   #copyright

Speed of light

2007 Schools Wikipedia Selection. Related subjects: General Physics

   The speed of light in a vacuum is an important physical constant
   denoted by the letter c for constant or the Latin word celeritas
   meaning "swiftness". It is the speed of all electromagnetic radiation
   in a vacuum, not just visible light.

   In metric units, c is exactly 299,792,458 metres per second
   (1,079,252,848.8 km/h). Note that this speed is a definition, not a
   measurement, since the fundamental SI unit of length, the metre, has
   been defined since October 21, 1983 in terms of the speed of light: one
   metre is the distance light travels in a vacuum in 1/299,792,458 of a
   second. Converted to imperial units, the speed of light is
   approximately 186,282.397 miles per second, or 670,616,629.384 miles
   per hour, or almost one foot per nanosecond.

   Through any transparent or translucent material medium, like glass or
   air, it has a lower speed than in a vacuum; the ratio of c to this
   slower speed is called the refractive index of the medium. Changes of
   gravity, however, warp the space the light has to travel through,
   making it appear to curve around massive objects. This gives rise to
   the phenomenon of gravitational lensing, in which large assemblies of
   matter can refract light from far away sources, so as to produce
   multiple images and similar optical distortions.

Overview

   One consequence of the laws of electromagnetism (such as Maxwell's
   equations) is that the speed c of electromagnetic radiation does not
   depend on the velocity of the object emitting the radiation; thus for
   instance the light emitted from a rapidly moving light source would
   travel at the same speed as the light coming from a stationary light
   source (although the colour, frequency, energy, and momentum of the
   light will be shifted, which is called the relativistic Doppler
   effect). If one combines this observation with the principle of
   relativity, one concludes that all observers will measure the speed of
   light in vacuum as being the same, regardless of the reference frame of
   the observer or the velocity of the object emitting the light. Because
   of this, one can view c as a fundamental physical constant. This fact
   can then be used as a basis for the theory of special relativity. It is
   worth noting that it is the constant speed c, rather than light itself,
   which is fundamental to special relativity; thus if light is somehow
   manipulated to travel at less than c, this will not directly affect the
   theory of special relativity.

   Observers travelling at large velocities will find that distances and
   times are distorted ("dilated") in accordance with the Lorentz
   transforms; however, the transforms distort times and distances in such
   a way that the speed of light remains constant. A person travelling
   near the speed of light would also find that colours of lights ahead
   were shifted toward the violet end of the spectrum and of those behind
   were redshifted, so that the Lorentz transformations and classical
   explanations of shifting are in harmony.

   If information could travel faster than c in one reference frame,
   causality would be violated: in some other reference frames, the
   information would be received before it had been sent, so the 'effect'
   could be observed before the 'cause' is. Due to special relativity's
   time dilation, the ratio between an external observer's perceived time
   and the time perceived by an observer moving closer and closer to the
   speed of light approaches zero. If something could move faster than
   light, this ratio would not be a real number. Such a violation of
   causality has never been observed.
   A light cone defines locations that are in causal contact and those
   that are not.
   Enlarge
   A light cone defines locations that are in causal contact and those
   that are not.

   To put it another way, information propagates to and from a point from
   regions defined by a light cone. The interval AB in the diagram to the
   right is ' time-like' (that is, there is a frame of reference in which
   event A and event B occur at the same location in space, separated only
   by their occurring at different times, and if A precedes B in that
   frame then A precedes B in all frames: there is no frame of reference
   in which event A and event B occur simultaneously). Thus, it is
   hypothetically possible for matter (or information) to travel from A to
   B, so there can be a causal relationship (with A the 'cause' and B the
   'effect').

   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 travelling 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.

   According to the currently prevailing definition, adopted in 1983, the
   speed of light is exactly 299,792,458 metres per second (approximately
   3 × 10^8 metres per second, or about thirty  centimetres (one foot) per
   nanosecond). The value of c defines the permittivity of free space
   (ε[0]) in SI units as:

          \varepsilon_0 = 10^{7}/4\pi c^2 \quad \mathrm{(in~ A^2\, s^4\,
          kg^{-1}\, m^{-3}, \, or \, F \, m^{-1})}

   The permeability of free space (μ[0]) is not dependent on c and is
   defined in SI units as:

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

   These constants appear in Maxwell's equations, which describe
   electromagnetism, and are related by:

          c= \frac {1} {\sqrt{\varepsilon_0\mu_0}}

   Astronomical distances are sometimes measured in light years (the
   distance that light would travel in one year, roughly
   9.46 × 10^12 kilometres or about 5.88 × 10^12 miles) especially in
   popularised texts. Also because light travels at a large but finite
   speed, it takes time for light to cover large distances. Thus, when we
   see the light of very distant objects in the universe, we are actually
   seeing light emitted from them a long time ago: we see them literally
   as they were in the distant past.

