Speed of light Information & Speed of light Links at HealthHaven.com
advertise
add site
services
publishers
database
health videos
Bookmark and Share

search wiki for    ?
web dir firms image gallery news hov pdf wiki shop video 
about
toolbar
stats
live show
health store
more stuff
JOIN/LOGIN
Featured Results:
Light and Optics | Speed of light - 3B Scientific
Light and Optics | Speed of light - 3B Scientific
a3bs.com		 Medical Light ing, Exam Light s, Headlights, Ultraviolet Light s, OR...
Medical Lighting, Exam Lights, Headlights, Ultraviolet Lights, OR...
a1medicalsales.com		 GE Multi Slice CT Light Speed QX/i (4 slice)
GE Multi Slice CT Light Speed QX/i (4 slice)
sunrisecorporate.com		 
For other uses, see Speed of light (disambiguation) and Lightspeed (disambiguation).
"Light barrier" redirects here. For the device, see Photoelectric sensor.
The Earth orbits the Sun at a distance of 150 million kilometres, and the Moon in turn orbits the Earth.
Sunlight takes approximately 8 minutes to reach Earth.
Speed of light in different units
metres per second 299,792,458 (exact)
kilometres per second ≈ 300 thousand
kilometres per hour ≈ 1,079 million
miles per second ≈ 186 thousand
miles per hour ≈ 671 million
astronomical units per day ≈ 173
natural units 1
Approximate length of time for light to travel:
One foot 1.0 nanoseconds
One metre 3.3 nanoseconds
One kilometre 3.3 microseconds
One statute mile 5.4 microseconds
To Earth from geostationary orbit 0.12 seconds
The length of 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
To Earth from the Andromeda Galaxy 2,500,000 years

The speed of light (usually denoted c) is a physical constant, and is the speed at which electromagnetic radiation, such as light, travels in vacuum. Its value is 299,792,458 metres per second. This constant is significant in the understanding and study of astronomy, space travel and other fields.

According to the theory of special relativity, c connects space and time in the unified structure of spacetime, and its square is the constant of proportionality between mass and energy (E = mc2).[1] In any inertial frame of reference, independently of the relative velocity of the emitter and the observer, c is the speed of all massless particles and associated fields, including all electromagnetic radiation in free space,[2] and it is believed to be the speed of gravity and of gravitational waves.[3][4] It is an upper bound on the speed at which energy, matter, and information can travel,[5][6] as surpassing it would be equivalent to travelling backwards in time;[7] its finite value is a limiting factor in the speed of operation of electronic devices.[8]

For much of human history, it was not known whether light was transmitted instantaneously or simply very quickly. In the 17th century, Ole Rømer first demonstrated that it travelled at a finite speed by studying the apparent motion of Jupiter's moon Io; using these observations, Christiaan Huygens estimated the speed of light to be at least 220,000 kilometres per second. Since then, scientists have devised increasingly sophisticated techniques to improve the precision of measurement. By 1975, the speed of light was known to be 299,792,458 m/s with a relative measurement uncertainty of 4 parts per billion (4 × 10−9), mostly due to the uncertainty in the length of the metre. In 1983, the metre was redefined in the International System of Units (SI) as the distance travelled by light in vacuum in 1⁄299,792,458 of a second. As a result, the numerical value of c in metres per second is now fixed and exact, by definition of the metre.[9][10]

The actual speed at which light propagates through transparent materials, such as glass or air, is less than c; the ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s; the refractive index of air is about 1.0003, so the speed of light in air is very close to c.

Contents

[edit] Numerical value, notation and units

The speed of light is a dimensional physical constant, so its numerical value depends upon the system of units used. In the International System of Units (SI), the metre is defined as the distance light travels in vacuum in 1⁄299,792,458 of a second (see "Redefinition of the metre", below). The effect of this definition is to fix the speed of light in vacuum at exactly 299,792,458 m/s.[11][12][13] Using the common official definitions of the mile (1609.344 metres), the yard (0.9144 metres), the foot (0.3048 metres) and the inch (0.0254 metres),[14] the speed of light can be expressed exactly in imperial units as 186,282 miles, 698 yards, 2 feet, and 5+21⁄127 inches per second.[15]

The speed of light in vacuum is usually denoted by c, for "constant" or the Latin celeritas (meaning "swiftness"). Originally, the symbol V was used, introduced by Maxwell in 1865; c was used in 1856 by Weber and Kohlrausch for a constant later shown to equal √2 times the speed of light in vacuum, and in 1894 Drude redefined it with the modern meaning. Einstein used V in his original 1905 German-language papers on special relativity, but in 1907 he switched to c, which by then had become the standard symbol.[16]

Some authors use c for the speed of waves in any material medium, and c0 for the speed of light in vacuum.[17] This subscripted notation, which is endorsed in official SI literature,[18] has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, and Z0 for the impedance of free space. However, in this article c will be exclusively used for the speed of light in vacuum.

In branches of physics in which the speed of light plays an important part, such as in relativity, it is common to use natural units, in which c = 1.[19][20] Thus, no symbol for the speed of light is required.

[edit] Fundamental importance in physics

[edit] Constant speed in inertial frames

See also: Introduction to special relativity and Special relativity

The speed of light has been shown experimentally to be independent of the motion of the source.[20][21] It has also been confirmed by the Michelson–Morley experiment and other experiments that the two-way speed of light (for example from a source to a mirror and back again) in an inertial frame is constant.[21][22][23][24]

It is not possible, however, 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.[21] Einstein (who was aware of this fact) adopted a synchronization method, the Einstein synchronization, by which the one-way speed of light becomes equal to the two-way speed of light and assumed that the synchronization method could be applied consistently all over the frame. Later it was proven that the assumption of consistency could be removed provided the two-way speed of light on the given inertial frame was a constant (see Einstein synchronisation) as experiments have indeed confirmed to be. Given this possibility, the clocks once synchronized measure a one-way speed which is a constant over the entire frame (homogeneity and isotropy). This is exactly the starting point which appeared as an assumption in Einstein's first works.

The constancy of the two-way speed, not only in the given inertial frame, but also with respect to changes of frame was then used by him to deduce the Lorentz transformations and the theory of special relativity.[25][26] Although the speed of propagation is independent of the motion of the source, the observed frequency can change due to the Doppler effect.

In non-inertial frames (gravitationally curved space or accelerated frames), the local speed of light is constant and equal to c, however the speed of light along a trajectory of finite length can differ from c depending on how distances and times are defined.

[edit] Spacetime constant

See also: Spacetime, Minkowski space, and Lorentz group
A hydrogen-2 nucleus (made of one proton and one neutron) and a hydrogen-3 nucleus (one proton and two neutrons) collide and turn into a neutron with 14.1 MeV and a helium-4 nucleus (two protons and two neutrons) with 3.5 Mev more energy.
Fusion of deuterium with tritium creating helium-4, freeing a neutron, and releasing 17.59 MeV of energy by conversion of mass in accord with E = mc2.[27]

In Einstein's theory of special relativity, space and time are viewed as a four-dimensional unification of space and time, known as spacetime,[28] with c playing the fundamental role of a conversion factor between the units of space and time,[29] and also between mass and energy according to the famous mass–energy equation E = mc2.[30]

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. These effects are very small when the speeds involved are much slower than c, in which case special relativity is closely approximated by Galilean relativity.

