fbpx
Wikipedia

Speed of light

May 02, 2024

"Lightspeed" redirects here. For other uses, see Speed of light (disambiguation) and Lightspeed (disambiguation).

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

Speed of light
On average, sunlight takes 8 minutes and 17 seconds to travel from the Sun to Earth.
Exact value
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
DistanceTime
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 Earth70000 years
across the Milky Way87400 years
from the Andromeda Galaxy to Earth2.5 million years

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

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

Massless particles and field perturbations, such as gravitational waves, also travel at speed c in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can be accelerated to approach c but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity, c interrelates space and time and appears in the famous mass–energy equivalence, E = mc2.[9]

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

The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of electromagnetic waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = 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.[10][11]

Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum.[12] This subscripted notation, which is endorsed in official SI literature,[13] has the same form as related electromagnetic constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, and Z0 for the impedance of free space. This article uses c exclusively for the speed of light in vacuum.

Use in unit systems

Further information: Metre § Speed of light definition

Since 1983, the constant c has been defined in the International System of Units (SI) as exactly 299792458 m/s; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1⁄299792458 of a second. By using the value of c, as well as an accurate measurement of the second, one can thus establish a standard for the metre.[14] 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.[Note 5][15][16]

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.[17][18] Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted.

Fundamental role in physics

See also: Special relativity and One-way speed of light

The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer.[Note 6] This invariance of the speed of light was postulated by Einstein in 1905,[8] after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for motion against the luminiferous aether.[19] It has since been consistently confirmed by many experiments.[Note 7] It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again) is frame-independent, because it is impossible 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 at the detector should be synchronized.[20][21]

By adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.[20][21] The special theory of relativity explores the consequences of this invariance of c with 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 in vacuum.[24][Note 8]

 
The Lorentz factor γ as a function of velocity. It starts at 1 and approaches infinity as v approaches c.

Special relativity has many counterintuitive and experimentally verified implications.[26] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 9] 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 99.5% the speed of light (v = 0.995 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.[29] 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,[30] and observations of gravitational waves have been consistent with this prediction.[31] 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 can differ from c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region.[32]

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.[33][34] No conclusive evidence for such changes has been found, but they remain the subject of ongoing research.[35][36]

It is generally assumed that the two-way speed of light is isotropic, meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear energy levels as a function of the orientation of the emitting nuclei in a magnetic field (see Hughes–Drever experiment), and of rotating optical resonators (see Resonator experiments) have put stringent limits on the possible two-way anisotropy.[37][38]

Upper limit on speeds

According to special relativity, the energy of an object with rest mass m and speed v is given by γmc2, where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to the famous E = mc2 formula for mass–energy equivalence. The γ factor approaches infinity as v approaches c, and 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, and individual photons cannot travel faster than the speed of light.[39] This is experimentally established in many tests of relativistic energy and momentum.[40]

 
Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame.

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 10][43] 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 such as the tachyonic antitelephone.[44]

Faster-than-light observations and experiments

See also: Faster-than-light and Superluminal motion

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,[45] but phase velocity does not determine the velocity at which waves convey information.[46]

If a laser beam is swept quickly across a distant object, the spot of light can move faster than c, although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed c. However, 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. Similarly, a shadow projected onto a distant object can be made to move faster than c, after a delay in time.[47] In neither case does any matter, energy, or information travel faster than light.[48]

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.[48]

Certain quantum effects appear to be transmitted instantaneously and therefore faster than c, 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. 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.[48][49]

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.[50][51] This could result in a virtual particle crossing a large gap faster than light. However, no information can be sent using this effect.[52]

So-called superluminal motion is seen in certain astronomical objects,[53] 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.[54]

A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error.[55][56]

In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. For example, galaxies far away from Earth are inferred to be moving away from the Earth with speeds proportional to their distances. Beyond a boundary called the Hubble sphere, the rate at which their distance from Earth increases becomes greater than the speed of light.[57] These recession rates, defined as the increase in proper distance per cosmological time, are not velocities in a relativistic sense. Faster-than-light cosmological recession speeds are only a coordinate artifact.

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[58]

 

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 travel at the speed of light in vacuum.[24]

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.[32] No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon.[59] The limit obtained depends on the model used: if the massive photon is described by Proca theory,[60] the experimental upper bound for its mass is about 10−57 grams;[61] if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14 eV/c2  (roughly 2 × 10−47 g).[60]

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.[62]

In a medium

See also: Refractive index

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.[63]

 
The blue dot moves at the speed of the ripples, the phase velocity; the green dot moves with the speed of the envelope, the group velocity; and the red dot moves with the speed of the foremost part of the pulse, the front velocity.

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.[64] Denser media, such as water,[65] glass,[66] and diamond,[67] 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. 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.[68]

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.[69] 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.[70][71] In practical terms, this means that in a material with refractive index less than 1, the wave will be absorbed quickly.[72]

A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light.[73] The opposite, group velocities exceeding c, was proposed theoretically in 1993 and achieved experimentally in 2000.[74] It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.[63]

None of these options allow information to be transmitted faster than c. It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to c.[63]

It is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than c). When a charged particle does that in a dielectric material, the electromagnetic equivalent of a shock wave, known as Cherenkov radiation, is emitted.[75]

Practical effects of finiteness

The speed of light is of relevance to communications: the one-way and round-trip delay time are greater than zero. This applies from small to astronomical scales. On the other hand, some techniques depend on the finite speed of light, for example in distance measurements.

Small scales

In computers, 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 clock cycle — in practice, this distance is even shorter since the printed circuit board refracts and slows down signals. Processors must therefore be placed close to each other, as well as memory chips, to minimize communication latencies, and care must be exercised when routing wires between them to ensure signal integrity. If clock frequencies continue to increase, the speed of light may eventually become a limiting factor for the internal design of single chips.[76][77]

Large distances on Earth

Acoustic representation of the speed of light, at every beep the light makes a full circle around the equator

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 traveling in optical fibre (a transparent material) the actual transit time is longer, in part because the speed of light is slower by about 35% in optical fibre, depending on its refractive index n.[Note 11] Straight lines are rare in global communications and the travel time increases when signals pass through electronic switches or signal regenerators.[79]

Although this distance is largely irrelevant for most applications, latency becomes important in fields such as 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 radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals.[80][81]

Spaceflight and astronomy

 
A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.

Similarly, 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 crewed spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three seconds for the answer to arrive.[82]

The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets. 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 5–20 minutes later. It would then take a further 5–20 minutes for commands to travel from Earth to Mars.[83]

Receiving light and other signals from distant astronomical sources takes much longer. For example, it takes 13 billion (13×109) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra-Deep Field images.[84][85] 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.[84] 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.[86]

Astronomical distances are sometimes expressed in light-years, especially in popular science publications and media.[87] 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.[88]

Distance measurement

Main article: 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 300000 kilometres (186000 mi) 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,[89] planets[90] and spacecraft,[91] respectively, by measuring round-trip transit times.

Measurement

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. 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 1⁄299792458 of a second",[92] 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

 
Measurement of the speed of light from the time it takes Io to orbit Jupiter, using eclipses of Io by Jupiter's shadow to precisely measure its orbit.

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.[93][94] 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 difference is small, but the cumulative time becomes significant when measured over months. 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 major moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.[93]

 
Aberration of light: light from a distant source appears to be from 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.[95] 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)[96] 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.[95]

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.[97][98] 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 12] The current definition uses the recommended value in metres for the previous definition of the astronomical unit, which was determined by measurement.[97] 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).[100]

Previously, the inverse of c expressed in seconds per astronomical unit was 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 could be obtained. For example, in 2009, the best estimate, as approved by the International Astronomical Union (IAU), was:[101][102]

light time for unit distance: tau = 499.004783836(10) s,
c = 0.00200398880410(4) AU/s = 173.144632674(3) AU/d.

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.[103] Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time in terms of the previous definition of the astronomical unit can also be interpreted as measuring the length of an AU (old definition) in metres.[Note 13]

Time of flight techniques

 
One of the last and most accurate time of flight measurements, Michelson, Pease and Pearson's 1930–1935 experiment used a rotating mirror and a one-mile (1.6 km) long vacuum chamber which the light beam traversed 10 times. It achieved accuracy of ±11 km/s.
 
Diagram of the Fizeau apparatus:
  1. Light source
  2. Beam-splitting semi-transparent mirror
  3. Toothed wheel-breaker of the light beam
  4. Remote mirror
  5. Telescopic tube

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 experiments by Hippolyte Fizeau and Léon Foucault.

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.[104]

The method of Foucault replaces the cogwheel with 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.[105] Foucault used this apparatus to measure the speed of light in air versus water, based on a suggestion by François Arago.[106]

Today, 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.[107]

Electromagnetic constants

An option for deriving c that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between c and the vacuum permittivity ε0 and vacuum permeability μ0 established by Maxwell's theory: c2 = 1/(ε0μ0). The vacuum permittivity may be determined by measuring the capacitance and dimensions of a capacitor, whereas the value of the vacuum permeability was historically fixed at exactly 4π×10−7 H⋅m−1 through the definition of the ampere. Rosa and Dorsey used this method in 1907 to find a value of 299710±22 km/s. Their method depended upon having a standard unit of electrical resistance, the "international ohm", and so its accuracy was limited by how this standard was defined.[108][109]

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 to determine the wavelength of the wave. In 1946, Louis Essen and A.C. Gordon-Smith established the frequency for a variety of normal modes of microwaves of a microwave cavity of precisely known dimensions. The dimensions were established to an accuracy of about ±0.8 μm using gauges calibrated by interferometry.[108] 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.[108][110]

The Essen–Gordon-Smith result, 299792±9 km/s, was substantially more precise than those found by optical techniques.[108] By 1950, repeated measurements by Essen established a result of 299792.5±3.0 km/s.[111]

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".[112][113]

Interferometry

 
An interferometric determination of length. Left: constructive interference; Right: destructive interference.

Interferometry is another method to find the wavelength of electromagnetic radiation for determining the speed of light.[Note 14] A coherent beam of light (e.g. from a laser), with a known frequency (f), is split to follow two paths and then recombined. By adjusting the path length while observing the interference pattern and carefully measuring the change in path length, the wavelength of the light (λ) can be determined. The speed of light is then calculated using the equation c = λf.

Before the advent of laser technology, coherent radio sources were used for interferometry measurements of the speed of light.[115] 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.[116]

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.[116] 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.[116][117]

History

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, Arabic 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 postulates that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.

History of measurements of c (in m/s)
<1638 Galileo, covered lanterns inconclusive[118][119][120]: 1252 [Note 15]
<1667 Accademia del Cimento, covered lanterns inconclusive[120]: 1253 [121]
1675 Rømer and Huygens, moons of Jupiter 220000000[94][122] −27%
1729 James Bradley, aberration of light 301000000[104] +0.40%
1849 Hippolyte Fizeau, toothed wheel 315000000[104] +5.1%
1862 Léon Foucault, rotating mirror 298000000±500000[104] −0.60%
1875 Werner Siemens 260 000 000[123]
1893 Heinrich Hertz 200 000 000[124]
1907 Rosa and Dorsey, EM constants 299710000±30000[108][109] −280 ppm
1926 Albert A. Michelson, rotating mirror 299796000±4000[125] +12 ppm
1950 Essen and Gordon-Smith, cavity resonator 299792500±3000[111] +0.14 ppm
1958 K. D. Froome, radio interferometry 299792500±100[115] +0.14 ppm
1972 Evenson et al., laser interferometry 299792456.2±1.1[117] −0.006 ppm
1983 17th CGPM, definition of the metre 299792458 (exact)[92]

Early history

Empedocles (c. 490–430 BCE) was the first to propose a theory of light[126] and claimed that light has a finite speed.[127] 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".[128] 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.[129]

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.[130] This led Alhazen to propose that light must have a finite speed,[128][131][132] and that the speed of light is variable, decreasing in denser bodies.[132][133] He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from the senses.[134] 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.[135]

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.[136][137] In the 1270s, Witelo considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.[138]

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. Although this argument fails when aberration of light is taken into account, the latter was not recognized until the following century.[139] 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.[128] Despite this, in his derivation of Snell's law, Descartes assumed that some kind of motion associated with light was faster in denser media.[140][141] 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.[142]

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.[118][119] 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.[143] The actual delay in this experiment would have been about 11 microseconds.

 
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 Rømer.[93][94] 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 estimated that it takes 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 220000 km/s, which is 27% lower than the actual value.[122]

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).[144] 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.[95] 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.[95]

Connections with electromagnetism

See also: History of electromagnetic theory and History of special relativity

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.[145] His method was improved upon by Léon Foucault who obtained a value of 298000 km/s in 1862.[104] 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.[146]

In the early 1860s, Maxwell showed that, according to the theory of electromagnetism he was working on, electromagnetic waves propagate in empty space[147] 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.[148] Maxwell backed up his claim with his own experiment published in the 1868 Philosophical Transactions which determined the ratio of the electrostatic and electromagnetic units of electricity.[149]

"Luminiferous aether"

Main article: Luminiferous aether

The wave properties of light were well known since Thomas Young. In the 19th century, physicists believed light was propagating in a medium called aether (or ether). But for electric force, it looks more like the gravitational force in Newton's law. A transmitting medium was not required. After Maxwell theory unified light and electric and magnetic waves, it was favored that both light and electric magnetic waves propagate in the same aether medium (or called the luminiferous aether).[150]

 
Hendrik Lorentz (right) with Albert Einstein (1921)

It was thought at the time that empty space was filled with a background medium called the luminiferous aether in which the electromagnetic field existed. Some physicists thought that this aether acted as a preferred frame of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is the experiment performed by Albert A. Michelson and Edward W. Morley in 1887.[151][152] The detected motion was found to always be nil (within observational error). Modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second.[153]

Because of this experiment Hendrik Lorentz proposed that the motion of the apparatus through the aether may cause the apparatus to contract along its length in the direction of motion, and he further assumed that the time variable for moving systems must also be changed accordingly ("local time"), which led to the formulation of the Lorentz transformation. Based on Lorentz's aether theory, Henri Poincaré (1900) showed that this local time (to first order in v/c) is indicated by clocks moving in the aether, which are synchronized under the assumption of constant light speed. In 1904, he speculated that the speed of light could be a limiting velocity in dynamics, provided that the assumptions of Lorentz's theory are all confirmed. In 1905, Poincaré brought Lorentz's aether theory into full observational agreement with the principle of relativity.[154][155]

Special relativity

In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.[156][157]

Increased accuracy of c and redefinition of the metre and second

See also: History of the 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. 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.[111] 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.[158]

In 1972, using the laser interferometer method and the new definitions, a group at the US National Bureau of Standards in Boulder, Colorado determined the speed of light in vacuum to be c = 299792456.2±1.1 m/s. This was 100 times less uncertain than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre.[Note 16][117] As similar experiments found comparable results for c, the 15th General Conference on Weights and Measures in 1975 recommended using the value 299792458 m/s for the speed of light.[161]

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".[92]

As a result of this definition, the value of the speed of light in vacuum is exactly 299792458 m/s[162][163] and has become a defined constant in the SI system of units.[14] 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.[164][165]

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."[166] This was one of the changes that was incorporated in the 2019 redefinition of the SI base units, also termed the New SI.[167]

