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The term '''speed of light''' generally refers to the [[speed]] of [[light]] in [[ |
The term '''speed of light''' generally refers to the [[speed]] of [[light]] in [[free space|vacuum]],<ref name=free_space> |
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In this context ''vacuum'' (or, more carefully, ''classical vacuum'' or [[free space]]) must be understood as an idealized vacuum, that can be approached in nature, but not actually realized. This use of "vacuum" is not to be confused with ''real'' vacua such as [[vacuum state|quantum vacuum]] or [[QCD vacuum]] that, in principle, ''are'' realizable media. |
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</ref> a fundamental [[physical constant]] usually denoted by the symbol ''c''. It is the speed of not just visible light, but of all [[electromagnetic radiation]], and it is believed to be the speed of anything having zero [[invariant mass|rest mass]],<ref name=Chow>{{cite book |
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| author = T.L. Chow |
| author = T.L. Chow |
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| year = 2006 |
| year = 2006 |
Revision as of 04:10, 20 July 2009
The term speed of light generally refers to the speed of light in vacuum,[2] a fundamental physical constant usually denoted by the symbol c. It is the speed of not just visible light, but of all electromagnetic radiation, and it is believed to be the speed of anything having zero rest mass,[3] and of gravitational waves. The speed of light in vacuum is exactly 299,792,458 metres per second (m/s)[4] since this is the way the metre is defined.
The speed of light is a fundamental constant of spacetime such that no matter or information can travel faster than the speed of light.[5][6] Speeds faster than that of light are encountered in physics but, in all such cases, no matter or information is transmitted faster than c.
For many practical purposes, the speed of light is so great that it can be regarded to travel instantaneously. An exception is where long distances or precise time measurements are involved. For example, in the Global Positioning System (GPS), a GPS receiver measures its distance to satellites based on how long it takes for a radio signal to arrive from the satellite. In astronomy, distances are often measured in light-years, the distance light travels in a year .[7]
The speed of light when it passes through a transparent or translucent material medium, like glass or air, is less than its speed in free space. The speed is inversely proportional to the refractive index of the medium. In specially-prepared media, the speed can be tiny, or even zero.
For many years the speed of light was the subject of speculation, some believing it to be infinite. The first effective measurements of the speed of light were made in the seventeenth century, and these were progressively refined until, in 1983, the speed of light in free space was fixed by definition.
Numerical value, notation and units
Speed of light in different units | |
---|---|
metres per second | 299,792,458 (exact) |
km per hour | 1,079,252,848.8 (exact) |
miles per hour | ≈ 670,616,629 |
miles per second | ≈ 186,282.397 |
Approximate length of time for light to travel... | |
One foot | 1.02 nanoseconds |
One metre | 3.3 nanoseconds |
One km | 3.3 microseconds |
One mile | 5.4 microseconds |
To Earth from geostationary orbit | 0.12 seconds |
Around Earth's equator | 0.13 seconds |
To Earth from the moon | 1.3 seconds |
To Earth from the sun | 8.3 minutes |
To Earth from Alpha Centauri | 4.4 years |
Across the Milky Way | 100,000 years |
The metre is defined as the distance light travels in vacuum in 1⁄299,792,458 of a second. The effect of this definition is to fix the speed of light in vacuum at exactly 299 792 458 m/s." NIST. As speed of light is fixed by definition and the value of the magnetic constant is defined [8] to be 4π×10−7 H/m the value of the electric constant is now also fixed.
By everyday standards, light travels very rapidly, roughly a million times faster than sound in air, and fast enough to circle the Earth more than 7 times in one second.
The symbol "c" for "constant" or the Latin celeritas (meaning “swiftness”)[9] is used for the speed of light in free space, and in this article c is used exclusively this way. Some authors, however, use "c" for the speed of light in any material medium, and "c0" for the speed of light in free space.[10] This subscripted notation, which is endorsed in official SI literature,[11][12] has the same form as other constants of free space; namely μ0, ε0 and Z0.
In branches of physics in which the speed of light plays an important part, such as in relativity, it is common to use a system of units known as natural units in which c is 1; thus no symbol for the speed of light is required.
Fundamental importance in physics
Light as electromagnetic radiation
Light is a form of electromagnetic radiation[13]. In the theory of classical electromagnetism it is described by the electromagnetic wave equation which is derived from Maxwell's equations. According to this theory, the speed of light in free space is related to the electric constant ε0 (also called the permittivity of free space) and the magnetic constant μ0 (also called the permeability of free space) by the equation c02=1/(ε0 μ0) in SI units.[14]
In Gaussian units, the speed of light fixes the ratio between electrostatic and electromagnetic units.
A more complete theory of light and its interaction with matter is given by quantum electrodynamics in which c plays the role of a fundamental constant.
Some theories of quantum gravity predict tiny variations of speed of light depending on the energy of the photon.[15] An established variation would be a strong confirmation of these theories, and experimentalists are searching for such variations. However, to date such variations, if any, are smaller than experimental errors of observation - the measured speed of electromagnetic radiation is the same for different frequencies to within very stringent experimental limits.[16][17][18]
Spacetime constant
Speed constant in all inertial frames
The speed of light is a fundamental constant of the spacetime in which we live. Light is measured to travel at the same speed in all inertial frames regardless of the motion of the source, although the observed frequency may change due to the Doppler effect.
