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Encyclopedia > Speed of light
A line showing the speed of light on a scale model of Earth and the Moon, taking about 1⅓ seconds to traverse that distance.
Light traveling through a medium such as air (for example, this laser) travels slower than light through a vacuum.

The speed of light in the vacuum of free space is an important physical constant usually denoted by the letter c.[1] It is the speed of all electromagnetic radiation, including visible light, in free space. It is the speed of anything having zero rest mass[2]. In metric units, the speed of light in vacuum is defined to be exactly 299,792,458 metres per second (1,079,252,849 km/h).[3] The speed of light can be assigned a definite numerical value because the fundamental SI unit of length, the metre, has been defined since October 21, 1983, as the distance light travels in a vacuum in 1/299,792,458 of a second; in other words, any increase in the measurement precision of the speed of light would refine the definition of the metre, but not alter the numerical value of c. The approximate value of 3×108 m/s is commonly used in rough estimates (the error is 0.07%). In imperial units, the speed of light is about 670,616,629.4 miles per hour or 983,571,056.4 feet per second, which is about 186,282.397 miles per second, or roughly one foot per nanosecond. See also the later section of this article at "Speed of light set by definition". Download high resolution version (1024x92, 4 KB)Self-made File links There are no pages that link to this file. ... Download high resolution version (1024x92, 4 KB)Self-made File links There are no pages that link to this file. ... This article is about Earth as a planet. ... This article is about Earths moon. ... Image File history File links Usaf-laser. ... Image File history File links Usaf-laser. ... For other uses, see Laser (disambiguation). ... A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... For other uses, see Light (disambiguation). ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... To help compare different orders of magnitude, the following list describes various speed levels between 1. ... Metre per second (U.S. spelling: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector), defined by distance in metres divided by time in seconds. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... This article is about the unit of length. ... is the 294th day of the year (295th in leap years) in the Gregorian calendar. ... For the Jimi Hendrix song, see 1983. ... This article is about the unit of time. ... This article is about post-1824 imperial units, see also English unit, U.S. customary units or Avoirdupois. ... Feet per second is a unit of speed; it expressses the number of feet traveled in one second. ... “Miles” redirects here. ... A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, ′ – a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ... To help compare orders of magnitude of different times this page lists times between 10−9 seconds and 10−8 seconds (1 nanosecond and 10 nanoseconds) See also times of other orders of magnitude. ... A line showing the speed of light on a scale model of Earth and the Moon, taking about 1â…“ seconds to traverse that distance. ...


The speed of light when it passes through a transparent or translucent material medium, like glass or air, is less than its speed in a vacuum. The ratio of the speed of light in the vacuum to the observed phase velocity is called the refractive index of the medium. See dispersion (optics). In general relativity c remains an important constant of spacetime, however the concepts of 'distance', 'time', and therefore 'speed' are not always unambiguously defined due to the curvature of spacetime caused by gravitation. When measured locally, light in a vacuum always passes an observer at c. Transparent glass ball In optics, transparency is the property of allowing light to pass. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... Dispersion of a light beam in a prism. ... For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ... Gravity redirects here. ... In mathematics, something is said to occur locally in the category of topological spaces if it occurs on small enough open sets. ...

Contents

Overview

The speed of light in vacuum is now viewed as a fundamental physical constant. This postulate, together with the principle of relativity that all inertial frames are equivalent, forms the basis of Einstein's theory of special relativity. According to the currently prevailing definition, adopted in 1983, the speed of light is exactly 299,792,458 metres per second (approximately 3×108 metres per second, or about 30 centimetres (1 foot) per nanosecond). See metre. For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ... A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, ′ – a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ... To help compare orders of magnitude of different times this page lists times between 10−9 seconds and 10−8 seconds (1 nanosecond and 10 nanoseconds) See also times of other orders of magnitude. ... This article is about the unit of length. ...


Experimental evidence has shown that the speed of light is independent of the motion of the source. It has also been confirmed experimentally that the two-way speed of light (for example from a source, to a mirror, and back again) is constant. It is not, however, possible to measure the 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 receiver should be synchronized[4]. Einstein (who was aware of this fact) postulated that the speed of light should be taken as constant in all cases, one-way and two-way.


It is worth noting that it is the constant speed c, rather than light itself, that is fundamental to special relativity; thus if light is somehow manipulated to travel at less than c, this manipulation will not directly affect the theory of special relativity.


Observers traveling at large velocities will find that distances and times are distorted in accordance with the Lorentz transforms; however, the transformations distort times and distances in such a way that the speed of light remains constant. An observer moving with respect to a collection of light sources would find that light from the sources ahead would be shifted toward the violet end of the spectrum while light from those behind was redshifted. In physics, the Lorentz transformation converts between two different observers measurements of space and time, where one observer is in constant motion with respect to the other. ... Blue shift is the opposite of redshift, the latter being much more noted due to its importance to modern astronomy. ... This article is about the physical phenomenon. ...


Use of the symbol 'c' for the speed of light

The symbol 'c' for 'constant' or the Latin celeritas ("swiftness")[5] is generally used for the speed of light. NIST and BIPM practice is to use c0 for the speed of light in vacuum. Occasionally, some writers use c for the speed of light in media other than vacuum. Throughout this article c is used exclusively to denote the speed of light in a vacuum. For other uses, see Latins and Latin (disambiguation). ... Celeritas is a Latin word, translated as swiftness or speed. It is often given as the origin of the symbol c, the universal notation for the speed of light in a vacuum, as popularised in Albert Einsteins famous equation E=mc². Also, according to Georges Dumézil, Celeres were... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ...


In branches of physics in which the speed of light plays an important part, for example relativity, it is common to use a system of units in which c is 1, thus no symbol for the speed of light is required.


Causality and information transfer

If information could travel faster than c in one reference frame, causality would be violated: in some other reference frames, the information would be received before it had been sent, so the "effect" could be observed before the "cause". Such a violation of causality has never been recorded[6]. Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ...

A light cone defines locations that are in causal contact and those that are not.
A light cone defines locations that are in causal contact and those that are not.

To put it another way, information propagates to and from a point from regions defined by a light cone. The interval AB in the diagram to the right is "time-like" (that is, there is a frame of reference in which event A and event B occur at the same location in space, separated only by their occurring at different times, and if A precedes B in that frame then A precedes B in all frames: there is no frame of reference in which event A and event B occur simultaneously). Thus, it is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the "cause" and B the "effect"). Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ... Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ... The term interval is used in the following contexts: cricket mathematics music time This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... In the context of special relativity, time-like separated points (or events) in spacetime have a spacetime interval greater than 0 (see sign convention). ...


On the other hand, the interval AC in the diagram to the right is "space-like" (that is, there is a frame of reference in which event A and event C occur simultaneously, separated only in space; see simultaneity). However, there are also frames in which A precedes C (as shown) or in which C precedes A. Barring some way of traveling faster than light, it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C. In the context of special relativity, space-like separated points (or events) in spacetime have a spacetime interval less than 0 (see sign convention). ... Simultaneity is the property of two events happening at the same time in at least ONE Reference frame. ... Faster than the speed of light redirects here. ...