See also

Notes

  1. ^ Exact value: (299792458 × 60 × 60 × 24 / 149597870700) AU/day.
  2. ^ Exact value: (999992651 π / 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 1⁄299792458 second. This particular value was chosen 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 exactly 186282 miles, 698 yards, 2 feet, and 5 21/127 inches per second.
  5. ^ The exact value is 149896229/152400000 ft/ns ≈ 0.98ft/ns.
  6. ^ However, the frequency of light can depend on the motion of the source relative to the observer, due to the Doppler effect.
  7. ^ See Michelson–Morley experiment and Kennedy–Thorndike experiment, for example.
  8. ^ 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.[25]
  9. ^ Whereas moving objects are measured to be shorter along the line of relative motion, they are also seen as being rotated. This effect, known as Terrell rotation, is due to the different times that light from different parts of the object takes to reach the observer.[27][28]
  10. ^ 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,[41] and it appears the special conditions in which this effect might occur would prevent one from using it to violate causality.[42]
  11. ^ A typical value for the refractive index of optical fibre is between 1.518 and 1.538.[78]
  12. ^ 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 1⁄365.256898 of a revolution) per day.[99]
  13. ^ Nevertheless, at this degree of precision, the effects of general relativity must be taken into consideration when interpreting the length. The metre is considered to be a unit of proper length, whereas the AU is usually used as a unit of observed length in a given frame of reference. The values cited here follow the latter convention, and are TDB-compatible.[102]
  14. ^ A detailed discussion of the interferometer and its use for determining the speed of light can be found in Vaughan (1989).[114]
  15. ^ According to Galileo, the lanterns he used were "at a short distance, less than a mile". Assuming the distance was not too much shorter than a mile, and that "about a thirtieth of a second is the minimum time interval distinguishable by the unaided eye", Boyer notes that Galileo's experiment could at best be said to have established a lower limit of about 60 miles per second for the velocity of light.[119]
  16. ^ 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".[159] 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.[160]

