Speed of light
Exact value | |
---|---|
metres per second | 299792458 |
Approximate values (to three significant digits) | |
kilometres per hour | 1080000000 |
miles per second | 186000 |
miles per hour[1] | 671000000 |
astronomical units per day | 173[Note 1] |
parsecs per year | 0.307[Note 2] |
Approximate light signal travel times | |
Distance | Time |
one foot | 1.0 ns |
one metre | 3.3 ns |
from geostationary orbit to Earth | 119 ms |
the length of Earth's equator | 134 ms |
from Moon to Earth | 1.3 s |
from Sun to Earth (1 AU) | 8.3 min |
one light-year | 1.0 year |
one parsec | 3.26 years |
from the nearest star to Sun (1.3 pc) | 4.2 years |
from the nearest galaxy to Earth | 70000 years |
across the Milky Way | 87400 years |
from the Andromeda Galaxy to Earth | 2.5 million years |
Special relativity |
---|
The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour).[Note 3] According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.[4][5][6]
All forms of
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.
In some cases, objects or waves may appear to travel
The speed at which light propagates through
Numerical value, notation, and units
The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin
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
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
The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the
By adopting
Special relativity has many counterintuitive and experimentally verified implications.
The results of special relativity can be summarized by treating space and time as a unified structure known as
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
Upper limit on speeds
According to special relativity, the energy of an object with
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
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
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
A 2011 experiment where
In models of the
Propagation of light
In
In modern
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
In a medium
In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity vp. A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocity vg, and its earliest part travels at the front velocity vf.[63]
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,
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.
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
Small scales
In
Large distances on Earth
Given that the equatorial circumference of the Earth is about 40075 km and that c is about 300000 km/s, the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is traveling in
Although this distance is largely irrelevant for most applications, latency becomes important in fields such as
Spaceflight and astronomy
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
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
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
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
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.
Another method is to use the
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
- 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
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
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
Cavity resonance
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
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
Interferometry
Before the advent of laser technology, coherent
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.
<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
In the 13th century,
In the early 17th century,
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.
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
Connections with electromagnetism
In the 19th century
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"
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]
It was thought at the time that empty space was filled with a background medium called the
Because of this experiment
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
Increased accuracy of c and redefinition of the metre and second
In the second half of the 20th century, much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. These were aided by new, more precise, definitions of the metre and second. In 1950,
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
- ^ Exact value: (299792458 × 60 × 60 × 24 / 149597870700) AU/day.
- ^ Exact value: (999992651 π / 10246429500) pc/y.
- ^ 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,
- ^ The exact value is 149896229/152400000 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 0.01720209895 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 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]
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Further reading
Historical references
- Rømer, O. (1676). "Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l'Academie Royale des Sciences" (PDF). Journal des sçavans (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". doi:10.1098/rstl.1677.0024. Archived from the originalon 29 July 2007.
- Translated as "A Demonstration concerning the Motion of Light".
- .
- Comptes rendus de l'Académie des sciences(in French). 29: 90–92, 132.
- Comptes rendus de l'Académie des sciences(in French). 55: 501–503, 792–796.
- Proceedings of the American Association for the Advancement of Science. 27: 71–77.
- Michelson, A. A.; S2CID 123010613.
- doi:10.1038/034029c0.
- Comptes rendus de l'Académie des sciences(in French). 131: 731–734.
Modern references
- Brillouin, L. (1960). Wave propagation and group velocity. Academic Press.
- 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. ISBN 978-1-58603-167-1.
- arXiv:hep-th/0208093.
External links
- "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