Light years

Astronomical distances are sometimes measured in light years (the distance that light would travel in one Earth year, roughly 9.46×1012 kilometres or about 5.88×1012 miles). Because light travels at a large but finite speed, it takes time for light to cover large distances. Thus, the light we observe from distant objects in the universe was emitted from them long ago: in effect, we see their distant past. For other uses, see Astronomy (disambiguation). ... A light-year or lightyear (symbol: ly) is a unit of measurement of length, specifically the distance light travels in vacuum in one year. ... To help compare different distances this page lists lengths starting at 1015 m (1,000,000 million km). ...


Communications and GPS

The speed of light is of relevance to communications. For example, given the equatorial circumference of the Earth is about 40,075 km and c about 300,000 km/s, the theoretical shortest amount of time for a piece of information to travel half the globe along the surface is 0.0668 s. Copy of the original phone of Alexander Graham Bell at the Musée des Arts et Métiers in Paris Telecommunication is the assisted transmission of signals over a distance for the purpose of communication. ... This article is about Earth as a planet. ...


The actual transit time is longer, in part because the speed of light is slower by about 30% in an optical fiber[citation needed] depending on its refractive index n, v = c / n and straight lines rarely occur in global communications situations, but also because delays are created when the signal passes through an electronic switch or signal regenerator. A typical time as of 2004 for a U.S. to Australia or Japan computer-to-computer ping is 0.18 s. The speed of light additionally affects wireless communications design. Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... For other uses of terms redirecting here, see US (disambiguation), USA (disambiguation), and United States (disambiguation) Motto In God We Trust(since 1956) (From Many, One; Latin, traditional) Anthem The Star-Spangled Banner Capital Washington, D.C. Largest city New York City National language English (de facto)1 Demonym American... For other uses, see Ping (disambiguation). ... It has been suggested that this article or section be merged with Wireless. ...


Another consequence of the finite speed of light is that communications with spacecraft are not instantaneous, and the gap becomes more noticeable as distances increase. This delay was significant for communications between Houston ground control and Apollo 8 when it became the first spacecraft to orbit the Moon: for every question, Houston had to wait nearly 3 seconds for the answer to arrive, even when the astronauts replied immediately. Houston redirects here. ... Ground Control was a real-time tactics game developed by Massive Entertainment and was at the time a forerunner in its genre, winning many industry awards. ... Apollo 8 was the Apollo space programs second successful manned mission. ... This article is about Earths moon. ... This article is about the unit of time. ...


This effect forms the basis of the Global Positioning System (GPS) and similar navigation systems. One's position can be determined by means of the delays in radio signals received from a number of satellites, each carrying a very accurate atomic clock, and very carefully synchronized. It is remarkable that, to work properly, this method requires that (among many other effects) the relative motion of satellite and receiver be taken into effect, which was how (on an interplanetary scale) the finite speed of light was originally discovered (see the following section). GPS redirects here. ... This article is about determination of position and direction on or above the surface of the earth. ... “Nuclear Clock” redirects here. ... Synchronization is coordination with respect to time. ...


Similarly, instantaneous remote control of interplanetary spacecraft is impossible because it takes time for the Earth-based controllers to receive information from the craft, and an equal time for instructions to be received by the craft. It can take hours for controllers to become aware of a problem, respond with instructions, and have the spacecraft receive the instructions.


The speed of light can also be of concern on very short distances. In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 GHz, a signal can only travel a maximum of 300 mm in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips. For other uses, see Supercomputer (disambiguation). ... CPU redirects here. ... A gigahertz is a billion hertz or a thousand megahertz, a measure of frequency. ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window, showing the integrated circuit inside. ...


Physics

Constant velocity from all inertial reference frames

Most individuals are accustomed to the addition rule of velocities: if two cars approach each other from opposite directions, each traveling at a speed of 50 km/h, relative to the road surface, one expects that each car will measure the other as approaching at a combined speed of 50 + 50 = 100 km/h to a very high degree of accuracy. Kilometres per hour (American spelling: kilometers per hour) is a unit of both speed (scalar) and velocity (vector). ...


However, as speeds increase this rule becomes less accurate. Two spaceships approaching each other, each traveling at 90% the speed of light relative to some third observer between them, do not measure each other as approaching at 90% + 90% = 180% the speed of light; instead they each measure the other as approaching at slightly less than 99.5% the speed of light. This last result is given by the Einstein velocity addition formula:[7] “Einstein” redirects here. ... A velocity addition formula appears in the special theory of relativity as a consequence of the Lorentz transformations. ...

u = {v + w over 1 + v w / {c}^2} ,!

where v and w are the (positive) velocities of the spaceships as measured by the third observer, and u is the measured velocity of either space ship as observed by the other.[8] This reduces to u = v + w for sufficiently small values of v and w (such as those typically encountered in common daily experiences), as the term vw / c2 approaches zero, reducing the denominator to 1.


If one of the velocities for the above formula (or both) are c, the final result is c, as is expected if the speed of light is the same in all reference frames. Another important result is that this formula always returns a value which is less than c whenever v and w are less than c: this shows that no acceleration in any frame of reference can cause one to exceed the speed of light with respect to another observer. Thus c acts as a speed limit for all objects with respect to all other objects in special relativity.


Luminiferous aether (discredited)

Interference pattern produced with a Michelson interferometer
Interference pattern produced with a Michelson interferometer

Before the advent of special relativity, it was believed that light travels through a medium called the luminiferous aether. Maxwell’s equations predict a given speed of light, in much the same way as is the speed of sound in air. The speed of sound in air is relative to the movement of the air itself, and the speed of sound in air with respect to an observer may be changed if the observer is moving with respect to the air (or vice versa). The speed of light was believed to be relative to a medium of transmission for light that acted as air does for the transmission of sound—the luminiferous aether. Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ... Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ... The luminiferous aether: it was hypothesised that the Earth moves through a medium of aether that carries light In the late 19th century luminiferous aether (light-bearing aether) was the term used to describe a medium for the propagation of light. ... For other uses, see Speed of sound (disambiguation). ... Look up air in Wiktionary, the free dictionary. ... For other uses, see Wind (disambiguation). ...


The Michelson–Morley experiment, arguably the most famous and useful failed experiment in the history of physics, was designed to detect the motion of the Earth through the luminiferous aether. It could not find any trace of this kind of motion, suggesting, as a result, that it is impossible to detect one's presumed absolute motion, that is, motion with respect to the hypothesized luminiferous aether. The Michelson–Morley experiment said little about the speed of light relative to the light’s source and observer’s velocity, as both the source and observer in this experiment were traveling at the same velocity together in space. The Michelson-Morley experiment, one of the most important and famous experiments in the history of physics, was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University, and is considered by some to be the first strong evidence against the theory of...