References

  1. ^ Larson, Ron; Hostetler, Robert P. (2007). Elementary and Intermediate Algebra: A Combined Course, Student Support Edition (4th illustrated ed.). Cengage Learning. p. 197. ISBN 978-0-618-75354-3.
  2. ^ a b "Definitions of the SI base units". physics.nist.gov. 29 May 2019. Retrieved 8 February 2022.
  3. ^ Penrose, R (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books. pp. 410–411. ISBN 978-0-679-77631-4. ... the most accurate standard for the metre is conveniently defined so that there are exactly 299792458 of them to the distance travelled by light in a standard second, giving a value for the metre that very accurately matches the now inadequately precise standard metre rule in Paris.
  4. ^ Moses Fayngold (2008). Special Relativity and How it Works (illustrated ed.). John Wiley & Sons. p. 497. ISBN 978-3-527-40607-4. Extract of page 497.
  5. ^ Albert Shadowitz (1988). Special Relativity (revised ed.). Courier Corporation. p. 79. ISBN 978-0-486-65743-1. Extract of page 79.
  6. ^ Peres, Asher; Terno, Daniel R. (6 January 2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797.
  7. ^ Gibbs, Philip (1997). . The Physics and Relativity FAQ. Archived from the original on 21 August 2015.
  8. ^ a b Stachel, J. J. (2002). Einstein from "B" to "Z" – Volume 9 of Einstein studies. Springer. p. 226. ISBN 978-0-8176-4143-6.
  9. ^ See, for example:
  10. ^ Gibbs, P. (2004) [1997]. . Usenet Physics FAQ. University of California, Riverside. Archived from the original on 25 March 2010. Retrieved 16 November 2009. "The origins of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch [...] Weber apparently meant c to stand for 'constant' in his force law, but there is evidence that physicists such as Lorentz and Einstein were accustomed to a common convention that c could be used as a variable for velocity. This usage can be traced back to the classic Latin texts in which c stood for 'celeritas', meaning 'speed'."
  11. ^ Mendelson, K. S. (2006). "The story of c". American Journal of Physics. 74 (11): 995–997. Bibcode:2006AmJPh..74..995M. doi:10.1119/1.2238887.
  12. ^ See, for example:
  13. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 112, ISBN 92-822-2213-6, (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  14. ^ a b See, for example:
    • Sydenham, P. H. (2003). "Measurement of length". In Boyes, W (ed.). Instrumentation Reference Book (3rd ed.). Butterworth–Heinemann. p. 56. ISBN 978-0-7506-7123-1. ... if the speed of light is defined as a fixed number then, in principle, the time standard will serve as the length standard ...
    • "CODATA value: Speed of Light in Vacuum". The NIST reference on Constants, Units, and Uncertainty. NIST. Retrieved 21 August 2009.
    • Jespersen, J.; Fitz-Randolph, J.; Robb, J. (1999). From Sundials to Atomic Clocks: Understanding Time and Frequency (Reprint of National Bureau of Standards 1977, 2nd ed.). Courier Dover. p. 280. ISBN 978-0-486-40913-9.
  15. ^ Mermin, N. David (2005). It's About Time: Understanding Einstein's Relativity. Princeton: Princeton University Press. p. 22. ISBN 0-691-12201-6. OCLC 57283944.
  16. ^ "Nanoseconds Associated with Grace Hopper". National Museum of American History. Retrieved 1 March 2022. Grace Murray Hopper (1906–1992), a mathematician who became a naval officer and computer scientist during World War II, started distributing these wire "nanoseconds" in the late 1960s in order to demonstrate how designing smaller components would produce faster computers.
  17. ^ Lawrie, I. D. (2002). "Appendix C: Natural units". A Unified Grand Tour of Theoretical Physics (2nd ed.). CRC Press. p. 540. ISBN 978-0-7503-0604-1.
  18. ^ Hsu, L. (2006). "Appendix A: Systems of units and the development of relativity theories". A Broader View of Relativity: General Implications of Lorentz and Poincaré Invariance (2nd ed.). World Scientific. pp. 427–428. ISBN 978-981-256-651-5.
  19. ^ Einstein, A. (1905). "Zur Elektrodynamik bewegter Körper". Annalen der Physik (Submitted manuscript) (in German). 17 (10): 890–921. Bibcode:1905AnP...322..891E. doi:10.1002/andp.19053221004. English translation: Perrett, W. Walker, J (ed.). "On the Electrodynamics of Moving Bodies". Fourmilab. Translated by Jeffery, G. B. Retrieved 27 November 2009.
  20. ^ a b Hsu, J.-P.; Zhang, Y. Z. (2001). Lorentz and Poincaré Invariance. Advanced Series on Theoretical Physical Science. Vol. 8. World Scientific. pp. 543ff. ISBN 978-981-02-4721-8.
  21. ^ a b c Zhang, Y. Z. (1997). Special Relativity and Its Experimental Foundations. Advanced Series on Theoretical Physical Science. Vol. 4. World Scientific. pp. 172–173. ISBN 978-981-02-2749-4. Retrieved 23 July 2009.
  22. ^ d'Inverno, R. (1992). Introducing Einstein's Relativity. Oxford University Press. pp. 19–20. ISBN 978-0-19-859686-8.
  23. ^ Sriranjan, B. (2004). "Postulates of the special theory of relativity and their consequences". The Special Theory to Relativity. PHI Learning Pvt. Ltd. pp. 20ff. ISBN 978-81-203-1963-9.
  24. ^ a b Ellis, George F. R.; Williams, Ruth M. (2000). Flat and Curved Space-times (2nd ed.). Oxford: Oxford University Press. p. 12. ISBN 0-19-850657-0. OCLC 44694623.
  25. ^ Antonioli, Pietro; Fienberg, Richard Tresch; Fleurot, Fabrice; Fukuda, Yoshiyuki; Fulgione, Walter; Habig, Alec; Heise, Jaret; McDonald, Arthur B.; Mills, Corrinne; Namba, Toshio; Robinson, Leif J. (2 September 2004). "SNEWS: the SuperNova Early Warning System". New Journal of Physics. 6: 114. arXiv:astro-ph/0406214. Bibcode:2004NJPh....6..114A. doi:10.1088/1367-2630/6/1/114. ISSN 1367-2630. S2CID 119431247.
  26. ^ Roberts, T.; Schleif, S. (2007). Dlugosz, J. M. (ed.). . Usenet Physics FAQ. University of California, Riverside. Archived from the original on 15 October 2009. Retrieved 27 November 2009.
  27. ^ Terrell, J. (1959). "Invisibility of the Lorentz Contraction". Physical Review. 116 (4): 1041–1045. Bibcode:1959PhRv..116.1041T. doi:10.1103/PhysRev.116.1041.
  28. ^ Penrose, R. (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society. 55 (1): 137–139. Bibcode:1959PCPS...55..137P. doi:10.1017/S0305004100033776. S2CID 123023118.
  29. ^ Hartle, J. B. (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 52–59. ISBN 978-981-02-2749-4.
  30. ^ Hartle, J. B. (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. p. 332. ISBN 978-981-02-2749-4.
  31. ^ See, for example:
    • Abbott, B. P.; et al. (2017). "Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A". The Astrophysical Journal Letters. 848 (2): L13. arXiv:1710.05834. Bibcode:2017ApJ...848L..13A. doi:10.3847/2041-8213/aa920c.
    • Cornish, Neil; Blas, Diego; Nardini, Germano (18 October 2017). "Bounding the Speed of Gravity with Gravitational Wave Observations". Physical Review Letters. 119 (16): 161102. arXiv:1707.06101. Bibcode:2017PhRvL.119p1102C. doi:10.1103/PhysRevLett.119.161102. PMID 29099221. S2CID 206300556.
    • Liu, Xiaoshu; He, Vincent F.; Mikulski, Timothy M.; Palenova, Daria; Williams, Claire E.; Creighton, Jolien; Tasson, Jay D. (7 July 2020). "Measuring the speed of gravitational waves from the first and second observing run of Advanced LIGO and Advanced Virgo". Physical Review D. 102 (2): 024028. arXiv:2005.03121. Bibcode:2020PhRvD.102b4028L. doi:10.1103/PhysRevD.102.024028. S2CID 220514677.
  32. ^ a b Gibbs, P. (1997) [1996]. Carlip, S. (ed.). . Usenet Physics FAQ. University of California, Riverside. Archived from the original on 2 April 2010. Retrieved 26 November 2009.
  33. ^ Ellis, G. F. R.; Uzan, J.-P. (2005). "'c' is the speed of light, isn't it?". American Journal of Physics. 73 (3): 240–227. arXiv:gr-qc/0305099. Bibcode:2005AmJPh..73..240E. doi:10.1119/1.1819929. S2CID 119530637. The possibility that the fundamental constants may vary during the evolution of the universe offers an exceptional window onto higher dimensional theories and is probably linked with the nature of the dark energy that makes the universe accelerate today.
  34. ^ Mota, D. F. (2006). Variations of the Fine Structure Constant in Space and Time (PhD). arXiv:astro-ph/0401631. Bibcode:2004astro.ph..1631M.
  35. ^ Uzan, J.-P. (2003). "The fundamental constants and their variation: observational status and theoretical motivations". Reviews of Modern Physics. 75 (2): 403. arXiv:hep-ph/0205340. Bibcode:2003RvMP...75..403U. doi:10.1103/RevModPhys.75.403. S2CID 118684485.
  36. ^ Amelino-Camelia, G. (2013). "Quantum Gravity Phenomenology". Living Reviews in Relativity. 16 (1): 5. arXiv:0806.0339. Bibcode:2013LRR....16....5A. doi:10.12942/lrr-2013-5. PMC 5255913. PMID 28179844.
  37. ^ Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E. V.; Peters, A. (2009). "Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level". Physical Review D. 80 (100): 105011. arXiv:1002.1284. Bibcode:2009PhRvD..80j5011H. doi:10.1103/PhysRevD.80.105011. S2CID 118346408.
  38. ^ Lang, K. R. (1999). Astrophysical formulae (3rd ed.). Birkhäuser. p. 152. ISBN 978-3-540-29692-8.
  39. ^ See, for example:
    • "It's official: Time machines won't work". Los Angeles Times. 25 July 2011.
    • "HKUST Professors Prove Single Photons Do Not Exceed the Speed of Light". The Hong Kong University of Science and Technology. 19 July 2011.
    • Shanchao Zhang; J. F. Chen; Chang Liu; M. M. T. Loy; G. K. L. Wong; Shengwang Du (16 June 2011). "Optical Precursor of a Single Photon" (PDF). Physical Review Letters. 106 (243602): 243602. Bibcode:2011PhRvL.106x3602Z. doi:10.1103/physrevlett.106.243602. PMID 21770570.
  40. ^ Fowler, M. (March 2008). "Notes on Special Relativity" (PDF). University of Virginia. p. 56. Retrieved 7 May 2010.
  41. ^ See, for example:
    • Ben-Menahem, Shahar (November 1990). "Causality between conducting plates". Physics Letters B. 250 (1–2): 133–138. Bibcode:1990PhLB..250..133B. doi:10.1016/0370-2693(90)91167-A. OSTI 1449261.
    • Fearn, H. (10 November 2006). "Dispersion relations and causality: does relativistic causality require that n (ω) → 1 as ω → ∞ ?". Journal of Modern Optics. 53 (16–17): 2569–2581. Bibcode:2006JMOp...53.2569F. doi:10.1080/09500340600952085. ISSN 0950-0340. S2CID 119892992.
    • Fearn, H. (May 2007). "Can light signals travel faster than c in nontrivial vacua in flat space-time? Relativistic causality II". Laser Physics. 17 (5): 695–699. arXiv:0706.0553. Bibcode:2007LaPhy..17..695F. doi:10.1134/S1054660X07050155. ISSN 1054-660X. S2CID 61962.
  42. ^ Liberati, S.; Sonego, S.; Visser, M. (2002). "Faster-than-c signals, special relativity, and causality". Annals of Physics. 298 (1): 167–185. arXiv:gr-qc/0107091. Bibcode:2002AnPhy.298..167L. doi:10.1006/aphy.2002.6233. S2CID 48166.
  43. ^ Taylor, E. F.; Wheeler, J. A. (1992). Spacetime Physics. W. H. Freeman. pp. 74–75. ISBN 978-0-7167-2327-1.
  44. ^ Tolman, R. C. (2009) [1917]. "Velocities greater than that of light". The Theory of the Relativity of Motion (Reprint ed.). BiblioLife. p. 54. ISBN 978-1-103-17233-7.
  45. ^ Hecht, E. (1987). Optics (2nd ed.). Addison-Wesley. p. 62. ISBN 978-0-201-11609-0.
  46. ^ Quimby, R. S. (2006). Photonics and lasers: an introduction. John Wiley and Sons. p. 9. ISBN 978-0-471-71974-8.
  47. ^ Wertheim, M. (20 June 2007). "The Shadow Goes". The New York Times. Retrieved 21 August 2009.
  48. ^ a b c Gibbs, P. (1997). . Usenet Physics FAQ. University of California, Riverside. Archived from the original on 10 March 2010. Retrieved 20 August 2008.
  49. ^ See, for example:
  50. ^ Muga, J. G.; Mayato, R. S.; Egusquiza, I. L., eds. (2007). Time in Quantum Mechanics. Springer. p. 48. ISBN 978-3-540-73472-7.
  51. ^ Hernández-Figueroa, H. E.; Zamboni-Rached, M.; Recami, E. (2007). Localized Waves. Wiley Interscience. p. 26. ISBN 978-0-470-10885-7.
  52. ^ Wynne, K. (2002). (PDF). Optics Communications. 209 (1–3): 84–100. Bibcode:2002OptCo.209...85W. doi:10.1016/S0030-4018(02)01638-3. Archived from the original (PDF) on 25 March 2009.
  53. ^ Rees, M. (1966). "The Appearance of Relativistically Expanding Radio Sources". Nature. 211 (5048): 468. Bibcode:1966Natur.211..468R. doi:10.1038/211468a0. S2CID 41065207.
  54. ^ Chase, I. P. "Apparent Superluminal Velocity of Galaxies". Usenet Physics FAQ. University of California, Riverside. Retrieved 26 November 2009.
  55. ^ Reich, Eugenie Samuel (2 April 2012). "Embattled neutrino project leaders step down". Nature News. doi:10.1038/nature.2012.10371. S2CID 211730430. Retrieved 11 February 2022.
  56. ^ OPERA Collaboration (12 July 2012). "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam". Journal of High Energy Physics. 2012 (10): 93. arXiv:1109.4897. Bibcode:2012JHEP...10..093A. doi:10.1007/JHEP10(2012)093. S2CID 17652398.
  57. ^ Harrison, E. R. (2003). Masks of the Universe. Cambridge University Press. p. 206. ISBN 978-0-521-77351-5.
  58. ^ Panofsky, W. K. H.; Phillips, M. (1962). Classical Electricity and Magnetism. Addison-Wesley. p. 182. ISBN 978-0-201-05702-7.
  59. ^ See, for example:
    • Schaefer, B. E. (1999). "Severe limits on variations of the speed of light with frequency". Physical Review Letters. 82 (25): 4964–4966. arXiv:astro-ph/9810479. Bibcode:1999PhRvL..82.4964S. doi:10.1103/PhysRevLett.82.4964. S2CID 119339066.
    • Ellis, J.; Mavromatos, N. E.; Nanopoulos, D. V.; Sakharov, A. S. (2003). "Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets". Astronomy & Astrophysics. 402 (2): 409–424. arXiv:astro-ph/0210124. Bibcode:2003A&A...402..409E. doi:10.1051/0004-6361:20030263. S2CID 15388873.
    • Füllekrug, M. (2004). "Probing the Speed of Light with Radio Waves at Extremely Low Frequencies". Physical Review Letters. 93 (4): 043901. Bibcode:2004PhRvL..93d3901F. doi:10.1103/PhysRevLett.93.043901. PMID 15323762.
    • Bartlett, D. J.; Desmond, H.; Ferreira, P. G.; Jasche, J. (17 November 2021). "Constraints on quantum gravity and the photon mass from gamma ray bursts". Physical Review D. 104 (10): 103516. arXiv:2109.07850. Bibcode:2021PhRvD.104j3516B. doi:10.1103/PhysRevD.104.103516. ISSN 2470-0010. S2CID 237532210.
  60. ^ a b Adelberger, E.; Dvali, G.; Gruzinov, A. (2007). "Photon Mass Bound Destroyed by Vortices". Physical Review Letters. 98 (1): 010402. arXiv:hep-ph/0306245. Bibcode:2007PhRvL..98a0402A. doi:10.1103/PhysRevLett.98.010402. PMID 17358459. S2CID 31249827.
  61. ^ Sidharth, B. G. (2008). The Thermodynamic Universe. World Scientific. p. 134. ISBN 978-981-281-234-6.
  62. ^ Amelino-Camelia, G. (2009). "Astrophysics: Burst of support for relativity". Nature. 462 (7271): 291–292. Bibcode:2009Natur.462..291A. doi:10.1038/462291a. PMID 19924200. S2CID 205051022.
  63. ^ a b c Milonni, Peter W. (2004). Fast light, slow light and left-handed light. CRC Press. pp. 25 ff. ISBN 978-0-7503-0926-4.
  64. ^ de Podesta, M. (2002). Understanding the Properties of Matter. CRC Press. p. 131. ISBN 978-0-415-25788-6.
  65. ^ "Optical constants of H2O, D2O (Water, heavy water, ice)". refractiveindex.info. Mikhail Polyanskiy. Retrieved 7 November 2017.
  66. ^ "Optical constants of Soda lime glass". refractiveindex.info. Mikhail Polyanskiy. Retrieved 7 November 2017.
  67. ^ "Optical constants of C (Carbon, diamond, graphite)". refractiveindex.info. Mikhail Polyanskiy. Retrieved 7 November 2017.
  68. ^ Cromie, William J. (24 January 2001). . Harvard University Gazette. Archived from the original on 28 October 2011. Retrieved 8 November 2011.
  69. ^ Milonni, P. W. (2004). Fast light, slow light and left-handed light. CRC Press. p. 25. ISBN 978-0-7503-0926-4.
  70. ^ Toll, J. S. (1956). "Causality and the Dispersion Relation: Logical Foundations". Physical Review. 104 (6): 1760–1770. Bibcode:1956PhRv..104.1760T. doi:10.1103/PhysRev.104.1760.
  71. ^ Wolf, Emil (2001). "Analyticity, Causality and Dispersion Relations". Selected Works of Emil Wolf: with commentary. River Edge, N.J.: World Scientific. pp. 577–584. ISBN 978-981-281-187-5. OCLC 261134839.
  72. ^ Libbrecht, K. G.; Libbrecht, M. W. (December 2006). "Interferometric measurement of the resonant absorption and refractive index in rubidium gas" (PDF). American Journal of Physics. 74 (12): 1055–1060. Bibcode:2006AmJPh..74.1055L. doi:10.1119/1.2335476. ISSN 0002-9505.
  73. ^ See, for example:
    • Hau, L. V.; Harris, S. E.; Dutton, Z.; Behroozi, C. H. (1999). "Light speed reduction to 17 metres per second in an ultracold atomic gas" (PDF). Nature. 397 (6720): 594–598. Bibcode:1999Natur.397..594V. doi:10.1038/17561. S2CID 4423307.
    • Liu, C.; Dutton, Z.; Behroozi, C. H.; Hau, L. V. (2001). "Observation of coherent optical information storage in an atomic medium using halted light pulses" (PDF). Nature. 409 (6819): 490–493. Bibcode:2001Natur.409..490L. doi:10.1038/35054017. PMID 11206540. S2CID 1894748.
    • Bajcsy, M.; Zibrov, A. S.; Lukin, M. D. (2003). "Stationary pulses of light in an atomic medium". Nature. 426 (6967): 638–641. arXiv:quant-ph/0311092. Bibcode:2003Natur.426..638B. doi:10.1038/nature02176. PMID 14668857. S2CID 4320280.
    • Dumé, B. (2003). . Physics World. Institute of Physics. Archived from the original on 5 December 2008. Retrieved 8 December 2008.
  74. ^ See, for example:
    • Chiao, R. Y. (1993). "Superluminal (but causal) propagation of wave packets in transparent media with inverted atomic populations". Physical Review A. 48 (1): R34–R37. Bibcode:1993PhRvA..48...34C. doi:10.1103/PhysRevA.48.R34. PMID 9909684.
    • Wang, L. J.; Kuzmich, A.; Dogariu, A. (2000). "Gain-assisted superluminal light propagation". Nature. 406 (6793): 277–279. doi:10.1038/35018520. PMID 10917523. S2CID 4358601.
    • Whitehouse, D. (19 July 2000). "Beam Smashes Light Barrier". BBC News. Retrieved 9 February 2022.
    • Gbur, Greg (26 February 2008). "Light breaking its own speed limit: how 'superluminal' shenanigans work". Retrieved 9 February 2022.