In Einstein's theory of general relativity, c is still an important constant of spacetime. This spacetime is curved by the presence of matter and energy causing gravitation.[31] Disturbances of this curvature, including gravitational waves, are predicted by the theory to propagate at the speed of light, although they have not been directly observed yet.[32][33]

[edit] Causality and information transfer

See also: Causal contact, Tachyonic antitelephone, and Horizon problem
A double cone, with the "time" axis passing in it through its vertex and the "space" axis perpendicular to it. Point A is the vertex of the cone, point B is inside the upper cone and point C is outside the cone.
A light cone defines locations that are in causal contact and those that are not.

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,[21] and would lead to paradoxes.[34]

Information propagates to and from a point forming regions defined by a light cone. The spacetime 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 Relativity of simultaneity). In some frames A precedes C (as shown), but in others C precedes A. Therefore there can be no causal connection between A and C, and in particular it is not possible for any matter (or information) to travel from A to C or from C to A.[35]

[edit] Composition of velocities

See also: Velocity addition formula and Fizeau–Foucault apparatus

If two cars approach each other from opposite directions, each travelling at a speed of 50 km/h relative to the road surface, according to intuitive Galilean relativity, one expects that an observer in one car will measure the speed of approach of the other car as 50 + 50 = 100 km/h. However, as speeds increase, the simple addition of speeds becomes less accurate. Two spaceships approaching each other, each travelling at 90% of the speed of light in opposite directions 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-addition formula, which in the case of two velocities in opposite directions along a line is:[36]

u = \frac{v_1 + v_2}{1 + v_1 v_2/{c^2}},

where v1 and v2 are the speeds of the spaceships as measured by the third observer, and u is the measured speed of either spaceship 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 v1v2/c2 becomes negligible, reducing the denominator to 1.

If one of the two speeds vi in the above formula is 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.

[edit] Variations with time

Main article: Variable speed of light

Some scientists have questioned why the fundamental constants of nature, including c, have the values they do, and whether they are changing as the universe evolves.[37][38][39] These questions remain an interest of ongoing research.[40][41][42][43][44][45]

[edit] Propagation of light

In classical physics, light is described as a type of electromagnetic wave. The classical behaviour of the electromagnetic field is described by Maxwell's equations, which predict that the speed c with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant ε0 and the magnetic constant μ0 by the equation c = 1/√ε0μ0).[46]

In modern quantum physics, the electromagnetic field is described by the theory of quantum electrodynamics (or QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field called photons. In QED, photons are massless particles and thus, according to special relativity, they must travel at the speed of light.

Extensions of QED in which the photon has a mass have been considered. In such a theory, their speed would depend on their frequency, and the invariant speed c of special relativity would then be the upper limit of the speed of light in vacuum.[47] To date no such effects have been observed[48][49][50] putting stringent limits of on the photon mass. The limit obtained depends on the used model: if the massive photon is described by Proca theory,[51] the experimental upper bound for its mass is about 10−57 grams.[52] If photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14 eV/c2[51] (equivalent to of the order of 10−47 g).

[edit] In a medium

See also: Refractive index and Dispersion (optics)
A white beam of light enters a prism and a spectrum comes out of it.
The light passing through this prism demonstrates refraction and, by the splitting of white light into a spectrum of colours, 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.[53] The refractive index of a transparent material is defined as the ratio of c to the speed of light v in the material. Larger indexes of refraction indicate smaller speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation. In many cases, though, it can be treated as a material-dependent constant. The refractive index in air is approximately 1.0003.[54] Denser media, such as water and glass, have refractive indexes of around 1.3 and 1.5 respectively for visible light. Diamond has a refractive index of about 2.4.

If the refractive index of a material dependence on the frequency of the light passing through the medium, there exist two notions of speed of light in the medium. The first is speed of a wave light of a single frequency f. This is called the phase velocity vp(f), and is related to (frequency dependent) refractive index n(f) by

vp = cn(f).

The second is average velocity of a pulse of light consisting of different frequencies of light. This is the called the group velocity and not only depends on the properties of the medium but also distribution of frequencies in the pulse. A pulse with different group and phase velocities is said to undergo dispersion.

Certain materials have an exceptionally high group index and a correspondingly low group velocity for light waves, a phenomenon called slow light. 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 (61 km/h; 38 mph);[55] in 2001, they were able to momentarily stop a beam.[56] In 2003, scientists at Harvard University and the Lebedev Physical 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.[57][58]

[edit] Faster-than-light observations and experiments

Main article: Faster-than-light
See also: Scharnhorst effect, Hartman effect, and Chronology protection conjecture

It is widely accepted that it is normally impossible for information or matter to travel faster than c for several reasons. One reason is that if an object were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame.[7] (It is thought that the Scharnhorst effect does allow signals to travel slightly faster than c, but the special conditions in which this effect can occur prevent one from using this effect to violate causality.[59]) However, there are many physical situations in which speeds greater than c are encountered. In some of these, entities travel faster than c in a particular reference frame. Even in these situations, however, neither matter, energy, nor information travels faster than the speed of light in a vacuum.

It is possible for the group velocity of light waves to exceed c.[60][61] In an experiment in 2000, laser beams travelled for extremely short distances through caesium atoms with a group velocity of 300 times c.[62] It is not possible to transmit information faster than c by this means because the speed of information transfer cannot exceed the front velocity of the wave pulse, which is always less than c.[63]

If a laser beam is swept quickly across a distant object, the spot of light can move faster than c.[64] Similarly, a shadow projected onto a distant object can be made to move faster than c.[65] In neither case does any matter or information travel faster than light.

In some interpretations of quantum mechanics, certain quantum effects may be transmitted faster than c. For example, the quantum states of two particles can be entangled. Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined immediately (i.e., faster than light could travel between the particles). However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.[66][67]

Another prediction of faster-than-light speeds occurs for quantum tunnelling and is called the Hartman effect.[68][69] However, no information can be sent using these effects.[70]

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,[71] 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.

[edit] Cherenkov radiation
Main article: Cherenkov radiation
A pool with blue-glowing water with some instruments immersed in it.
The blue glow in this "swimming pool" nuclear reactor is Cherenkov radiation, emitted as a result of electrons travelling faster than the speed of light in water.

It is possible for shock waves to be formed with electromagnetic radiation.[72][73] If a charged particle travels through an electrical insulator faster than the speed of light in that medium (but always slower than the speed of light in vacuum) then electromagnetic radiation is emitted which is analogous to a sonic boom and is known as Cherenkov radiation.

[edit] Galaxies moving faster than light
See also: Metric expansion of space, Hubble's Law, Observable universe, and Cosmological horizon

In models of the expanding universe, the farther 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.