Experimental evidence has shown that the speed of light is independent of the motion of the source. [19] [20] It has also been confirmed by the Michelson-Morley experiment and others that the two-way speed of light (for example from a source, to a mirror, and back again) is constant.[21][22] 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 detector should be synchronized.[19] 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.
Relativity
The postulate that the speed of light is the same in all inertial frames, together with the principle of relativity that all inertial frames are equivalent, forms the basis of Einstein's theory of special relativity, in which space and time are viewed as a four dimensional unification of space and time, known as spacetime,[24] with c playing the fundamental role of a conversion factor between the units of space and time, and mass and energy according to the famous mass-energy equation E = mc2. [25]
The finite speed of light in relativity leads to some counter-intuitive consequences, which include length contraction, time dilation and the relativity of simultaneity, this last item contradicting the classical notion that the duration of the time interval between two events is equal for all observers.
In Einstein's general theory of relativity, spacetime is curved by the presence of matter and energy causing gravitation.[26] Disturbances in this curvature, including gravitational waves, propagate at the speed of light.[27][28]
Causality and information transfer
According to the theory of special relativity, causality would be violated if information could travel faster than c in some reference frame, 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.[19]
Information propagates to and from a point forming 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"). In other words, c represents the maximum speed at which matter, energy, or information can be transmitted.
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.[29]
Composition 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, according to intuitive Galilean relativity, one expects that each car will measure the other as approaching at a speed of 50 + 50 = 100 km/h. However, as speeds increase the simple addition of speeds becomes less accurate. Two spaceships approaching each other, each traveling at 90% the speed of light relative to some third observer, would 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 velocity-composition formula[30]
where v1 and v2 are the 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. This reduces to u = v1 + v2 for sufficiently small values of v1 and v2 (such as those typically encountered in common daily experiences), as the term (v1·v2)/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 inertial reference frames. Another important result is that this formula never returns a value greater than c, this is consistent with c being the maximum possible speed.
Speed of light in cosmology
Some scientists have questioned why the fundamental constants of nature, including the speed of light, have the values they do, and whether they are changing as the universe evolves.[31][32][33] These questions remain an interest of on-going research.[34][35][36][37][38]
Others have suggested that the speed of light may exhibit dispersion.[39] However, observations of astrophysical events at high redshifts can be used to place severe limits on the variation of the speed of light with frequency, as well as on the photon mass mγ. [40]
Light in transparent media
Refractive index and refraction
When light travels through a transparent material, it travels more slowly that it does through free space. This is due to the interaction of the light with the electrons bound to the atoms in the material[41] . The refractive index of a transparent material indicates how much slower light propagates in that medium than in a vacuum, being the ratio of the c to the phase velocity of light in the material. In the simple case the refractive index is taken to be a constant but in some materials it may depend on the light's frequency, intensity, polarization, or direction of propagation. The refractive index in air is only slightly larger than one [1]. Denser media, such as water and glass, have refractive indices of between 1.3 and 1.5 for visible light. Diamond has a refractive index of about 2.4.
Classically, when an electromagnetic wave meets the surface of a dielectric material at an angle, the leading edge is slowed while the trailing edge continues normally. This causes the wave to change direction. This is called refraction and the change in direction may be calculated from the refractive index using Snell's law[42].
Dispersion
The dependence of the speed of light in a material on its frequency is known as dispersion.
When a light pulse comprised of multiple frequencies passes through transparent materials, the speed of light is characterized by two speeds: the phase velocity and the group velocity. The phase velocity of light may be found from knowledge of the frequency-dependent refractive index:
where εr is the material's relative permittivity, and μr is its relative permeability.
The group velocity of the wave is the speed at which the envelope of the pulse travels through the medium, and is dependent on the frequency content of the pulse as well as the properties of the medium. A wave with different group and phase velocities is said to undergo dispersion.
When light enters materials its energy is absorbed. In the case of transparent materials (dielectrics) this energy is quickly re-radiated. However, this absorption and re-radiation introduces a delay. As light propagates through dielectric material it undergoes continuous absorption and re-radiation. Therefore when the speed of light in a medium is said to be less than c, this should be read as the speed of energy propagation at the macroscopic level. At an atomic level, electromagnetic waves always travel at c in the empty space between atoms. Two factors influence this slowing; stronger absorption leading to shorter path length between each re-radiation cycle and longer delays. The slowing is therefore the product of these two factors. This reduction in speed is also responsible for bending of light at an interface between two materials with different refractive indices, a phenomenon known as refraction.
General media
In real materials the current and charge densities appearing in Maxwell's equations are determined by the way charges respond to the electromagnetic fields. One approach to describing this behavior is the calculation of constitutive equations, which describe how charges behave within the medium, usually using a linear approximation. (Ohm's law is an example.) In simplest form, the constitutive equations replace the electric constant and magnetic constant of free space by the electric permittivity and magnetic permeability of the medium. However, nonlinear behavior also occurs, as in ferroelectric materials, for example. A consequence of the charge response to fields is that the speed of light may become dependent upon field amplitudes, polarization, direction of propagation, and frequency. One field concerned with the calculation of these relationships is condensed matter physics.