Interaction with transparent materials

The refractive index of a material indicates how much slower the speed of light is in that medium than in a vacuum. The slower speed of light in materials can cause refraction, as demonstrated by this prism (in the case of a prism splitting white light into a spectrum of colours, the refraction is known as dispersion).
The refractive index of a material indicates how much slower the speed of light is in that medium than in a vacuum. The slower speed of light in materials can cause refraction, as demonstrated by this prism (in the case of a prism splitting white light into a spectrum of colours, the refraction is known as dispersion).

In passing through materials, the observed speed of light can differ from c. The ratio of c to the phase velocity of light in the material is called the refractive index. The speed of light in air is only slightly less than c. Denser media, such as water and glass, can slow light much more, to fractions such as tfrac{1}{2} and tfrac{2}{3} of c. Through diamond, light is much slower—only about 124,000 kilometres per second, less than tfrac{1}{2} of c.[9] This reduction in speed is also responsible for bending of light at an interface between two materials with different indices, a phenomenon known as refraction. prism splitting light Source: NASA File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... prism splitting light Source: NASA File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... For the property of metals, see refraction (metallurgy). ... Diagram of a triangular prism, dispersing light Lamps as seen through a prism. ... Visible light redirects here. ... Dispersion of a light beam in a prism. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... Air redirects here. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... This article is about the material. ... For the property of metals, see refraction (metallurgy). ...


Since the speed of light in a material depends on the refractive index, and the refractive index may depend on the frequency of the light, light at different frequencies can travel at different speeds through the same material. This effect is called dispersion. Dispersion can mean any of several things: A phenomenon that causes the separation of a wave into components of varying frequency. ...


Classically, considering electromagnetic radiation to be a wave, the charges of each atom (primarily the electrons) interact with the electric and magnetic fields of the radiation, slowing its progress. For other uses, see Electron (disambiguation). ...


A more complete description of the passage of light through a medium is given by quantum electrodynamics. Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. ...


Accelerated frames of reference and general relativity

Since the early part of the 20th century lightspeed in vacuum has been considered a property of our spacetime metric, i.e. an exchange rate between seconds and meters and thus an effective "limit speed for energy" in general[10]. In general relativity, the metric tensor (or simply the metric) is the fundamental object of study. ...


Although it is constant in inertial frames of reference in special relativity, the speed of light can vary based on its position for accelerated frames of reference in special relativity and in general relativity. Before heading into this discussion, it must first be noted that in all cases the speed of light locally remains c in these cases. So when an observer measures the speed of light at his own position, the constancy of its speed holds. The issue arises at positions distant from the observer in these situations.


The cause of this change is gravitational time dilation. As clocks at lower gravitational potentials tick slower, a beam of light will take longer to move along a rod at a lower gravitational potential than it would take to move along an identical rod at ones own potential. This light is considered to be moving more slowly at lower potentials. This slowdown becomes extreme as the light approaches the event horizon of a black hole, where both time and light will appear to stop. Similarly, light will appear to go faster at higher gravitational potentials. Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... For the science fiction film, see Event Horizon (film). ... For other uses, see Black hole (disambiguation). ...


In general relativity, the curvature of spacetime can also affect the number of rods between certain positions. This will add another factor to magnitude of the apparent speed change.


Faster-than-light observations and experiments

Main article: Faster-than-light
The blue glow in this "swimming pool" nuclear reactor is Čerenkov radiation, emitted as a result of electrons traveling faster than the speed of light in water.
The blue glow in this "swimming pool" nuclear reactor is Čerenkov radiation, emitted as a result of electrons traveling faster than the speed of light in water.

It is generally considered that it is impossible for any information or matter to travel faster than c. The equations of relativity show that, for an object travelling faster than c, some physical quantities would be not represented by real numbers. However, there are many physical situations in which speeds greater than c are encountered. Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... Image File history File links Question_book-3. ... Image File history File links TrigaReactorCore. ... Image File history File links TrigaReactorCore. ... Core of a small nuclear reactor used for research. ... ÄŒerenkov radiation glowing in the core of a TRIGA reactor ÄŒerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. ... For other uses, see Electron (disambiguation). ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... This article is about matter in physics and chemistry. ... Please refer to Real vs. ...


Things which can travel faster than c

Wave velocities and synchronized events

It has long been known theoretically that it is possible for the "group velocity" of light to exceed c.[11] One recent experiment made the group velocity of laser beams travel for extremely short distances through caesium atoms at 300 times c. In 2002, at the Université de Moncton, physicist Alain Haché made history by sending pulses at a group velocity of three times light speed over a long distance for the first time, transmitted through a 120-metre cable made from a coaxial photonic crystal.[12] However, it is not possible to use this technique to transfer information faster than c: the velocity of information transfer depends on the front velocity (the speed at which the first rise of a pulse above zero moves forward) and the product of the group velocity and the front velocity is equal to the square of the normal speed of light in the material. The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... For other uses, see Laser (disambiguation). ... General Name, Symbol, Number caesium, Cs, 55 Chemical series alkali metals Group, Period, Block 1, 6, s Appearance silvery gold Standard atomic weight 132. ... The Université de Moncton is a French language university in Moncton, New Brunswick serving the Acadian community of Atlantic Canada. ... The opal in this bracelet contains a natural periodic microstructure responsible for its iridescent color. ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... Front velocity is the speed at which the first rise of a pulse above zero moves forward. ...


Exceeding the group velocity of light in this manner is comparable to exceeding the speed of sound by arranging people distantly spaced in a line, and asking them all to shout "I'm here!", one after another with short intervals, each one timing it by looking at their own wristwatch so they don't have to wait until they hear the previous person shouting. Another example can be seen when watching ocean waves washing up on shore. With a narrow enough angle between the wave and the shoreline, the breakers travel along the waves' length much faster than the waves' movement inland.


Light spots and shadows

If a laser is swept across a distant object, the spot of light can easily be made to move at greater than c[13]. Similarly, a shadow projected onto a distant object can be made to move faster than c. In neither case does any matter or information travel faster than light.


Quantum mechanics

The speed of light may also appear to be exceeded in some phenomena involving evanescent waves, such as tunnelling. Experiments indicate that the phase velocity and the group velocity of evanescent waves may exceed c; however, it would appear that the front velocity does not exceed c, so, again, it is not possible for information to be transmitted faster than c. An evanescent wave is an electromagnetic wave that decays exponentially with distance. ... In quantum mechanics, quantum tunnelling is a micro and nanoscopic phenomenon in which a particle violates principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...