[edit] Practical effect of the finite speed of light

The speed of light plays an important part in many modern sciences and technologies. In electronic systems, despite their small size, the speed of light can become a limiting factor in their maximum speed of operation.[8]

[edit] Transit time

See also: Transit time and Light year
The diameter of the moon is about one quarter of that of Earth, and their distance is about thirty times the diameter of Earth. A beam of light starts from the Earth and reaches the Moon in about a second and a quarter.
A beam of light is depicted travelling between the Earth and the Moon in the same time it takes light to scale the distance between them: 1.255 seconds at its mean orbital (surface to surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.

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 Lunar Laser Ranging Experiment, radar astronomy and the Deep Space Network determine the distances to the Moon, planets and spacecraft respectively by measuring the round-trip travel time.

The finite 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 (13 × 109) 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, when the universe was less than a billion years old. 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, of galaxies, and of the universe itself.

Astronomical distances are sometimes expressed in light-years, especially in popular science publications.[74] A light‑year is the distance light travels in one year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs. Next to the Sun, the closest star to Earth, Proxima Centauri, is around 4.2 light‑years away.[75]

[edit] Doppler effect

Main article: Relativistic Doppler effect
See also: Redshift and Blue shift
Two light spectra with some black lines on them. The pattern of the line is the same for both spectra, but in the lower spectrum the lines are shifted toward the red end.

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blue shift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us, that is, the radial velocity. This is used to detect if an apparently single star is, in reality, a close binary star and even to measure the rotational speed of stars and galaxies.

[edit] Stellar aberration

Main article: Stellar aberration

Stellar aberration is the apparent motion of celestial objects about their real locations due to the finite speed of light and the motion of Earth. It was discovered and later explained by the third Astronomer Royal, James Bradley, in 1725.[76]

Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light, a phenomenon known as the aberration of light.

The figure to the left examines how light from a star (at location 1) travels down a telescope idealized as a narrow tube and moving at a speed v to the right. (This motion is largely due to the Earth as it orbits the Sun.) 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 the light is detected by an observer. During the transit of the light, the tube moves a distance vh/c. Consequently, for the light ray to reach the bottom of the tube, where the tube must be inclined at an angle φ different from θ, resulting in an apparent position of the star at angle φ.

The maximum amount of the aberrational displacement of a star is approximately 20 arcseconds. Although this is a relatively small value, it was well within the observational capability of the instruments available in the early eighteenth century.

[edit] Terrell rotation

Main article: Terrell rotation

Whereas objects passing rapidly by an observer will be measured to have shrunk along the line of relative motion due to Lorentz contraction, they will be actually seen as being rotated. This is due to the differences in time that it takes light to reach the eye of the observer from different parts of the object.[77][78] This effect is known as Terrell rotation.

[edit] History

[edit] Ancient, medieval and early modern speculation

Until relatively recent times, it was not known whether light travelled instantaneously or at a finite speed. The first extant recorded examination of this subject was in ancient Greece. Empedocles maintained that light was something in motion, and therefore must take some time to travel. Aristotle argued, to the contrary, that "light is due to the presence of something, but it is not a movement".[79] Euclid and Ptolemy advanced the emission theory of vision, where light is 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 Islamic philosophers initially agreed with the Aristotelian view that light had no speed of travel. 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 now accepted intromission theory of vision, where light moves from an object into the eye.[80] This led Alhazen to propose that light must therefore have a finite speed,[79][81][82] and that the speed of light is variable, decreasing in denser bodies.[82][83] He argued that light is a "substantial matter", the propagation of which requires time "even if this is hidden to our senses".[84]

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.[85] Roger Bacon argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle.[86][87] In the 1270s, Witelo considered the possibility of light travelling at infinite speed in a vacuum but slowing down in denser bodies.[88] A comment on a verse in the Rigveda by the 14th century Indian scholar Sayana mentioned a speed of light, about 186,400 miles per second, that was chosen so that light would encircle the Puranic universe in one day, making it a "blind hit".[89][90] 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 very distant, to reach the Earth.[91]

In the early 17th century, Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it. 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 were found to be finite, his whole system of philosophy might be demolished.[79]

[edit] First measurement attempts

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 was unable to distinguish whether light travel was instaneous or not, but concluded that if it weren't, it must nevertheless be extraordinarily rapid.[92][93] Galileo's experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile, 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.

[edit] Early astronomical techniques

Rømer's observations of the occultations of Io from Earth
Main article: Rømer's determination of the speed of light

The first quantitative estimate of the speed of light was made in 1676 by Ole Christensen Rømer, one of a group of astronomers of the French Royal Academy of Sciences who were studying the motion of Jupiter's moons.[94] [95] One of the group's discoveries, announced by Cassini in 1675, was that the periods of the moons appeared to be shorter when the Earth was approaching Jupiter than when it was receding from it. Rømer suggested that this occurred because the speed of light was finite. In September 1676, on the basis of this assumption, he predicted that on the following ninth of November, Io, Jupiter's innermost moon, would emerge from Jupiter's shadow 10 minutes later than had been expected from calculations based on its mean motion and the times of previous emersions observed during the preceding August.[96]

After Rømer's prediction was fulfilled (to the second, according to Rømer himself),[97] he read a report to a meeting of the French Academy of Sciences[98] in which he explained how he had derived it.[99] The procedure was illustrated with the aid of a diagram reproduced at the right.[100] The points L and K represent positions of the Earth (moving away from Jupiter at B) at which observations are made of Io emerging from Jupiter's shadow at D. Because light takes a finite time to travel from D to L or K, these observations will occur later than the actual times at which the emersions themselves did. If the actual time interval between the two emersions is p,[101] then the time interval between their observations at L and K will be p + Δ, where Δ is the time taken by light to travel the distance from L to K. But, for the same reason, the time interval between two observations, at F and G, of Io entering into Jupiter's shadow at C, as the Earth moves towards it, will be p − Δ (asssuming the distance from G to F is the same as that from L to K).

If only one revolution of Io occurs between the two observed emersions or immersions, then Δ will only be about 20 seconds[102]—too small to obtain a reliable estimate of the speed of light. But Rømer realized that when many revolutions of Io occurred between two observations, the time lag Δ would be proportionately larger, and would therefore make a useful estimate possible.[103] Using the available observations, he estimated that it would take 22 minutes for light to cross the diameter of the Earth's orbit.[104]

Rømer did not express his estimate in terms of conventional units of length,[105] except to say that light took less than a second to travel a distance of 3,000 leagues—a distance on the order of the diameter of the earth. Christiaan Huygens, however, on reading the English translation of Rømer's account, wrote to him for confirmation of the estimate, and using it and the then estimated size of the astronomical unit (roughly, the Earth-to-Sun distance),[106] estimated the speed of light to be at least 110,000,000 toises per second.[107] 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.[108]

Isaac Newton also accepted the finite speed. In his 1704 book Opticks he gives a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8 minutes 19 seconds).[109] 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.