Slow light
Certain materials have an exceptionally high group index and a correspondingly low group velocity for light waves. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light pulse to about 17 m/s;[43] in 2001, they were able to momentarily stop a beam.[44]
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.[45][46]
Faster-than-light observations and experiments
It is generally considered that it is impossible for any information or matter to travel faster than c, because it would travel backwards in time relative to some observers.[47] However, there are many physical situations in which speeds greater than c are encountered.
Some of these situations involve entities that actually travel faster than c in a particular reference frame but none involves either matter, energy, or information traveling faster than the speed of light in vacuum.
It is possible for the group velocity of light to exceed c[48][49] and in an experiment in 2000 laser beams traveled for extremely short distances through caesium atoms with a group velocity of 300 times c.[50] It is not, however, possible to use this technique to transfer information faster than c since the velocity of information transfer depends on the front velocity, which is always less than c.[51]
If a laser is swept across a distant object, the spot of light can easily be made to move at a speed greater than c.[52] Similarly, a shadow projected onto a distant object can be made to move faster than c.[53] In neither case does any matter or information travel faster than light.
In some interpretations of quantum mechanics, certain quantum effects may be transmitted at speeds greater than c. For example, the quantum states of two particles can be entangled. Until the particles are observed, they exist in a superposition of two quantum states. 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 and faster than a light signal could travel between the two particles. 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.
Another prediction of faster-than-light speeds occurs for quantum tunneling and is called the Hartman effect.[54][55] However, no information can be sent using these effects.[56]
Closing speeds and proper speeds are examples of calculated speeds that may have value in excess of c but that do not represent the speed of an object as measured in a single inertial frame.
So-called superluminal motion is seen in certain astronomical objects,[57] 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.
Čerenkov radiation
It is possible for shock waves to be formed with electromagnetic radiation.[58][59] If a charged particle travels through an insulating medium faster than the speed of light in that medium (but always slower than the speed of light in free space) then electromagnetic radiation is emitted which is analogous to a sonic boom and is known as Čerenkov radiation.
Galaxies moving faster than light
In models of the expanding universe, the further things are from Earth, the faster they move away from us. This movement is not considered to be a straightforward travel, like a rocket for example, but a movement due to the expansion of space itself. This expansion moves distant objects away from us faster and faster the further away they are. At a boundary called the Hubble sphere, the recessional velocity is the speed of light.
Practical effect of the finite speed of light
The speed of light plays an important part in many modern sciences and technologies. Radar systems measure the distance to a target by measuring the time taken for an echo of the light pulse to return. Similarly, a global positioning system (GPS) receiver measures its distance to satellites based on how long it takes for a radio signal to arrive from the satellite. The distances to the moon, planets, and spacecraft are determined by measuring the round-trip travel time.
Another effect of the finite speed of light is stellar aberration. Suppose we look at a star with a telescope idealized as a narrow tube. The light enters the tube from a star at angle θ and travels at speed c taking a time h/c to reach the bottom of the tube, where our eye detects the light. Suppose observations are made from Earth, which is moving with a speed v. During the transit of the light, the tube moves a distance vh/c. Consequently, for the photon to reach the bottom of the tube, the tube must be inclined at an angle φ different from θ , resulting in an apparent position of the star at angle φ.
In astronomy beyond the solar system, distances are often measured in light-years, the distance light travels in a year.
In electronic systems, despite their small size, the speed of light can become a limiting factor in their maximum speed of operation.[60][61]
Speed of light in astronomy
The speed of light is particularly important in astronomy. Due to the vast distances involved it can take a very long time for light to travel from its source to Earth. For example, it takes 13 billion years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago (near the beginning of the universe). The fact that farther-away objects appear younger (due to the finite speed of light) is crucial in astronomy, allowing astronomers to infer the evolution of stars, galaxies, and the universe itself.
Astronomical distances are sometimes measured in light-years, the distance light travels in one year. A light‑year is around 9 trillion km, 6 trillion miles, or 0.3 parsecs. Next to the Sun, the closest star to Earth, Proxima Centauri, is around 4.2 light‑years away.[62]
History
Until relatively recent times, whether the speed of light was infinite was unknown. The debate began in ancient Greece. Empedocles maintained that light was something in motion, and therefore there had to be some time elapsed in traveling. Aristotle said that, on the contrary, "light is due to the presence of something, but it is not a movement".[63] Euclid and Ptolemy advanced the emission theory of vision, which claimed light was emitted from the eye, thus enabling sight. Using that 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.
Early Muslim philosophers initially agreed with the Aristotelian view of the speed of light being infinite. In 1021, Iraqi physicist Alhazen (Ibn al-Haytham) published the Book of Optics, in which he used experiments related to the camera obscura to support the intromission theory of vision, which claimed that light moves from an object into the eye.[64] This led to Alhazen proposing that light must therefore have a finite speed,[63][65][66] and that the speed of light is variable, with its speed decreasing in denser bodies.[66][67] He argued that light is a “substantial matter”, the propagation of which requires time "even if this is hidden to our senses".[68] This debate continued in Europe and the Middle East throughout the Middle Ages.
