# Speed ​​of Light

Physical constant
Surname Speed ​​of light (in vacuum)
Formula symbol ${\ displaystyle c, \, c_ {0}}$
Size type speed
value
SI 299 792 458${\ displaystyle \ textstyle {\ frac {\ mathrm {m}} {\ mathrm {s}}}}$
Uncertainty  (rel.) (exactly)
Gauss 2.997 924 58e10 ${\ displaystyle \ textstyle {\ frac {\ mathrm {cm}} {\ mathrm {s}}}}$
Planck units 1
Relation to other constants
${\ displaystyle c = {\ frac {1} {\ sqrt {\ varepsilon _ {0} \ mu _ {0}}}}}$(in SI and Planck)  -  Electric field constant  -  Magnetic field constant
${\ displaystyle \ varepsilon _ {0} \,}$
${\ displaystyle \ mu _ {0} \,}$
Sources and Notes
Source for the SI value: CODATA  2014 ( direct link )

The speed of light ( from Latin celeritas: speed) is usually understood as the speed of propagation of light in a vacuum . In addition to light, all other electromagnetic waves as well as gravitational waves propagate at this speed. It is a fundamental natural constant whose meaning in the special and general theory of relativity goes far beyond the description of electromagnetic wave propagation. ${\ displaystyle c}$${\ displaystyle c}$

In a material medium , the speed of propagation of light is usually lower. If one wants to differentiate oneself clearly, one speaks of the vacuum speed of light, otherwise of the speed of propagation of light (in a medium). In dispersive media, a distinction is also made between phase and group velocity .

According to Maxwell's equations of electrodynamics, the speed of light does not depend on the speed of the light source. From this statement, together with the principle of relativity, it follows that the speed of light does not depend on the state of motion of the receiver used to measure it. From this Albert Einstein developed the theory of relativity . It says, among other things, that the vacuum speed of light represents an insurmountable speed limit for the movement of mass and for the transmission of energy and information in the universe. Particles without mass, like photons , always move at this limit speed, all particles with mass always move more slowly. As a consequence of the special theory of relativity (SRT) , the natural constant connects the previously independent concepts of energy and mass in the equivalence of mass and energy . Place and time are combined into space-time and described by the four-vector in a four-dimensional space. Since 1983, the meter has been defined as the distance that light travels in seconds in a vacuum . ${\ displaystyle c}$${\ displaystyle c}$${\ displaystyle E}$${\ displaystyle m}$ ${\ displaystyle E = mc ^ {2}}$${\ displaystyle c}$ ${\ displaystyle (ct, x, y, z)}$${\ displaystyle 1/299 \, 792 \, 458}$

The speed of light is so high that for a long time it was assumed that the ignition of a light can be felt everywhere at the same time. In 1676, Ole Rømer found that the observed orbital period of Jupiter's moon Io fluctuates regularly depending on the distance between Jupiter and Earth. From this he correctly concluded that light propagates with a finite speed. The value he determined was already in the right order of magnitude , but still deviated from the actual value by 30 percent. The measuring methods for determining the speed of light became more and more precise in the period that followed.

The formula symbol is also used in many cases for the different propagation speed in materials such as glass , air or electrical cables . If it does not result from the context, word additions make it clear whether the speed of light is meant in a vacuum or in a material. Occasionally the index zero is used for the speed of light in a vacuum ( ). ${\ displaystyle c}$${\ displaystyle c_ {0}}$

## value

Timely representation of a ray of light traveling from the earth to the moon; Duration: about 1.3 seconds

Before 1983, the meter was defined as a multiple of the wavelength of a particular atomic transition . The speed of light was a result of measurements given in the derived unit meters per second . The 17th  General Conference on Weights and Measures reversed the relationship between the speed of light and the definition of the meter in 1983. Since then, the relationship between the wavelength of the transition and the meter has been considered as a result of measurements. In return, the relationship between the meter and the speed of light could be defined by a definition, i.e. H. without measurement.

One meter is the distance that light travels in a vacuum in a matter of seconds.${\ displaystyle 1/299 \, 792 \, 458}$

After this determination, the speed of light in the vacuum is exactly

${\ displaystyle c = 299 \, 792 \, 458 \ {\ frac {\ text {m}} {\ text {s}}},}$

so about or a little more than a billion kilometers per hour. ${\ displaystyle 300 \, 000 \; {\ text {km / s}}}$

The exact numerical value was chosen in such a way that it coincided with the best measurement result at that time. It will remain valid even if more precise speed measurements are possible. Such measurements then give a more accurate determination of the length of one meter.