  75. ^ Cherenkov, Pavel A. (1934). "Видимое свечение чистых жидкостей под действием γ-радиации" [Visible emission of pure liquids by action of γ radiation]. Doklady Akademii Nauk SSSR. 2: 451. Reprinted: Cherenkov, P. A. (1967). "Видимое свечение чистых жидкостей под действием γ-радиации" [Visible emission of pure liquids by action of γ radiation]. Usp. Fiz. Nauk. 93 (10): 385. doi:10.3367/ufnr.0093.196710n.0385., and in A. N. Gorbunov; E. P. Čerenkova, eds. (1999). Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie [Pavel Alekseyevich Čerenkov: Man and Discovery]. Moscow: Nauka. pp. 149–153.
  76. ^ Parhami, B. (1999). Introduction to parallel processing: algorithms and architectures. Plenum Press. p. 5. ISBN 978-0-306-45970-2.
  77. ^ Imbs, D.; Raynal, Michel (2009). Malyshkin, V. (ed.). Software Transactional Memories: An Approach for Multicore Programming. 10th International Conference, PaCT 2009, Novosibirsk, Russia, 31 August – 4 September 2009. Springer. p. 26. ISBN 978-3-642-03274-5.
  78. ^ Midwinter, J. E. (1991). Optical Fibers for Transmission (2nd ed.). Krieger Publishing Company. ISBN 978-0-89464-595-2.
  79. ^ . Pingdom. June 2007. Archived from the original on 2 September 2010. Retrieved 5 May 2010.
  80. ^ Buchanan, Mark (11 February 2015). "Physics in finance: Trading at the speed of light". Nature. 518 (7538): 161–163. Bibcode:2015Natur.518..161B. doi:10.1038/518161a. PMID 25673397.
  81. ^ "Time is money when it comes to microwaves". Financial Times. 10 May 2013. Archived from the original on 10 December 2022. Retrieved 25 April 2014.
  82. ^ . The Apollo 8 Flight Journal. NASA. Archived from the original on 4 January 2011. Retrieved 16 December 2010.
  83. ^ "Communications". Mars 2020 Mission Perseverance Rover. NASA. Retrieved 14 March 2020.
  84. ^ a b "Hubble Reaches the "Undiscovered Country" of Primeval Galaxies" (Press release). Space Telescope Science Institute. 5 January 2010.
  85. ^ "The Hubble Ultra Deep Field Lithograph" (PDF). NASA. Retrieved 4 February 2010.
  86. ^ Mack, Katie (2021). The End of Everything (Astrophysically Speaking). London: Penguin Books. pp. 18–19. ISBN 978-0-141-98958-7. OCLC 1180972461.
  87. ^ "The IAU and astronomical units". International Astronomical Union. Retrieved 11 October 2010.
  88. ^ Further discussion can be found at "StarChild Question of the Month for March 2000". StarChild. NASA. 2000. Retrieved 22 August 2009.
  89. ^ Dickey, J. O.; et al. (July 1994). "Lunar Laser Ranging: A Continuing Legacy of the Apollo Program" (PDF). Science. 265 (5171): 482–490. Bibcode:1994Sci...265..482D. doi:10.1126/science.265.5171.482. PMID 17781305. S2CID 10157934.
  90. ^ Standish, E. M. (February 1982). "The JPL planetary ephemerides". Celestial Mechanics. 26 (2): 181–186. Bibcode:1982CeMec..26..181S. doi:10.1007/BF01230883. S2CID 121966516.
  91. ^ Berner, J. B.; Bryant, S. H.; Kinman, P. W. (November 2007). "Range Measurement as Practiced in the Deep Space Network" (PDF). Proceedings of the IEEE. 95 (11): 2202–2214. doi:10.1109/JPROC.2007.905128. S2CID 12149700.
  92. ^ a b c "Resolution 1 of the 17th CGPM". BIPM. 1983. Retrieved 23 August 2009.
  93. ^ a b c Cohen, I. B. (1940). "Roemer and the first determination of the velocity of light (1676)". Isis. 31 (2): 327–379. doi:10.1086/347594. hdl:2027/uc1.b4375710. S2CID 145428377.
  94. ^ a b c "Demonstration tovchant le mouvement de la lumiere trouvé par M. Rŏmer de l'Académie Royale des Sciences" [Demonstration to the movement of light found by Mr. Römer of the Royal Academy of Sciences] (PDF). Journal des sçavans (in French): 233–236. 1676.
    Translated in "A demonstration concerning the motion of light, communicated from Paris, in the Journal des Sçavans, and here made English". Philosophical Transactions of the Royal Society. 12 (136): 893–895. 1677. Bibcode:1677RSPT...12..893.. doi:10.1098/rstl.1677.0024.
    Reproduced in Hutton, C.; Shaw, G.; Pearson, R., eds. (1809). "On the Motion of Light by M. Romer". The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665, in the Year 1800: Abridged. Vol. II. From 1673 to 1682. London: C. & R. Baldwin. pp. 397–398.
    The account published in Journal des sçavans was based on a report that Rømer read to the French Academy of Sciences in November 1676 (Cohen, 1940, p. 346).
  95. ^ a b c d Bradley, J. (1729). "Account of a new discovered Motion of the Fix'd Stars". Philosophical Transactions. 35: 637–660.
  96. ^ Duffett-Smith, P. (1988). Practical Astronomy with your Calculator. Cambridge University Press. p. 62. ISBN 978-0-521-35699-2. Extract of page 62.
  97. ^ a b "Resolution B2 on the re-definition of the astronomical unit of length" (PDF). International Astronomical Union. 2012.
  98. ^ "Supplement 2014: Updates to the 8th edition (2006) of the SI Brochure" (PDF). The International System of Units. International Bureau of Weights and Measures: 14. 2014.
  99. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN 92-822-2213-6, (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  100. ^ Brumfiel, Geoff (14 September 2012). "The astronomical unit gets fixed". Nature. doi:10.1038/nature.2012.11416. ISSN 1476-4687. S2CID 123424704.
  101. ^ See the following:
    • Pitjeva, E. V.; Standish, E. M. (2009). "Proposals for the masses of the three largest asteroids, the Moon–Earth mass ratio and the Astronomical Unit". Celestial Mechanics and Dynamical Astronomy. 103 (4): 365–372. Bibcode:2009CeMDA.103..365P. doi:10.1007/s10569-009-9203-8. S2CID 121374703.
    • "Astrodynamic Constants". Solar System Dynamics. Jet Propulsion Laboratory. Retrieved 10 February 2022.
  102. ^ a b IAU Working Group on Numerical Standards for Fundamental Astronomy. . US Naval Observatory. Archived from the original on 8 December 2009. Retrieved 25 September 2009.
  103. ^ . UK National Physical Laboratory. Archived from the original on 31 August 2010. Retrieved 28 October 2009.
  104. ^ a b c d e Gibbs, P. (1997). . Usenet Physics FAQ. University of California, Riverside. Archived from the original on 21 August 2015. Retrieved 13 January 2010.
  105. ^ Fowler, M. "The Speed of Light". University of Virginia. Retrieved 21 April 2010.
  106. ^ Hughes, Stephan (2012). Catchers of the Light: The Forgotten Lives of the Men and Women Who First Photographed the Heavens. ArtDeCiel Publishing. p. 210. ISBN 978-1-62050-961-6.
  107. ^ See, for example:
    • Cooke, J.; Martin, M.; McCartney, H.; Wilf, B. (1968). "Direct determination of the speed of light as a general physics laboratory experiment". American Journal of Physics. 36 (9): 847. Bibcode:1968AmJPh..36..847C. doi:10.1119/1.1975166.
    • Aoki, K.; Mitsui, T. (2008). "A small tabletop experiment for a direct measurement of the speed of light". American Journal of Physics. 76 (9): 812–815. arXiv:0705.3996. Bibcode:2008AmJPh..76..812A. doi:10.1119/1.2919743. S2CID 117454437.
    • James, M. B.; Ormond, R. B.; Stasch, A. J. (1999). "Speed of light measurement for the myriad". American Journal of Physics. 67 (8): 681–714. Bibcode:1999AmJPh..67..681J. doi:10.1119/1.19352.
  108. ^ a b c d e Essen, L.; Gordon-Smith, A. C. (1948). "The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator". Proceedings of the Royal Society of London A. 194 (1038): 348–361. Bibcode:1948RSPSA.194..348E. doi:10.1098/rspa.1948.0085. JSTOR 98293.
  109. ^ a b Rosa, E. B.; Dorsey, N. E. (1907). "A new determination of the ratio of the electromagnetic to the electrostatic unit of electricity". Bulletin of the Bureau of Standards. 3 (6): 433. doi:10.6028/bulletin.070.
  110. ^ Essen, L. (1947). "Velocity of Electromagnetic Waves". Nature. 159 (4044): 611–612. Bibcode:1947Natur.159..611E. doi:10.1038/159611a0. S2CID 4101717.
  111. ^ a b c Essen, L. (1950). "The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator". Proceedings of the Royal Society of London A. 204 (1077): 260–277. Bibcode:1950RSPSA.204..260E. doi:10.1098/rspa.1950.0172. JSTOR 98433. S2CID 121261770.
  112. ^ Stauffer, R. H. (April 1997). "Finding the Speed of Light with Marshmallows". The Physics Teacher. 35 (4): 231. Bibcode:1997PhTea..35..231S. doi:10.1119/1.2344657. Retrieved 15 February 2010.
  113. ^ "BBC Look East at the speed of light". BBC Norfolk website. Retrieved 15 February 2010.
  114. ^ Vaughan, J. M. (1989). The Fabry-Perot interferometer. CRC Press. pp. 47, 384–391. ISBN 978-0-85274-138-2.
  115. ^ a b Froome, K. D. (1958). "A New Determination of the Free-Space Velocity of Electromagnetic Waves". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 247 (1248): 109–122. Bibcode:1958RSPSA.247..109F. doi:10.1098/rspa.1958.0172. JSTOR 100591. S2CID 121444888.
  116. ^ a b c Sullivan, D. B. (2001). "Speed of Light from Direct Frequency and Wavelength Measurements". In Lide, D. R. (ed.). (PDF). CRC Press. pp. 191–193. ISBN 978-0-8493-1247-2. Archived from the original (PDF) on 13 August 2009.
  117. ^ a b c Evenson, K. M.; et al. (1972). "Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser". Physical Review Letters. 29 (19): 1346–1349. Bibcode:1972PhRvL..29.1346E. doi:10.1103/PhysRevLett.29.1346. S2CID 120300510.
  118. ^ a b Galilei, G. (1954) [1638]. . Crew, H.; de Salvio A. (trans.). Dover Publications. p. 43. ISBN 978-0-486-60099-4. Archived from the original on 30 January 2019. Retrieved 29 January 2019.
  119. ^ a b c Boyer, C. B. (1941). "Early Estimates of the Velocity of Light". Isis. 33 (1): 24. doi:10.1086/358523. S2CID 145400212.
  120. ^ a b Foschi, Renato; Leone, Matteo (2009), "Galileo, measurement of the velocity of light, and the reaction times", Perception, 38 (8): 1251–1259, doi:10.1068/p6263, hdl:2318/132957, PMID 19817156, S2CID 11747908
  121. ^ Magalotti, Lorenzo (2001) [1667], Saggi di Naturali Esperienze fatte nell' Accademia del Cimento (digital, online ed.), Florence: Istituto e Museo di Storia delle Scienze, pp. 265–266, retrieved 25 September 2015
  122. ^ a b Huygens, C. (1690). Traitée de la Lumière (in French). Pierre van der Aa. pp. 8–9.
  123. ^ Buchwald, Jed; Yeang, Chen-Pang; Stemeroff, Noah; Barton, Jenifer; Harrington, Quinn (1 March 2021). "What Heinrich Hertz discovered about electric waves in 1887–1888". Archive for History of Exact Sciences. 75 (2): 125–171. doi:10.1007/s00407-020-00260-1. ISSN 1432-0657. S2CID 253895826.
  124. ^ Hertz, Heinrich (1893). Electric Waves. London: Macmillan and Co.
  125. ^ Michelson, A. A. (1927). "Measurement of the Velocity of Light Between Mount Wilson and Mount San Antonio". The Astrophysical Journal. 65: 1. Bibcode:1927ApJ....65....1M. doi:10.1086/143021.
  126. ^ Weiner, John; Nunes, Frederico (2013). Light-Matter Interaction: Physics and Engineering at the Nanoscale (illustrated ed.). OUP Oxford. p. 1. ISBN 978-0-19-856766-0. Extract of page 1.
  127. ^ Sarton, G. (1993). Ancient science through the golden age of Greece. Courier Dover. p. 248. ISBN 978-0-486-27495-9.
  128. ^ a b c MacKay, R. H.; Oldford, R. W. (2000). "Scientific Method, Statistical Method and the Speed of Light". Statistical Science. 15 (3): 254–278. doi:10.1214/ss/1009212817. (click on "Historical background" in the table of contents)
  129. ^ Ahmed, Sherif Sayed (2014). Electronic Microwave Imaging with Planar Multistatic Arrays. Logos Verlag Berlin. p. 1. ISBN 978-3-8325-3621-3. Extract of page 1
  130. ^ Gross, C. G. (1999). "The Fire That Comes from the Eye". Neuroscientist. 5: 58–64. doi:10.1177/107385849900500108. S2CID 84148912.
  131. ^ Hamarneh, S. (1972). "Review: Hakim Mohammed Said, Ibn al-Haitham". Isis. 63 (1): 119. doi:10.1086/350861.
  132. ^ a b Lester, P. M. (2005). Visual Communication: Images With Messages. Thomson Wadsworth. pp. 10–11. ISBN 978-0-534-63720-0.
  133. ^ O'Connor, J. J.; Robertson, E. F. "Abu Ali al-Hasan ibn al-Haytham". MacTutor History of Mathematics archive. University of St Andrews. Retrieved 12 January 2010.
  134. ^ Lauginie, P. (2004). (PDF). Fifth International Conference for History of Science in Science Education. Keszthely, Hungary. pp. 75–84. Archived from the original (PDF) on 4 July 2015. Retrieved 12 August 2017.
  135. ^ O'Connor, J. J.; Robertson, E. F. "Abu han Muhammad ibn Ahmad al-Biruni". MacTutor History of Mathematics archive. University of St Andrews. Retrieved 12 January 2010.
  136. ^ Lindberg, D. C. (1996). Roger Bacon and the origins of Perspectiva in the Middle Ages: a critical edition and English translation of Bacon's Perspectiva, with introduction and notes. Oxford University Press. p. 143. ISBN 978-0-19-823992-5.
  137. ^ Lindberg, D. C. (1974). "Late Thirteenth-Century Synthesis in Optics". In Edward Grant (ed.). A source book in medieval science. Harvard University Press. p. 396. ISBN 978-0-674-82360-0.
  138. ^ Marshall, P. (1981). "Nicole Oresme on the Nature, Reflection, and Speed of Light". Isis. 72 (3): 357–374 [367–374]. doi:10.1086/352787. S2CID 144035661.
  139. ^ Sakellariadis, Spyros (1982). "Descartes' Experimental Proof of the Infinite Velocity of Light and Huygens' Rejoinder". Archive for History of Exact Sciences. 26 (1): 1–12. doi:10.1007/BF00348308. ISSN 0003-9519. JSTOR 41133639. S2CID 118187860.
  140. ^ Cajori, Florian (1922). A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories. Macmillan. p. 76.
  141. ^ Smith, A. Mark (1987). "Descartes's Theory of Light and Refraction: A Discourse on Method". Transactions of the American Philosophical Society. 77 (3): i–92. doi:10.2307/1006537. ISSN 0065-9746. JSTOR 1006537.
  142. ^ Boyer, Carl Benjamin (1959). The Rainbow: From Myth to Mathematics. Thomas Yoseloff. pp. 205–206. OCLC 763848561.
  143. ^ Foschi, Renato; Leone, Matteo (August 2009). "Galileo, Measurement of the Velocity of Light, and the Reaction Times". Perception. 38 (8): 1251–1259. doi:10.1068/p6263. hdl:2318/132957. ISSN 0301-0066. PMID 19817156. S2CID 11747908.
  144. ^ Newton, I. (1704). "Prop. XI". Optiks. The text of Prop. XI is identical between the first (1704) and second (1719) editions.
  145. ^ Guarnieri, M. (2015). "Two Millennia of Light: The Long Path to Maxwell's Waves". IEEE Industrial Electronics Magazine. 9 (2): 54–56, 60. doi:10.1109/MIE.2015.2421754. S2CID 20759821.
  146. ^ Kirchhoff, G. (1857). "Über die Bewegung der Elektricität". Ann. Phys. 178 (12): 529–244. Bibcode:1857AnP...178..529K. doi:10.1002/andp.18571781203.
  147. ^ See, for example:
    • Giordano, Nicholas J. (2009). College physics: reasoning and relationships. Cengage Learning. p. 787. ISBN 978-0-534-42471-8. Extract of page 787
    • Bergmann, Peter Gabriel (1992). The riddle of gravitation. Courier Dover Publications. p. 17. ISBN 978-0-486-27378-5. Extract of page 17
    • Bais, Sander (2005). The equations: icons of knowledge. Harvard University Press. p. 40. ISBN 978-0-674-01967-6. Extract of page 40
  148. ^ O'Connor, J. J.; Robertson, E. F. (November 1997). . School of Mathematics and Statistics, University of St Andrews. Archived from the original on 28 January 2011. Retrieved 13 October 2010.
  149. ^ Campbell, Lewis; Garnett, William; Rautio, James C. "The Life of James Clerk Maxwell", p. 544, ISBN 978-1773751399.
  150. ^ Watson, E. C. (1 September 1957). "On the Relations between Light and Electricity". American Journal of Physics. 25 (6): 335–343. Bibcode:1957AmJPh..25..335W. doi:10.1119/1.1934460. ISSN 0002-9505.
  151. ^ Consoli, Maurizio; Pluchino, Alessandro (2018). Michelson-Morley Experiments: An Enigma for Physics & The History of Science. World Scientific. pp. 118–119. ISBN 978-9-813-27818-9. Retrieved 4 May 2020.
  152. ^ Michelson, A. A.; Morley, E. W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether". American Journal of Science. 34 (203): 333–345. doi:10.1366/0003702874447824. S2CID 98374065.
  153. ^ French, A. P. (1983). Special relativity. Van Nostrand Reinhold. pp. 51–57. ISBN 978-0-442-30782-0.
  154. ^ Darrigol, O. (2000). Electrodynamics from Ampére to Einstein. Clarendon Press. ISBN 978-0-19-850594-5.
  155. ^ Galison, P. (2003). Einstein's Clocks, Poincaré's Maps: Empires of Time. W. W. Norton. ISBN 978-0-393-32604-8.
  156. ^ Miller, A. I. (1981). Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911). Addison–Wesley. ISBN 978-0-201-04679-3.
  157. ^ Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 978-0-19-520438-4.
  158. ^ . BIPM. 1967. Archived from the original on 11 April 2021. Retrieved 14 March 2021.
  159. ^ "Resolution 6 of the 15th CGPM". BIPM. 1967. Retrieved 13 October 2010.
  160. ^ Barger, R.; Hall, J. (1973). "Wavelength of the 3.39-μm laser-saturated absorption line of methane". Applied Physics Letters. 22 (4): 196. Bibcode:1973ApPhL..22..196B. doi:10.1063/1.1654608. S2CID 1841238.
  161. ^ "Resolution 2 of the 15th CGPM". BIPM. 1975. Retrieved 9 September 2009.
  162. ^ Taylor, E. F.; Wheeler, J. A. (1992). Spacetime Physics: Introduction to Special Relativity (2nd ed.). Macmillan. p. 59. ISBN 978-0-7167-2327-1.
  163. ^ Penzes, W. B. (2009). "Time Line for the Definition of the Meter" (PDF). NIST. Retrieved 11 January 2010.
  164. ^ Adams, S. (1997). Relativity: An Introduction to Space–Time Physics. CRC Press. p. 140. ISBN 978-0-7484-0621-0. One peculiar consequence of this system of definitions is that any future refinement in our ability to measure c will not change the speed of light (which is a defined number), but will change the length of the meter!
  165. ^ Rindler, W. (2006). Relativity: Special, General, and Cosmological (2nd ed.). Oxford University Press. p. 41. ISBN 978-0-19-856731-8. Note that [...] improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light!
  166. ^ . BIPM. 2011. Archived from the original on 11 August 2014.
  167. ^ See, for example:

Further reading

Historical references

Modern references

  • Brillouin, L. (1960). Wave propagation and group velocity. Academic Press.
  • Jackson, J. D. (1975). Classical Electrodynamics (2nd ed.). John Wiley & Sons. ISBN 978-0-471-30932-1.
  • Keiser, G. (2000). Optical Fiber Communications (3rd ed.). McGraw-Hill. p. 32. ISBN 978-0-07-232101-2.
  • Ng, Y. J. (2004). "Quantum Foam and Quantum Gravity Phenomenology". In Amelino-Camelia, G; Kowalski-Glikman, J (eds.). Planck Scale Effects in Astrophysics and Cosmology. Springer. pp. 321ff. ISBN 978-3-540-25263-4.
  • Helmcke, J.; Riehle, F. (2001). "Physics behind the definition of the meter". In Quinn, T. J.; Leschiutta, S.; Tavella, P. (eds.). Recent advances in metrology and fundamental constants. IOS Press. p. 453. ISBN 978-1-58603-167-1.
  • Duff, M. J. (2004). "Comment on time-variation of fundamental constants". arXiv:hep-th/0208093.

External links

 
Wikiquote has quotations related to Speed of light.
  • "Test Light Speed in Mile Long Vacuum Tube". Popular Science Monthly, September 1930, pp. 17–18.
  • Definition of the metre (International Bureau of Weights and Measures, BIPM)
  • Speed of light in vacuum (National Institute of Standards and Technology, NIST)
  • (download data gathered by Albert A. Michelson)
  • Subluminal (Java applet by Greg Egan demonstrating group velocity information limits)
  • Light discussion on adding velocities
  • Speed of Light (Sixty Symbols, University of Nottingham Department of Physics [video])
  • Speed of Light, BBC Radio 4 discussion (In Our Time, 30 November 2006)
  • Speed of Light (Live-Counter – Illustrations)
  • Speed of Light – animated demonstrations
  • "The Velocity of Light", Albert A. Nicholson, Scientific American, 28 September 1878, p. 193