Also in the 11th century, Abū Rayhān al-Bīrūnī agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.[69] In the 1270s, Witelo considered the possibility of light traveling at infinite speed in a vacuum but slowing down in denser bodies.[70] A comment on a verse in the Rigveda by the 14th century Indian scholar Sayana[71] may be interpreted as suggesting an estimate for the speed of light that is in good agreement with its actual speed. In 1574, the Ottoman astronomer and physicist Taqi al-Din concluded that the speed of light is constant, but variable in denser bodies, and suggested that it would take a long time for light from the stars which are millions of kilometres away to reach the Earth.[72]
Early attempts to measure the speed of light
In the early 17th century, Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it. Francis Bacon argued that the speed of light was 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 was infinite. Descartes speculated that if the speed of light was found to be finite, his whole system of philosophy might be demolished.[63]
In 1629, Isaac Beeckman proposed an experiment in which a person would observe the flash of a cannon reflecting off a mirror about one mile (1.6 km) away. In 1638, Galileo Galilei proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He concluded that the speed of light is ten times faster than the speed of sound, a figure now known to be much too slow.[66] Galileo's experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile (1.6 km), but no delay was observed. Based on the modern value of the speed of light, the actual delay in this experiment would be about 11 microseconds. 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.
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 points C and D in the diagram at right). 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. He realized that these exit "signals" took longer to reach Earth as a result of the extra time it took for light to cross the extra distance between the moving planets. The opposite is the case when they are approaching (as from F to G). Rømer observed 40 orbits of Io when Earth was approaching Jupiter to be 22 minutes shorter than 40 orbits of Io when Earth was moving away from Jupiter.[73] On the basis of those observations, Rømer concluded that it took light 22 minutes to cross the distance the Earth traversed in 80 orbits of Io.[73] This means that in traveling from L to K and F to G, whereas the earth took 80 periods of Io's orbits (42.5 hours), the light only took 22 minutes. This corresponds to a ratio between the speed of light and the speed at which the Earth travels in its orbit around the sun of 9,300. The modern value of the ratio is about 10,100.
Around the same time, the astronomical unit (roughly, the Earth-to-Sun distance) was estimated to be about 140 million kilometres (87 million miles). 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, based on having misinterpreted Rømer's value of 22 minutes to mean the time it would take light to cross the diameter of the orbit of the Earth.[73] 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.
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. The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. 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.
In 1728, James 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 (186,000 miles per second).
Earth-bound techniques
The first successful entirely earthbound measurement of the speed of light was carried out by Hippolyte Fizeau in 1849. Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror 8 km 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. 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.
In 1861 Maxwell proposed a theory which linked the speed of light to the electromagnetic field.[74] In 1864 Maxwell compared known measurements of the speed of light with the ratio of electrostatic to electromagnetic units by Weber and Kohlrausch to support the connection between light and electromagnetic phenomena.[74] Maxwell’s equations allow the speed of light to be calculated, in much the same way as the speed of sound can be calculated in normal matter.
The 'luminiferous aether'
After some proposals in the 17th and 18th century, Augustin Fresnel in 1818 argued that light moved through a rigid and stationary aether as a way to explain the existence of aberration and polarization. And because of James Clerk Maxwell's (1861) aether based concept of electromagnetism, the existence of the aether was widely accepted. In 1887, physicists Albert Michelson and Edward Morley designed an experiment to measure the velocity of the Earth through the aether.[75] As the Earth is in orbit round the sun, and the aether was assumed to be fixed, the Earth would be expected to be in motion with respect to the aether for at least some of the time.[76] 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 then recombined to produce a pattern of constructive and destructive interference. Any slight change in speed of light along one arm of the interferometer compared with its speed along the other arm would then be observed as a change in the pattern of interference. The experiment gave a null result. Some interesting details of these experiments are found in Hollberg et al.[77] Later experiments confirmed this result to a much higher accuracy.[78][79]
At the beginning the experiment was not understood as disproving the existence of the luminiferous aether, and so some hypothesis (like the Aether drag hypothesis or the Lorentz–Fitzgerald contraction) were made to explain the result within the framework of an aether. So it lasted until the beginning of the 20th century, when some physicists cast doubt on the existence of the aether. Eventually Einstein showed that the aether was not necessary. His theory of special relativity explains the null result of the Michelson–Morley experiment by postulating that the speed of light is always the same for all inertial observers. This means that the speed of light will always be the same in both arms of the interferometer, regardless of their orientation or state of inertial motion, thus no changes in the observed fringes would be expected when it was rotated. Einstein later published his general theory of relativity, which extended his special theory to include gravitation, and the concept of aether rapidly fell into disuse and it forms no part of physics today.
Modern 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 and A.C. Gordon-Smith used a microwave cavity of precisely known dimensions to establish the frequency for a variety of normal modes of microwaves. 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.