## Natural units

Many representations of relativistic physics give lengths in terms of the times of flight of light or, conversely, times in terms of the length of the path that light travels during this time. A light year is then shorter than a year. In these units of measurement (see Planck units ) the following applies

${\ displaystyle 1 {\ text {light second}} = 299 \, 792 \, 458 {\ text {meter}}}$

and light has the dimensionless speed of one second per second

${\ displaystyle c = 1}$.

The formula of physical relationships is simplified by this choice of units, for example the relationship between energy and momentum of a particle of mass is no longer , but . ${\ displaystyle E}$ ${\ displaystyle {\ vec {p}}}$ ${\ displaystyle m}$${\ displaystyle E ^ {2} = m ^ {2} c ^ {4} + {\ vec {p}} ^ {\, 2} c ^ {2}}$${\ displaystyle E ^ {2} = m ^ {2} + {\ vec {p}} ^ {\, 2}}$

If you want to recover the equation in the International System of Units (SI) from an equation in natural units , you have to multiply each summand by so many factors that both sides of the equation and each summand have the same SI units. For example, in SI, energy has the unit of measurement of a mass times the square of a speed and an impulse has the unit of measurement of a mass times a speed. So that in the formula on the right-hand side in the SI there are quantities of the same unit of measurement, energy times energy, as on the left-hand side, the square of mass must be multiplied by and the square of momentum by. This gives the equation valid in the SI${\ displaystyle c}$${\ displaystyle E ^ {2} = m ^ {2} + {\ vec {p}} ^ {\, 2}}$${\ displaystyle c ^ {4}}$${\ displaystyle c ^ {2}}$${\ displaystyle E ^ {2} = m ^ {2} \, c ^ {4} + {\ vec {p}} ^ {\, 2} \, c ^ {2}.}$

## Technical importance

Information in telecommunications systems spreads at 70 percent (glass fibers) to 100 percent (vacuum, space, practically also air) of the speed of light. This results in delay times that cannot be avoided. The maximum distance between two places along the earth's surface is approximately . At the speed of light in a vacuum, this would correspond to transit time. The actual transfer time is always longer. In the case of atmospheric transmission, the wave is reflected in the different layers of the atmosphere and on the ground and thus has to travel a longer distance. ${\ displaystyle 20 \, 000 \; {\ text {km}}}$${\ displaystyle 67 \; {\ text {ms}}}$

Microprocessors today work with clock frequencies in the order of 1 to 4  GHz . During a cycle, electrical signals travel between and back in circuits with low-k dielectric . When designing circuits, these run times are not negligible. ${\ displaystyle 5 \; {\ text {cm}}}$${\ displaystyle 20 \; {\ text {cm}}}$

Geostationary satellites are located over the equator. In order to receive an answer to telephone or television signals in this way, the signal must at least have traveled: from the transmitter to the satellite, then to the receiver, then the same way back. This running time is about . ${\ displaystyle 35 \, 786 \; {\ text {km}}}$${\ displaystyle 144 \, 000 \; {\ text {km}}}$${\ displaystyle 480 \; {\ text {ms}}}$

Space probes are often located many millions or billions of kilometers from Earth at their destinations. Even at the speed of light, the radio signals travel to you for several minutes to hours. The answer back to earth takes the same time again. Extraterrestrial vehicles such as the Mars rover Opportunity must therefore be able to steer automatically and recognize dangers, because the ground station can only react to incidents minutes later.

## Speed ​​of light and electrodynamics

From Maxwell's equations it follows that electric and magnetic fields can oscillate and transport energy through empty space. The fields obey a wave equation , similar to that for mechanical waves and water waves. The electromagnetic waves transmit energy and information, which is used in technical applications for radio, radar or laser.

### Plane wave or spherical wave in a vacuum

The speed of plane or spherical electromagnetic waves in a vacuum is, according to Maxwell's equations, the reciprocal of the square root of the product of the electric field constant and the magnetic field constant${\ displaystyle \ varepsilon _ {0}}$ ${\ displaystyle \ mu _ {0}:}$

${\ displaystyle c = {\ frac {1} {\ sqrt {\ varepsilon _ {0} \, \ mu _ {0}}}}}$

From this, Maxwell calculated in 1865 with the then known values ​​for and the value of and concluded:${\ displaystyle \ varepsilon _ {0}}$${\ displaystyle \ mu _ {0}}$${\ displaystyle 310 \, 740 \; {\ text {km / s}}}$

"This speed is so close to the speed of light that we have strong reason to believe that light itself (including thermal radiation and other radiation, if any) is an electromagnetic wave."

Maxwell's assumption has been confirmed in all observations on electromagnetic radiation.