Between 1725 and 1728, James Bradley, while searching for stellar parallax, observed the apparent motion of the star γ Draconis (Eltanin) depending on the season of the year. He realized that the motion (about 39 arcseconds) could not be a parallax (it was in the wrong direction at any given time) and, after ruling out several other possible causes, produced the theory of the aberration of light,[110] a vector addition of the velocity of light arriving from the star and the velocity of the Earth around its orbit. The effect is that an observer on the Earth will see the light coming from a slightly different angle than the "true" value which, for a star in the sky, means a slightly different position. The effect is greatest near the orbital pole which, for the Earth, is close to γ Draconis, and almost zero for stars on the ecliptic.[111] Bradley was able to predict the aberration for several other stars, and confirm his predictions by observation.[110] His observations on γ Draconis gave a ratio of the speed of light to the mean linear speed of the Earth's orbital motion: Bradley's figure was that light travelled 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8 minutes and 12 seconds to travel from the Sun to the Earth.[110]

[edit] Earth-bound techniques

See also: Fizeau–Foucault apparatus
A light ray passes horizontally through a half-mirror and a rotating cog wheel, is reflected back by a mirror, passes through the cog wheel, and is reflected by the half-mirror into a monocular.
Diagram of the Fizeau apparatus

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 km/s. Léon Foucault improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estimate, published in 1862, was 298,000 km/s.

[edit] Cavity resonance

Electromagnetic standing waves in a cavity. Sinusoidal waves at the top have larger frequencies than below and are shifted upward for clarity. The conductive walls require the nodes of the standing wave to be at the wall surfaces, so the allowed wavelengths are: λ/2 = W, λ = W, 3λ/2 = W where W = width of cavity.

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±1.0 km/s, which became the value adopted by the 12th General Assembly of the Radio-Scientific Union in 1957.[citation needed]

[edit] Heterodyne laser measurements

An idealized interferometric determination of wavelength obtained by looking at interference fringes between two coherent beams recombined after travelling different distances. Top: Constructive interference (in phase); If the difference in path length is a multiple of a wavelength, the recombined beams support one another and reconstitute the original beam. Bottom: Destructive interference (out of phase); If the two paths differ by half a wavelength, the recombined beams are out of phase and cancel each other. The bottom panel in the figure suggests the path length has been increased by half a wavelength by moving the right-hand point of reflection further out.

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.[112] A coherent light beam with a known frequency (f), 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 (λ) can be determined, which is related to the speed of light by the equation c = λf.

The main problem with interferometry is to measure the frequency of light in or near the optical region. This was first overcome by a group at the NIST laboratories in Boulder, Colorado, in 1972.[113] By a series of photodiodes and specially constructed metal–insulator–metal diodes, they succeeded in linking the frequency of the caesium transition used in atomic clocks to the frequency of a methane-stabilized laser (nearly 10,000 times higher).[114] Their results were

f = 88.376181627(50) THz
λ = 3.392231376(12) μm
c = 299792456.2(1.1) m/s

nearly a hundred times more precise than previous measurements of the speed of light.[113][114]

[edit] Redefinition of the metre

See also: Metre

The 1972 measurement, with a relative uncertainty of 4×10−9, was not only a feat of experimental precision: it also demonstrated a fundamental limit to how precisely the speed of light could be measured at that time using any technique. The remaining uncertainty in the value was almost completely attributable to uncertainty in the realization of the metre.[113][114][115]

Since 1960, the metre had been defined as a given number of wavelengths of the light of one of the spectral lines of a krypton lamp,[116] but it turned out that the chosen spectral line was not perfectly symmetrical.[114] This gave an uncertainty in its wavelength, and hence in the length of the metre. By analogy with a metal measuring stick, it was as if the stick were slightly fuzzy at each end, although if it were a real measuring stick, the fuzziness at the ends of a one-metre stick would only be apparent at the atomic scale.

To get round this problem, the 15th Conférence Générale des Poids et Mesures (CGPM) in 1975 recommended the use of the value 299,792,458 m/s for "the speed of propagation of electromagnetic waves in vacuum".[115] The 17th CGPM in 1983 decided to redefine the metre to be "the length of the path travelled by light in vacuum during a time interval of 1⁄299,792,458 of a second".[117]

The effect of this definition gives the speed of light the exact value 299,792,458 m/s, which is nearly the same as the value 299,792,456.2(1.1) m/s obtained in the 1972 experiment. This number was chosen in order to ensure that the change in the value of the metre was minimised, being limited to the elimination of the measurement uncertainty (then four parts per billion, 4 × 10−9).[118][119] As a result, within the SI system of units, the speed of light is now a defined constant[13] and no longer something to be measured.[114] Improved experimental techniques do not affect the value of the speed of light in SI units, but do result in a better realization of the SI metre.[120][121]

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.[122] 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.[123][124]

[edit] Modern astronomical measurements

The overriding problem with any modern measurement of the speed of light is the definition of a precise standard of length. For practical length measurements on Earth, the speed of light is the length standard, through the 1983 definition of the metre, but it is still possible to define other standards and hence to measure the speed of light against those standards.

In astronomy and satellite communication, it is useful to use standards based on the mass of either the Sun or the Earth. This is transformed into a length standard by saying that the standard length is the distance from the centre of the body at which a planet or satellite would have a given orbital velocity. The method was first used by Carl Friedrich Gauss in 1801 to calculate the orbit of Ceres, and was refined by Simon Newcomb in his Tables of the Sun (1895).

The astronomical unit is one example of such a length standard, based on the solar mass and approximately equal to the average distance between the Earth and the Sun. The "light time per unit distance" is an essential parameter in calculating planetary ephemerides, and is simply the inverse of the speed of light in astronomical units per second. It is measured by comparing the time taken for radio signals to reach different spacecraft in the Solar System with their position as caculated from the gravitational effects of the Sun and the various planets. By combining many such measurements, a "best fit" value for the light time per unit distance can be obtained. The 2009 best estimate, as approved by the International Astronomical Union (IAU), is:[125][126][127]

light time per unit distance: 499.004783836(10) s
c = 0.00200398880410(4) AU/s = 173.144632674(3) AU/day

The relative uncertainty in these measurements is 0.02 parts per billion (0.02 × 10−9), equivalent to the uncertainty in Earth-based measurements of length by interferometry.[128][129]

The light time per unit distance is effectively the same quantity that was measured by Rømer and Cassini in the late 17th century, where they gave a value of "ten to eleven minutes"[130], slightly longer than the currently accepted value of 8 minutes 19 seconds.