The Essen-Gordon-Smith result, 299 792 ± 3 km/s, was substantially more precise 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, which became the value adopted by the 12th General Assembly of the Radio-Scientific Union in 1957.
An alternative to the cavity resonator method to find the wavelength for determining the speed of light is to use a form of interferometer, indicated schematically in the figure.[80] A coherent light beam with a known frequency, as from a laser, is split to follow two paths and then recombined. By carefully changing the path length and observing the interference pattern, the wavelength of the light can be determined, which can be related to the speed of light.
With modern electronics, particularly oscilloscopes with time resolutions of less than one nanosecond, 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, although this method is less precise than either the cavity resonator or the interferometric methods.[81][82][83]
Speed of light set by definition
For reasons stated in Resolution 1,[84] in 1983 the 17th Conférence Générale des Poids et Mesures defined the metre in terms of the distance traveled by light in a given time in perfect vacuum:[11]
"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."
According to NIST[85] "Note that the effect of this definition is to fix the speed of light in vacuum at exactly c = 299 792 458 m/s." According to NIST [86] "A consequence of this definition [adopted by CGPM in 1983] is that the speed of light is now a defined constant, not to be measured again."
A perfect vacuum or free space is a reference state. Like absolute zero, it is an idealized state that only can be approximated in the physical world. Measurements in any real-world medium, such as air[87][88] or a medium perturbed by gravity must be corrected so as to relate to free space.
Because the second can be precisely realized, the new definition allows for a more precise definition of the metre, assuming an adequate realization of "vacuum" is available.
Rather than measure a time-of-flight, one implementation of this definition is to use a recommended source with established frequency(f), and delineate the metre in terms of the wavelength(λ) of this light as determined using the defined numerical value of c and the relationship λ = c / f.[89] Practical realizations of the metre use recommended wavelengths of visible light in a laboratory vacuum with corrections being applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum.
See also
- Faster-than-light
- Electromagnetic wave equation
- Mathematical descriptions of the electromagnetic field
- Maxwell's equations
- Quantum electrodynamics
- Sinusoidal plane-wave solutions of the electromagnetic wave equation
- Slow light
References
Footnotes
- ^ a b Michael De Podesta (2002). Understanding the Properites of Matter. CRC Press. p. 131. ISBN 0415257883.
- ^ In this context vacuum (or, more carefully, classical vacuum or free space) must be understood as an idealized vacuum, that can be approached in nature, but not actually realized. This use of "vacuum" is not to be confused with real vacua such as quantum vacuum or QCD vacuum that, in principle, are realizable media.
- ^ T.L. Chow (2006). Electromagnetic theory. Sudbury MA: Jones and Bartlett. pp. 391–392. ISBN 0-7637-3827-1.
- ^ "Fundamental Physical Constants: Speed of light in vacuum; c, c0". physics.nist.gov.
- ^ Brian Greene (2003). The Elegant Universe. WW Norton & Co. p. 56. ISBN 0393058581.
- ^ PCW Davies (1979). The Forces of Nature. Cambridge University Press. p. 128. ISBN 052122523X.
- ^ Astronomers also use the parsec as a unit of length, which is unrelated to the speed of light.
- ^ "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). Committee on Data for Science and Technology (CODATA): See Table 1. NIST.
- ^ P. Gibbs (1997). "Why is c the symbol for the speed of light?". University of California, Riverside. Retrieved 2008-08-20.
- ^ See, for example, some handbooks:
- D.R. Lide (2004). CRC Handbook of Chemistry and Physics. CRC Press. pp. 2–9. ISBN 0849304857.
- J.W. Harris, W. Benenson, H. Stoecker, H. Lutz (2002). Handbook of Physics. Springer. p. 499.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - J.C. Whitaker (2005). The Electronics Handbook. CRC Press. p. 235. ISBN 0849318890.
- E Richard Cohen; et al. (2007). Quantities, Units and Symbols in Physical Chemistry (3rd ed.). Royal Society of Chemistry. p. 184. ISBN 0854044337.
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: Explicit use of et al. in:|author=
(help)
- ^ a b Le Système international d’unités [The International System of Units] (PDF) (in French and English) (9th ed.), International Bureau of Weights and Measures, 2019, p. 112, ISBN 978-92-822-2272-0
- ^ B.N. Taylor (ed.), A. Thompson (ed.) (2008). The International System of Units (SI): NIST Special Publication 330 (PDF). Washington, DC: NIST. pp. 11, 33–34.
{{cite book}}
:|author=
has generic name (help) - ^ http://www.geo.mtu.edu/rs/back/spectrum/
- ^ W Panofsky, M Phillips (1962). Classical Electricity and Magnetism. Addison Wesley. p. 182.
- ^ Christopher Wanjek. "Quantum Gravity - revealed by gamma ray bursts?". Astronomy Today.
- ^ |title=Severe limits on variations of the speed of light with frequency |author=Bradley E Shaefer |doi=10.1103/PhysRevLett.82.4964}}
- ^ J. Ellis, N.E. Mavromatos, D.V. Nanopoulos, A.S. Sakharov (2003). "Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets". Astron.Astrophys. 403: 409–424. doi:10.1051/0004-6361:20030263.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ Martin Füllekrug (2004). "Probing the Speed of Light with Radio Waves at Extremely Low Frequencies". Phys Rev Lett. 93: 043901. doi:10.1103/PhysRevLett.93.043901.