### Plane wave or spherical wave in a medium

In a medium, the two field constants are changed by the material, which is taken into account by the factors relative permittivity and relative permeability . Both depend on the frequency. The speed of light in the medium is accordingly ${\ displaystyle \ varepsilon _ {\ mathrm {r}}}$ ${\ displaystyle \ mu _ {\ mathrm {r}}}$

${\ displaystyle c _ {\ text {medium}} = {\ frac {1} {\ sqrt {\ varepsilon \, \ mu}}} = {\ frac {1} {\ sqrt {\ varepsilon _ {0} \, \ varepsilon _ {\ mathrm {r}} \, \ mu _ {0} \, \ mu _ {\ mathrm {r}}}}} = {\ frac {c} {\ sqrt {\ varepsilon _ {\ mathrm {r}} \, \ mu _ {\ mathrm {r}}}}}}$.

The ratio of the speed of light in a vacuum to that in a medium is the ( frequency-dependent ) refractive index of the medium. The relationship between the refractive index and the relative permittivity and relative permeability is also called Maxwell's relation:${\ displaystyle n}$

${\ displaystyle n = {\ frac {c} {c _ {\ text {medium}}}} = {\ sqrt {\ varepsilon _ {\ mathrm {r}} \, \ mu _ {\ mathrm {r}}} }}$
The red point moves with the (mean) phase velocity, the green points with the group velocity.

Because of the generally given dependence on and on the frequency of the wave, it should be noted that the phase velocity in the medium is the term used for the progression of points of the same phase (e.g. minima or maxima) of a plane wave with constant amplitude. The envelope of a spatially limited wave packet , on the other hand, propagates with the group speed . In media, these two speeds differ more or less from each other. In particular, a refractive index only means that the wave crests are spreading faster than they are . Wave packets that are used to transport information and energy are still slower than . ${\ displaystyle \ varepsilon _ {\ mathrm {r}}}$${\ displaystyle \ mu _ {\ mathrm {r}}}$${\ displaystyle c _ {\ mathrm {medium}}}$${\ displaystyle n <1}$${\ displaystyle c}$${\ displaystyle c}$

### Transversely modulated wave in a vacuum

According to Maxwell's equations, the speed of light u is independent of the wavelength . a. for the case of a plane wave that is infinitely extended in a vacuum and has a well-defined direction of propagation. In contrast, every practically realizable light wave always has a certain beam profile. If this is represented as a superposition of plane waves with slightly changed directions of propagation, the individual plane waves all have the speed of light in a vacuum , but this does not necessarily apply to the wave created by the superposition. The result is a slightly slowed wave. This could also be demonstrated with specially shaped Bessel rays from microwaves and visible light, even for the speed of individual photons. With all practically realizable light waves, even with sharply bundled laser beams, this effect is negligibly small. ${\ displaystyle c = 1 / {\ sqrt {\ varepsilon _ {0} \, \ mu _ {0}}}}$${\ displaystyle c}$

## Speed ​​of light in matter

In matter , light is slower than in a vacuum, and indeed, as was deduced above, it has a refractive index that is greater than 1. ${\ displaystyle c _ {\, \ mathrm {Medium}} = {c} / {n}}$ ${\ displaystyle n}$

In air close to the ground, the speed of light is around 0.28 ‰ lower than in a vacuum (i.e. around 299,710 km / s), in water it is around 225,000 km / s (−25%) and in glasses with a high refractive index down to 160,000 km / s (-47%).

In some media such as Bose-Einstein condensates or photonic crystals , there is a very large dispersion for certain wavelengths . Light spreads in them much more slowly. In 1999 , the research group of the Danish physicist Lene Hau was able to bring light to a group speed of around 17 m / s.

If two transparent media border one another, the different speeds of light in both media cause the light to refract at the interface. Since the speed of light in the medium also depends on the wavelength of the light, light of different colors is refracted differently, and white light is split into its different color components. This effect can be z. B. observe directly with the help of a prism .

Particles in a medium can be faster than light in the same medium. When they are electrically charged, such as electrons or protons , the Cherenkov effect occurs: The particles emit light, just like a supersonic airplane drags a sonic boom behind it. This can be observed , for example, in swimming pool reactors. In them there is water between the fuel elements . The beta radiation from the fission products consists of electrons that are faster than the speed of light in water. The Cherenkov light they emit makes the water glow blue.

The Cherenkov effect is used in particle detectors to detect faster charged particles.