In quantum mechanics, certain quantum effects may be transmitted at speeds greater than c (indeed, action at a distance has long been perceived by some as a problem with quantum mechanics: see EPR paradox, interpretations of quantum mechanics). For example, the quantum states of two particles can be entangled, so the state of one particle fixes the state of the other particle (say, one must have spin +½ and the other must have spin −½). Until the particles are observed, they exist in a superposition of two quantum states, (+½, −½) and (−½, +½). If the particles are separated and one of them is observed to determine its quantum state then the quantum state of the second particle is determined automatically. If, as in some interpretations of quantum mechanics, one presumes that the information about the quantum state is local to one particle, then one must conclude that second particle takes up its quantum state instantaneously, as soon as the first observation is carried out. However, it is impossible to control which quantum state the first particle will take on when it is observed, so no information can be transmitted in this manner. The laws of physics also appear to prevent information from being transferred through more clever ways and this has led to the formulation of rules such as the no-cloning theorem and the no-communication theorem. For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ... In a nontechnical sense, an interpretation of quantum mechanics is an attempt to answer the question: what exactly is quantum mechanics talking about? Quantum mechanics has been very successful in predicting experimental results. ... Probability densities for the electron at different quantum numbers (l) In quantum mechanics, the quantum state of a system is a set of numbers that fully describe a quantum system. ... It has been suggested that Quantum coherence be merged into this article or section. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... Quantum superposition is the application of the superposition principle to quantum mechanics. ... The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. ... In quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible. ...


Closing speeds

If two objects are travelling towards one another, each at 0.8c as measured in a particular inertial frame of reference, then they are getting closer together at 1.6c as measured in that frame[14]. This is called a closing speed. Note that a closing speed does not represent the speed of any object in an inertial frame.


Proper Speeds

If a spaceship travels to a planet one light year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance travelled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a proper velocity. There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. Note that a light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller.


Things which only appear to travel faster than c

So-called superluminal motion is seen in certain astronomical objects, such as the 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 at a small angle to the line of sight. In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, quasars and recently also in some galactic sources called microquasars. ... Relativistic Jet. ... An active galaxy is a galaxy where a significant fraction of the energy output is not emitted by the normal components of a galaxy: stars, dust and interstellar gas. ... This article is about the astronomical object. ... The word projection can mean more than one thing. ... This article is about angles in geometry. ...


Travel faster than the speed of light in a medium

Although it may sound paradoxical, it is possible for shock waves to be formed with electromagnetic radiation. As a charged particle travels through an insulating medium, it disrupts the local electromagnetic field in the medium. Electrons in the atoms of the medium will be displaced and polarised by the passing field of the charged particle, and photons are emitted as the electrons in the medium restore themselves to equilibrium after the disruption has passed. (In a conductor, the equilibrium can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves travel, as when a charged particle exceeds the speed of light in that medium, the photons constructively interfere and intensify the observed radiation. The result (analogous to a sonic boom) is known as Čerenkov radiation. Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ... This article or section is in need of attention from an expert on the subject. ... In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ... In science and engineering, conductors are materials that contain movable charges of electricity. ... For other uses, see Sonic boom (disambiguation). ... ÄŒerenkov radiation glowing in the core of a TRIGA reactor ÄŒerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. ...


General relativity

Some topics (such as the expansion of the universe, and wormholes) require the application of general relativity and are covered in the main faster than light article. For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ...


Other theories concerning the speed of light

Particles that travel faster than light, dubbed tachyons, have been proposed by particle physicists but have yet to be observed, and would potentially violate causality if they were. A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Causality or causation denotes the relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first. ...


Some physicists, notably João Magueijo and John Moffat, have proposed that in the past light traveled much faster than the current speed of light. This theory is called variable speed of light (VSL) and its supporters claim that it has the ability to explain many cosmological puzzles better than its rival, the inflation model of the universe. However, it has not gained wide acceptance. João Magueijo at the journée de la Science at the EPFL, on the 11th of November 2005 João Magueijo is a cosmologist and lecturer in theoretical physics at Imperial College London. ... John Moffat is a Professor Emeritus in physics at the University of Toronto. ... The variable speed of light (VSL) concept states that the speed of light in vacuum, usually denoted by c, may not be constant, for some reason. ... This article is about the physics subject. ... For other uses, see Universe (disambiguation). ...


Science fiction

The ability to communicate or travel faster than light is a popular topic in science fiction. In Orson Scott Card's Ender novels a device known as the ansible has the ability to transmit instant data between communicators that are lightyears apart. Faster than the speed of light redirects here. ... Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ... Orson Scott Card (born August 24, 1951)[1] is a bestselling American author, as well as being a critic, political writer, and speaker. ... Book one in the Enders Game series The Enders Game Series (or simply Ender Series) is a series of science fiction books by Orson Scott Card, started with the short story Enders Game, which was later expanded into the novel Enders Game. ... An ansible is a hypothetical machine, capable of superluminal communication, and used as a plot device in science fiction literature. ... A light year, abbreviated ly, is the distance light travels in one year: roughly 9. ...


Slow light

Main article: Slow light
Refractive phenomena, such as this rainbow, are due to the slower speed of light in a medium (water, in this case).
Refractive phenomena, such as this rainbow, are due to the slower speed of light in a medium (water, in this case).

Light traveling through a medium other than a vacuum travels below c as a result of the time lag between the polarization response of the medium and the incident light. However, certain materials have an exceptionally high group index and a correspondingly low group velocity. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light pulse to about 17 metres per second[15]; in 2001, they were able to momentarily stop a beam.[16] Refractive phenomena, such as this rainbow, are due to the slower speed of light in a medium (water, in this case). ... Image File history File links Supernumerary_rainbow_03_contrast. ... Image File history File links Supernumerary_rainbow_03_contrast. ... For the property of metals, see refraction (metallurgy). ... For other uses, see Rainbow (disambiguation). ... In classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. ... The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... Lene Vestergaard Hau (born Vejle, Denmark November 13, 1959) is a Danish physicist. ...


In 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light by directing it into a Bose–Einstein condensate of the element rubidium, the atoms of which, in Lukin's words, behaved "like tiny mirrors" due to an interference pattern in two "control" beams.[17] Harvard redirects here. ... The Lebedev Physical Institute of the Russian Academy of Sciences is a Russian research institute specializing in physics. ... For other uses, see Moscow (disambiguation). ... A Bose–Einstein condensate (BEC) is a state of matter formed by a system of bosons confined in an external potential and cooled to temperatures very near to absolute zero (0 kelvin or −273. ... General Name, Symbol, Number rubidium, Rb, 37 Chemical series alkali metals Group, Period, Block 1, 5, s Appearance grey white Standard atomic weight 85. ...


History

Until relatively recent times, the speed of light was largely a matter of conjecture. Empedocles maintained that light was something in motion, and therefore there had to be some time elapsed in travelling. Aristotle said that, on the contrary, "light is due to the presence of something, but it is not a movement". Furthermore, if light had a finite speed, it would have to be very great; Aristotle asserted "the strain upon our powers of belief is too great" to believe this. Empedocles (Greek: , ca. ... For other uses, see Aristotle (disambiguation). ...


One of the ancient theories of vision was that light was emitted from the eye, instead of entering the eye from another source. Using this theory, Heron of Alexandria advanced the argument that the speed of light must be infinite, since distant objects such as stars appear immediately upon opening the eyes. Heros aeolipile Hero (or Heron) of Alexandria (c. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...


