The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is exactly 7008299792458000000
299792458metres per second, as the length of the metre is defined from this constant and the international standard for time.Penrose, R (2004). special relativity, c is the maximum speed at which all matter and information in the universe can travel. It is the speed at which all massless particles and changes of the associated fields (including electromagnetic radiation such as light and gravitational waves) travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial frame of reference of the observer. In the theory of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E=mc2.The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n=c/v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 7008200000000000000
200000km/s; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 7008299700000000000299700km/s or 700490000000000000090km/s slower than c.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 communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip. The speed of light can be used with time of flight measurements to measure large distances to high precision.
Ole Rømer first demonstrated in 1676 that light travels at a finite speed (as opposed to instantaneously) by studying the apparent motion of Jupiter's moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism.Albert Einstein postulated that the speed of light with respect to any inertial frame is independent of the motion of the light source,Stachel, JJ (2002). special theory of relativity and showing that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 7008299792458000000
299792458m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units (SI) as the distance travelled by light in vacuum in 1/7008299792458000000299792458 of a second. As a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre.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"). Originally, the symbol V was used for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum. 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.
Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum.
- Lide, DR (2004). [5] has the same form as other related 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.
Since 1983, the metre has been defined in the International System of Units (SI) as the distance light travels in vacuum in 1/7008299792458000000299792458 of a second. This definition fixes the speed of light in vacuum at exactly 7008299792458000000299792458m/s. As a dimensional physical constant, the numerical value of c is different for different unit systems. Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result.
Fundamental role in physics
See also: Introduction to special relativity, 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 3] This invariance of the speed of light was postulated by Einstein in 1905,[4] after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether;Einstein, A (1905). \"Zur Elektrodynamik bewegter Körper\". 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. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.Hsu, J-P; Zhang, YZ (2001). [14]Zhang, YZ (1997). 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.d'Inverno, R (1992). Introducing Einstein's Relativity. massless particles and waves, including light, must travel in vacuum.
The Lorentz factor γ as a function of velocity. It starts at 1 and approaches infinity as v approachesc.
Special relativity has many counterintuitive and experimentally verified implications. The factorγ 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 thanc, 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.
The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (withc relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameterc.Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. As such, the parameterc is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts thatc is also the speed of gravity and of gravitational waves.Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. non-inertial frames of reference (gravitationally curved space or accelerated reference frames), the local speed of light is constant and equal toc, but the speed of light along a trajectory of finite length can differ fromc, depending on how distances and times are defined.[25]
It is generally assumed that the 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.Herrmann, S et al. (2009). \"Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level\".
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 approachesc, 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. This is experimentally established in many tests of relativistic energy and momentum.
EventA precedesB in the red frame, is simultaneous withB in the green frame, and followsB in the blue frame.
More generally, it is normally impossible for information or energy to travel faster thanc. 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 eventsA andB is greater than the time interval between them multiplied byc then there are frames of reference in whichA precedesB, others in whichB precedesA, and others in which they are simultaneous. As a result, if something were travelling faster thanc relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated.\n{{cite journal\n |last=Liberati |first=S |last2=Sonego |first2=S |last3=Visser |first3=M\n |year=2002\n |title=Faster-than-''c'' signals, special relativity, and causality and would lead to paradoxes such as the tachyonic antitelephone.
Faster-than-light observations and experiments
Main article: Faster-than-light
Further information: Superluminal motion
There are situations in which it may seem that matter, energy, or information travels at speeds greater thanc, 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. For example, the phase velocity of X-rays through most glasses can routinely exceed c,
If a laser beam is swept quickly across a distant object, the spot of light can move faster thanc, although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speedc. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speedc from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster thanc, after a delay in time.
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 ofc. However, this does not represent the speed of any single object as measured in a single inertial frame.[39]
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 (i.e., faster than light could travel from one particle to the other). However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.
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.This could result in a virtual particle crossing a large gap faster-than-light. However, no information can be sent using this effect.
So-called superluminal motion is seen in certain astronomical objects,Rees, M (1966). \"The Appearance of Relativistically Expanding Radio Sources\". 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.
In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion through space, but rather to the expansion of space itself.[39] For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere, the rate at which their distance from Earth increases becomes greater than the speed of light.
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 speedc with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant ε0 and the magnetic constant μ0 by the equation c = 1/√ε0μ0.Panofsky, WKH; Phillips, M (1962). Classical Electricity and Magnetism. Addison-Wesley. p. 182. 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.
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 speedc of special relativity would then be the upper limit of the speed of light in vacuum.Gibbs, P (1997) [1996]. Carlip, S, ed. Proca theory,Adelberger, E; Dvali, G; Gruzinov, A (2007). \"Photon Mass Bound Destroyed by Vortices\". Physical Review Letters 98 (1): 010402. grams;Sidharth, BG (2008). Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14 eV/c2[51] (roughly 2×10−47g).
Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of the spectrum of gamma-ray burst GRB 090510 did not find any difference in the speeds of photons of different energies, confirming that Lorentz invariance is verified at least down to the scale of the Planck length (lP=√ħG/c3≈ 69651616300000000001.6163×10−35m) divided by 1.2.Amelino-Camelia, G (2009). \"Astrophysics: Burst of support for relativity\".