Mnemonic

   Since a nine-digit sequence is a bit hard to remember, there are
   several useful mnemonics for c in m/s, which use the letters on a
   telephone keypad:
     * Constant Which We Remember Well Because It's Light's Velocity.
     * A Way We Remember What Constant Is Light's Velocity.

   For either of these, one can obtain the number 299,792,458 by
   translating the bolded letters to digits.

Communications and GPS

   The speed of light is of relevance to communications. For example,
   given that the equatorial circumference of the Earth is 40100 km and
   c = 300000 km/s, the theoretical shortest amount of time for a piece of
   information to travel half the globe along the surface is 0.0668 s.

   The actual transit time is longer, in part because the speed of light
   is slower by about 30% in an optical fibre and straight lines rarely
   occur in global communications situations, but also because delays are
   created when the signal passes through an electronic switch or signal
   regenerator. A typical time as of 2004 for an Australia or Japan to US
   computer-to-computer ping is 0.18 s. The speed of light additionally
   affects wireless communications design.

   Another consequence of the finite speed of light is that communications
   with spacecraft are not instantaneous, especially as distances
   increase. This delay was significant for the communication of Houston
   ground control and Apollo 8 when it became the first spacecraft to
   orbit the Moon: For every question, Houston had to wait nearly 3
   seconds for the answer to arrive, even when the astronauts replied
   immediately.

   This effect forms the basis of the Global Positioning System (GPS), and
   similar navigation systems. One's position can be determined by means
   of the delays in light signals received from a number of satellites,
   each carrying a very accurate atomic clock, and very carefully
   synchronized. It is remarkable that, to work properly, this method
   requires to take into account (among many other effects) the relative
   motion of satellite and receiver, which was how (on an interplanetary
   scale) the finite speed of light was originally discovered (see the
   following).
   A line showing the speed of light on a scale model of Earth and the
   Moon
   Enlarge
   A line showing the speed of light on a scale model of Earth and the
   Moon

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

   The speed of light can also be of concern on short distances. In
   supercomputers, the speed of light imposes a limit on how quickly data
   can be sent between processors. If a processor operates at 1  GHz, a
   signal can only travel a maximum of 300 mm in a single cycle.
   Processors must therefore be placed close to each other to minimise
   communication latencies. If clock frequencies continue to increase, the
   speed of light will eventually become a limiting factor for the
   internal design of single chips.

Physics

Interaction with transparent materials

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

   In passing through materials, light is slowed to less than c by the
   ratio called the refractive index of the material. The speed of light
   in air is only slightly less than c. Denser media, such as water and
   glass, can slow light much more, to fractions such as ¾ and 2/3 of c.
   This reduction in speed is also responsible for bending of light at an
   interface between two materials with different indices, a phenomenon
   known as refraction.

   Since the speed of light in a material depends on the refractive index,
   and the refractive index depends on the frequency of the light, light
   at different frequencies travels at different speeds through the same
   material. This can cause distortion of electromagnetic waves that
   consist of multiple frequencies, called dispersion.

   Note that the speed of light referred to is the observed or measured
   speed in some medium and not the true speed of light (as observed in
   vacuum). It may be noted, that once the light has emerged from the
   medium it changes back to its original speed and this is without
   gaining any energy. This can mean only one thing—that the light's speed
   itself was never altered in the first place.

   It is sometimes claimed that light is slowed on its passage through a
   block of media by being absorbed and re-emitted by the atoms, only
   travelling at full speed through the vacuum between atoms. This
   explanation is incorrect and runs into problems if you try to use it to
   explain the details of refraction beyond the simple slowing of the
   signal.