May 02, 2024
speed, light, lightspeed, redirects, here, other, uses, disambiguation, lightspeed, disambiguation, speed, light, vacuum, commonly, denoted, universal, physical, constant, that, exactly, equal, metres, second, approximately, kilometres, second, miles, second, . Lightspeed redirects here For other uses see Speed of light disambiguation and Lightspeed disambiguation The speed of light in vacuum commonly denoted c is a universal physical constant that is exactly equal to 299 792 458 metres per second approximately 300 000 kilometres per second 186 000 miles per second 671 million miles per hour Note 3 According to the special theory of relativity c is the upper limit for the speed at which conventional matter or energy and thus any signal carrying information can travel through space 4 5 6 Speed of lightOn average sunlight takes 8 minutes and 17 seconds to travel from the Sun to Earth Exact valuemetres per second299792 458Approximate values to three significant digits kilometres per hour1080 000 000miles per second186000miles per hour 1 671000 000astronomical units per day173 Note 1 parsecs per year0 307 Note 2 Approximate light signal travel timesDistanceTimeone foot1 0 nsone metre3 3 nsfrom geostationary orbit to Earth119 msthe length of Earth s equator134 msfrom Moon to Earth1 3 sfrom Sun to Earth 1 AU 8 3 minone light year1 0 yearone parsec3 26 yearsfrom the nearest star to Sun 1 3 pc 4 2 yearsfrom the nearest galaxy to Earth70000 yearsacross the Milky Way87400 yearsfrom the Andromeda Galaxy to Earth2 5 million years All forms of electromagnetic radiation including visible light travel at the speed of light For many practical purposes light and other electromagnetic waves will appear to propagate instantaneously but for long distances and very sensitive measurements their finite speed has noticeable effects Any starlight viewed on Earth is from the distant past allowing humans to study the history of the universe by viewing distant objects When communicating with distant space probes it can take minutes to hours for signals to travel In computing the speed of light fixes the ultimate minimum communication delay The speed of light can be used in time of flight measurements to measure large distances to extremely high precision Ole Romer first demonstrated in 1676 that light does not travel instantaneously by studying the apparent motion of Jupiter s moon Io Progressively more accurate measurements of its speed came over the following centuries In a paper published in 1865 James Clerk Maxwell proposed that light was an electromagnetic wave and therefore travelled at speed c 7 In 1905 Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and is independent of the motion of the light source 8 He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism Massless particles and field perturbations such as gravitational waves also travel at speed c in vacuum Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer Particles with nonzero rest mass can be accelerated to approach c but can never reach it regardless of the frame of reference in which their speed is measured In the theory of relativity c interrelates space and time and appears in the famous mass energy equivalence E mc2 9 In some cases objects or waves may appear to travel faster than light e g phase velocities of waves the appearance of certain high speed astronomical objects and particular quantum effects The expansion of the universe is understood to exceed the speed of light beyond a certain boundary The speed at which light propagates through transparent materials such as glass or air is less than c similarly the speed of electromagnetic waves in wire cables is slower than c The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material n 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 Contents 1 Numerical value notation and units 1 1 Use in unit systems 2 Fundamental role in physics 2 1 Upper limit on speeds 3 Faster than light observations and experiments 4 Propagation of light 4 1 In a medium 5 Practical effects of finiteness 5 1 Small scales 5 2 Large distances on Earth 5 3 Spaceflight and astronomy 5 4 Distance measurement 6 Measurement 6 1 Astronomical measurements 6 1 1 Astronomical unit 6 2 Time of flight techniques 6 3 Electromagnetic constants 6 4 Cavity resonance 6 5 Interferometry 7 History 7 1 Early history 7 2 First measurement attempts 7 3 Connections with electromagnetism 7 4 Luminiferous aether 7 5 Special relativity 7 6 Increased accuracy of c and redefinition of the metre and second 7 7 Defined as an explicit constant 8 See also 9 Notes 10 References 11 Further reading 11 1 Historical references 11 2 Modern references 12 External linksNumerical value notation and unitsThe 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 10 11 Sometimes c is used for the speed of waves in any material medium and c 0 for the speed of light in vacuum 12 This subscripted notation which is endorsed in official SI literature 13 has the same form as related electromagnetic constants namely m0 for the vacuum permeability or magnetic constant e0 for the vacuum permittivity or electric constant and Z0 for the impedance of free space This article uses c exclusively for the speed of light in vacuum Use in unit systems Further information Metre Speed of light definition Since 1983 the constant c has been defined in the International System of Units SI as exactly 299792 458 m s this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1 299792 458 of a second By using the value of c as well as an accurate measurement of the second one can thus establish a standard for the metre 14 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 Note 5 15 16 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 17 18 Using these units c does not appear explicitly because multiplication or division by 1 does not affect the result Its unit of light second per second is still relevant even if omitted Fundamental role in physicsSee also Special relativity and One way speed of light The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer Note 6 This invariance of the speed of light was postulated by Einstein in 1905 8 after being motivated by Maxwell s theory of electromagnetism and the lack of evidence for motion against the luminiferous aether 19 It has since been consistently confirmed by many experiments Note 7 It is only possible to verify experimentally that the two way speed of light for example from a source to a mirror and back again is frame independent because it is impossible 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 at the detector should be synchronized 20 21 By adopting Einstein synchronization for the clocks the one way speed of light becomes equal to the two way speed of light by definition 20 21 The special theory of relativity explores the consequences of this invariance of c with 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 in vacuum 24 Note 8 nbsp The Lorentz factor g as a function of velocity It starts at 1 and approaches infinity as v approaches c Special relativity has many counterintuitive and experimentally verified implications 26 These include the equivalence of mass and energy E mc2 length contraction moving objects shorten Note 9 and time dilation moving clocks run more slowly The factor g by which lengths contract and times dilate is known as the Lorentz factor and is given by g 1 v2 c2 1 2 where v is the speed of the object The difference of g 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 g 2 occurs at a relative velocity of 86 6 of the speed of light v 0 866 c Similarly a time dilation factor of g 10 occurs at 99 5 the speed of light v 0 995 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 29 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 30 and observations of gravitational waves have been consistent with this prediction 31 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 can differ from c when measured from a remote frame of reference depending on how measurements are extrapolated to the region 32 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 33 34 No conclusive evidence for such changes has been found but they remain the subject of ongoing research 35 36 It is generally assumed that the two way speed of light is isotropic meaning that it has the same value regardless of the direction in which it is measured Observations of the emissions from nuclear energy levels as a function of the orientation of the emitting nuclei in a magnetic field see Hughes Drever experiment and of rotating optical resonators see Resonator experiments have put stringent limits on the possible two way anisotropy 37 38 Upper limit on speeds According to special relativity the energy of an object with rest mass m and speed v is given by gmc2 where g is the Lorentz factor defined above When v is zero g is equal to one giving rise to the famous E mc2 formula for mass energy equivalence The g factor approaches infinity as v approaches c and 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 and individual photons cannot travel faster than the speed of light 39 This is experimentally established in many tests of relativistic energy and momentum 40 nbsp Event A precedes B in the red frame is simultaneous with B in the green frame and follows B in the blue frame 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 10 43 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 such as the tachyonic antitelephone 44 Faster than light observations and experimentsSee also Faster than light and Superluminal motion 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 45 but phase velocity does not determine the velocity at which waves convey information 46 If a laser beam is swept quickly across a distant object the spot of light can move faster than c although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed c However 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 Similarly a shadow projected onto a distant object can be made to move faster than c after a delay in time 47 In neither case does any matter energy or information travel faster than light 48 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 48 Certain quantum effects appear to be transmitted instantaneously and therefore faster than c 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 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 48 49 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 50 51 This could result in a virtual particle crossing a large gap faster than light However no information can be sent using this effect 52 So called superluminal motion is seen in certain astronomical objects 53 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 54 A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error 55 56 In models of the expanding universe the farther galaxies are from each other the faster they drift apart For example galaxies far away from Earth are inferred to be moving away from the Earth with speeds proportional to their distances Beyond a boundary called the Hubble sphere the rate at which their distance from Earth increases becomes greater than the speed of light 57 These recession rates defined as the increase in proper distance per cosmological time are not velocities in a relativistic sense Faster than light cosmological recession speeds are only a coordinate artifact Propagation of lightIn 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 e0 and the magnetic constant m0 by the equation 58 c 1 e 0 m 0 displaystyle c frac 1 sqrt varepsilon 0 mu 0 nbsp 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 travel at the speed of light in vacuum 24 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 32 No variation of the speed of light with frequency has been observed in rigorous testing putting stringent limits on the mass of the photon 59 The limit obtained depends on the model used if the massive photon is described by Proca theory 60 the experimental upper bound for its mass is about 10 57 grams 61 if photon mass is generated by a Higgs mechanism the experimental upper limit is less sharp m 10 14 eV c2 roughly 2 10 47 g 60 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 62 In a medium See also Refractive index 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 63 nbsp The blue dot moves at the speed of the ripples the phase velocity the green dot moves with the speed of the envelope the group velocity and the red dot moves with the speed of the foremost part of the pulse the front velocity 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 64 Denser media such as water 65 glass 66 and diamond 67 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 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 68 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 69 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 70 71 In practical terms this means that in a material with refractive index less than 1 the wave will be absorbed quickly 72 A pulse with different group and phase velocities which occurs if the phase velocity is not the same for all the frequencies of the pulse smears out over time a process known as dispersion Certain materials have an exceptionally low or even zero group velocity for light waves a phenomenon called slow light 73 The opposite group velocities exceeding c was proposed theoretically in 1993 and achieved experimentally in 2000 74 It should even be possible for the group velocity to become infinite or negative with pulses travelling instantaneously or backwards in time 63 None of these options allow information to be transmitted faster than c It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse the front velocity It can be shown that this is under certain assumptions always equal to c 63 It is possible for a particle to travel through a medium faster than the phase velocity of light in that medium but still slower than c When a charged particle does that in a dielectric material the electromagnetic equivalent of a shock wave known as Cherenkov radiation is emitted 75 Practical effects of finitenessThe speed of light is of relevance to communications the one way and round trip delay time are greater than zero This applies from small to astronomical scales On the other hand some techniques depend on the finite speed of light for example in distance measurements Small scales In computers 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 clock cycle in practice this distance is even shorter since the printed circuit board refracts and slows down signals Processors must therefore be placed close to each other as well as memory chips to minimize communication latencies and care must be exercised when routing wires between them to ensure signal integrity If clock frequencies continue to increase the speed of light may eventually become a limiting factor for the internal design of single chips 76 77 Large distances on Earth source source Acoustic representation of the speed of light at every beep the light makes a full circle around the equator 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 traveling in optical fibre a transparent material the actual transit time is longer in part because the speed of light is slower by about 35 in optical fibre depending on its refractive index n Note 11 Straight lines are rare in global communications and the travel time increases when signals pass through electronic switches or signal regenerators 79 Although this distance is largely irrelevant for most applications latency becomes important in fields such as 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 radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals 80 81 Spaceflight and astronomy nbsp A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them 1 255 seconds at their mean orbital surface to surface distance The relative sizes and separation of the Earth Moon system are shown to scale Similarly 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 crewed spacecraft to orbit the Moon for every question the ground control station had to wait at least three seconds for the answer to arrive 82 The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets 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 5 20 minutes later It would then take a further 5 20 minutes for commands to travel from Earth to Mars 83 Receiving light and other signals from distant astronomical sources takes much longer For example it takes 13 billion 13 109 years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images 84 85 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 84 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 86 Astronomical distances are sometimes expressed in light years especially in popular science publications and media 87 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 88 Distance measurement Main article 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 300000 kilometres 186000 mi 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 89 planets 90 and spacecraft 91 respectively by measuring round trip transit times MeasurementThere 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 It is also possible to determine c from other physical laws where it appears for example by determining the values of the electromagnetic constants e0 and m0 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 1 299792 458 of a second 92 fixing the value of the speed of light at 299792 458 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 nbsp Measurement of the speed of light from the time it takes Io to orbit Jupiter using eclipses of Io by Jupiter s shadow to precisely measure its orbit 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 Romer used an astronomical measurement to make the first quantitative estimate of the speed of light in the year 1676 93 94 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 difference is small but the cumulative time becomes significant when measured over months 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 Romer observed this effect for Jupiter s innermost major moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth s orbit 93 nbsp Aberration of light light from a distant source appears to be from 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 95 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 96 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 95 Astronomical unit An astronomical unit AU is approximately the average distance between the Earth and Sun It was redefined in 2012 as exactly 149597 870 700 m 97 98 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 12 The current definition uses the recommended value in metres for the previous definition of the astronomical unit which was determined by measurement 97 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 100 Previously the inverse of c expressed in seconds per astronomical unit was 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 could be obtained For example in 2009 the best estimate as approved by the International Astronomical Union IAU was 101 102 light time for unit distance tau 499 004783 836 10 s c 0 002003 988 804 10 4 AU s 173 144632 674 3 AU d 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 103 Since the metre is defined to be the length travelled by light in a certain time interval the measurement of the light time in terms of the previous definition of the astronomical unit can also be interpreted as measuring the length of an AU old definition in metres Note 13 Time of flight techniques nbsp One of the last and most accurate time of flight measurements Michelson Pease and Pearson s 1930 1935 experiment used a rotating mirror and a one mile 1 6 km long vacuum chamber which the light beam traversed 10 times It achieved accuracy of 11 km s nbsp Diagram of the Fizeau apparatus Light sourceBeam splitting semi transparent mirrorToothed wheel breaker of the light beamRemote mirrorTelescopic tube 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 experiments by Hippolyte Fizeau and Leon Foucault 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 104 The method of Foucault replaces the cogwheel with 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 105 Foucault used this apparatus to measure the speed of light in air versus water based on a suggestion by Francois Arago 106 Today 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 107 Electromagnetic constants An option for deriving c that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between c and the vacuum permittivity e0 and vacuum permeability m0 established by Maxwell s theory c2 1 e0m0 The vacuum permittivity may be determined by measuring the capacitance and dimensions of a capacitor whereas the value of the vacuum permeability was historically fixed at exactly 4p 10 7 H m 1 through the definition of the ampere Rosa and Dorsey used this method in 1907 to find a value of 299710 22 km s Their method depended upon having a standard unit of electrical resistance the international ohm and so its accuracy was limited by how this standard was defined 108 109 Cavity resonance nbsp Electromagnetic standing waves in a cavity Another way to measure the speed of light is to independently measure the frequency f and wavelength l of an electromagnetic wave in vacuum The value of c can then be found by using the relation c fl 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 to determine the wavelength of the wave In 1946 Louis Essen and A C Gordon Smith established the frequency for a variety of normal modes of microwaves of a microwave cavity of precisely known dimensions The dimensions were established to an accuracy of about 0 8 mm using gauges calibrated by interferometry 108 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 108 110 The Essen Gordon Smith result 299792 9 km s was substantially more precise than those found by optical techniques 108 By 1950 repeated measurements by Essen established a result of 299792 5 3 0 km s 111 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 112 113 Interferometry nbsp An interferometric determination of length Left constructive interference Right destructive interference Interferometry is another method to find the wavelength of electromagnetic radiation for determining the speed of light Note 14 A coherent beam of light e g from a laser with a known frequency f is split to follow two paths and then recombined By adjusting the path length while observing the interference pattern and carefully measuring the change in path length the wavelength of the light l can be determined The speed of light is then calculated using the equation c lf Before the advent of laser technology coherent radio sources were used for interferometry measurements of the speed of light 115 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 116 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 116 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 9 116 117 HistoryUntil 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 Arabic scholars and classical European scientists long debated this until Romer provided the first calculation of the speed of light Einstein s theory of special relativity postulates that the speed of light is constant regardless of one s frame of reference Since then scientists have provided increasingly accurate measurements History of measurements of c in m s lt 1638 Galileo covered lanterns inconclusive 118 119 120 1252 Note 15 lt 1667 Accademia del Cimento covered lanterns inconclusive 120 1253 121 1675 Romer and Huygens moons of Jupiter 220000 000 94 122 27 1729 James Bradley aberration of light 301000 000 104 0 40 1849 Hippolyte Fizeau toothed wheel 315000 000 104 5 1 1862 Leon Foucault rotating mirror 298000 000 500000 104 0 60 1875 Werner Siemens 260 000 000 123 1893 Heinrich Hertz 