## Speed ​​of light and particle physics

The vacuum speed of light as the limit speed of massive particles: If their speed goes against the speed of light, the energy grows, i.e. over all limits.${\ displaystyle E (v)}$

Particles without mass always move at the speed of light in every inertial system . The best known massless particle that shows this property is the photon . It mediates the electromagnetic interaction that determines a large part of everyday physics. Other massless particles in the standard model of particle physics are the gluons , the mediator particles of the strong interaction . Particles with a mass other than zero are always slower than light. When it is accelerated, its energy grows accordingly because of the relativistic energy-momentum relationship${\ displaystyle E (v)}$

${\ displaystyle E (v) = {\ frac {m \, c ^ {2}} {\ sqrt {1- {v} ^ {2} / c ^ {2}}}}.}$

It is the speed of the particle in relation to the inertial, which is chosen for the description of the process. The closer the magnitude of the particle speed is to the speed of light , the closer the quotient approaches the value 1 and the smaller the root of the denominator becomes. The closer the particle speed approaches the speed of light, the greater the energy required for it. With finitely high energy you can accelerate a particle as close as you want to the speed of light, but you cannot reach it. ${\ displaystyle v}$${\ displaystyle v}$${\ displaystyle c}$${\ displaystyle v ^ {2} / c ^ {2}}$

The relationship between energy and speed, as predicted by the theory of relativity, has been proven in various experiments .

He has u. a. Effects on the technology of particle accelerators . The period of rotation of a z. B. in a synchrotron orbiting bundle of electrons hardly changes with further acceleration; the synchronization of the individual accelerating alternating fields can therefore be constant. On the other hand, for heavier particles that are fed in at a lower speed, it must be continuously adapted to the increasing speed.

## Faster than light

There is speculation about particles moving faster than the speed of light. One example are hypothetical particles called tachyons . According to the theory of relativity , tachyons could not interact with normal matter: Otherwise one would not be able to distinguish between cause and effect, the same for all observers. The theoretical basis of the tachyon concept is controversial. An experimental proof of tachyons has not yet been successful.

In addition, publications in recent years that claim that the speed of light has been observed has attracted particular attention. However, it could either be shown that the apparently faster than light signal transmission was caused by a misinterpretation of the data (faster than light jets , superluminal tunneling), or the measurements could not be reproduced and ultimately turned out to be faulty (see, for example, measurements of neutrino speed ).

## Historical background

Historically assumed speed of light
Year (approximately) Researcher Speed ​​of Light
450 BC Chr. Empedocles at last
350 BC Chr. Aristotle infinite
100 Heron of Alexandria infinite
1000 Avicenna / Alhazen at last
1350 Sayana at last
1600 Johannes Kepler infinite
1620 René Descartes infinite
1620 Galileo Galilei at last

The question of whether light spreads infinitely fast or whether it has a finite speed was already of interest in ancient philosophy. Light travels a kilometer in just three microseconds. With the observation possibilities of antiquity, a ray of light is inevitably already at its destination at the moment of its emergence.

Nevertheless, Empedocles already believed (around 450 BC ) that light was something that was in motion and therefore needed time to cover distances. Aristotle , on the other hand, said that light comes from the mere presence of objects, but that it is not in motion. He argued that otherwise the speed would have to be so enormous that it would be beyond the human imagination. Because of his reputation and influence, Aristotle's theory found general acceptance.

An ancient theory of vision assumed that the light needed to see is emitted by the eye. An object should therefore be visible when the light rays from the eye hit it. Building on this idea, Heron of Alexandria also endorsed the Aristotelian theory. He stated that the speed of light must be infinite, since one can see even the distant stars as soon as one opens one's eyes.

In the oriental world, on the other hand, the idea of ​​a finite speed of light was also widespread. In particular, the Persian philosophers and scientists Avicenna and Alhazen (both around the year 1000) believed that light has a finite speed. But their supporters were in the minority compared to the supporters of the Aristotelian theory.

At the beginning of the 17th century, the astronomer Johannes Kepler believed that the speed of light, at least in a vacuum, was infinite, since empty space was no obstacle for light. Here the idea already appears that the speed of a light beam could depend on the medium it traversed.

Francis Bacon argued that light does not necessarily have to be infinitely fast, but maybe just faster than perceptible.

René Descartes assumed an infinitely great speed of light. The sun, moon and earth are in a line during a solar eclipse . Descartes argued that these celestial bodies would appear to be out of line to an observer at this point in time if the speed of light was finite. Since such an effect was never observed, his assumption was confirmed. Descartes believed in the infinitely great speed of light so strongly that he was convinced that his worldview would collapse when it were finite.

This contrasts with the theories of Isaac Newton and Christiaan Huygens with finite speed of light around the year 1700 . Newton saw light as a stream of particles, while Huygens saw light as a wave. Both were able to explain the law of refraction by using the speed of light proportional (Newton) or inversely proportional (Huygens) to the refractive index. Newton's idea has been disproved since the 19th century when interference and diffraction could be observed and the speed measured in media.

Since the first measurement of the speed of light took place in Huygens time, which in his opinion was far too high for bodies with mass to be able to reach it, he proposed ether, an elastic (neither visible nor measurable) background medium that would allow the propagation of waves, similar to sound in the air.