Medieval and early modern theories

Early Muslim philosophers initially agreed with Aristotle's view that light has an infinite speed. In the 11th century, however, Muslim scientists realized that light has a finite speed. The Iraqi scientist Ibn al-Haytham (Alhacen), the father of optics, using an early experimental scientific method in his Book of Optics, discovered that light has a finite speed. Some of his contemporaries, notably the Persian scientists Avicenna and al-Biruni, also agreed with Alhacen that light has a finite speed. Avicenna "observed that if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite".[18] Al-Biruni further discovered that the speed of light is much faster than the speed of sound.[19] Early Muslim philosophy is considered influential in the rise of modern philosophy. ... For other uses, see Aristotle (disambiguation). ... In the history of science, Islamic science refers to the science developed under the Islamic civilisation between the 8th and 15th centuries (the Islamic Golden Age). ... (Arabic: أبو علي الحسن بن الحسن بن الهيثم, Latinized: Alhacen or (deprecated) Alhazen) (965 – 1039), was an Arab[1] Muslim polymath[2][3] who made significant contributions to the principles of optics, as well as to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, visual perception, and to science in general with his introduction of the... For the book by Sir Isaac Newton, see Opticks. ... In the scientific method, an experiment (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena. ... Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ... The title page of a 1572 Latin manuscript of Ibn al-Haythams Book of Optics The Book of Optics (Arabic: Kitab al-Manazir, Latin: De Aspectibus or Perspectiva) was a seven volume treatise on optics written by the Iraqi Muslim scientist Ibn al-Haytham (Latinized as Alhacen or Alhazen... This article is about the Persian people, an ethnic group found mainly in Iran. ... (Persian: ابن سينا) (c. ... (September 15, 973 in Kath, Khwarezm – December 13, 1048 in Ghazni) was a Persian[1][2][3] Muslim polymath[4] of the 11th century, whose experiments and discoveries were as significant and diverse as those of Leonardo da Vinci or Galileo, five hundred years before the Renaissance; al-Biruni was... For other uses, see Speed of sound (disambiguation). ...


Commenting on a verse in the Rigveda ("Swift and all beautiful art thou, O Surya, maker of the light; illuminating all the radiant realm."),[20] the 14th century Indian scholar Sayana wrote "Thus it is remembered: [O Sun] you who traverse 2202 yojanas [1 yojana is about 9 miles] [ca. 14,000 to 30,000 km] in half a nimesa [ca. 0.1 to 0.2 s]", corresponding to between 65,000 and 300,000 km/s, for high values of yojana and low values of nimesa consistent with the actual speed of light.[21][22] Rig veda is the oldest text in the world. ... Sayana (सायण) was the great 14th century commentator on the Vedas. ... Please wikify (format) this article or section as suggested in the Guide to layout and the Manual of Style. ... It has been suggested that Time in Hindu mythology be merged into this article or section. ...


Johannes Kepler believed that the speed of light is infinite since empty space presents no obstacle to it. Francis Bacon argued that the speed of light is not necessarily infinite, since something can travel too fast to be perceived. René Descartes argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light is infinite. Descartes speculated that if the speed of light was found to be finite, his whole system of philosophy might be demolished.[23] Kepler redirects here. ... Sir Francis Bacon Francis Bacon, 1st Viscount St Albans, KC (22 January 1561 – 9 April 1626) was an English astrologer, philosopher, statesman, spy, freemason and essayist. ... Descartes redirects here. ... Sol redirects here. ... This article is about Earth as a planet. ... This article is about Earths moon. ... Time lapse movie of the 3 March 2007 lunar eclipse A lunar eclipse occurs whenever the Moon passes through some portion of the Earth’s shadow. ...


Measurement of the speed of light

Early attempts

Isaac Beeckman proposed an experiment (1629) in which a person would observe the flash of a cannon reflecting off a mirror about one mile away. Galileo proposed an experiment (1638), 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. This experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile. No delay was observed. Robert Hooke explained the negative results as Galileo had by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great. Isaac Beeckman (December 10, 1588 - May 19, 1637) was a Dutch philosopher and scientist. ... For other uses, see Cannon (disambiguation). ... A mirror, reflecting a vase. ... Galileo redirects here. ... For other uses, see Lantern (disambiguation). ... The Accademia del Cimento (Academy of Experiment), a early scientific society, was founded in Florence 1657 by students of Galileo, Evangelista Torricelli and Vincenzo Viviani. ... Florence (or Firenze, Florentia and Fiorenza) is the capital city of the Italian region of Tuscany, and of the province of Florence. ... Robert Hooke, FRS (July 18, 1635 – March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ...

Rømer's observations of the occultations of Io from Earth.
Rømer's observations of the occultations of Io from Earth.

Image File history File links Download high-resolution version (436x825, 46 KB) A diagram of Jupiter (B) eclipsing its moon Io (DC) as viewed from different points in earths orbit around the sun. ... Image File history File links Download high-resolution version (436x825, 46 KB) A diagram of Jupiter (B) eclipsing its moon Io (DC) as viewed from different points in earths orbit around the sun. ...

Astronomical techniques

The first quantitative estimate of the speed of light was made in 1676 by Ole Christensen Rømer, who was studying the motions of Jupiter's moon, Io, with a telescope. It is possible to time the orbital revolution of Io because it enters and exits Jupiter's shadow at regular intervals (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5 hours when Earth was closest to Jupiter (at H). He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. This was as a result of the extra time it took for light to cross the extra distance between the planets, time which had accumulated in the interval between one signal and the next. The opposite is the case when they are approaching (as from F to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the astronomical unit); the modern estimate is about 16 minutes and 40 seconds. Ole Rømer. ... This article or section is in need of attention from an expert on the subject. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Atmosphere Surface pressure: trace Composition: 90% sulfur dioxide Io (eye-oe, IPA: , Greek Ῑώ) is the innermost of the four Galilean moons of Jupiter and, with a diameter of 3,642 kilometers, is the fourth largest moon in the Solar System. ... This article does not cite any references or sources. ... Orbital revolution is the cyclical path taken by one object around another object (or point, line, etc. ... With regards to time, an interval is the duration between two events or occurrences of similar events. ... The hour (symbol: h) is a unit of time. ... This article is about Earth as a planet. ... The astronomical unit (AU or au or a. ...


Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by Christiaan Huygens, who estimated the speed of light to be 1,000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), 26% lower than the currently accepted value, but still very much faster than any physical phenomenon then known. Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629 – July 8, 1698), was a Dutch mathematician, astronomer and physicist; born in The Hague as the son of Constantijn Huygens. ...


