Speed of light

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.

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.

For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects.

In 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.

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.

[Note 5] This invariance of the speed of light was postulated by Einstein in 1905,[6] after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for motion against the luminiferous aether.

[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.

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.

[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.

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.

[76][77] 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 10] Straight lines are rare in global communications and the travel time increases when signals pass through electronic switches or signal regenerators.

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.

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.

[85] 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.

The Lunar Laser Ranging experiment, radar astronomy and the Deep Space Network determine distances to the Moon,[90] planets[91] and spacecraft,[92] respectively, by measuring round-trip transit times.

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.

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.

It was redefined in 2012 as exactly 149597870700 m.[98][99] 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.

[101] 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.

The ancient Greeks, Arabic scholars, and classical European scientists long debated this until Rømer provided the first calculation of the speed of light.

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.

[136] 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.

[141][142] Pierre de Fermat derived Snell's law using the opposing assumption, the denser the medium the slower light travelled.

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.

[96] 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.

[151] 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.

[159] 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.

[Note 15][118] 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.

γ starts at 1 when v equals zero and stays nearly constant for small v's, then it sharply curves upwards and has a vertical asymptote, diverging to positive infinity as v approaches c.
The Lorentz factor γ as a function of velocity. It starts at 1 and approaches infinity as v approaches c .
Three pairs of coordinate axes are depicted with the same origin A; in the green frame, the x axis is horizontal and the ct axis is vertical; in the red frame, the x′ axis is slightly skewed upwards, and the ct′ axis slightly skewed rightwards, relative to the green axes; in the blue frame, the x′′ axis is somewhat skewed downwards, and the ct′′ axis somewhat skewed leftwards, relative to the green axes. A point B on the green x axis, to the left of A, has zero ct, positive ct′, and negative ct′′.
Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame.
A modulated wave moves from left to right. There are three points marked with a dot: A blue dot at a node of the carrier wave, a green dot at the maximum of the envelope, and a red dot at the front of the envelope.
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.
Acoustic representation of the speed of light, at every beep the light makes a full circle around the equator
The diameter of the moon is about one quarter of that of Earth, and their distance is about thirty times the diameter of Earth. A beam of light starts from the Earth and reaches the Moon in about a second and a quarter.
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.
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.
A star emits a light ray that hits the objective of a telescope. While the light travels down the telescope to its eyepiece, the telescope moves to the right. For the light to stay inside the telescope, the telescope must be tilted to the right, causing the distant source to appear at a different location to the right.
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.
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.
A light ray passes horizontally through a half-mirror and a rotating cog wheel, is reflected back by a mirror, passes through the cog wheel, and is reflected by the half-mirror into a monocular.
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 box with three waves in it; there are one and a half wavelength of the top wave, one of the middle one, and a half of the bottom one.
Electromagnetic standing waves in a cavity
Schematic of the working of a Michelson interferometer.
An interferometric determination of length. Left: constructive interference ; Right: destructive interference .
A diagram of a planet's orbit around the Sun and of a moon's orbit around another planet. The shadow of the latter planet is shaded.
Rømer's observations of the occultations of Io from Earth
Hendrik Lorentz (right) with Albert Einstein (1921)