### Measurement of the speed of light

Experimental setup of the Fizeau experiment
Experimental setup for Foucault's experiment

Around 1600, Galileo Galilei was the first to try to measure the speed of light using scientific methods by positioning himself and an assistant with a signal lamp each on two hills with a known distance. The assistant should return Galileo's signal immediately. He had already successfully determined the speed of sound using a comparable method. To his astonishment, after subtracting the assistant's reaction time, there was no repeatable, measurable time. This did not change when the distance was increased to the maximum possible visibility of the lanterns. Isaac Beeckman proposed a modified version of the experiment in 1629, in which the light should be reflected by a mirror. Descartes criticized such experiments as superfluous, since more precise observations with the help of solar eclipses had already been carried out and had given a negative result. Nevertheless, the Accademia del Cimento repeated the experiment in Florence in 1667. The lamps were about a mile apart. Again, no delay could be observed. Descartes confirmed this in his assumption of an infinitely rapid spread of light. Galilei and Robert Hooke, however, interpreted the result in such a way that the speed of light is so high that it could not be determined with this experiment.

The first proof that the speed of light is finite came from the Danish astronomer Ole Rømer in 1676. He found seasonal fluctuations for clock signals from Jupiter (entry of Jupiter's moon Io into Jupiter's shadow), while on this side the earth's rotation served as a stable time reference. He specified a transit time of the light of 22 minutes for the earth orbit diameter. The correct value is shorter (16 min 38 s). Since Rømer did not know the diameter of the earth's orbit, he did not give a value for the speed of light. Christiaan Huygens did so two years later. He related the travel time given by Rømer to the almost correct diameter of the earth's orbit around the sun , which Cassini accidentally gave in 1673 (see solar parallax for the gradual improvement of this value) and came to the speed of light . ${\ displaystyle 213 \, 000 \; {\ text {km / s}}}$

James Bradley found another astronomical method in 1728 by determining the fluctuations in the star positions by an angle of 20 "during the earth's orbit around the sun ( aberration ). His measurements were an attempt to observe the parallax of fixed stars in order to determine their distances. From this, Bradley calculated that light is times faster than the earth in its orbit (measurement error 2%). Its measurement (published in 1729) was then seen as further evidence of a finite speed of light and - at the same time - of the Copernican world system . To calculate the speed of light, however, he also needed the earth's orbit radius. ${\ displaystyle 10 \, 210}$

Armand Fizeau succeeded in determining the speed of light for the first time using the gear wheel method . In 1849 he sent light through a rotating gear to a mirror several kilometers away, which reflected it back through the gear. Depending on how fast the gear wheel rotates, the reflected light that has passed a gap in the gear wheel on the way there either falls on a tooth or it passes through a gap again and only then can it be seen. Fizeau came up with a value that was 5% too high.

Léon Foucault further improved the method in 1850 by significantly shortening the measuring distances with the rotating mirror method . This enabled him to demonstrate for the first time the material dependence of the speed of light: light spreads more slowly in other media than in air . In the experiment, light falls on a rotating mirror. From this it is deflected onto a fixed mirror, where it is reflected back onto the rotating mirror. However, since the rotating mirror has continued to rotate in the meantime, the light beam is no longer reflected onto the starting point. By measuring the displacement of the point, with a known frequency of rotation and known distances, it is possible to determine the speed of light. Foucault published his results in 1862 and gave to to kilometers per second. ${\ displaystyle c}$${\ displaystyle 298 \, 000}$

Simon Newcomb and Albert A. Michelson again built on Foucault's apparatus and improved the principle again. In 1926, in California , Michelson also used rotating prism mirrors to send a beam of light from Mount Wilson to Mount San Antonio and back. He received just 12 ppm above today's level. ${\ displaystyle 299 \, 796 \; {\ text {km / s}}}$

Historical values ​​for the speed of light
year Researcher method Speed ​​of light in km / s
around 1620 Galileo Galilei Time delay in observing lanterns that have been covered by hand At least several km / s
1676/78 Ole Rømer / Christiaan Huygens Time delay in astronomical observations ${\ displaystyle 213 \, 000}$
1728 James Bradley Aberration ${\ displaystyle 301 \, 000}$
around 1775 ? Venus transit 1769 ${\ displaystyle 285 \, 000}$
1834 Charles Wheatstone Rotating mirror method for measuring the speed of electric current ${\ displaystyle 402 \, 336}$
1849 Armand Fizeau Gear method ${\ displaystyle 315 \, 000}$
1851 Léon Foucault Rotating mirror method ${\ displaystyle 298 \, 000 \ pm 500}$
1865 James Clerk Maxwell Maxwell's equations ${\ displaystyle 310 \, 740}$
1875 Alfred Cornu Rotating mirror method ${\ displaystyle 299 \, 990}$
1879 Albert A. Michelson Rotating mirror method ${\ displaystyle 299 \, 910 \ pm 50}$
1888 Heinrich Hertz Frequency and wavelength measurement of standing radio waves ${\ displaystyle 300 \, 000}$
1926 Albert A. Michelson Rotating mirror method ${\ displaystyle 299 \, 796 \ pm 4}$
1947 Louis Essen , Albert Gordon-Smith Electric cavity resonator ${\ displaystyle 299 \, 792 \ pm 3}$
1958 Keith Froome Interferometer ${\ displaystyle 299 \, 792 {,} 5 \ pm 0 {,} 1}$
1973 Boulder group at the NBS Laser measurement ${\ displaystyle 299 \, 792 {,} 4574 \ pm 0 {,} 001}$
1983 Definition of the CGPM Determination of the speed of light by redefining the meter ${\ displaystyle 299 \, 792 {,} 458}$