Isaac Newton also accepted the finite speed. In his 1704 book Opticks he reports the value of 16.6 Earth diameters per second (210,000 kilometres per second, 30% less than the actual value), which it seems he inferred for himself (whether from Rømer's data, or otherwise, is not known). The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. And later observations also showed the effect with the three other Galilean moons, where it was more difficult to observe, thus laying to rest some further objections that had been raised. Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Opticks or a treatise of the reflections, refractions, inflections and colours of light Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. ...


Even if, by these observations, the finite speed of light may not have been established to everyone's satisfaction (notably Jean-Dominique Cassini's), after the observations of James Bradley (1728), the hypothesis of infinite speed was considered discredited. Bradley deduced that starlight falling on the Earth should appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit to the speed of light. This "aberration of light", as it is called, was observed to be about 1/200 of a degree. Bradley calculated the speed of light as about 298,000 kilometres per second (185,000 miles per second). This is only slightly less than the currently accepted value (less than one percent). The aberration effect has been studied extensively over the succeeding centuries, notably by Friedrich Georg Wilhelm Struve and de:Magnus Nyrén. Giovanni Domenico (Jean-Dominique) Cassini Portrait Giovanni Domenico Cassini (June 8, 1625–September 14, 1712) was an Italian astronomer, engineer, and astrologer. ... James Bradley (March 1693 – July 13, 1762) was an English astronomer, Astronomer Royal from 1742. ... The aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects. ... Friedrich Georg Wilhelm von Struve Friedrich Georg Wilhelm von Struve (April 15, 1793 – November 23, 1864 (Julian calendar: November 11)) was a German-Russian astronomer. ...

Diagram of the Fizeau-Foucault apparatus.
Diagram of the Fizeau-Foucault apparatus.

Drawn by Theresa Knott File links The following pages link to this file: Speed of light Fizeau-Foucault apparatus User:Theresa knott/image gallery Categories: GFDL images ... Drawn by Theresa Knott File links The following pages link to this file: Speed of light Fizeau-Foucault apparatus User:Theresa knott/image gallery Categories: GFDL images ... The Fizeau-Foucault apparatus (1850) was designed by the French physicists Hippolyte Fizeau and Léon Foucault for measuring the speed of light. ...

Earth-bound techniques

The first successful measurement of the speed of light using an earthbound apparatus was carried out by Hippolyte Fizeau in 1849. (This measures the speed of light in air, which is slower than the speed of light in vacuum by a factor of the refractive index of air, about 1.0003.) Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror several thousand metres away. On the way from the source to the mirror, the beam passed through a rotating cog wheel. At a certain rate of rotation, the beam could pass through one gap on the way out and another on the way back. But at slightly higher or lower rates, the beam would strike a tooth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 kilometres per second. Fizeau's method was later refined by Marie Alfred Cornu (1872) and Joseph Perrotin (1900). Armand Hippolyte Louis Fizeau Armand Hippolyte Louis Fizeau (September 23, 1819-1896), French physicist, was born in Paris. ... Marie Alfred Cornu (March 6, 1841—April 12, 1902) was a French physicist. ... Henri Joseph Anastase Perrotin (December 19, 1845 – February 29, 1904) was a French astronomer. ...


Leon Foucault improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estimate, published in 1862, was 298,000 kilometres per second. Foucault's method was also used by Simon Newcomb and Albert A. Michelson. Michelson began his lengthy career by replicating and improving on Foucault's method. J. B. Léon Foucault Jean Bernard Léon Foucault (18 September 1819–11 February 1868) was a French physicist best known for the invention of the Foucault pendulum, a device demonstrating the effect of the Earths rotation. ... Simon Newcomb. ... Albert Abraham Michelson. ...


In 1926, Michelson used a rotating prism to measure the time it took light to make a round trip from Mount Wilson to Mount San Antonio in California, a distance of about 22 miles (36 km). The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second). If a shaft of light entering a prism is sufficiently narrow, a spectrum results. ... Mount Wilson is one of the more prominent peaks in the San Gabriel Mountains, part of the Angeles National Forest in Los Angeles County, California, USA. It is the location of the Mount Wilson Observatory and has become the astronomical center of Southern California with 60 inch (1524 mm) and... Mount San Antonio, better known to most Angelenos as Old Baldy or Mount Baldy, is the highest peak in the San Gabriel Mountains of Southern California, USA. While not as unique in its landscape as Seattles Mount Rainier, they are similar in being easily sighted for miles around their... This article is about the U.S. state. ...


Laboratory-based methods

During World War II, the development of the cavity resonance wavemeter for use in radar, together with precision timing methods, opened the way to laboratory-based measurements of the speed of light. In 1946, Louis Essen in collaboration with A.C. Gordon-Smith used a microwave cavity of precisely known dimensions to establish the frequency for a variety of normal modes of microwaves—which, in common with all electromagnetic radiation, travels at the speed of light in vacuum. As the wavelength of the modes was known from the geometry of the cavity and from electromagnetic theory, knowledge of the associated frequencies enabled a calculation of the speed of light. Their result, 299,792±3 km/s, was substantially greater than those found by optical techniques, and prompted much controversy. However, by 1950 repeated measurements by Essen established a result of 299,792.5±1 km/s; this became the value adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. Most subsequent measurements have been consistent with this value. Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... It has been suggested that this article or section be merged into resonator. ... For other uses, see Radar (disambiguation). ... Louis Essen (September 6, 1908 – August 24, 1997) was an English physicist whose most notable achievements were in the precise measurement of time and the determination of the speed of light. ... This article is about the type of Electromagnetic radiation. ... For other uses, see Frequency (disambiguation). ... For other types of mode, see mode. ... For other uses, see Wavelength (disambiguation). ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Essen is a city in the center of the Ruhr Area in North Rhine-Westphalia, Germany. ... The International Union of Radio Science (in French, LUnion radio-scientifique internationale - URSI) is one of 26 international scientific unions affiliated to the International Council for Science. ...


With modern electronics (and most particularly the availability of oscilloscopes with time resolutions in the sub-nanosecond regime) the speed of light can now be directly measured by timing the delay of a light pulse from a laser or a LED in reflecting from a mirror, and this kind of experiment is now routine in undergraduate physics laboratories.[24][25][26]


Speed of light set by definition

In 1983, the 17th Conférence Générale des Poids et Mesures defined the metre in terms of the distance traveled by light in a given amount of time, which amounts to adopting a standard value for the speed of light in vacuum:[27] The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures (CGPM, sometimes written in English Conférence Générale des Poids et Mesures). ... This article is about the unit of length. ...

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.[3]

Here, the term vacuum is meant in the technical sense of free space. This definition of the metre relies on the definition of the second, which is: In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... This article is about the unit of time. ...