- ^ a b c Y.Z. Zhang, Y.-C. Chang (1998). Special Relativity and Its Experimental Foundations. World Scientific. p. 173. ISBN 9810227493. Cite error: The named reference "Zhang_Chang" was defined multiple times with different content (see the help page).
- ^ P. Beckman, P. Mandics (1965). "Test of the constancy of the velocity of electromagnetic radiation in high vacuum". J. Res. Natl. Bur. Std. 69D (4): 623. OSTI 4619000.
- ^ R.J. Kennedy, E.M. Thorndike (1932). "Experimental Establishment of the Relativity of Time". Physical Review. 42 (3): 400–418. doi:10.1103/PhysRev.42.400.
- ^ D. Hils, J.L. Hall (1990). "Improved Kennedy-Thorndike experiment to test special relativity". Physical Review Letters. 64 (15): 1697–1700. doi:10.1103/PhysRevLett.64.1697.
- ^ J. Kenneth Shultis, Richard E. Faw (2002). Fundamentals of nuclear science and engineering. CRC Press. p. 151. ISBN 0824708342.
- ^ James B Hartle (2003). Gravity (An introduction to Einstein's general relativity). Addison Wesley. pp. 52–59. ISBN 9810227493.
- ^ D.M. Harrison (1999). "The Special Theory of Relativity". University of Toronto, Department of Physics. Retrieved 2008-12-08.
- ^ John Archibald Wheeler (1990). A journey into Gravity and Spacetime. Scientific American Library. pp. 68–81. ISBN 0-7167-5016-3.
- ^ James B Hartle (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. p. 332. ISBN 0805386629.
- ^ D. Baskaran, A. G. Polnarev, M. S. Pshirkov, K. A. Postnov (2008). "Limits on the speed of gravitational waves from pulsar timing". Phys. Rev. D.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ James B Hartle (2003). Gravity - An introduction to Einstein's General Relativity'. Addison Wesley. p. 59. ISBN 0-8053-8662-9.
- ^ R d'Inverno (1999). Introducing Einstein's Relativity. OUP. p. 34.
- ^ Weyl, H.: Annalen der Physik, vol. 359, Issue 18, pp.117-145 (1917); Weyl, H.: Annalen der Physik, vol. 364, Issue 10, pp.101-133 (1919)
- ^ AS Eddington (1931). "On the instability of Einstein's spherical world". Monthly Notices of the Royal Astronomical Society. 90: 669–678.
- ^ PAM Dirac (1937). "The Cosmological Constants". Nature. 139: 323.
- ^ An overview can be found in the dissertation of DF Mota (2006). "Variations of the Fine Structure Constant in Space and Time". ArXiv version of dissertation.
- ^ Jean-Philippe Uzan (2003). "The fundamental constants and their variation: observational status and theoretical motivations". Rev.Mod.Phys. 74: 403.
- ^ Menas Kafatos, Sisir Roy, Malabika Roy (2005). "Variation of Physical Constants, Redshift and the Arrow of Time". Acta Phys.Polon. B36: 3139–3162.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ DJ Farrell & J Dunning-Davies (2007). "The constancy, or otherwise, of the speed of light". In Louis V. Ross (ed.). New Research on Astrophysics, Neutron Stars and Galaxy Clusters. Nova Publishers. pp. 71ff. ISBN 1600211100.
- ^ Giovanni Amelino-Camelia (2008). "Quantum Gravity Phenomenology". ArXiv preprint.
- ^ Rodolfo Gambini & Jorge Pullin (1999). "Nonstandard optics from quantum spacetime". Phys.Rev. D59.
- ^ Bradley E Shaefer (1999). "Severe limits on variations of the speed of light with frequency". Phys. Rev. Lett. 82: 4964–4966. doi:10.1103/PhysRevLett.82.4964.
- ^ R P Feynman (1963). Lectures on Physics Vol II. Addison-Wesley. pp. 32-1 to 32-3.
- ^ Snell's Law
- ^
L.V. Hau, S.E. Harris, Z. Dutton, C.H. Behroozi (1999). "Light speed reduction to 17 metres per second in an ultracold atomic gas". Nature. 397: 594–598. doi:10.1038/17561.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^
C. Liu, Z. Dutton, C.H. Behroozi, L.V. Hau (2001). "Observation of coherent optical information storage in an atomic medium using halted light pulses" (PDF). Nature. 409: 490–493. doi:10.1038/35054017.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^
M. Bajcsy, A.S. Zibrov, M.D. Lukin (2003). "Stationary pulses of light in an atomic medium". Nature. 426: 638–641. doi:10.1038/nature02176.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ B. Dumé (2003). "Switching light on and off". PhysicsWorld.com. Retrieved 2008-12-08.
- ^ E.F. Taylor, J.A. Wheeler (1992). Spacetime Physics. W. H. Freeman. pp. 74–75. ISBN 0716723271.