   Classically, considering electromagnetic radiation to be like a wave,
   the charges of each atom (primarily the electrons) interfere with the
   electric and magnetic fields of the radiation, slowing its progress.

   The full quantum-mechanical explanation is essentially the same, but
   has to cope with the discrete particle nature (see Photons in matter):
   The E-field creates phonons in the media, and the photons mix with the
   phonons. The resulting mixture, called a polariton, travels with a
   speed slower than light.

"Faster-than-light" observations and experiments

   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.
   Enlarge
   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 has long been known theoretically that it is possible for the "
   phase velocity" of light to exceed c. One recent experiment made the
   group velocity of laser beams travel for extremely short distances
   through caesium atoms at 300 times c. However, it is not possible to
   use this technique to transfer information faster than c: the velocity
   of information transfer depends on the front velocity (the speed at
   which the first rise of a pulse above zero moves forward) and the
   product of the group velocity and the front velocity is equal to the
   square of the normal speed of light in the material.

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

   The speed of light may also appear to be exceeded in some phenomena
   involving evanescent waves, such as tunnelling. Experiments indicate
   that the phase velocity of evanescent waves may exceed c; however, it
   would appear that neither the group velocity nor the front velocity
   exceed c, so, again, it is not possible for information to be
   transmitted faster than c.

   In quantum mechanics, certain quantum effects may be transmitted at
   speeds greater than c (indeed, action at a distance has long been
   perceived by some as a problem with quantum mechanics: see EPR paradox,
   interpretations of quantum mechanics). For example, the quantum states
   of two particles can be entangled, so the state of one particle fixes
   the state of the other particle (say, one must have spin +½ and the
   other must have spin −½). Until the particles are observed, they exist
   in a superposition of two quantum states, (+½, −½) and (−½, +½). If the
   particles are separated and one of them is observed to determine its
   quantum state then the quantum state of the second particle is
   determined automatically. If, as in some interpretations of quantum
   mechanics, one presumes that the information about the quantum state is
   local to one particle, then one must conclude that second particle
   takes up its quantum state instantaneously, as soon as the first
   observation is carried out. However, it is impossible to control which
   quantum state the first particle will take on when it is observed, so
   no information can be transmitted in this manner. The laws of physics
   also appear to prevent information from being transferred through more
   clever ways and this has led to the formulation of rules such as the
   no-cloning theorem and the no-communication theorem.

   So-called superluminal motion is also seen in certain astronomical
   objects, such as the jets of radio galaxies and quasars. However, these
   jets are not actually 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.

   Although it may sound paradoxical, it is possible for shock waves to be
   formed with electromagnetic radiation. As a charged particle travels
   through an insulating medium, it disrupts the local electromagnetic
   field in the medium. Electrons in the atoms of the medium will be
   displaced and polarised by the passing field of the charged particle,
   and photons are emitted as the electrons in the medium restore
   themselves to equilibrium after the disruption has passed. (In a
   conductor, the disruption can be restored without emitting a photon.)
   In normal circumstances, these photons destructively interfere with
   each other and no radiation is detected. However, if the disruption
   travels faster than the photons themselves travel, the photons
   constructively interfere and intensify the observed radiation. The
   result (analogous to a sonic boom) is known as Cherenkov radiation.

   The ability to communicate or travel faster-than-light is a popular
   topic in science fiction. Particles that travel faster than light,
   dubbed tachyons, have been proposed by particle physicists but have yet
   to be observed.

   Some physicists, notably João Magueijo and John Moffat, have proposed
   that in the past light travelled much faster than the current speed of
   light. This theory is called variable speed of light (VSL) and its
   supporters claim that it has the ability to explain many cosmological
   puzzles better than its rival, the inflation model of the universe.
   However, it has yet to gain wide acceptance.

   In 2002, physicists Alain Haché and Louis Poirier made history by
   sending pulses at a group velocity of three times light speed over a
   long distance for the first time, transmitted through a 120-metre cable
   made from a coaxial photonic crystal.

"Slow Light" Experiments

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

   Any light travelling through a medium other than a vacuum travels below
   c as a result of the time lag between the polarization response of the
   medium and the incident light. However, certain materials have an
   exceptionally high group index and a correspondingly low group
   velocity. In 1999, a team of scientists led by Lene Hau were able to
   slow the speed of a light pulse to about 17 metres per second, and in
   2001, they were able to momentarily stop a beam.