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.[28][29]

The consequence of this definition is that further refinements in the current experimental value of the speed of light would only adjust the length of a metre.[30] This point is made explicit by nondimensionalization in the article on Maxwell's equations. The value of c, or c0[31], namely: Nondimensionalization refers to the partial or full removal of units from a mathematical equation by a suitable substitution of variables. ... For thermodynamic relations, see Maxwell relations. ...

 c = c_0  stackrel{mathrm{def}}{=} 299,792,458  mathrm {m/s}  ,

combined with the definition of magnetic constant μ0, also defines the electric constant ε0 in SI units. The magnetic constant μ0 is not dependent on c and as a result of the definition of the ampere, has a standard value in SI units of:[32] The magnetic constant () is the permeability of vacuum. ... The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The magnetic constant () is the permeability of vacuum. ... For other uses, see Ampere (disambiguation). ... Look up si, Si, SI in Wiktionary, the free dictionary. ...

 mu_0  stackrel{mathrm{def}}{=} 4,pi,times 10^{-7} quad mathrm{(in~ kg, m, s^{-2}, A^{-2}, , or , N , A^{-2})}  ..

The electric constant has then the exact value [33]

 varepsilon_0  stackrel{mathrm{def}}{=} frac {1}{mu_0 {c}^2} approx 8.854187817 ldots times 10^{-12} quad mathrm{(in~ A^2, s^4, kg^{-1}, m^{-3}, , or , F , m^{-1})}  .

These constants appear in Maxwell's equations. For thermodynamic relations, see Maxwell relations. ...


Special relativity

After the work of James Clerk Maxwell, it was believed that light travelled at a constant speed relative to the "luminiferous aether", the medium that was then thought to be necessary for the transmission of light. This speed was determined by the (permittivity and permeability) of the aether. James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... The luminiferous aether: it was hypothesised that the Earth moves through a medium of aether that carries light In the late 19th century luminiferous aether (light-bearing aether) was the term used to describe a medium for the propagation of light. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ...

A schematic representation of a Michelson interferometer, as used for the Michelson-Morley experiment.
A schematic representation of a Michelson interferometer, as used for the Michelson-Morley experiment.

In 1887, the physicists Albert Michelson and Edward Morley performed the influential Michelson-Morley experiment to measure the speed of light relative to the motion of the earth, the goal being to measure the velocity of the Earth through the aether. As shown in the diagram of a Michelson interferometer, a half-silvered mirror was used to split a beam of monochromatic light into two beams traveling at right angles to one another. After leaving the splitter, each beam was reflected back and forth between mirrors several times (the same number for each beam to give a long but equal path length; the actual Michelson-Morley experiment used more mirrors than shown) then recombined to produce a pattern of constructive and destructive interference. Any slight change in speed of light along each arm of the interferometer (because the apparatus was moving with the Earth through the proposed "aether") would change the amount of time that the beam spent in transit, which would then be observed as a change in the pattern of interference. In the event, the experiment gave a null result. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Albert Abraham Michelson. ... Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ... Albert Abraham Michelson. ... Edward Morley (1887). ... The Michelson-Morley experiment, one of the most important and famous experiments in the history of physics, was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University, and is considered by some to be the first strong evidence against the theory of... This article is about Earth as a planet. ... Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ... A beam splitter is an optical device, that splits a beam of light in two. ... Something which is monochromatic has a single color. ... This article is about angles in geometry. ... A mirror, reflecting a vase. ... A mirror, reflecting a vase. ... For other uses, see Interference (disambiguation). ... Generally, a null result is a result which is null (nothing): that is, the absence of an observable result. ...


Ernst Mach was among the first physicists to suggest that the experiment amounted to a disproof of the aether theory. Developments in theoretical physics had already begun to provide an alternative theory, Fitzgerald-Lorentz contraction, which explained the null result of the experiment. Ernst Mach Ernst Mach (February 18, 1838 – February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ... The Lorentz-FitzGerald contraction hypothesis was proposed by George FitzGerald and independently proposed and extended by Hendrik Lorentz to explain the negative result of the Michelson-Morley experiment, which attempted to detect Earths motion relative to the luminiferous aether. ...


It is uncertain whether Albert Einstein knew the results of the Michelson-Morley experiment, but the null result of the experiment greatly assisted the acceptance of his theory of relativity. The constant speed of light is one of the fundamental Postulates (together with causality and the equivalence of inertial frames) of special relativity. “Einstein” redirects here. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... The theory of Special Relativity states that there are no privileged frames of reference, or in other words, there is no place to stand still and observe the rest of the universe. ...


See also

ÄŒerenkov radiation glowing in the core of a TRIGA reactor ÄŒerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. ... Lasers used for visual effects during a musical performance. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental forces of nature. ... For thermodynamic relations, see Maxwell relations. ... The metre, or meter (symbol: m) is the SI base unit of length. ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... Perhaps the most useful solutions to the electromagnetic wave equation are sinusoidal plane-wave solutions. ... For other uses, see Speed of sound (disambiguation). ... In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ...

References

Footnotes

  1. ^ NIST and BIPM practice is to use c0 for the speed of light in vacuum in accord with international standard ISO 31-5. See NIST Special Publication 330, Appendix 2, p. 45 : "Current practice is to use c0 to denote the speed of light in vacuum (ISO 31)." However older publications use just c and many physicists may continue to do this in cases where there is no ambiguity.
  2. ^ Tai L. Chow (2006). Electromagnetic theory. Sudbury MA: Jones and Bartlett, 391-392. ISBN 0-7637-3827-1. 
  3. ^ a b BIPM. Unit of length (metre). SI brochure, Section 2.1.1.1. BIPM. Retrieved on 2007-11-28.
  4. ^ Zhang, Yuan Zhong. Special Relativity and its Experimental Foundations. World Scientific, p171. 
  5. ^ Why is c the symbol for the speed of light?. Retrieved on 2007-06-05.
  6. ^ Zhang, Yuan Zhong. Special Relativity and its Experimental Foundations. World Scientific, p31. 
  7. ^ Current practice is to use c0 to denote the speed of light in vacuum ISO 31. In the original Recommendation of 1983, the symbol c was used for this purpose.
  8. ^ Francis Weston Sears, Introduction to the Theory of Relativity, p. 24, footnote:

    Except in giving a name to [this equation], the term "velocity" is used in this book to mean the speed and direction of motion. Velocity is a vector quantity, whereas speed refers only to the magnitude of the velocity. Since we have restricted motion to a single dimension (along the x-axis), we have not needed to introduce the concept of velocity here. As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 332nd day of the year (333rd in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 156th day of the year (157th in leap years) in the Gregorian calendar. ... International Standard ISO 31 (Quantities and units, International Organization for Standardization, 1992) is the most widely respected style guide for the use of units of measurement, and formulas involving them, in scientific and educational documents worldwide. ...