### To the constancy of the speed of light

#### First considerations

With his investigations on aberration from 1728, James Bradley was not only able to determine the speed of light himself, but also for the first time to make statements about its constancy. He observed that the aberration for all stars in the same line of sight varies in an identical way over a year. From this he concluded that the speed with which starlight arrives on earth is the same for all stars within the scope of his measurement accuracy of about one percent.

However, this measurement accuracy was not sufficient to clarify whether this speed of arrival depends on whether the earth moves towards or away from a star on its way around the sun. François Arago first investigated this question in 1810 by measuring the deflection angle of starlight in a glass prism. According to the corpuscular theory of light that was accepted at the time, he expected this angle to change in a measurable order of magnitude, since the speed of the incident starlight should add to the speed of the earth on its way around the sun. However, there were no measurable fluctuations in the deflection angle over the course of the year. Arago explained this result with the thesis that starlight is a mixture of different speeds, while the human eye can only perceive one of them. From today's perspective, however, its measurement can be regarded as the first experimental proof of the constancy of the speed of light.

With the emergence of the idea of ​​light as a wave phenomenon, Augustin Fresnel formulated another interpretation of the Arago experiment in 1818. Thereafter, the analogy between mechanical waves and light waves included the idea that light waves must propagate in a certain medium, the so-called ether , just as water waves propagate in water. The aether should represent the reference point for a preferred inertial system. Fresnel explained the result of Arago by assuming that this ether is partly carried along inside matter, in this case in the prism used. The degree of entrainment would depend in a suitable manner on the refractive index .

#### Michelson-Morley experiment

Schematic setup of the Michelson-Morley experiment

In 1887 Albert A. Michelson and Edward W. Morley conducted a significant experiment to determine the speed of the earth relative to this assumed ether. For this purpose, the dependence of the light transit times on the state of motion of the ether was examined. Contrary to expectations, the experiment always resulted in the same running times. Repetitions of the experiment at different phases of the earth's orbit around the sun always led to the same result. An explanation based on a long-range aether carryover through the earth as a whole failed because in this case there would be no aberration for stars perpendicular to the direction of movement of the earth.

A solution compatible with Maxwell's electrodynamics was achieved with the length contraction proposed by George FitzGerald and Hendrik Lorentz . Lorentz and Henri Poincaré developed this hypothesis further by introducing time dilation , but combined this with the assumption of a hypothetical aether whose state of motion could not have been determined in principle. That means that in this theory the speed of light "real" is only constant in the ether system, independent of the movement of the source and the observer. This means, among other things, that Maxwell's equations should only take on the usual form in the ether system. However, Lorentz and Poincaré took this into account by introducing the Lorentz transformation in such a way that the “apparent” speed of light is also constant in all other reference systems and thus everyone can claim to be at rest in the ether. (The Lorentz transformation was only interpreted as a mathematical construction, while Einstein (1905) was supposed to revolutionize all previous ideas about the structure of space-time on its basis, see below). In 1904 Poincaré stated that the main feature of Lorentz's theory was that the speed of light cannot be exceeded by all observers, regardless of their state of motion relative to the ether (see Lorentz's theory of ether ). This means that even for Poincaré existed the ether.

However, a theory in which the ether system was assumed to exist, but remained undetectable, was very unsatisfactory. Einstein (1905) found a solution to the dilemma with the special theory of relativity by giving up the conventional ideas of space and time and replacing them with the principle of relativity and the constancy of light as the starting points or postulates of his theory. This solution was formally identical to the theory of H. A. Lorentz, however, like an emission theory, it managed without any “ether”. He took the light constancy from Lorentz's ether, as he explained in 1910, whereby, in contrast to Poincaré and Lorentz, he explained that precisely because of the equality of the reference systems and thus the undetectability of the ether, the concept of aether is meaningless at all. In 1912 he summed it up as follows:

“It is generally known that a theory of the laws of transformation of space and time cannot be based on the principle of relativity alone. As is well known, this has to do with the relativity of the terms “simultaneity” and “shape of moving bodies”. In order to fill this gap, I introduced the principle of the constancy of the speed of light, borrowed from HA Lorentz's theory of the quiescent light ether, which, like the principle of relativity, contains a physical assumption that only appeared to be justified by relevant experience (experiments by Fizeau, Rowland, etc.) . "

The independence of the speed of light from the speed of the uniformly moving observer is therefore the basis of the theory of relativity. This theory has been generally accepted for decades due to many very precise experiments.