- ^ G. Egan (2000). "Subluminal". Retrieved 2007-02-06.
- ^
L.J. Wang, A. Kuzmich, A. Dogariu (2000). "Gain-assisted superluminal light propagation". Nature. 406 (406): 277. doi:10.1038/35018520.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ D. Whitehouse (2000). "Beam smashes light barrier". BBC News. Retrieved 2008-12-08.
- ^
N. Brunner, V. Scarani, M. Wegmüller, M. Legré, N. Gisin (2004). "Direct Measurement of Superluminal Group Velocity and Signal Velocity in an Optical Fiber". Physical Review Letters. 93 (20): 203902. doi:10.1103/PhysRevLett.93.203902.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ P. Gibbs (1997). "Is Faster-Than-Light Travel or Communication Possible?". University of California, Riverside. Retrieved 2008-08-20.
- ^ M. Wertheim (2007). "The Shadow Goes". New York Times.
- ^ Time in Quantum Mechanics. Springer. 2007. p. 48. ISBN 3540734724.
{{cite book}}
: Unknown parameter|editors=
ignored (|editor=
suggested) (help) - ^ Hugo E. Hernández-Figueroa, Michel Zamboni-Rached, Erasmo Recami (2007). Localized Waves. Wiley-Interscience. p. 26. ISBN 0470108851.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ^ Klaas Wynne (2002). "Causality and the nature of information" (PDF). Optics Communications. 209: 84–100.
- ^ M. Rees (1966). "The Appearance of Relativistically Expanding Radio Sources". Nature. 211: 468. doi:10.1038/211468a0.
- ^ P.A. Čerenkov (1934). "Visible Emission of Clean Liquids by Action of γ Radiation". Dokl. Akad. Nauk SSSR. 2: 451.. Reprinted in "Selected Papers of Soviet Physicists". Usp. Fiz. Nauk. 93: 385. 1967.
- ^ A.N. Gorbunova (ed.), E.P. Čerenkov (1999), Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie, Nauka, pp. 149–153
- ^ Hall, S.H. and Hall, G.W. and McCall, J.A. (2000). High Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices. Wiley New York.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ^ E Gad, M Nakla & R Achar (2008). "Model-order reduction of high-speed interconnects using integrated congruence transform". Model Order Reduction. Springer. p. 362. ISBN 3540788409.
{{cite book}}
: Unknown parameter|editors=
ignored (|editor=
suggested) (help) - ^ Further discussion can be found at NASA StarChild
- ^ a b c R.J. MacKay, R.W. Oldford (2000). "Scientific Method, Statistical Method and the Speed of Light". Statistical Science. 15 (3): 254–278. doi:10.1214/ss/1009212817.
- ^ B. Steffens (2006). "Chapter Five – The Scholar of Cairo". Ibn al-Haytham: First Scientist. Morgan Reynolds. ISBN 1599350246.
- ^ S. Hamarneh (1972). "Review: Hakim Mohammed Said, Ibn al-Haitham". Isis. 63 (1): 119. doi:10.1086/350861.
- ^ a b c P.M. Lester (2005). Visual Communication: Images With Messages. Thomson Wadsworth. pp. 10–11. ISBN 0534637205.
- ^ O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics Archive, University of St Andrews
- ^ P. Lauginie (2005). "Measuring: Why? How? What?" (PDF). Eighth International History, Philosophy, Sociology & Science Teaching Conference. Retrieved 2008-07-18.
- ^ O'Connor, John J.; Robertson, Edmund F., "Abu Arrayhan Muhammad ibn Ahmad al-Biruni", MacTutor History of Mathematics Archive, University of St Andrews
- ^ P. Marshall (1981). "Nicole Oresme on the Nature, Reflection, and Speed of Light". Isis. 72 (3): 357–374 [367–74]. doi:10.1086/352787.
- ^ Sayana-commentary on Rigveda 1.50, see: M. Müller (ed.) (1890), Rig-Veda-Samhita, together with the Commentary of Sayana, London: Oxford University Press
{{citation}}
:|author=
has generic name (help) - ^ H.G. Topdemir (1999), Takîyüddîn'in Optik Kitabi, Ankara: Ministry of Culture Press (cf. H.G. Topdemir (2008), Taqi al-Din ibn Ma‘ruf and the Science of Optics: The Nature of Light and the Mechanism of Vision, FSTC, retrieved 2007-07-04)
- ^ a b c
Teuber, Jan (2004), "Ole Rømer og den bevægede Jord – en dansk førsteplads?", in Friedrichsen, Per; Henningsen, Ole; Olsen, Olaf; Thykier, Claus; Tortzen, Chr. Gorm (ed.), Ole Rømer – videnskabsmand og samfundstjener, Kroppedal, Studier i astronomi, Nyere tid, Arkæologi, Gads, pp. 217–219, ISBN 87-12-04139-4
{{citation}}
: CS1 maint: multiple names: editors list (link) Template:Da icon - ^ a b See Maxwell p. 499 in A Dynamical Theory of the Electromagnetic Field (1864) and Maxwell On physical lines of force (1861).