200 000 000 124 1907 Rosa and Dorsey EM constants 299710 000 30000 108 109 280 ppm 1926 Albert A Michelson rotating mirror 299796 000 4000 125 12 ppm 1950 Essen and Gordon Smith cavity resonator 299792 500 3000 111 0 14 ppm 1958 K D Froome radio interferometry 299792 500 100 115 0 14 ppm 1972 Evenson et al laser interferometry 299792 456 2 1 1 117 0 006 ppm 1983 17th CGPM definition of the metre 299792 458 exact 92 Early history Empedocles c 490 430 BCE was the first to propose a theory of light 126 and claimed that light has a finite speed 127 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 128 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 129 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 130 This led Alhazen to propose that light must have a finite speed 128 131 132 and that the speed of light is variable decreasing in denser bodies 132 133 He argued that light is substantial matter the propagation of which requires time even if this is hidden from the senses 134 Also in the 11th century Abu Rayhan al Biruni agreed that light has a finite speed and observed that the speed of light is much faster than the speed of sound 135 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 136 137 In the 1270s Witelo considered the possibility of light travelling at infinite speed in vacuum but slowing down in denser bodies 138 In the early 17th century Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it Rene 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 Although this argument fails when aberration of light is taken into account the latter was not recognized until the following century 139 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 128 Despite this in his derivation of Snell s law Descartes assumed that some kind of motion associated with light was faster in denser media 140 141 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 142 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 118 119 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 143 The actual delay in this experiment would have been about 11 microseconds nbsp Romer s observations of the occultations of Io from Earth The first quantitative estimate of the speed of light was made in 1676 by Ole Romer 93 94 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 estimated that it takes 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 220000 km s which is 27 lower than the actual value 122 In his 1704 book Opticks Isaac Newton reported Romer 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 144 Newton queried whether Romer 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 95 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 95 Connections with electromagnetism See also History of electromagnetic theory and History of special relativity 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 145 His method was improved upon by Leon Foucault who obtained a value of 298000 km s in 1862 104 In the year 1856 Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge 1 e0m0 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 146 In the early 1860s Maxwell showed that according to the theory of electromagnetism he was working on electromagnetic waves propagate in empty space 147 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 148 Maxwell backed up his claim with his own experiment published in the 1868 Philosophical Transactions which determined the ratio of the electrostatic and electromagnetic units of electricity 149 Luminiferous aether Main article Luminiferous aetherThe wave properties of light were well known since Thomas Young In the 19th century physicists believed light was propagating in a medium called aether or ether But for electric force it looks more like the gravitational force in Newton s law A transmitting medium was not required After Maxwell theory unified light and electric and magnetic waves it was favored that both light and electric magnetic waves propagate in the same aether medium or called the luminiferous aether 150 nbsp Hendrik Lorentz right with Albert Einstein 1921 It was thought at the time that empty space was filled with a background medium called the luminiferous aether in which the electromagnetic field existed Some physicists thought that this aether acted as a preferred frame of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium by measuring the isotropy of the speed of light Beginning in the 1880s several experiments were performed to try to detect this motion the most famous of which is the experiment performed by Albert A Michelson and Edward W Morley in 1887 151 152 The detected motion was found to always be nil within observational error Modern experiments indicate that the two way speed of light is isotropic the same in every direction to within 6 nanometres per second 153 Because of this experiment Hendrik Lorentz proposed that the motion of the apparatus through the aether may cause the apparatus to contract along its length in the direction of motion and he further assumed that the time variable for moving systems must also be changed accordingly local time which led to the formulation of the Lorentz transformation Based on Lorentz s aether theory Henri Poincare 1900 showed that this local time to first order in v c is indicated by clocks moving in the aether which are synchronized under the assumption of constant light speed In 1904 he speculated that the speed of light could be a limiting velocity in dynamics provided that the assumptions of Lorentz s theory are all confirmed In 1905 Poincare brought Lorentz s aether theory into full observational agreement with the principle of relativity 154 155 Special relativity In 1905 Einstein postulated from the outset that the speed of light in vacuum measured by a non accelerating observer is independent of the motion of the source or observer Using this and the principle of relativity as a basis he derived the special theory of relativity in which the speed of light in vacuum c featured as a fundamental constant also appearing in contexts unrelated to light This made the concept of the stationary aether to which Lorentz and Poincare still adhered useless and revolutionized the concepts of space and time 156 157 Increased accuracy of c and redefinition of the metre and second See also History of the 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 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 111 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 133 158 In 1972 using the laser interferometer method and the new definitions a group at the US National Bureau of Standards in Boulder Colorado determined the speed of light in vacuum to be c 299792 456 2 1 1 m s This was 100 times less uncertain than the previously accepted value The remaining uncertainty was mainly related to the definition of the metre Note 16 117 As similar experiments found comparable results for c the 15th General Conference on Weights and Measures in 1975 recommended using the value 299792 458 m s for the speed of light 161 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 299792 458 of a second 92 As a result of this definition the value of the speed of light in vacuum is exactly 299792 458 m s 162 163 and has become a defined constant in the SI system of units 14 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 164 165 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 299792 458 when it is expressed in the SI unit m s 1 166 This was one of the changes that was incorporated in the 2019 redefinition of the SI base units also termed the New SI 167 See also nbsp Physics portal nbsp Astronomy portal nbsp Outer space portal Light second Speed of electricity Speed of gravity Speed of sound Velocity factor Warp factor fictional Notes Exact value 299792 458 60 60 24 149597 870 700 AU day Exact value 999992 651 p 10246 429 500 pc y 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 1 299792 458 second This particular value was chosen 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 9192 631 770 cycles of the radiation emitted by a caesium 133 atom in a transition between two specified energy states 2 The speed of light in imperial and United States customary units is based on an inch of exactly 2 54 cm and is exactly 299792 458 m s 100 cm m 1 2 54 in cm which is exactly 186282 miles 698 yards 2 feet and 5 21 127 inches per second The exact value is 149896 229 152400 000 ft ns 0 98ft ns However the frequency of light can depend on the motion of the source relative to the observer due to the Doppler effect See Michelson Morley experiment and Kennedy Thorndike experiment for example 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 25 Whereas moving objects are measured to be shorter along the line of relative motion they are also seen as being rotated This effect known as Terrell rotation is due to the different times that light from different parts of the object takes to reach the observer 27 28 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 41 and it appears the special conditions in which this effect might occur would prevent one from using it to violate causality 42 A typical value for the refractive index of optical fibre is between 1 518 and 1 538 78 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 017202 098 95 radians approximately 1 365 256898 of a revolution per day 99 Nevertheless at this degree of precision the effects of general relativity must be taken into consideration when interpreting the length The metre is considered to be a unit of proper length whereas the AU is usually used as a unit of observed length in a given frame of reference The values cited here follow the latter convention and are TDB compatible 102 A detailed discussion of the interferometer and its use for determining the speed of light can be found in Vaughan 1989 114 According to Galileo the lanterns he used were at a short distance less than a mile Assuming the distance was not too much shorter than a mile and that about a thirtieth of a second is the minimum time interval distinguishable by the unaided eye Boyer notes that Galileo s experiment could at best be said to have established a lower limit of about 60 miles per second for the velocity of light 119 Between 1960 and 1983 the metre was defined as the length equal to 1650 763 73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom 159 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 160 References Larson Ron Hostetler Robert P 2007 Elementary and Intermediate Algebra A Combined Course Student Support Edition 4th illustrated ed Cengage Learning p 197 ISBN 978 0 618 75354 3 a b Definitions of the SI base units physics nist gov 29 May 2019 Retrieved 8 February 2022 Penrose R 2004 The Road to Reality A Complete Guide to the Laws of the Universe Vintage Books pp 410 411 ISBN 978 0 679 77631 4 the most accurate standard for the metre is conveniently defined so that there are exactly 299792 458 of them to the distance travelled by light in a standard second giving a value for the metre that very accurately matches the now inadequately precise standard metre rule in Paris Moses Fayngold 2008 Special Relativity and How it Works illustrated ed John Wiley amp Sons p 497 ISBN 978 3 527 40607 4 Extract of page 497 Albert Shadowitz 1988 Special Relativity revised ed Courier Corporation p 79 ISBN 978 0 486 65743 1 Extract of page 79 Peres Asher Terno Daniel R 6 January 2004 Quantum information and relativity theory Reviews of Modern Physics 76 1 93 123 arXiv quant ph 0212023 Bibcode 2004RvMP 76 93P doi 10 1103 RevModPhys 76 93 ISSN 0034 6861 S2CID 7481797 Gibbs Philip 1997 How is the speed of light measured The Physics and Relativity FAQ Archived from the original on 21 August 2015 a b Stachel J J 2002 Einstein from B to Z Volume 9 of Einstein studies Springer p 226 ISBN 978 0 8176 4143 6 See for example Feigenbaum Mitchell J Mermin N David January 1988 E mc2 American Journal of Physics 56 1 18 21 Bibcode 1988AmJPh 56 18F doi 10 1119 1 15422 ISSN 0002 9505 Uzan J P Leclercq B 2008 The Natural Laws of the Universe Understanding Fundamental Constants Springer pp 43 44 ISBN 978 0 387 73454 5 Gibbs P 2004 1997 Why is c the symbol for the speed of light Usenet Physics FAQ University of California Riverside Archived from the original on 25 March 2010 Retrieved 16 November 2009 The origins of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch Weber apparently meant c to stand for constant in his force law but there is evidence that physicists such as Lorentz and Einstein were accustomed to a common convention that c could be used as a variable for velocity This usage can be traced back to the classic Latin texts in which c stood for celeritas meaning speed Mendelson K S 2006 The story of c American Journal of Physics 74 11 995 997 Bibcode 2006AmJPh 74 995M doi 10 1119 1 2238887 See for example Lide D R 2004 CRC Handbook of Chemistry and Physics CRC Press pp 2 9 ISBN 978 0 8493 0485 9 Harris J W et al 2002 Handbook of Physics Springer p 499 ISBN 978 0 387 95269 7 Whitaker J C 2005 The Electronics Handbook CRC Press p 235 ISBN 978 0 8493 1889 4 Cohen E R et al 2007 Quantities Units and Symbols in Physical Chemistry 3rd ed Royal Society of Chemistry p 184 ISBN 978 0 85404 433 7 International Bureau of Weights and Measures 2006 The International System of Units SI PDF 8th ed p 112 ISBN 92 822 2213 6 archived PDF from the original on 4 June 2021 retrieved 16 December 2021 a b See for example Sydenham P H 2003 Measurement of length In Boyes W ed Instrumentation Reference Book 3rd ed Butterworth Heinemann p 56 ISBN 978 0 7506 7123 1 if the speed of light is defined as a fixed number then in principle the time standard will serve as the length standard CODATA value Speed of Light in Vacuum The NIST reference on Constants Units and Uncertainty NIST Retrieved 21 August 2009 Jespersen J Fitz Randolph J Robb J 1999 From Sundials to Atomic Clocks Understanding Time and Frequency Reprint of National Bureau of Standards 1977 2nd ed Courier Dover p 280 ISBN 978 0 486 40913 9 Mermin N David 2005 It s About Time Understanding Einstein s Relativity Princeton Princeton University Press p 22 ISBN 0 691 12201 6 OCLC 57283944 Nanoseconds Associated with Grace Hopper National Museum of American History Retrieved 1 March 2022 Grace Murray Hopper 1906 1992 a mathematician who became a naval officer and computer scientist during World War II started distributing these wire nanoseconds in the late 1960s in order to demonstrate how designing smaller components would produce faster computers Lawrie I D 2002 Appendix C Natural units A Unified Grand Tour of Theoretical Physics 2nd ed CRC Press p 540 ISBN 978 0 7503 0604 1 Hsu L 2006 Appendix A Systems of units and the development of relativity theories A Broader View of Relativity General Implications of Lorentz and Poincare Invariance 2nd ed World Scientific pp 427 428 ISBN 978 981 256 651 5 Einstein A 1905 Zur Elektrodynamik bewegter Korper Annalen der Physik Submitted manuscript in German 17 10 890 921 Bibcode 1905AnP 322 891E doi 10 1002 andp 19053221004 English translation Perrett W Walker J ed On the Electrodynamics of Moving Bodies Fourmilab Translated by Jeffery G B Retrieved 27 November 2009 a b Hsu J P Zhang Y Z 2001 Lorentz and Poincare Invariance Advanced Series on Theoretical Physical Science Vol 8 World Scientific pp 543ff ISBN 978 981 02 4721 8 a b c Zhang Y Z 1997 Special Relativity and Its Experimental Foundations Advanced Series on Theoretical Physical Science Vol 4 World Scientific pp 172 173 ISBN 978 981 02 2749 4 Retrieved 23 July 2009 d Inverno R 1992 Introducing Einstein s Relativity Oxford University Press pp 19 20 ISBN 978 0 19 859686 8 Sriranjan B 2004 Postulates of the special theory of relativity and their consequences The Special Theory to Relativity PHI Learning Pvt Ltd pp 20ff ISBN 978 81 203 1963 9 a b Ellis George F R Williams Ruth M 2000 Flat and Curved Space times 2nd ed Oxford Oxford University Press p 12 ISBN 0 19 850657 0 OCLC 44694623 Antonioli Pietro Fienberg Richard Tresch Fleurot Fabrice Fukuda Yoshiyuki Fulgione Walter Habig Alec Heise Jaret McDonald Arthur B Mills Corrinne Namba Toshio Robinson Leif J 2 September 2004 SNEWS the SuperNova Early Warning System New Journal of Physics 6 114 arXiv astro ph 0406214 Bibcode 2004NJPh 6 114A doi 10 1088 1367 2630 6 1 114 ISSN 1367 2630 S2CID 119431247 Roberts T Schleif S 2007 Dlugosz J M ed What is the experimental basis of Special Relativity Usenet Physics FAQ University of California Riverside Archived from the original on 15 October 2009 Retrieved 27 November 2009 Terrell J 1959 Invisibility of the Lorentz Contraction Physical Review 116 4 1041 1045 Bibcode 1959PhRv 116 1041T doi 10 1103 PhysRev 116 1041 Penrose R 1959 The Apparent Shape of a Relativistically Moving Sphere Proceedings of the Cambridge Philosophical Society 55 1 137 139 Bibcode 1959PCPS 55 137P doi 10 1017 S0305004100033776 S2CID 123023118 Hartle J B 2003 Gravity An Introduction to Einstein s General Relativity Addison Wesley pp 52 59 ISBN 978 981 02 2749 4 Hartle J B 2003 Gravity An Introduction to Einstein s General Relativity Addison Wesley p 332 ISBN 978 981 02 2749 4 See for example Abbott B P et al 2017 Gravitational Waves and Gamma Rays from a Binary Neutron Star Merger GW170817 and GRB 170817A The Astrophysical Journal Letters 848 2 L13 arXiv 1710 05834 Bibcode 2017ApJ 848L 13A doi 10 3847 2041 8213 aa920c Cornish Neil Blas Diego Nardini Germano 18 October 2017 Bounding the Speed of Gravity with Gravitational Wave Observations Physical Review Letters 119 16 161102 arXiv 1707 06101 Bibcode 2017PhRvL 119p1102C doi 10 1103 PhysRevLett 119 161102 PMID 29099221 S2CID 206300556 Liu Xiaoshu He Vincent F Mikulski Timothy M Palenova Daria Williams Claire E Creighton Jolien Tasson Jay D 7 July 2020 Measuring the speed of gravitational waves from the first and second observing run of Advanced LIGO and Advanced Virgo Physical Review D 102 2 024028 arXiv 2005 03121 Bibcode 2020PhRvD 102b4028L doi 10 1103 PhysRevD 102 024028 S2CID 220514677 a b Gibbs P 1997 1996 Carlip S ed Is The Speed of Light Constant Usenet Physics FAQ University of California Riverside Archived from the original on 2 April 2010 Retrieved 26 November 2009 Ellis G F R Uzan J P 2005 c is the speed of light isn t it American Journal of Physics 73 3 240 227 arXiv gr qc 0305099 Bibcode 2005AmJPh 73 240E doi 10 1119 1 1819929 S2CID 119530637 The possibility that the fundamental constants may vary during the evolution of the universe offers an exceptional window onto higher dimensional theories and is probably linked with the nature of the dark energy that makes the universe accelerate today Mota D F 2006 Variations of the Fine Structure Constant in Space and Time PhD arXiv astro ph 0401631 Bibcode 2004astro ph 1631M Uzan J P 2003 The fundamental constants and their variation observational status and theoretical motivations Reviews of Modern Physics 75 2 403 arXiv hep ph 0205340 Bibcode 2003RvMP 75 403U doi 10 1103 RevModPhys 75 403 S2CID 118684485 Amelino Camelia G 2013 Quantum Gravity Phenomenology Living Reviews in Relativity 16 1 5 arXiv 0806 0339 Bibcode 2013LRR 16 5A doi 10 12942 lrr 2013 5 PMC 5255913 PMID 28179844 Herrmann S Senger A Mohle K Nagel M Kovalchuk E V Peters A 2009 Rotating optical cavity experiment testing Lorentz invariance at the 10 17 level Physical Review D 80 100 105011 arXiv 1002 1284 Bibcode 2009PhRvD 80j5011H doi 10 1103 PhysRevD 80 105011 S2CID 118346408 Lang K R 1999 Astrophysical formulae 3rd ed Birkhauser p 152 ISBN 978 3 540 29692 8 See for example It s official Time machines won t work Los Angeles Times 25 July 2011 HKUST Professors Prove Single Photons Do Not Exceed the Speed of Light The Hong Kong University of Science and Technology 19 July 2011 Shanchao Zhang J F Chen Chang Liu M M T Loy G K L Wong Shengwang Du 16 June 2011 Optical Precursor of a Single Photon PDF Physical Review Letters 106 243602 243602 Bibcode 2011PhRvL 106x3602Z doi 10 1103 physrevlett 106 243602 PMID 21770570 Fowler M March 2008 Notes on Special Relativity PDF University of Virginia p 56 Retrieved 7 May 2010 See for example Ben Menahem Shahar November 1990 Causality between conducting plates Physics Letters B 250 1 2 133 138 Bibcode 1990PhLB 250 133B doi 10 1016 0370 2693 90 91167 A OSTI 1449261 Fearn H 10 November 2006 Dispersion relations and causality does relativistic causality require that n w 1 as w Journal of Modern Optics 53 16 17 2569 2581 Bibcode 2006JMOp 53 2569F doi 10 1080 09500340600952085 ISSN 0950 0340 S2CID 119892992 Fearn H May 2007 Can light signals travel faster than c in nontrivial vacua in flat space time Relativistic causality II Laser Physics 17 5 695 699 arXiv 0706 0553 Bibcode 2007LaPhy 17 695F doi 10 1134 S1054660X07050155 ISSN 1054 660X S2CID 61962 Liberati S Sonego S Visser M 2002 Faster than c signals special relativity and causality Annals of Physics 298 1 167 185 arXiv gr qc 0107091 Bibcode 2002AnPhy 298 167L doi 10 1006 aphy 2002 6233 S2CID 48166 Taylor E F Wheeler J A 1992 Spacetime Physics W H Freeman pp 74 75 ISBN 978 0 7167 2327 1 Tolman R C 2009 1917 Velocities greater than that of light The Theory of the Relativity of Motion Reprint ed BiblioLife p 54 ISBN 978 1 103 17233 7 Hecht E 1987 Optics 2nd ed Addison Wesley p 62 ISBN 978 0 201 11609 0 Quimby R S 2006 Photonics and lasers an introduction John Wiley and Sons p 9 ISBN 978 0 471 71974 8 Wertheim M 20 June 2007 The Shadow Goes The New York Times Retrieved 21 August 2009 a b c Gibbs P 1997 Is Faster Than Light Travel or Communication Possible Usenet Physics FAQ University of California Riverside Archived from the original on 10 March 2010 Retrieved 20 August 2008 See for example Sakurai J J 1994 Tuan S F ed Modern Quantum Mechanics Revised ed Addison Wesley pp 231 232 ISBN 978 0 201 53929 5 Peres Asher 1993 Quantum Theory Concepts and Methods Kluwer p 170 ISBN 0 7923 2549 4 OCLC 28854083 Caves Carlton M 2015 Quantum Information Science Emerging No More OSA Century of Optics Optica pp 320 326 arXiv 1302 1864 ISBN 978 1 943 58004 0 I t was natural to dream that quantum correlations could be used for faster than light communication but this speculation was quickly shot down and the shooting established the principle that quantum states cannot be copied Muga J G Mayato R S Egusquiza I L eds 2007 Time in Quantum Mechanics Springer p 48 ISBN 978 3 540 73472 7 Hernandez Figueroa H E Zamboni Rached M Recami E 2007 Localized Waves Wiley Interscience p 26 ISBN 978 0 470 10885 7 Wynne K 2002 Causality and the nature of information PDF Optics Communications 209 1 3 84 100 Bibcode 2002OptCo 209 85W doi 10 1016 S0030 4018 02 01638 3 Archived from the original PDF on 25 March 2009 Rees M 1966 The Appearance of Relativistically Expanding Radio Sources Nature 211 5048 468 Bibcode 1966Natur 211 468R doi 10 1038 211468a0 S2CID 41065207 Chase I P Apparent Superluminal Velocity of Galaxies Usenet Physics FAQ University of California Riverside Retrieved 26 November 2009 Reich Eugenie Samuel 2 April 2012 Embattled neutrino project leaders step down Nature News doi 10 1038 nature 2012 10371 S2CID 211730430 Retrieved 11 February 2022 OPERA Collaboration 12 July 2012 Measurement of the neutrino velocity with the OPERA detector in the CNGS beam Journal of High Energy Physics 2012 10 93 arXiv 1109 4897 Bibcode 2012JHEP 10 093A doi 10 1007 JHEP10 2012 093 S2CID 17652398 Harrison E R 2003 Masks of the Universe Cambridge University Press p 206 ISBN 978 0 521 77351 5 Panofsky W K H Phillips M 1962 Classical Electricity and Magnetism Addison Wesley p 182 ISBN 978 0 201 05702 7 See for example Schaefer B E 1999 Severe limits on variations of the speed of light with frequency Physical Review Letters 82 25 4964 4966 arXiv astro ph 9810479 Bibcode 1999PhRvL 82 4964S doi 10 1103 PhysRevLett 82 