   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 mass of hot rubidium gas, the atoms of which, in
   Lukin's words, behaved "like tiny mirrors", due to an interference
   pattern in two "control" beams.

History

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

   One of the ancient theories of vision is that light is emitted from the
   eye, instead of being reflected into the eye from another source. On
   this theory, Heron of Alexandria advanced the argument that the speed
   of light must be infinite, since distant objects such as stars appear
   immediately when one opens one's eyes.

Medieval and early modern theories

   The Islamic philosophers Avicenna and Alhazen believed that light has a
   finite speed, although most philosophers agreed with Aristotle on this
   point.

   The philosophers of ancient India also held the speed of light to be
   finite. The 14th century scholar Sayana wrote in a comment on verse
   1.50 of the Rig Veda:

          "Thus it is remembered: [O Sun] you who traverse 2202 yojanas in
          half a nimesa."

   Sayana's statement comes very close to the actual speed of light, and
   has been called the most astonishing "blind hit" in the history of
   science.

   Johannes Kepler believed that the speed of light is infinite since
   empty space presents no obstacle to it. Francis Bacon argued that the
   speed of light is not necessarily infinite, since something can travel
   too fast to be perceived. René Descartes argued that if the speed of
   light were finite, the Sun, Earth, and Moon would be noticeably out of
   alignment during a lunar eclipse. Since such misalignment had not been
   observed, Descartes concluded the speed of light is infinite. In fact,
   Descartes was convinced that if the speed of light were finite, his
   whole system of philosophy would be demolished.

Measurement of the speed of light

   Isaac Beeckman proposed an experiment ( 1629) in which a person would
   observe the flash of a cannon reflecting off a mirror about one mile
   away. Galileo proposed an experiment (1638), with an apparent claim to
   having performed it some years earlier, to measure the speed of light
   by observing the delay between uncovering a lantern and its perception
   some distance away. This experiment was carried out by the Accademia
   del Cimento of Florence in 1667, with the lanterns separated by about
   one mile. No delay was observed. Robert Hooke explained the negative
   results as Galileo had: by pointing out that such observations did not
   establish the infinite speed of light, but only that the speed must be
   very great. Descartes criticised this experiment as superfluous, in
   that the observation of eclipses, which had more power to detect a
   finite speed, gave a negative result.
   Rømer's observations of the occultations of Io from Earth.
   Enlarge
   Rømer's observations of the occultations of Io from Earth.

   The first quantitative estimate of the speed of light was made in 1676
   by Ole Rømer, who was studying the motions of Jupiter's satellite Io
   with a telescope. It is possible to time the orbital revolution of Io
   because it enters and exits Jupiter's shadow at regular intervals (at C
   or D). Rømer observed that Io revolved around Jupiter once every 42.5
   hours when Earth was closest to Jupiter. He also observed that, as
   Earth and Jupiter moved apart (as from L to K), Io's exit from the
   shadow would begin progressively later than predicted. It was clear
   that these exit "signals" took longer to reach Earth, as Earth and
   Jupiter moved further apart. As a result of the extra time it took for
   light to cross the extra distance between the planets, which had
   accumulated in the interval between one signal and the next. The
   opposite is the case when they are approaching (as from F (not shown
   but opposite of K) to G). Quite as in the familiar Doppler effect. On
   the basis of his observations, Rømer estimated that it would take light
   22 minutes to cross the diameter of the orbit of the Earth (that is,
   twice the astronomical unit); the modern estimate is closer to 16
   minutes and 40 seconds.

   Around the same time, the astronomical unit was estimated to be about
   140 million kilometres. The astronomical unit and Rømer's time estimate
   were combined by Christiaan Huygens, who estimated the speed of light
   to be 1000 Earth diameters per minute. This is about 220,000 kilometres
   per second (136,000 miles per second), well below the currently
   accepted value, but still very much faster than any physical phenomenon
   then known.

   Isaac Newton also accepted the finite speed. In his book " Opticks" he,
   in fact, reports the more accurate value of 16.6 Earth diameters per
   second, which it seems he inferred for himself (whether from Rømer's
   data, or otherwise, is not known). The same effect was subsequently
   observed by Rømer for a "spot" rotating with the surface of Jupiter.
   And later observations also showed the effect with the three other
   Galilean moons, where it was more difficult to observe, thus laying to
   rest some further objections that had been raised.