#### Independence from the source

With the Michelson-Morley experiment, although the constant speed of light has been confirmed for a co-moving with the light source observers, but not for a not moved along with the source observer. Because the experiment can also be explained with an emission theory, according to which the speed of light in all reference systems is only constant relative to the emission source (i.e. in systems where the source moves with ± v, the light would consequently propagate with c ± v) . Even Albert Einstein moved before 1905 such a hypothesis briefly consider what the reason was that he indeed always, but not used in his writings the MM experiment to confirm the principle of relativity as confirmation of light consistency.

However, an emission theory would require a complete reformulation of electrodynamics, against which the great success of Maxwell's theory spoke. The emission theory has also been refuted experimentally. For example, the orbits of binary stars observed from Earth would have to be distorted at different speeds of light, but this was not observed. The decay with almost of itself moving π 0 - meson the photons resulting would assume the speed of mesons and should move almost double the speed of light, but that was not the case. The Sagnac effect also demonstrates the independence of the speed of light from the movement of the source. All these experiments find their explanation in the special theory of relativity, which u. a. says: light does not overtake light.${\ displaystyle c}$

#### Variable speed of light and constancy in the observable universe

Although the constancy of the speed of light has been proven experimentally, there is as yet no sufficiently convincing explanation for its constancy and its special value. The loop quantum gravity , for example, dictates that the speed of a photon can not be defined as a constant, but that their value by the photo frequency depends. In fact, there are theories that the speed of light changes with the age of the universe and that it was not constant in the early universe. Albrecht and Magueijo show that the cosmological evolution equations together with a variable speed of light can solve the problems of the horizon, flatness and the cosmological constant . The assumption of spacetime with three space and two time dimensions gives a natural explanation for the constancy of the speed of light in the observable universe and also for the fact that the speed of light varied in the early universe.

## literature

Original works:

• Ole Rømer: Demonstration touchant le mouvement de la lumière . In: Journal des Sçavans . de Boccard, Paris 1676 ( PDF - Engl. Version ( Memento of December 21, 2008 in the Internet Archive )).
• Edmund Halley: Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London . In: Philosophical Transactions . tape 18 . London 1694, p. 237-256 ( archive.org ).
• HL Fizeau: Sur une expérience relative à la vitesse de propagation de la lumière . In: Comptes rendus de l'Académie des sciences . tape 29 . Gauthier-Villars, Paris 1849 ( academie-sciences.fr [PDF]).
• JL Foucault: Détermination expérimentale de la vitesse de la lumière, parallaxe du Soleil . In: Comptes Rendus . tape 55 . Gauthier-Villars, 1862, ISSN  0001-4036 .
• AA Michelson: Experimental Determination of the Velocity of Light . In: Proceedings of the American Association for the Advancement of Science . Philadelphia 1878 ( Gutenberg Project ).
• Simon Newcomb: The Velocity of Light . In: Nature . London May 13th 1886.
• Joseph Perrotin: Sur la vitesse de la lumière . In: Comptes Rendus . No. 131 . Gauthier-Villars, 1900, ISSN  0001-4036 .
• AA Michelson, FG Pease, F. Pearson: Measurement of the Velocity of Light In a Partial Vacuum . In: Astrophysical Journal . tape 81 . Univ. Press, 1935, ISSN  0004-637X , pp. 100-101 .

Otherwise:

• JH Sanders (ed. And introduction): The speed of light. Introduction and original texts, WTB Scientific Pocket Books series, Volume 57, Akademie Verlag / Vieweg 1970
• Subhash Kak: The Speed ​​of Light and Puranic Cosmology. Annals Bhandarkar Oriental Research Institute 80, 1999, pp. 113-123, arxiv : physics / 9804020 .
• S. Débarbat, C. Wilson: The galilean satellites of Jupiter from Galileo to Cassini, Römer and Bradley . In: René Taton (Ed.): Planetary astronomy from the Renaissance to the rise of astrophysics. Part A: Tycho Brahe to Newton . Univ. Press, Cambridge 1989, ISBN 0-521-24254-1 , pp. 144-157 .
• G. Sarton: Discovery of the aberration of light (with facsimile of Bradley's letter to Halley 1729) . In: Isis . tape 16 , no. 2 . Univ. Press, November 1931, ISSN  0021-1753 , pp. 233-248 .
• George FR Ellis, Jean-Philippe Uzan: 'c' is the speed of light, isn't it? In: Am J Phys. 73, 2005, pp. 240-247, doi: 10.1119 / 1.1819929 , arxiv : gr-qc / 0305099 .
• Jürgen Bortfeldt: Units and fundamental constants in physics and chemistry, Subvolume B . In: B. Kramer, Werner Martienssen (Eds.): Numerical data and functional relationships in science and technology . tape 1 . Springer, Berlin 1992, ISBN 3-540-54258-2 .
• John H. Spence: Lightspeed: The Ghostly Aether and the Race to Measure the Speed ​​of Light , Oxford UP 2019