4964 S2CID 119339066 Ellis J Mavromatos N E Nanopoulos D V Sakharov A S 2003 Quantum Gravity Analysis of Gamma Ray Bursts using Wavelets Astronomy amp Astrophysics 402 2 409 424 arXiv astro ph 0210124 Bibcode 2003A amp A 402 409E doi 10 1051 0004 6361 20030263 S2CID 15388873 Fullekrug M 2004 Probing the Speed of Light with Radio Waves at Extremely Low Frequencies Physical Review Letters 93 4 043901 Bibcode 2004PhRvL 93d3901F doi 10 1103 PhysRevLett 93 043901 PMID 15323762 Bartlett D J Desmond H Ferreira P G Jasche J 17 November 2021 Constraints on quantum gravity and the photon mass from gamma ray bursts Physical Review D 104 10 103516 arXiv 2109 07850 Bibcode 2021PhRvD 104j3516B doi 10 1103 PhysRevD 104 103516 ISSN 2470 0010 S2CID 237532210 a b Adelberger E Dvali G Gruzinov A 2007 Photon Mass Bound Destroyed by Vortices Physical Review Letters 98 1 010402 arXiv hep ph 0306245 Bibcode 2007PhRvL 98a0402A doi 10 1103 PhysRevLett 98 010402 PMID 17358459 S2CID 31249827 Sidharth B G 2008 The Thermodynamic Universe World Scientific p 134 ISBN 978 981 281 234 6 Amelino Camelia G 2009 Astrophysics Burst of support for relativity Nature 462 7271 291 292 Bibcode 2009Natur 462 291A doi 10 1038 462291a PMID 19924200 S2CID 205051022 a b c Milonni Peter W 2004 Fast light slow light and left handed light CRC Press pp 25 ff ISBN 978 0 7503 0926 4 de Podesta M 2002 Understanding the Properties of Matter CRC Press p 131 ISBN 978 0 415 25788 6 Optical constants of H2O D2O Water heavy water ice refractiveindex info Mikhail Polyanskiy Retrieved 7 November 2017 Optical constants of Soda lime glass refractiveindex info Mikhail Polyanskiy Retrieved 7 November 2017 Optical constants of C Carbon diamond graphite refractiveindex info Mikhail Polyanskiy Retrieved 7 November 2017 Cromie William J 24 January 2001 Researchers now able to stop restart light Harvard University Gazette Archived from the original on 28 October 2011 Retrieved 8 November 2011 Milonni P W 2004 Fast light slow light and left handed light CRC Press p 25 ISBN 978 0 7503 0926 4 Toll J S 1956 Causality and the Dispersion Relation Logical Foundations Physical Review 104 6 1760 1770 Bibcode 1956PhRv 104 1760T doi 10 1103 PhysRev 104 1760 Wolf Emil 2001 Analyticity Causality and Dispersion Relations Selected Works of Emil Wolf with commentary River Edge N J World Scientific pp 577 584 ISBN 978 981 281 187 5 OCLC 261134839 Libbrecht K G Libbrecht M W December 2006 Interferometric measurement of the resonant absorption and refractive index in rubidium gas PDF American Journal of Physics 74 12 1055 1060 Bibcode 2006AmJPh 74 1055L doi 10 1119 1 2335476 ISSN 0002 9505 See for example Hau L V Harris S E Dutton Z Behroozi C H 1999 Light speed reduction to 17 metres per second in an ultracold atomic gas PDF Nature 397 6720 594 598 Bibcode 1999Natur 397 594V doi 10 1038 17561 S2CID 4423307 Liu C Dutton Z Behroozi C H Hau L V 2001 Observation of coherent optical information storage in an atomic medium using halted light pulses PDF Nature 409 6819 490 493 Bibcode 2001Natur 409 490L doi 10 1038 35054017 PMID 11206540 S2CID 1894748 Bajcsy M Zibrov A S Lukin M D 2003 Stationary pulses of light in an atomic medium Nature 426 6967 638 641 arXiv quant ph 0311092 Bibcode 2003Natur 426 638B doi 10 1038 nature02176 PMID 14668857 S2CID 4320280 Dume B 2003 Switching light on and off Physics World Institute of Physics Archived from the original on 5 December 2008 Retrieved 8 December 2008 See for example Chiao R Y 1993 Superluminal but causal propagation of wave packets in transparent media with inverted atomic populations Physical Review A 48 1 R34 R37 Bibcode 1993PhRvA 48 34C doi 10 1103 PhysRevA 48 R34 PMID 9909684 Wang L J Kuzmich A Dogariu A 2000 Gain assisted superluminal light propagation Nature 406 6793 277 279 doi 10 1038 35018520 PMID 10917523 S2CID 4358601 Whitehouse D 19 July 2000 Beam Smashes Light Barrier BBC News Retrieved 9 February 2022 Gbur Greg 26 February 2008 Light breaking its own speed limit how superluminal shenanigans work Retrieved 9 February 2022 Cherenkov Pavel A 1934 Vidimoe svechenie chistyh zhidkostej pod dejstviem g radiacii Visible emission of pure liquids by action of g radiation Doklady Akademii Nauk SSSR 2 451 Reprinted Cherenkov P A 1967 Vidimoe svechenie chistyh zhidkostej pod dejstviem g radiacii Visible emission of pure liquids by action of g radiation Usp Fiz Nauk 93 10 385 doi 10 3367 ufnr 0093 196710n 0385 and in A N Gorbunov E P Cerenkova eds 1999 Pavel Alekseyevich Cerenkov Chelovek i Otkrytie Pavel Alekseyevich Cerenkov Man and Discovery Moscow Nauka pp 149 153 Parhami B 1999 Introduction to parallel processing algorithms and architectures Plenum Press p 5 ISBN 978 0 306 45970 2 Imbs D Raynal Michel 2009 Malyshkin V ed Software Transactional Memories An Approach for Multicore Programming 10th International Conference PaCT 2009 Novosibirsk Russia 31 August 4 September 2009 Springer p 26 ISBN 978 3 642 03274 5 Midwinter J E 1991 Optical Fibers for Transmission 2nd ed Krieger Publishing Company ISBN 978 0 89464 595 2 Theoretical vs real world speed limit of Ping Pingdom June 2007 Archived from the original on 2 September 2010 Retrieved 5 May 2010 Buchanan Mark 11 February 2015 Physics in finance Trading at the speed of light Nature 518 7538 161 163 Bibcode 2015Natur 518 161B doi 10 1038 518161a PMID 25673397 Time is money when it comes to microwaves Financial Times 10 May 2013 Archived from the original on 10 December 2022 Retrieved 25 April 2014 Day 4 Lunar Orbits 7 8 and 9 The Apollo 8 Flight Journal NASA Archived from the original on 4 January 2011 Retrieved 16 December 2010 Communications Mars 2020 Mission Perseverance Rover NASA Retrieved 14 March 2020 a b Hubble Reaches the Undiscovered Country of Primeval Galaxies Press release Space Telescope Science Institute 5 January 2010 The Hubble Ultra Deep Field Lithograph PDF NASA Retrieved 4 February 2010 Mack Katie 2021 The End of Everything Astrophysically Speaking London Penguin Books pp 18 19 ISBN 978 0 141 98958 7 OCLC 1180972461 The IAU and astronomical units International Astronomical Union Retrieved 11 October 2010 Further discussion can be found at StarChild Question of the Month for March 2000 StarChild NASA 2000 Retrieved 22 August 2009 Dickey J O et al July 1994 Lunar Laser Ranging A Continuing Legacy of the Apollo Program PDF Science 265 5171 482 490 Bibcode 1994Sci 265 482D doi 10 1126 science 265 5171 482 PMID 17781305 S2CID 10157934 Standish E M February 1982 The JPL planetary ephemerides Celestial Mechanics 26 2 181 186 Bibcode 1982CeMec 26 181S doi 10 1007 BF01230883 S2CID 121966516 Berner J B Bryant S H Kinman P W November 2007 Range Measurement as Practiced in the Deep Space Network PDF Proceedings of the IEEE 95 11 2202 2214 doi 10 1109 JPROC 2007 905128 S2CID 12149700 a b c Resolution 1 of the 17th CGPM BIPM 1983 Retrieved 23 August 2009 a b c Cohen I B 1940 Roemer and the first determination of the velocity of light 1676 Isis 31 2 327 379 doi 10 1086 347594 hdl 2027 uc1 b4375710 S2CID 145428377 a b c Demonstration tovchant le mouvement de la lumiere trouve par M Rŏmer de l Academie Royale des Sciences Demonstration to the movement of light found by Mr Romer of the Royal Academy of Sciences PDF Journal des scavans in French 233 236 1676 Translated in A demonstration concerning the motion of light communicated from Paris in the Journal des Scavans and here made English Philosophical Transactions of the Royal Society 12 136 893 895 1677 Bibcode 1677RSPT 12 893 doi 10 1098 rstl 1677 0024 Reproduced in Hutton C Shaw G Pearson R eds 1809 On the Motion of Light by M Romer The Philosophical Transactions of the Royal Society of London from Their Commencement in 1665 in the Year 1800 Abridged Vol II From 1673 to 1682 London C amp R Baldwin pp 397 398 The account published in Journal des scavans was based on a report that Romer read to the French Academy of Sciences in November 1676 Cohen 1940 p 346 a b c d Bradley J 1729 Account of a new discovered Motion of the Fix d Stars Philosophical Transactions 35 637 660 Duffett Smith P 1988 Practical Astronomy with your Calculator Cambridge University Press p 62 ISBN 978 0 521 35699 2 Extract of page 62 a b Resolution B2 on the re definition of the astronomical unit of length PDF International Astronomical Union 2012 Supplement 2014 Updates to the 8th edition 2006 of the SI Brochure PDF The International System of Units International Bureau of Weights and Measures 14 2014 International Bureau of Weights and Measures 2006 The International System of Units SI PDF 8th ed p 126 ISBN 92 822 2213 6 archived PDF from the original on 4 June 2021 retrieved 16 December 2021 Brumfiel Geoff 14 September 2012 The astronomical unit gets fixed Nature doi 10 1038 nature 2012 11416 ISSN 1476 4687 S2CID 123424704 See the following Pitjeva E V Standish E M 2009 Proposals for the masses of the three largest asteroids the Moon Earth mass ratio and the Astronomical Unit Celestial Mechanics and Dynamical Astronomy 103 4 365 372 Bibcode 2009CeMDA 103 365P doi 10 1007 s10569 009 9203 8 S2CID 121374703 Astrodynamic Constants Solar System Dynamics Jet Propulsion Laboratory Retrieved 10 February 2022 a b IAU Working Group on Numerical Standards for Fundamental Astronomy IAU WG on NSFA Current Best Estimates US Naval Observatory Archived from the original on 8 December 2009 Retrieved 25 September 2009 NPL s Beginner s Guide to Length UK National Physical Laboratory Archived from the original on 31 August 2010 Retrieved 28 October 2009 a b c d e Gibbs P 1997 How is the speed of light measured Usenet Physics FAQ University of California Riverside Archived from the original on 21 August 2015 Retrieved 13 January 2010 Fowler M The Speed of Light University of Virginia Retrieved 21 April 2010 Hughes Stephan 2012 Catchers of the Light The Forgotten Lives of the Men and Women Who First Photographed the Heavens ArtDeCiel Publishing p 210 ISBN 978 1 62050 961 6 See for example Cooke J Martin M McCartney H Wilf B 1968 Direct determination of the speed of light as a general physics laboratory experiment American Journal of Physics 36 9 847 Bibcode 1968AmJPh 36 847C doi 10 1119 1 1975166 Aoki K Mitsui T 2008 A small tabletop experiment for a direct measurement of the speed of light American Journal of Physics 76 9 812 815 arXiv 0705 3996 Bibcode 2008AmJPh 76 812A doi 10 1119 1 2919743 S2CID 117454437 James M B Ormond R B Stasch A J 1999 Speed of light measurement for the myriad American Journal of Physics 67 8 681 714 Bibcode 1999AmJPh 67 681J doi 10 1119 1 19352 a b c d e Essen L Gordon Smith A C 1948 The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator Proceedings of the Royal Society of London A 194 1038 348 361 Bibcode 1948RSPSA 194 348E doi 10 1098 rspa 1948 0085 JSTOR 98293 a b Rosa E B Dorsey N E 1907 A new determination of the ratio of the electromagnetic to the electrostatic unit of electricity Bulletin of the Bureau of Standards 3 6 433 doi 10 6028 bulletin 070 Essen L 1947 Velocity of Electromagnetic Waves Nature 159 4044 611 612 Bibcode 1947Natur 159 611E doi 10 1038 159611a0 S2CID 4101717 a b c Essen L 1950 The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator Proceedings of the Royal Society of London A 204 1077 260 277 Bibcode 1950RSPSA 204 260E doi 10 1098 rspa 1950 0172 JSTOR 98433 S2CID 121261770 Stauffer R H April 1997 Finding the Speed of Light with Marshmallows The Physics Teacher 35 4 231 Bibcode 1997PhTea 35 231S doi 10 1119 1 2344657 Retrieved 15 February 2010 BBC Look East at the speed of light BBC Norfolk website Retrieved 15 February 2010 Vaughan J M 1989 The Fabry Perot interferometer CRC Press pp 47 384 391 ISBN 978 0 85274 138 2 a b Froome K D 1958 A New Determination of the Free Space Velocity of Electromagnetic Waves Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 247 1248 109 122 Bibcode 1958RSPSA 247 109F doi 10 1098 rspa 1958 0172 JSTOR 100591 S2CID 121444888 a b c Sullivan D B 2001 Speed of Light from Direct Frequency and Wavelength Measurements In Lide D R ed A Century of Excellence in Measurements Standards and Technology PDF CRC Press pp 191 193 ISBN 978 0 8493 1247 2 Archived from the original PDF on 13 August 2009 a b c Evenson K M et al 1972 Speed of Light from Direct Frequency and Wavelength Measurements of the Methane Stabilized Laser Physical Review Letters 29 19 1346 1349 Bibcode 1972PhRvL 29 1346E doi 10 1103 PhysRevLett 29 1346 S2CID 120300510 a b Galilei G 1954 1638 Dialogues Concerning Two New Sciences Crew H de Salvio A trans Dover Publications p 43 ISBN 978 0 486 60099 4 Archived from the original on 30 January 2019 Retrieved 29 January 2019 a b c Boyer C B 1941 Early Estimates of the Velocity of Light Isis 33 1 24 doi 10 1086 358523 S2CID 145400212 a b Foschi Renato Leone Matteo 2009 Galileo measurement of the velocity of light and the reaction times Perception 38 8 1251 1259 doi 10 1068 p6263 hdl 2318 132957 PMID 19817156 S2CID 11747908 Magalotti Lorenzo 2001 1667 Saggi di Naturali Esperienze fatte nell Accademia del Cimento digital online ed Florence Istituto e Museo di Storia delle Scienze pp 265 266 retrieved 25 September 2015 a b Huygens C 1690 Traitee de la Lumiere in French Pierre van der Aa pp 8 9 Buchwald Jed Yeang Chen Pang Stemeroff Noah Barton Jenifer Harrington Quinn 1 March 2021 What Heinrich Hertz discovered about electric waves in 1887 1888 Archive for History of Exact Sciences 75 2 125 171 doi 10 1007 s00407 020 00260 1 ISSN 1432 0657 S2CID 253895826 Hertz Heinrich 1893 Electric Waves London Macmillan and Co Michelson A A 1927 Measurement of the Velocity of Light Between Mount Wilson and Mount San Antonio The Astrophysical Journal 65 1 Bibcode 1927ApJ 65 1M doi 10 1086 143021 Weiner John Nunes Frederico 2013 Light Matter Interaction Physics and Engineering at the Nanoscale illustrated ed OUP Oxford p 1 ISBN 978 0 19 856766 0 Extract of page 1 Sarton G 1993 Ancient science through the golden age of Greece Courier Dover p 248 ISBN 978 0 486 27495 9 a b c MacKay R H Oldford R W 2000 Scientific Method Statistical Method and the Speed of Light Statistical Science 15 3 254 278 doi 10 1214 ss 1009212817 click on Historical background in the table of contents Ahmed Sherif Sayed 2014 Electronic Microwave Imaging with Planar Multistatic Arrays Logos Verlag Berlin p 1 ISBN 978 3 8325 3621 3 Extract of page 1 Gross C G 1999 The Fire That Comes from the Eye Neuroscientist 5 58 64 doi 10 1177 107385849900500108 S2CID 84148912 Hamarneh S 1972 Review Hakim Mohammed Said Ibn al Haitham Isis 63 1 119 doi 10 1086 350861 a b Lester P M 2005 Visual Communication Images With Messages Thomson Wadsworth pp 10 11 ISBN 978 0 534 63720 0 O Connor J J Robertson E F Abu Ali al Hasan ibn al Haytham MacTutor History of Mathematics archive University of St Andrews Retrieved 12 January 2010 Lauginie P 2004 Measuring Speed of Light Why Speed of what PDF Fifth International Conference for History of Science in Science Education Keszthely Hungary pp 75 84 Archived from the original PDF on 4 July 2015 Retrieved 12 August 2017 O Connor J J Robertson E F Abu han Muhammad ibn Ahmad al Biruni MacTutor History of Mathematics archive University of St Andrews Retrieved 12 January 2010 Lindberg D C 1996 Roger Bacon and the origins of Perspectiva in the Middle Ages a critical edition and English translation of Bacon s Perspectiva with introduction and notes Oxford University Press p 143 ISBN 978 0 19 823992 5 Lindberg D C 1974 Late Thirteenth Century Synthesis in Optics In Edward Grant ed A source book in medieval science Harvard University Press p 396 ISBN 978 0 674 82360 0 Marshall P 1981 Nicole Oresme on the Nature Reflection and Speed of Light Isis 72 3 357 374 367 374 doi 10 1086 352787 S2CID 144035661 Sakellariadis Spyros 1982 Descartes Experimental Proof of the Infinite Velocity of Light and Huygens Rejoinder Archive for History of Exact Sciences 26 1 1 12 doi 10 1007 BF00348308 ISSN 0003 9519 JSTOR 41133639 S2CID 118187860 Cajori Florian 1922 A History of Physics in Its Elementary Branches Including the Evolution of Physical Laboratories Macmillan p 76 Smith A Mark 1987 Descartes s Theory of Light and Refraction A Discourse on Method Transactions of the American Philosophical Society 77 3 i 92 doi 10 2307 1006537 ISSN 0065 9746 JSTOR 1006537 Boyer Carl Benjamin 1959 The Rainbow From Myth to Mathematics Thomas Yoseloff pp 205 206 OCLC 763848561 Foschi Renato Leone Matteo August 2009 Galileo Measurement of the Velocity of Light and the Reaction Times Perception 38 8 1251 1259 doi 10 1068 p6263 hdl 2318 132957 ISSN 0301 0066 PMID 19817156 S2CID 11747908 Newton I 1704 Prop XI Optiks The text of Prop XI is identical between the first 1704 and second 1719 editions Guarnieri M 2015 Two Millennia of Light The Long Path to Maxwell s Waves IEEE Industrial Electronics Magazine 9 2 54 56 60 doi 10 1109 MIE 2015 2421754 S2CID 20759821 Kirchhoff G 1857 Uber die Bewegung der Elektricitat Ann Phys 178 12 529 244 Bibcode 1857AnP 178 529K doi 10 1002 andp 18571781203 See for example Giordano Nicholas J 2009 College physics reasoning and relationships Cengage Learning p 787 ISBN 978 0 534 42471 8 Extract of page 787 Bergmann Peter Gabriel 1992 The riddle of gravitation Courier Dover Publications p 17 ISBN 978 0 486 27378 5 Extract of page 17 Bais Sander 2005 The equations icons of knowledge Harvard University Press p 40 ISBN 978 0 674 01967 6 Extract of page 40 O Connor J J Robertson E F November 1997 James Clerk Maxwell School of Mathematics and Statistics University of St Andrews Archived from the original on 28 January 2011 Retrieved 13 October 2010 Campbell Lewis Garnett William Rautio James C The Life of James Clerk Maxwell p 544 ISBN 978 1773751399 Watson E C 1 September 1957 On the Relations between Light and Electricity American Journal of Physics 25 6 335 343 Bibcode 1957AmJPh 25 335W doi 10 1119 1 1934460 ISSN 0002 9505 Consoli Maurizio Pluchino Alessandro 2018 Michelson Morley Experiments An Enigma for Physics amp The History of Science World Scientific pp 118 119 ISBN 978 9 813 27818 9 Retrieved 4 May 2020 Michelson A A Morley E W 1887 On the Relative Motion of the Earth and the Luminiferous Ether American Journal of Science 34 203 333 345 doi 10 1366 0003702874447824 S2CID 98374065 French A P 1983 Special relativity Van Nostrand Reinhold pp 51 57 ISBN 978 0 442 30782 0 Darrigol O 2000 Electrodynamics from Ampere to Einstein Clarendon Press ISBN 978 0 19 850594 5 Galison P 2003 Einstein s Clocks Poincare s Maps Empires of Time W W Norton ISBN 978 0 393 32604 8 Miller A I 1981 Albert Einstein s special theory of relativity Emergence 1905 and early interpretation 1905 1911 Addison Wesley ISBN 978 0 201 04679 3 Pais A 1982 Subtle is the Lord The Science and the Life of Albert Einstein Oxford University Press ISBN 978 0 19 520438 4 Resolution 1 of the 15th CGPM BIPM 1967 Archived from the original on 11 April 2021 Retrieved 14 March 2021 Resolution 6 of the 15th CGPM BIPM 1967 Retrieved 13 October 2010 Barger R Hall J 1973 Wavelength of the 3 39 mm laser saturated absorption line of methane Applied Physics Letters 22 4 196 Bibcode 1973ApPhL 22 196B doi 10 1063 1 1654608 S2CID 1841238 Resolution 2 of the 15th CGPM BIPM 1975 Retrieved 9 September 2009 Taylor E F Wheeler J A 1992 Spacetime Physics Introduction to Special Relativity 2nd ed Macmillan p 59 ISBN 978 0 7167 2327 1 Penzes W B 2009 Time Line for the Definition of the Meter PDF NIST Retrieved 11 January 2010 Adams S 1997 Relativity An Introduction to Space Time Physics CRC Press p 140 ISBN 978 0 7484 0621 0 One peculiar consequence of this system of definitions is that any future refinement in our ability to measure c will not change the speed of light which is a defined number but will change the length of the meter Rindler W 2006 Relativity Special General and Cosmological 2nd ed Oxford University Press p 41 ISBN 978 0 19 856731 8 Note that improvements in experimental accuracy will modify the meter relative to atomic wavelengths but not the value of the speed of light The explicit constant formulation BIPM 2011 Archived from the original on 11 August 2014 See for example Conover Emily 2 November 2016 Units of measure are getting a fundamental upgrade Science News Retrieved 6 February 2022 Knotts Sandra Mohr Peter J Phillips William D January 2017 An Introduction to the New SI The Physics Teacher 55 1 16 21 Bibcode 2017PhTea 55 16K doi 10 1119 1 4972491 ISSN 0031 921X S2CID 117581000 SI Redefinition National Institute of Standards and Technology 11 May 2018 Retrieved 6 February 2022 Further readingHistorical references Romer O 1676 Demonstration touchant le mouvement de la lumiere trouve par M Romer de l Academie Royale des Sciences PDF Journal des scavans in French 223 236 Archived from the original PDF on 8 September 2022 Retrieved 10 March 2020 Translated as A Demonstration concerning the Motion of Light Philosophical Transactions of the Royal Society 12 136 893 894 1677 Bibcode 1677RSPT 12 893 doi 10 1098 rstl 1677 0024 Archived from the original on 29 July 2007 Halley E 1694 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 of the Royal Society 18 214 237 256 Bibcode 1694RSPT 18 237C doi 10 1098 rstl 1694 0048 Fizeau H L 1849 Sur une experience relative a la vitesse de propagation de la lumiere PDF Comptes rendus de l Academie des sciences in French 29 90 92 132 Foucault J L 1862 Determination experimentale de la vitesse de la lumiere parallaxe du Soleil Comptes rendus de l Academie des sciences in French 55 501 503 792 796 Michelson A A 1878 Experimental Determination of the Velocity of Light Proceedings of the American Association for the Advancement of Science 27 71 77 Michelson A A Pease F G Pearson F 1935 Measurement of the Velocity of Light in a Partial Vacuum Astrophysical Journal 82 2091 26 61 Bibcode 1935ApJ 82 26M doi 10 1086 143655 PMID 17816642 S2CID 123010613 Newcomb S 1886 The Velocity of Light Nature 34 863 29 32 Bibcode 1886Natur 34 29 doi 10 1038 034029c0 Perrotin J 1900 Sur la vitesse de la lumiere Comptes rendus de l Academie des sciences in French 131 731 734 Modern references Brillouin L 1960 Wave propagation and group velocity Academic Press Jackson J D 1975 Classical Electrodynamics 2nd ed John Wiley amp Sons ISBN 978 0 471 30932 1 Keiser G 2000 Optical Fiber Communications 3rd ed McGraw Hill p 32 ISBN 978 0 07 232101 2 Ng Y J 2004 Quantum Foam and Quantum Gravity Phenomenology In Amelino Camelia G Kowalski Glikman J eds Planck Scale Effects in Astrophysics and Cosmology Springer pp 321ff ISBN 978 3 540 25263 4 Helmcke J Riehle F 2001 Physics behind the definition of the meter In Quinn T J Leschiutta S Tavella P eds Recent advances in metrology and fundamental constants IOS Press p 453 ISBN 978 1 58603 167 1 Duff M J 2004 Comment on time variation of fundamental constants arXiv hep th 0208093 External links nbsp Wikiquote has quotations related to Speed of light Test Light Speed in Mile Long Vacuum Tube Popular Science Monthly September 1930 pp 17 18 Definition of the metre International Bureau of Weights and Measures BIPM Speed of light in vacuum National Institute of Standards and Technology NIST Data Gallery Michelson Speed of Light Univariate Location Estimation download data gathered by Albert A Michelson Subluminal Java applet by Greg Egan demonstrating group velocity information limits Light discussion on adding velocities Speed of Light Sixty Symbols University of Nottingham Department of Physics video Speed of Light BBC Radio 4 discussion In Our Time 30 November 2006 Speed of Light Live Counter Illustrations Speed of Light animated demonstrations The Velocity of Light Albert A Nicholson Scientific American 28 September 1878 p 193 Retrieved from https en wikipedia org w index php title Speed of light amp oldid 1220012310, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.