[edit] Laboratory demonstration

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 an LED reflected from a mirror, although this method is less precise than either the cavity resonator or the interferometric methods.[131][132][133]

[edit] See also

[edit] References

[edit] Citations

  1. ^ Uzan, J-P; Leclercq, B (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Springer. pp. 43–44. ISBN 0387734546. http://books.google.com/books?id=dSAWX8TNpScC&pg=PA43. 
  2. ^ Duke, PJ (2000). "Electromagnetic waves in free space – no electric charges or currents". Synchrotron Radiation: Production and Properties. Oxford University Press. p. 53. ISBN 0198517580. http://books.google.com/books?id=x4zDe7Aa-iUC&pg=PA53. 
  3. ^ Schwinger, JS (2002) [1986]. "Gravitational waves". Einstein's Legacy: The Unity of Space and Time (Reprint ed.). Courier Dover. p. 223. ISBN 0486419746. 
  4. ^ Wei-Tou Ni (2005). "Empirical foundation of the relativistic gravity". International Journal of Modern Physics D 14: 901–21. doi:10.1142/S0218271805007139. http://astronomy.nju.edu.cn/~tyhuang/jiaoxue/Ni2005.pdf. 
  5. ^ Greene, G (2003). The Elegant Universe. W. W. Norton. pp. 55–56. ISBN 0393058581. http://books.google.com/books?id=FH3o-WVDECwC&pg=PA55. 
  6. ^ Davies, PCW (1979). The Forces of Nature. Cambridge University Press. pp. 127–28. ISBN 052122523X. http://books.google.com/books?id=Av08AAAAIAAJ&pg=PA127. 
  7. ^ a b Taylor, EF; Wheeler, JA (1992). Spacetime Physics. W. H. Freeman. pp. 74–75. ISBN 0716723271. 
  8. ^ a b Kirk, AG (2006). "Free-space optical interconnects". in Pavesi, L; Guillot, G. Optical Interconnects: The silicon approach. Birkhäuser. p. 343. ISBN 3540289100. 
    Hall, SG; Hall, GW; McCall, JA (2000). High Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices. Wiley. ISBN 0471360902. 
    Gad, E; Nakla, M; Achar, R (2008). "Model-order reduction of high-speed interconnects using integrated congruence transform". in Schilders, WHA; van der Vorst, HA; Rommes, J;. Model Order Reduction. Springer. p. 362. ISBN 3540788409. 
  9. ^ Penrose, R (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books. pp. 410–411. ISBN 9780679776314. "The reader might well be puzzled that the speed of light comes out as an exact integer when measured in metres per second. This is no accident, but merely a reflection of the fact that very accurate distance measurements are now much harder to ascertain than very accurate time measurements. Accordingly, the most accurate standard for the metre is conveniently defined so that there are exactly 299,792,458 of them to the distance travelled by light in a standard second, giving a value for the metre that very accurately matches the now inadequately precise standard metre rule in Paris." 
  10. ^ The official statement is provided in the BIPM SI Units brochure, § 2.1.1.1, p. 112
  11. ^ Sydenham, PH (2003). "Measurement of length". in Boyes, W. Instrumentation Reference Book (3rd ed.). Butterworth-Heinemann. p. 56. ISBN 0750671238. "... if the speed of light is defined as a fixed number then, in principle, the time standard will serve as the length standard ..." 
  12. ^ "Fundamental Physical Constants: Speed of Light in Vacuum". NIST. http://physics.nist.gov/cgi-bin/cuu/Value?c. Retrieved 2009-08-21. 
  13. ^ a b Jespersen, J; Fitz-Randolph, J; Robb, J (1999). From Sundials to Atomic Clocks: Understanding time and frequency (Reprint of National Bureau of Standards 1977, 2nd ed.). Courier Dover. p. 280. ISBN 0486409139. http://books.google.com/books?id=Z7chuo4ebUAC&pg=PA280. 
  14. ^ Barbrow, Louis E. and Lewis V. Judson, (1976), pp. 16, 17, 20. Weights and Measures Standards of the United States: a brief history.
  15. ^ Online calculation of c back into metric
  16. ^ Gibbs, P (2004). "Why is c the symbol for the speed of light?". University of California, Riverside. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html. Retrieved 2009-10-22. 
  17. ^ See for example:
  18. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 112, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 
  19. ^ Lawrie, ID (2002). "Appendix C: Natural units". A unified grand tour of theoretical physics (2nd ed.). CRC Press. p. 540. ISBN 0750306041. 
  20. ^ a b Hsu, L (2006). "Appendix A: Systems of units and the development of relativity theories". A broader view of relativity: general implications of Lorentz and Poincaré invariance (2nd ed.). World Scientific. pp. 427–428. ISBN 9812566511. 
  21. ^ a b c d Zhang, YZ (1997). Special Relativity and Its Experimental Foundations. Advanced Series on Theoretical Physical Science. 4. World Scientific. pp. 172–173. ISBN 9810227493. http://www.worldscibooks.com/physics/3180.html. 
  22. ^ Sklar, L (1977). Space, Time, and Spacetime. University of California Press. pp. 245–247. ISBN 0520031741. http://books.google.com/books?id=cPLXqV3QwuMC&pg=PA245. 
  23. ^ Kennedy, RJ; Thorndike, EM (1932). "Experimental establishment of the relativity of time". Physical Review 42 (3): 400–418. doi:10.1103/PhysRev.42.400. 
  24. ^ Hils, D; Hall, JL (1990). "Improved Kennedy–Thorndike experiment to test special relativity". Physical Review Letters 64 (15): 1697–1700. doi:10.1103/PhysRevLett.64.1697. 
  25. ^ d'Inverno, R (1992). Introducing Einstein's Relativity. Oxford University Press. pp. 19–20. ISBN 0198596863. 
  26. ^ Sriranjan, B (2004). "Postulates of the special theory of relativity and their consequences". The Special Theory to Relativity. PHI Learning. pp. 20 ff. ISBN 812031963X. http://books.google.com/books?id=FsRfMvyudlAC&pg=PA20#v=onepage&q=&f=false. 
  27. ^ Shultis, JK; Faw, RE (2002). Fundamentals of nuclear science and engineering. CRC Press. p. 151. ISBN 0824708342. http://books.google.com/books?id=SO4Lmw8XoEMC&pg=PA151. 
  28. ^ Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 52–59. ISBN 9810227493. 
  29. ^ Sachs, M (1993). Relativity in our time. CRC Press. p. 49. ISBN 0748401180. http://books.google.com/books?id=-8g1ekO8FmMC&pg=PA49. 
  30. ^ Harrison, DM (1999). "The Special Theory of Relativity". University of Toronto, Department of Physics. http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html. Retrieved 2008-12-08. 
  31. ^ Wheeler, JA (1990). A Journey into Gravity and Spacetime. Scientific American. pp. 68–81. ISBN 0-7167-5016-3. 
  32. ^ Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 332. ISBN 9810227493. 
  33. ^ Baskaran, D; Polnarev, AG; Pshirkov, MS; Postnov, KA (2008). "Limits on the speed of gravitational waves from pulsar timing". Physical Review D. arΧiv:0805.3103. 