   Even if, by these observations, the finite speed of light may not have
   been established to everyone's satisfaction (notably Jean-Dominique
   Cassini's), after the observations of James Bradley ( 1728), the
   hypothesis of infinite speed was considered discredited. Bradley
   deduced that starlight falling on the Earth should appear to come from
   a slight angle, which could be calculated by comparing the speed of the
   Earth in its orbit to the speed of light. This "aberration of light",
   as it is called, was observed to be about 1/200 of a degree. Bradley
   calculated the speed of light as about 298,000 kilometres per second
   (185,000 miles per second). This is only slightly less than the
   currently accepted value. The aberration effect has been studied
   extensively over the succeeding centuries, notably by Friedrich Georg
   Wilhelm Struve and Magnus Nyren.
   Diagram of the Fizeau-Foucault apparatus.
   Enlarge
   Diagram of the Fizeau-Foucault apparatus.

   The first successful measurement of the speed of light using an
   earthbound apparatus 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 several
   thousand metres away. On the way from the source to the mirror, the
   beam passed through a rotating cog wheel. At a certain rate of
   rotation, the beam could pass through one gap on the way out and
   another on the way back. But at slightly higher or lower rates, the
   beam would strike a tooth and not pass through the wheel. Knowing the
   distance to the mirror, the number of teeth on the wheel, and the rate
   of rotation, the speed of light could be calculated. Fizeau reported
   the speed of light as 313,000 kilometres per second. Fizeau's method
   was later refined by Marie Alfred Cornu ( 1872) and Joseph Perrotin (
   1900).

   Leon Foucault improved on Fizeau's method by replacing the cogwheel
   with a rotating mirror. Foucault's estimate, published in 1862, was
   298,000 kilometres per second. Foucault's method was also used by Simon
   Newcomb and Albert A. Michelson. Michelson began his lengthy career by
   replicating and improving on Foucault's method.

   In 1926, Michelson used a rotating prism to measure the time it took
   light to make a round trip from Mount Wilson to Mount San Antonio in
   California. The precise measurements yielded a speed of 186,285 miles
   per second (299,796 kilometres per second).

Relativity

   From the work of James Clerk Maxwell, it was known that the speed of
   electromagnetic radiation was a constant defined by the electromagnetic
   properties of the vacuum ( permittivity and permeability).
   A schematic representation of a Michelson interferometer, as used for
   the Michelson-Morley experiment.
   Enlarge
   A schematic representation of a Michelson interferometer, as used for
   the Michelson-Morley experiment.

   In 1887, the physicists Albert Michelson and Edward Morley performed
   the influential Michelson-Morley experiment to measure the speed of
   light relative to the motion of the earth, the goal being to measure
   the velocity of the Earth through the "luminiferous aether", the medium
   that was then thought to be necessary for the transmission of light. 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
   travelling at right angles to one another. After leaving the splitter,
   each beam was reflected back and forth between mirrors several times
   (the same number for each beam to give a long but equal path length;
   the actual Michelson-Morley experiment used more mirrors than shown)
   then recombined to produce a pattern of constructive and destructive
   interference. Any slight change in speed of light along each arm of the
   interferometer (because the apparatus was moving with the Earth through
   the proposed "aether") would change the amount of time that the beam
   spent in transit, which would then be observed as a change in the
   pattern of interference. In the event, the experiment gave a null
   result.

   Ernst Mach was among the first physicists to suggest that the
   experiment actually amounted to a disproof of the aether theory.
   Developments in theoretical physics had already begun to provide an
   alternate theory, Fitzgerald-Lorentz contraction, which explained the
   null result of the experiment.

   It is uncertain whether Albert Einstein knew the results of the
   Michelson-Morley experiment, but the null result of the experiment
   greatly assisted the acceptance of his theory of relativity. Einstein's
   theory did not require an aether and was entirely consistent with the
   null result of the experiment: the aether did not exist and the speed
   of light was the same in each direction. The constant speed of light is
   one of the fundamental Postulates (together with causality and the
   equivalence of inertial frames) of special relativity.

   Retrieved from " http://en.wikipedia.org/wiki/Speed_of_light"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