  9. ^ Refraction, Snell's law, and total internal reflection. Boston University Physics. Retrieved on 2007-01-24.
  10. ^ L. de Broglie, Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis (Paris), 1924; L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925). Reprinted in Ann. Found. Louis de Broglie 17 (1992) p. 22. translation
  11. ^ Egan, Greg (2000-08-17). Applets Gallery / Subluminal. Retrieved on 2007-02-06.
    References LJ Wang; A Kuzmich & A Dogariu (2000-07-20). "Gain-assisted superluminal light propagation". Nature (406): p277. 
  12. ^ Electrical pulses break light speed record, physicsweb, 22 January 2002; see also A Haché and L Poirier (2002), Appl. Phys. Lett. v.80 p.518.
  13. ^ Shadows and Light Spots. Retrieved on 2008-03-02.
  14. ^ Third Party Observers. Retrieved on 2008-03-02.
  15. ^ L.V. Hau, S.E. Harris, Z. Dutton, and C.H. Behroozi (1999-02-18). "Light speed reduction to 17 metres per second in an ultracold atomic gas" (HTML). Nature 397: 594–598. doi:10.1038/17561. 
  16. ^ C. Liu, Z. Dutton, C.H. Behroozi, and L.V. Hau (2001-01-25). "Observation of coherent optical information storage in an atomic medium using halted light pulses" (PDF). Nature 409: 490–493. doi:10.1038/35054017. 
  17. ^ M. Bajcsy1, A.S. Zibrov, and M.D. Lukin (2003-12-11). "Stationary pulses of light in an atomic medium". Nature 426: 638–641. doi:10.1038/nature02176. 
  18. ^ George Sarton, Introduction to the History of Science, Vol. 1, p. 710.
  19. ^ O'Connor, John J. & Robertson, Edmund F., "Al-Biruni", MacTutor History of Mathematics archive 
  20. ^ RV 1.50.4, How did Indians know about the speed of light even before it was discovered in 1675?
  21. ^ Subhash Kak, "The Speed of light and Puranic cosmology"PDF (107 KiB), Annals of the Bhandarkar Oriental Research Institute 80 (1999) 113–123.
  22. ^ Subhash C. Kak, "Sayana's astronomy"PDF (83.4 KiB), Indian Journal of the History of Science 33 (1998) 31–36.
  23. ^ Historical Background, footnote 5. Statistics and Actuarial Science, University of Waterloo. Retrieved on 2007-08-03.
  24. ^ J. Cooke, M. Martin, . McCartney and H. Wilf, “Direct determination of the speed of light as a general physics laboratory experiment”, American Journal of Physics, Volume 36, p. 847 (1968). See also Ulabe and Hauk, Proc. of the IEEE
  25. ^ Kenichiro Aoki� and Takahisa Mitsui, "A small tabletop experiment for a direct measurement of the speed of light," available from ArXiv (3/20/2008)
  26. ^ Mary B. James, Robert B. Ormond, and Aric J. Stasch, "Speed of light measurement for the myriad," American Journal of Physics, Volume 67, Issue 8, August 1999 pp. 681-684, doi:10.1119/1.19352 Available from AIP (3/20/2008)
  27. ^ This definition raises an interesting question: What really is a vacuum? For a discussion, see the article free space.
  28. ^ BIPM. Unit of time (second). SI brochure, Section 2.1.1.1. BIPM. Retrieved on 2008-01-30.
  29. ^ This definition is subject to a note: This definition refers to a caesium atom at rest at a temperature of 0 K. This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K.
  30. ^ "The new definition of the meter, accepted by the 17th Conférence Générale des Poids et Mesures in 1983, was quite simple and elegant: [See definition in text]. A consequence of this definition is that the speed of light is now a defined constant, not to be measured again." NIST
  31. ^ International standards agencies now use c0 to denote the speed of light in vacuum, following standard ISO 31-5. See, for example, the BIPM SI Units brochure, 8th Edition.
  32. ^ NIST magnetic constant
  33. ^ NIST electric constant

Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 24th day of the year in the Gregorian calendar. ... Greg Egan (August 20, 1961, Perth, Western Australia) is an Australian computer programmer and science fiction author. ... Year 2000 (MM) was a leap year starting on Saturday. ... is the 229th day of the year (230th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 37th day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 61st day of the year (62nd in leap years) in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 61st day of the year (62nd in leap years) in the Gregorian calendar. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... George Alfred Leon Sarton (1884-1956) was a seminal Belgian-American polymath and historian of science. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The first Mandala of the Rig Veda has 191 hymns. ... “PDF” redirects here. ... A kibibyte (a contraction of kilo binary byte) is a unit of information or computer storage, commonly abbreviated KiB (never kiB). 1 kibibyte = 210 bytes = 1,024 bytes The kibibyte is closely related to the kilobyte, which can be used either as a synonym for kibibyte or to refer to... “PDF” redirects here. ... A kibibyte (a contraction of kilo binary byte) is a unit of information or computer storage, commonly abbreviated KiB (never kiB). 1 kibibyte = 210 bytes = 1,024 bytes The kibibyte is closely related to the kilobyte, which can be used either as a synonym for kibibyte or to refer to... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 215th day of the year (216th in leap years) in the Gregorian calendar. ... In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 30th day of the year in the Gregorian calendar. ...

Historical references

  • Ole Rømer. "Démonstration touchant le mouvement de la lumière", Journal des sçavans, 7 Décembre 1676, pp. 223–236. Translated as "A Demonstration concerning the Motion of Light", Philosophical Transactions of the Royal Society no. 136, pp. 893–894; June 25, 1677. (Rømer's 1676 paper, in English and French, as bitmap images, and in French as plain text)
  • 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", Philosophical Transactions XVIII, No. 214, pp 237–256, Nov.–Dec., 1694.
  • H.L. Fizeau. "Sur une expérience relative à la vitesse de propagation de la lumière", Comptes Rendus 29, 90–92, 132, 1849.
  • J.L. Foucault. "Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil", Comptes Rendus 55, 501–503, 792–796, 1862.
  • A.A. Michelson. "Experimental Determination of the Velocity of Light", Proceedings of the American Association for the Advancement of Science 27, 71–77, 1878. (Project Gutenberg Etext version)
  • Simon Newcomb. "The Velocity of Light", Nature, pp 29–32, May 13, 1886.
  • Joseph Perrotin. "Sur la vitesse de la lumière", Comptes Rendus 131, 731–734, 1900.
  • A.A. Michelson, F.G. Pease, and F. Pearson. "Measurement Of The Velocity Of Light In A Partial Vacuum", Astrophysical Journal 82, 26–61, 1935.

The first issue of the Journal des sçavans (title page) The Journal des sçavans (later renamed Journal des savants), founded by Denis de Sallo, was the earliest scientific journal published in Europe. ... For other uses, see Royal Society (disambiguation). ...

Modern references

  • Léon Brillouin. Wave propagation and group velocity. Academic Press Inc., 1960.
  • John David Jackson. Classical electrodynamics. John Wiley & Sons, 2nd edition, 1975; 3rd edition, 1998. ISBN 0-471-30932-X
  • R.J. MacKay and R.W. Oldford. "Scientific Method, Statistical Method and the Speed of Light", Statistical Science 15(3):254–278, 2000.
  • Gerd Keiser. Optical Fiber Communications, pp 32.Mcgraw-Hill, 3rd edition, 2000. ISBN 0072321016.

External links

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