  34. ^ One such paradox is called the tachyonic antitelephone. See Tolman, RC (1917). The Theory of the Relativity of Motion. p. 54. 
  35. ^ Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 59. ISBN 9810227493. 
  36. ^ d'Inverno, R (1999). Introducing Einstein's Relativity. Oxford University Press. pp. 34. ISBN 0198596863. 
  37. ^ Weyl, H (1917). "Zur Gravitationstheorie". Annalen der Physik 359 (18): 117–145. doi:10.1002/andp.19173591804. 
    Weyl, H (1919). "Eine neue Erweiterung der Relativitätstheorie". Annalen der Physik 364 (10): 101–133. doi:10.1002/andp.19193641002. 
  38. ^ Eddington, AS (1931). "On the instability of Einstein's spherical world". Monthly Notices of the Royal Astronomical Society 90: 669–678. Bibcode: 1930MNRAS..90..668E. 
  39. ^ Dirac, PAM (1937). "The Cosmological Constants". Nature 139: 323. doi:10.1038/139323a0. 
  40. ^ Ellis, GFR; Uzan, J-P (2005). "‘c’ is the speed of light, isn’t it?". American Journal of Physics 73: 240–247. doi:10.1119/1.1819929. arΧiv:gr-qc/0305099. "The possibility that the fundamental constants may vary during the evolution of the universe offers an exceptional window onto higher dimensional theories and is probably linked with the nature of the dark energy that makes the universe accelerate today.". 
  41. ^ An overview can be found in the dissertation of Mota, DF (2006). "Variations of the fine structure constant in space and time". arΧiv: astro-ph/0401631` [astro-ph]. 
  42. ^ Uzan, J-P (2003). "The fundamental constants and their variation: observational status and theoretical motivations". Reviews of Modern Physics 74: 403. arΧiv:hep-ph/0205340. 
  43. ^ Kafatos, M; Roy, S; Roy, M (2005). "Variation of Physical Constants, Redshift and the Arrow of Time". Acta Physica Polonica B 36: 3139–3162. arΧiv:astro-ph/0305117. 
  44. ^ Farrell, DJ; Dunning-Davies, J (2007). "The constancy, or otherwise, of the speed of light". in Ross, LV. New Research on Astrophysics, Neutron Stars and Galaxy Clusters. Nova Publishers. pp. 71ff. ISBN 1600211100. 
  45. ^ Amelino-Camelia, G (2008). "Quantum Gravity Phenomenology". arΧiv: 0806.0339 [gr-qc]. 
  46. ^ Panofsky, W; Phillips, M (1962). Classical Electricity and Magnetism. Addison-Wesley. pp. 182. 
  47. ^ "Is The Speed of Light Constant?". Usenet Physics FAQ. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html. Retrieved 2009-09-12. 
  48. ^ Schaefer, BE (1999). "Severe limits on variations of the speed of light with frequency". Physical Review Letters 82: 4964–4966. doi:10.1103/PhysRevLett.82.4964. arΧiv:astro-ph/9810479. 
  49. ^ Ellis, J; Mavromatos, DV; Sakharov, AS (2003). "Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets". Astronomy & Astrophysics 403: 409–424. doi:10.1051/0004-6361:20030263. arΧiv:astro-ph/0210124. 
  50. ^ Füllekrug, M (2004). "Probing the Speed of Light with Radio Waves at Extremely Low Frequencies". Physical Review Letters 93: 043901. doi:10.1103/PhysRevLett.93.043901. 
  51. ^ a b Adelberger, E; Dvali, G; Gruzinov, A (2007). "Photon Mass Bound Destroyed by Vortices". Physical Review Letters 98: 010402. doi:10.1103/PhysRevLett.98.010402. arΧiv:hep-ph/0306245. 
  52. ^ Sidharth, BG (2008). The Thermodynamic Universe. World Scientific. p. 134. ISBN 9812812342. http://books.google.com/books?id=OUfHR36wSfAC&pg=PA134. 
  53. ^ Feynman, RP (1963). Lectures on Physics Volume II. Addison-Wesley. pp. 32:1–32:3. 
  54. ^ de Podesta, M (2002). Understanding the Properties of Matter. CRC Press. p. 131. ISBN 0415257883. http://books.google.com/books?id=h8BNvnR050cC&pg=PA131&lpg=PA131. 
  55. ^ Hau, LV; Harris, SE; Dutton, Z; Behroozi, CH (1999). "Light speed reduction to 17 metres per second in an ultracold atomic gas". Nature 397: 594–598. doi:10.1038/17561. http://www.nature.com/nature/journal/v397/n6720/pdf/397594a0.pdf. 
  56. ^ Liu, C; Dutton, Z; Behroozi, CH; Hau, LV (2001). "Observation of coherent optical information storage in an atomic medium using halted light pulses". Nature 409 (6819): 490–493. doi:10.1038/35054017. PMID 11206540. http://www.nature.com/nature/journal/v409/n6819/pdf/409490a0.pdf. 
  57. ^ Bajcsy, M; Zibrov, AS; Lukin, MD (2003). "Stationary pulses of light in an atomic medium". Nature 426 (6967): 638–641. doi:10.1038/nature02176. PMID 14668857. 
  58. ^ Dumé, B (2003). "Switching light on and off". Physics World. http://physicsweb.org/article/news/7/12/5. Retrieved 2008-12-08. 
  59. ^ S. Liberati S. Sonego, and M. Visser , Faster-than-c signals, special relativity, and causality, Annals Phys. 298, 167-185 (2002) preprint
  60. ^ Egan, G. (2000). "Subluminal". http://gregegan.customer.netspace.net.au/APPLETS/20/20.html. Retrieved 2007-02-06. 
  61. ^ Wang, LJ; Kuzmich, A; Dogario, A (2000). "Gain-assisted superluminal light propagation". Nature 406 (406): 277. doi:10.1038/35018520. PMID 10917523. 
  62. ^ Whitehouse, D (2000). "Beam smashes light barrier". BBC News. http://news.bbc.co.uk/hi/english/sci/tech/newsid_841000/841690.stm. Retrieved 2008-12-08. 
  63. ^ Brunner, N; Scarani, V; Wegmüller, M; Legré, M; Gisin, N (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. 
  64. ^ Gibbs, P (1997). "Is Faster-Than-Light Travel or Communication Possible?". University of California, Riverside. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html. Retrieved 2008-08-20. 
  65. ^ Wertheim, M (2007). "The Shadow Goes". New York Times. http://www.nytimes.com/2007/06/20/opinion/20wertheim.html?_r=1&scp=1&sq=%27the%20shadow%20goes%27&st=cse&oref=slogin. Retrieved 2009-08-21. 
  66. ^ Sakurai, JJ (1994). T, San Fu. ed. Modern Quantum Mechanics (Revised ed.). Addison-Wesley. pp. 231–232. ISBN 0-201-53929-2. 
  67. ^ "Faster Than Light: EPR Paradox". Usenet Physics FAQ. http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#9. Retrieved 2009-09-03. 
  68. ^ Muga, JG; Mayato, RS; Egusquiza, IL, eds (2007). Time in Quantum Mechanics. Springer. p. 48. ISBN 3540734724. http://books.google.com/books?id=InKru6zHQWgC&pg=PA48. 
  69. ^ Hernández-Figueroa, HE; Zamboni-Rached, M; Recami, E (2007). Localized Waves. Wiley Interscience. p. 26. ISBN 0470108851. http://books.google.com/books?id=xxbXgL967PwC&pg=PA26. 
  70. ^ Wynne, K (2002). "Causality and the nature of information". Optics Communications 209: 84–100. doi:10.1016/S0030-4018(02)01638-3. http://bcp.phys.strath.ac.uk/the_group/r/uf/2002-OC-causality.pdf. 
  71. ^ Rees, M (1966). "The Appearance of Relativistically Expanding Radio Sources". Nature 211: 468. doi:10.1038/211468a0. 