- ^ Michelson, Albert Abraham & Morley, Edward Williams (1887),
{{citation}}
: CS1 maint: multiple names: authors list (link) , American Journal of Science, 34: 333–345 - ^ Berkley Physics Course, Vol 1, Kittel, Knight, Ruderman, Helmholtz, Moyer, McGraw Hill, ISBN 0-07-004880-0 pp. 312-317
- ^ L Hollberg; et al. (2005). "Optical frequency/wavelength references" (PDF). J Phys B: At Mol Opt Phys. 38: S473 ff. doi:10.1088/0953-4075/38/9/003.
{{cite journal}}
: Explicit use of et al. in:|author=
(help) - ^ R C Cialdea, Lett Nuovo Cimento 4 (1972) 821
- ^ D C Champeny, G R Isaak, and A M Kahn, Phys Lett 7 (1963) 241
- ^ A detailed discussion of the interferometer and its use for determining the speed of light can be found in J. M. Vaughan (1989). The Fabry-Perot interferometer. CRC Press. p. 47. ISBN 0852741383. and pp. 384-391.
- ^
J. Cooke, M. Martin, H. McCartney, B. Wilf (1968). "Direct determination of the speed of light as a general physics laboratory experiment". American Journal of Physics. 36 (9): 847. doi:10.1119/1.1975166.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ K. Aoki, T. Mitsui (2008). "A small tabletop experiment for a direct measurement of the speed of light". American Journal of Physics. 76 (9): 812–815. doi:10.1119/1.2919743.
- ^
M.B. James, R.B. Ormond, A.J. Stasch (1999). "Speed of light measurement for the myriad". American Journal of Physics. 67 (8): 681–684. doi:10.1119/1.19352.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ Resolution 1
- ^ Definition of the meter
- ^ NIST document p. 191
- ^ BG Zagar (1999). "Laser Interferometer Displacement Sensors; §6.5". In JG Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. p. 6-69. ISBN 0849383471.
- ^ J Flügge; et al. (2004). "Fundamental length metrology: Practical issues; §D.2.1.3". In CE Webb & JDC Jones (ed.). Handbook of Laser Technology and Applications. Taylor & Francis. pp. 1737 ff. ISBN 0750309660.
{{cite book}}
: Explicit use of et al. in:|author=
(help) - ^ BIPM mise-en-pratique method b.
Historical references
- Rømer, Ole (1676). "Démonstration touchant le mouvement de la lumière". Journal des sçavans: 223–236. Template:Fr icon. Translated as "A Demonstration concerning the Motion of Light". Philosophical Transactions of the Royal Society (136): 893–894. 1677.
- Halley, Edmund (1694). "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 of the Royal Society. 18 (214): 237–256.
- Fizeau, H. L. (1849). Sur une expérience relative à la vitesse de propagation de la lumière. Comptes rendus de l'Académie des sciences (Paris). Vol. 29. pp. 90–92, 132. Template:Fr icon
- Foucault, J. L. (1862). Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil. Comptes rendus de l'Académie des sciences (Paris). Vol. 55. pp. 501–503, 792–796.
- Michelson, A. A. (1878). Experimental Determination of the Velocity of Light. Proceedings of the American Association of Advanced Science. Vol. 27. pp. 71–77.
- Newcomb, Simon (1886), "The Velocity of Light", Nature: 29–32
- Perrotin, Joseph (1900), "Sur la vitesse de la lumière", C. R. Acad. Sci. Paris, 131: 731–734 Template:Fr icon
- Michelson, A. A.; Pease, F. G.; Pearson, F. (1935), "Measurement Of The Velocity Of Light In A Partial Vacuum", Astrophys. J., 82: 26–61, doi:10.1086/143655
Modern references
- Brillouin, Léon (1960), Wave propagation and group velocity, Academic Press
- Jackson, John David (1975), Classical electrodynamics (2nd ed.), John Wiley & Sons, ISBN 0-471-30932-X
- MacKay, R. J.; Oldford, R. W. (2000), "Scientific Method, Statistical Method and the Speed of Light", Statistical Science, 15 (3): 254–278, doi:10.1214/ss/1009212817
- Keiser, Gerd (2000), Optical Fiber Communications (3rd ed.), McGraw-Hill, p. 32, ISBN 0072321016
- Y Jack Ng (2004). "Quantum Foam and Quantum Gravity Phenomenology". In Giovanni Amelino-Camelia & Jerzy Kowalski-Glikman (editors) (ed.). Planck Scale Effects in Astrophysics and Cosmology. Springer. pp. 321ff. ISBN 3540252630.
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has generic name (help)
External links
- Speed of light in vacuum (at NIST)
- Definition of the metre (BIPM)
- Data Gallery: Michelson Speed of Light (Univariate Location Estimation) (download data gathered by A.A. Michelson)
- Subluminal (Java applet demonstrating group velocity information limits)
- De Mora Luminis at MathPages
- Light discussion on adding velocities
- Speed of Light (University of Colorado Department of Physics)
- How is the speed of light measured?
- The Fizeau "Rapidly Rotating Toothed Wheel" Method