. His method was improved upon by [|Léon Foucault] who obtained a value of 298,000 km/s in 1862.[|[82]] [|James Clerk Maxwell] observed that this value was very close to the parameter //c// appearing in his theory of [|electromagnetism] as the propagation **speed** of the electromagnetic field, and suggested that **light** was an electromagnetic wave.[|[114]] It was thought at the time that electromagnetic field existed in some background medium called the [|luminiferous aether]. This aether acted as an absolute reference frame for all physics and should be possible to measure the motion of the Earth with respect to this medium. In the second half of the 19th century and the beginning of the 20th century several experiments were performed to try to detect this motion, the most famous of which is [|the experiment] performed by [|Albert Michelson] and [|Edward Morley] in 1887.[|[115]] None of the experiments found any hint of the motion, finding that the **speed** of **light** was the same in every direction.[|[116]] In 1905 [|Albert Einstein] proposed that the **speed** of **light** was independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived his [|special theory of relativity], in which the **speed** of **light** //c// featured as a fundamental parameter, also appearing in contexts unrelated to **light**.[|[117]]

[[|edit]] Increased accuracy and redefinition of the metre
See also: [|Metre] 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. In 1972, using the latter method, a team at the US [|National Institute of Standards and Technology] (NIST) laboratories in [|Boulder, Colorado] determined the **speed** of **light** to be //c// = 299,792,456.2 ± 1.1 m/s .[|[94]][|[95]] Almost all the uncertainty in this measurement of the **speed** of **light** was due to uncertainty in the length of the metre.[|[95]][|[94]][|[118]] Since 1960, the metre had been defined as a given number of wavelengths of the **light** of one of the [|spectral lines] of a [|krypton] &amp,[|[Note 9]] but it turned out that the chosen spectral line was not perfectly symmetrical.[|[95]] This made its wavelength, and hence the length of the metre, uncertain, because the definition did not specify what point on the line profile (e.g., its maximum-intensity point or its centre of gravity) it referred to.[|[Note 10]] To get around this problem, in 1975, the 15th [|Conférence Générale des Poids et Mesures] (CGPM) recommended using 299,792,458 metres per second for "the **speed** of propagation of electromagnetic waves in vacuum".[|[118]] Based on this recommendation, the 17th CGPM in 1983 redefined the metre as "the length of the path travelled by **light** in vacuum during a time interval of 1 ⁄ 299,792,458 of a second".[|[120]] The effect of this definition gives the **speed** of **light** the exact value 299,792,458 m/s, which is nearly the same as the value 299,792,456.2 ± 1.1 m/s obtained in the 1972 experiment. The CGPM chose this value to minimise any change in the length of the metre.[|[121]][|[122]] As a result, in the SI system of units the **speed** of **light** is now a defined constant.[|[14]] Improved experimental techniques do not affect the value of the **speed** of **light** in SI units, but do result in a more precise realisation of the SI metre.[|[123]][|[124]]