Wiktionary: speed of light  - explanations of meanings, word origins, synonyms, translations
Commons : Speed ​​of Light  - collection of images, videos and audio files

1. ^ Resolution on the definition of the meter as a result of the 17th  CGPM conference. "The meter is the length of the path traveled by light in vacuum during a time interval of a second."${\ displaystyle 1/299 \, 792 \, 458}$
2. The relationships for the phase velocity or the group velocity are mathematically particularly simple if one uses the angular frequency instead of the frequency and the reciprocal quantity instead of the wavelength , the so-called "wave number": Then the phase velocity is given by the quotient , the group velocity by the Derivation of the function${\ displaystyle f}$${\ displaystyle \ omega = 2 \ pi f}$${\ displaystyle \ lambda}$${\ displaystyle k: = 2 \ pi \ lambda}$${\ displaystyle v_ {P} = \ omega k}$${\ displaystyle v_ {G} = \ mathrm {d} \ omega / \ mathrm {d} k}$${\ displaystyle \ omega (k).}$
3. D. Giovannini et al. a .: Spatially structured photons that travel in free space slower than the speed of light. On: sciencemag.org. January 22, 2015. doi: 10.1126 / science.aaa3035 .
4. Light quanta dawdle in a vacuum. On: pro-physik.de. January 22, 2015.
5. Strictly speaking, it is assumed that transient processes have already subsided and that one is dealing with stationary conditions. Interestingly enough, analogous formulas apply in matter for the so-called retarded potential and vector potentials as in a vacuum, i.e. That means, there, too, the retardation takes place with the vacuum speed of light: The polarization effects of the matter are only in the second terms of the effective charge and current densities to be retarded and this corresponds precisely to the following text.${\ displaystyle \ rho _ {E} \, \, (= \ mathrm {div} \, \, (\ mathbf {DP}))}$${\ displaystyle \ mathbf {j} _ {B} \, \, (= \ mathrm {red \, \,} (\ mathbf {H + M}))).}$
6. Slow light in photonic resonances.
7. Light speed reduction to 17 meters per second in an ultracold atomic gas. Article in Nature on the slowing down of light in a Bose-Einstein condensate.
8. A. Einstein: About the development of our views on the nature and constitution of radiation . In: Physikalische Zeitschrift . tape 10 , no. 22 , 1909, pp. 817–825 ( WikiSource (English) , PDF (German) ).
9. A. Einstein: Relativity and Gravitation. Reply to a remark by M. Abraham . In: Annals of Physics . tape 38 , 1912, pp. 1059-1064 , doi : 10.1002 / andp.19123431014 ( PDF (German) ).
10. ^ JD Norton: Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905 . In: Archive for History of Exact Sciences . tape 59 , 2004, p. 45-105 , doi : 10.1007 / s00407-004-0085-6 ( pitt.edu ).
11. ^ J. Stachel: Einstein and Michelson: the Context of Discovery and Context of Justification . In: Astronomical News . tape 303 , no. 1 , 1982, pp. 47-53 , doi : 10.1002 / asna.2103030110 .
12. G. Amelino-Camelia, John Ellis, NE Mavromatos, DV Nanopoulos, Subir Sarkar: Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo . In: Nature . tape 393 , 1998, pp. 763–765 (English, online [PDF; 247 kB ; accessed on September 29, 2018]).
13. ^ Andreas Albrecht, Joao Magueijo: A Time Varying Speed ​​of Light as a Solution to Cosmological Puzzles . In: Physical Review D . tape 59 , no. 4 , 1999, doi : 10.1103 / PhysRevD.59.043516 .
14. Christoph Köhn: The Planck Length and the Constancy of the Speed ​​of Light in Five Dimensional Spacetime Parametrized with Two Time Coordinates . In: J. High Energy Phys., Grav and Cosm. tape 3 , no. 4 , 2017, p. 635-650 , arxiv : 1612.01832 [abs] (English).
 This article was added to the list of excellent articles on May 17, 2006 in this version .