The speed of light is the speed of electromagnetic waves. Light travels at slower speed inside materials like glass or water; its highest speed is in a vacuum. The speed of light in vacuum is a universal physical constant denoted (in ISO and IEC standards ), exactly equal to It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of second. The value . For other approximations of , valid for various units and size scales see the infobox. The shorter form, speed of light, means speed of light in vacuum in any context where the vacuum is implied.
All forms of electromagnetic radiation, including visible light, travel in vacuum at the speed c as do massless particles and field perturbations, such as gravitational waves. The speed of light in vacuum is the same for all observers, no matter their relative velocity. As a result, massless particles and waves travel at in a vacuum regardless of the motion of the source or the inertial reference frame of the observer. The speed of light in vacuum is the upper limit for the speed at which information, matter, or energy can travel through space. Extract of page 497. Extract of page 79. Particles with nonzero rest mass can be accelerated to approach but can never reach it, regardless of the frame of reference in which their speed is measured.
For long distances and sensitive measurements, the finite speed of light has noticeable effects. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take hours for signals to travel. In computing, the speed of light fixes the ultimate minimum communication delay. The speed of light in vacuum can be used in time of flight measurements to measure large distances to extremely high precision.
The speed at which light propagates through transparent materials, such as glass or air, is less than ; similarly, the speed of electromagnetic waves around wire cables (the speed of electricity) is slower than . The ratio between and the speed at which light travels in a material is called the refractive index of the material (). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about slower than .
In the context of relativity, luminal speed may be used. In some cases, objects or waves may appear to travel faster than light, also called superluminal speed. Simplistic calculations of the speed of distant galaxies due to the expansion of the universe appear to exceed the speed of light, but only local velocity can be defined uniquely. Ole Rømer first demonstrated that light does not travel instantaneously by studying the apparent motion of Jupiter's moon Io. In an 1865 paper, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed . Albert Einstein postulated that the speed of light with respect to any inertial frame of reference is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity, and so showed that the parameter had relevance outside of the context of light and electromagnetism. In the theory of relativity, interrelates space and time and appears in the famous mass–energy equivalence, .See, for example:
Notation The speed of light in vacuum is usually denoted by a lowercase . The origin of the letter choice is unclear, with guesses including "c" for "constant" or the Latin (meaning 'swiftness, celerity'). The "c" was used for "celerity" meaning a velocity in books by Leonhard Euler and others, but this velocity was not specifically for light; Isaac Asimov wrote a popular science article, "C for Celeritas", but did not explain the origin. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used for a different constant that was later shown to equal times the speed of light in vacuum. Historically, the symbol was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1903, Max Abraham used with its modern meaning in a widely read textbook on electromagnetism. Einstein used in his original German-language papers on special relativity in 1905, but in 1907 he switched to , which by then had become the standard symbol for the speed of light."The origins of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch [...] Weber apparently meant c to stand for 'constant' in his force law, but there is evidence that physicists such as Lorentz and Einstein were accustomed to a common convention that c could be used as a variable for velocity. This usage can be traced back to the classic Latin texts in which c stood for 'celeritas', meaning 'speed'."
Sometimes is used for the speed of waves in any material medium, and 0 for the speed of light in vacuum.See, for example:
In unit systems
The constant is defined in the International System of Units (SI) as . This fixed value is used to define the metre as exactly the distance that light travels in vacuum in of a second. The second is, in turn, defined to be the length of time occupied by of the radiation emitted by a caesium-133 atom in a transition between two specified energy states. By using the fixed value of and an accurate measurement of the second, the value for the standard metre is defined.See, for example:
Prior to 1983, the meter was defined separately from the second and the speed of light was measured experimentally. The particular value adopted for the fixed speed of light in the current unit system was chosen to agree with the best measurements available before 1983. The current definition of the second was adopted in 1967.
As a dimensional physical constant, the numerical value of is different for different unit systems. For example, in imperial units, the speed of light is approximately miles per second. The speed of light is less than 2% different from 1 billion feet per second or one foot per nanosecond. Naval officer and computer scientist Grace Murray Hopper distributed foot-long wires to colleagues in the late 1960s to visually illustrate the importance of designing smaller components to increase computing speed.
In branches of physics in which appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where . Using these units, does not appear explicitly because multiplication or division by1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted.
Role in physics Boundary for effects of special relativity
The speed at which light waves propagate in vacuum is independent of the speed of the wave source relative to any observer. The invariance of the speed of light has been verified by experiments such as the Kennedy–Thorndike experiment and the Ives–Stilwell experiment. This invariance of combined with the assumption that the laws of physics are the same for all interactions between objects outside of gravitational fields results in the special theory of relativity.
Special relativity has many experimentally verified but counterintuitive implications. These include the equivalence of mass and energy (), length contraction (moving objects shorten), Terrell rotation (apparent rotation), and time dilation (moving clocks run more slowly). These implications are only evident in circumstances when relative velocities approach the speed of light. Thus the speed of light acts as a boundary between those domains where non-relativistic models are adequate and those domains where relativity must be included.
One way to characterize the transition to relativistic effects is the Lorentz factor. This is the factor by which lengths contract and times dilate and is given bywhere is the speed of the object. The difference of from1 is negligible for speeds much slower than , such as most everyday speedsin which case special relativity is closely approximated by Galilean relativitybut it increases at relativistic speeds and diverges to infinity as approaches . For example, a time dilation factor of occurs at a relative velocity of approximately 86.6% of the speed of light (). Similarly, a time dilation factor of occurs at approximately 99.5% the speed of light ().
Synthesis of space and time
The speed of light relates the units of space and time in the unified geometry called spacetime. Distances are generalized in spacetime to Lorentz intervals
where differences in space () are combined with differences in time using a factor of and a negative sign.
All physical theories based on spacetime satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter . Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. As such, the parameter is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that is also the speed of gravity and of gravitational waves, and observations of gravitational waves have been consistent with this prediction.See, for example:
In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the speed of light is constant and equal to , but the speed of light can differ from when measured from a remote frame of reference, depending on how measurements are extrapolated to the region.
Mass and massless particles Massless particles travel at the speed of light.See appendix 1, The speed of light is an unattainable speed for objects with positive rest mass. An object with rest mass and speed relative to a laboratory has kinetic energy with respect to that lab, where is the Lorentz factor defined above. The factor approaches infinity as approaches , and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. Analysis of individual photons confirm that information cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum.
Causality
More generally, it is impossible for signals or energy to travel faster than . One argument for this is known as causality. If the spatial distance between two events and is greater than the time interval between them multiplied by then there are frames of reference in which precedes , others in which precedes , and others in which they are simultaneous. As a result, if something were travelling faster than relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone.
In some theoretical treatments, the Scharnhorst effect allows signals to travel faster than , by one part in 1036.De Clark, S. G. (2016). The scharnhorst effect: Superluminality and causality in effective field theories. The University of Arizona. However other approaches to the same physical set up show no such effect.See, for example:
and it appears the special conditions in which this effect might occur would prevent one from using it to violate causality.
One-way speed of light