  72. ^ Čerenkov, PA (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. 
  73. ^ Čerenkov, EP (1999). Gorbunova, AN. ed. Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie. Nauka. pp. 149–153. 
  74. ^ "The IAU and astronomical units". International Astronomical Union. http://www.iau.org/public_press/themes/measuring/. Retrieved 2009-10-27. 
  75. ^ Further discussion can be found at "StarChild Question of the Month for March 2000". StarChild. NASA. 2000. http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question19.html. Retrieved 2009-08-22. 
  76. ^ Hirschfeld, A (2001). Parallax:The Race to Measure the Cosmos. Henry Holt. ISBN 0-8050-7133-4. 
  77. ^ Terrel, J (1959). "Invisibility of the Lorentz Contraction". Physical Review 116: 1041–1045. doi:10.1103/PhysRev.116.1041. 
  78. ^ Penrose, R (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society 55: 137–139. doi:10.1017/S0305004100033776. 
  79. ^ a b c MacKay, RH; Oldford, RW (2000). "Scientific Method, Statistical Method and the Speed of Light". Statistical Science 15 (3): 254–278. doi:10.1214/ss/1009212817. http://www.stats.uwaterloo.ca/~rwoldfor/papers/sci-method/paperrev. 
  80. ^ Steffens, B (2006). "Chapter Five – The Scholar of Cairo". Ibn al-Haytham: First Scientist. Morgan Reynolds. ISBN 1599350246. 
  81. ^ Hamarneh, S (1972). "Review: Hakim Mohammed Said, Ibn al-Haitham". Isis 63 (1): 119. doi:10.1086/350861. 
  82. ^ a b Lester, PM (2005). Visual Communication: Images With Messages. Thomson Wadsworth. pp. 10–11. ISBN 0534637205. 
  83. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive .
  84. ^ Lauginie, P (2005). "Measuring: Why? How? What?". Proceedings of the 8th International History, Philosophy, Sociology & Science Teaching Conference. 
  85. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Arrayhan Muhammad ibn Ahmad al-Biruni", MacTutor History of Mathematics archive .
  86. ^ Lindberg, DC (1996). Roger Bacon and the origins of Perspectiva in the Middle Ages: a critical edition and English translation of Bacon's Perspectiva, with introduction and notes. Oxford University Press. p. 143. ISBN 0198239920. http://books.google.com/books?id=jSPHMKbjYkQC&pg=PA143. 
  87. ^ Lindberg, DC (1974). "Late Thirteenth-Century Synthesis in Optics". in Edward Grant. A source book in medieval science. Harvard University Press. p. 396. ISBN 9780674823600. http://books.google.com/books?id=fAPN_3w4hAUC&pg=RA1-PA395&dq=roger-bacon+speed-of-light&as_brr=3&ei=UJV0SsnfOpCqkATpnqybCw#v=onepage&q=roger-bacon%20speed-of-light&f=false. 
  88. ^ Marshall, P (1981). "Nicole Oresme on the Nature, Reflection, and Speed of Light". Isis 72 (3): 357–374 [367–374]. doi:10.1086/352787. 
  89. ^ Kak, Subhash (2001). "The speed of light and Puranic cosmology". http://arxiv.org/abs/physics/9804020. Retrieved 5 November 2009. 
  90. ^ Kak, Subhash (1998). "Sayana's astronomy". Indian Journal of History of Science 33: 31–36. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_31.pdf. 
  91. ^ Topdemir, HG (1999). Takîyüddîn'in Optik Kitabi. Ankara: Ministry of Culture Press.  (cf. Topdemir, HG (2008). Taqi al-Din ibn Ma‘ruf and the Science of Optics: The Nature of Light and the Mechanism of Vision. FSTC. http://muslimheritage.com/topics/default.cfm?ArticleID=951. Retrieved 2007-07-04. )
  92. ^ Boyer, CB (1941). "Early Estimates of the Velocity of Light". Isis 33 (1): 24. doi:10.1086/358523. 
  93. ^ Galilei, G (1954) [1638]. Dialogues Concerning Two New Sciences. translated by Henry Crew and Alfonso de Salvio. Dover Publications. p. 43. ISBN 486-60099-8. http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=753&layout=html#a_2288356. 
  94. ^ Cohen, IB (1940). "Roemer and the first determination of the velocity of light (1676)". Isis 31 (2): 327–379. doi:10.1086/347594. 
    Besides Rømer, the group included Giovanni Domenico Cassini and Jean Picard.
  95. ^ Rømer, O (1676). "Touchant le mouvement de la lumiere trouvé par M. Rŏmer de l'Académie Royale des Sciences". Journal des Sçavans: 233–236. http://www-obs.univ-lyon1.fr/labo/fc/ama09/pages_jdsc/pages/jdsc_1676_lumiere.pdf. 
    Although Rømer read a report on his work to the French Academy of Sciences in November 1676 (Cohen, 1940, p.346), he does not appear to have written the published account. An electronic copy of the latter (French) and one of a 1677 English translation are available online.
  96. ^ Cohen (1940, pp.328, 351–52); Rømer (1676, p.235). The term "eclipse", with which Cohen refers to these emersions, is used by him to refer to both the moons' immersions into, and their emersions out of, Jupiter's shadow. It is impossible, from the Earth, to view both the immersion and the emersion of Io for the same passage through Jupiter's shadow, as one or the other will always be masked by Jupiter itself.
  97. ^ Cohen (1940, p.353). Cohen raises some doubt about whether the predicted emersion did occur precisely when Rømer claimed. He cites a historical record by a later astronomer, Pierre Charles le Monnier, which placed the event two minutes later.
  98. ^ On the 21st of November (Cohen, 1940, p.346).
  99. ^ Rømer (1676).
  100. ^ Rømer (1676, p.234). The label on the point F was missing from the original copy. Also, the diagram illustrates only a simple special case. In general, neither the points D, K and L, nor the points C, G and F, would be collinear.
  101. ^ p will be approximately equal to Io's mean period of about 42.5 hours multiplied by the number of revolutions it has made between the two emersions.
  102. ^ Cohen (1940, p.351).
  103. ^ Rømer (1676, p.235). In the report of his work, 40 revolutions are mentioned as an example, but it is not clear whether that is the number he actually used.
  104. ^ Cohen (1940, pp.328, 351–52).
  105. ^ A wide variety of such estimates have nevertheless been erroneously attributed to Rømer in physics textbooks and popular historical accounts. See Boyer (1941), Wróblewski, Andrzej (1985). "de Mora Luminis: A spectacle in two acts with a prologue and an epilogue". Am. J. Phys. 53 (7): 620–30. doi:10.1119/1.14270.  and French, AP (1990). "Roemer: a cautionary tale". in Roche, J. Physicists look back: studies in the history of physics. CRC Press. pp. 120–121. ISBN 0852740018. http://books.google.com/books?id=5H3Oo0iicrkC&pg=PA120. 
  106. ^ Then estimated to be about 33 million lieuës (leagues), or 11,500 times the diameter of the earth. Godin, Louis; Fontenelle, Bernard de, eds (1729–34). Mémoires de l'Académie royale des sciences depuis 1666 jusqu'en 1699. Paris: Compagnie des libraires. pp. 112–15. http://gallica.bnf.fr/ark:/12148/bpt6k56063967. 
  107. ^ Huygens, Christiaan (1690). Traitée de la Lumière. Leiden: Pierre van der Aa. pp. 8–9. http://books.google.com.au/books?id=No8PAAAAQAAJ&printsec=frontcover. 
  108. ^ Huygens' estimate of the speed of light in ground based units (110,000,000 toises per second) is deliberately conservative. "Que si l'on considère la vaste étendue du diametre K L, qui selon moy est de quelques 24 mille diamteres de la la Terre, l'on connoitra l'extreme vistesse de la lumiere. Car supposé que K L ne soit que 22 mille de ces diametres, il paroit que estans passez en 22 minutes…" "If we consider the vast size of the diameter K L, which according to me is some 24,000 Earth diameters, we we realise the extreme rapidity of light. Because supposing that K L is only 22,000 of these diameters, it seems that there are passed in 22 minutes…" Huygens is taking a small value for the diameter of the Earth's orbit (which also simplifies his calculation) and a value at the high end of the range (20–22 minutes) found by Cassini and Rømer for the time taken for light to travel the diameter of the orbit.
  109. ^ Newton, Issac (1704). "Prop. XI". Optiks. http://gallica.bnf.fr/ark:/12148/bpt6k3362k.image.f235.vignettesnaviguer. . The text of Prop. XI is identical between the first (1704) and second (1719) editions.
  110. ^ a b c Bradley, James (1729), "Account of a new discoved Motion of the Fix'd Stars", Phil. Trans. 35: 637–60, http://gallica.bnf.fr/ark:/12148/bpt6k55840n.image.f375.langEN .
  111. ^ For stars on the ecliptic, the annual aberration, which is what Bradley was observing and theorizing, is zero. There is a much smaller effect, called the daily aberration, which is due to the Earth's rotation on its axis and which does affect stars on the ecliptic.
  112. ^ A detailed discussion of the interferometer and its use for determining the speed of light can be found in Vaughan, JM (1989). The Fabry-Perot interferometer. CRC Press. p. 47 & pp. 384–391. ISBN 0852741383. http://books.google.com/books?id=mMLuISueDKYC&printsec=frontcover#PPA47,M1. 
  113. ^ a b c Evenson, K. M.; Wells, J. S.; Petersen, F. R.; Danielson, B. L.; Day, G. W.; Barger, R. L.; Hall, J. L. (1972), "Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser", Phys. Rev. Lett. 29: 1346–49, doi:10.1103/PhysRevLett.29.1346 .
  114. ^ a b c d e Sullivan, D. B.. "Speed of Light From Direct Frequency and Wavelength Measurements". NIST. p. 191–93. http://nvl.nist.gov/pub/nistpubs/sp958-lide/191-193.pdf. Retrieved 2009-08-22. 
  115. ^ a b "Resolution 2 of the 15th CGPM". Conférence Générale des Poids et Mesures. BIPM. 1975. http://www.bipm.org/en/CGPM/db/15/2/. Retrieved 2009-09-09. 
  116. ^ The metre was defined (1960–1983) as "the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom." "Resolution 6 of the 11th CGPM", Conférence Générale des Poids et Mesures (BIPM), 1960, http://www.bipm.org/en/CGPM/db/11/6/, retrieved 2009-10-18 .
  117. ^ "Resolution 1 of the 17th CGPM". Conférence Générale des Poids et Mesures. BIPM. 1983. http://www.bipm.org/en/CGPM/db/17/1/. Retrieved 2009-08-23. 
  118. ^ Taylor, EF; Wheeler, JA (1992). Spacetime physics: introduction to special relativity (2nd ed.). Macmillan. ISBN 0716723271. http://books.google.com/books?id=PDA8YcvMc_QC&pg=PA59#v=onepage&q=&f=false. 
  119. ^ "NIST timeline of definitions of the metre". http://www.nist.gov/mel/ped/museum-timeline.cfm. 
  120. ^ Adams, S (1997). Relativity: An Introduction to Space-Time Physics. CRC Press. p. 140. ISBN 0748406212. http://books.google.com/books?id=1RV0AysEN4oC&pg=PA140. "One peculiar consequence of this system of definitions is that any future refinement in our ability to measure c will not change the speed of light (which is a defined number), but will change the length of the meter!" 
  121. ^ Rindler, W (2006). Relativity: Special, General, and Cosmological (2nd ed.). Oxford University Press. p. 41. ISBN 0198567316. http://books.google.com/books?id=MuuaG5HXOGEC&pg=PT41. "Note that [...] improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light!" 
  122. ^ A list of the resulting wavelengths based upon these frequencies and λ = c/f is found at BIPM mise-en-pratique, method b.
  123. ^ Zagar, BG (1999). "Laser Interferometer Displacement Sensors; §6.5". in JG Webster, JG. The Measurement, Instrumentation, and Sensors Handbook. CRC Press. p. 6-69. ISBN 0849383471. 
  124. ^ Flügge, J; et al. (2004). "Fundamental length metrology: Practical issues; §D.2.1.3". in Webb, CE; JDC Jones, JDC. Handbook of Laser Technology and Applications. Taylor & Francis. pp. 1737 ff. ISBN 0750309660. 
  125. ^ Pitjeva, E. V.; Standish, E. M. (2009), "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit", Celest. Mech. Dynam. Astron. 103 (4): 365–72, doi:10.1007/s10569-009-9203-8, http://www.springerlink.com/content/21885q7262104u76/ .
  126. ^ IAU WG on NSFA Current Best Estimates, http://maia.usno.navy.mil/NSFA/CBE.html, retrieved 2009-09-25 .
  127. ^ "The Final Session of the General Assembly", Estrella d'Alva: 1, 2009-08-14, http://www.astronomy2009.com.br/10.pdf .
  128. ^ Length (poster), UK National Physical Laboratory, http://www.npl.co.uk/educate-explore/posters/length/length-%28poster%29, retrieved 2009-10-28 .
  129. ^ Mise en pratique 2003 – Iodine (λ ≈ 633 nm), Bureau international des poids et mesures (BIPM), 2003 .
  130. ^ Cette seconde inégalité paraît venir de ce que la lumière emploie quelques temps à venir du satellite jusqu'à nous, et qu'elle met environ dix à onze minutes à parcourir un espace égal au demi-diamètre de l'orbite terrestre. also found in "L'expérience de Römer". 1675. http://www.la-cite.org/citadins/chris/tipeI/node11.html. Retrieved 2008-10-21. 
  131. ^ Cooke, J (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. 
  132. ^ Aoki, K; Mitsui, T (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. arΧiv:0705.3996. 
  133. ^ James, MB; Ormond, RB; Stasch, AJ (1999). "Speed of light measurement for the myriad". American Journal of Physics 67 (8): 681–684. doi:10.1119/1.19352. 

[edit] Historical references

[edit] Modern references

[edit] External links


v • d • e
Extremes of motion
Speed
Distance
See also

Retrieved from "http://en.wikipedia.org/wiki/Speed_of_light"



Product Results (view all...)

search wiki for    ?
web dir firms image gallery news hov pdf wiki shop video 



↑ top of page ↑about thumbshots