The 'speed of light in vacuum' is an important
physical constant denoted by the letter ''c'' for ''constant'' or the
Latin word ''
celeritas'' meaning "swiftness".
[1] It is the speed of all
electromagnetic radiation, including visible
light, in a
vacuum. More generally, it is the speed of anything having zero
rest mass.
A line showing the speed of light on a scale model of
Earth and the
Moon, about 1.2 seconds.
In metric units, ''c'' is exactly '
299,792,458'
metres per second (1,079,252,848.8 km/h).
[2] The fundamental
SI unit of length, the
metre, has been defined since
October 21,
1983, as the distance light travels in a vacuum in 1/299,792,458 of a
second; any increase in the precision of the measurement of the speed of light would refine the definition of the metre, but not alter the numerical value of ''c''. The approximate value of 3 m/s is commonly used in rough estimates. In
imperial units, the speed of light is about 670,616,629.2 miles per hour or 983,571,056
feet per second, which is about 186,282.397
miles per second, or roughly one
foot per
nanosecond.
The speed of light when it passes through a
transparent or translucent material medium, like glass or air, is slower than its speed in a vacuum. The ratio of ''c'' to the observed
phase velocity is called the
refractive index of the medium.
General relativity explains how a
gravitational potential can affect the apparent speed of distant light in a vacuum, but locally light in a vacuum always passes an observer at a rate of ''c''.
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 fact, one can view ''c'' as a fundamental physical constant. This logic is the basis of the theory of
special relativity.
[3]
Observers traveling at large velocities will find that distances and times are distorted in accordance with the
Lorentz transforms; however, the transformations distort times and distances in such a way that the speed of light remains constant. A light sensor traveling 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 frequency 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'. 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 recorded.
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 traveling
faster than light, it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C.
According to the currently prevailing definition, adopted in
1983, the speed of light is exactly 299,792,458 metres per second (approximately 3 metres per second, or about thirty
centimetres (one
foot) per
nanosecond). The value of
defines the
permittivity of free space (
) in
SI units as:
:
The
magnetic constant is not dependent on
and is defined in
SI units as:
:
.
These constants appear in Maxwell's equations, which describe
electromagnetism, and are related by:
:
Astronomical distances are sometimes measured in
light years (the distance that light would travel in one year, roughly
9.46 kilometres or about 5.88 miles). 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.
Communications and GPS
The speed of light is of relevance to
communications. For example, given the equatorial circumference of the
Earth is km and ''c'' = km/s, the theoretical shortest amount of time for a piece of information to travel half the globe along the surface is s.
The actual transit time is longer, in part because the speed of light is slower by about 30% in an
optical fiber and straight lines rarely occur in global communications situations, but also because delays are created when the signal passes through an electronic switch or signal regenerator. A typical time as of
2004 for a
U.S. to
Australia or
Japan computer-to-computer
ping is 0.18 s. The speed of light additionally affects
wireless communications design.
Another consequence of the finite speed of light is that communications with spacecraft are not instantaneous, and the gap becomes more noticeable as distances increase. This delay was significant for communications between
Houston ground control and
Apollo 8 when it became the first spacecraft to orbit the
Moon: For every question, Houston had to wait nearly 3
seconds for the answer to arrive, even when the astronauts replied immediately.
This effect forms the basis of the
Global Positioning System (GPS), and similar
navigation systems. One's position can be determined by means of the delays in radio signals received from a number of satellites, each carrying a very accurate
atomic clock, and very carefully
synchronized. It is remarkable that, to work properly, this method requires that (among many other effects) the relative motion of satellite and receiver be taken into effect, which was how (on an interplanetary scale) the finite speed of light was originally discovered (see the following section).
Similarly, instantaneous remote control of interplanetary spacecraft is impossible because it takes time for the Earth-based controllers to receive information from the craft, and an equal time for instructions to be received by the craft. It can take hours for controllers to become aware of a problem, respond with instructions, and have the spacecraft receive the instructions.
The speed of light can also be of concern on very short distances. In
supercomputers, the speed of light imposes a limit on how quickly data can be sent between
processors. If a processor operates at 1
GHz, a signal can only travel a maximum of 300 mm in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single
chips.
Physics
Constant velocity from all inertial reference frames
Most individuals are accustomed to the addition rule of velocities: if two cars approach each other from opposite directions, each traveling at a speed of 50
km/h, relative to the road surface, one expects that each car will perceive the other as approaching at a combined speed of 50 + 50 = 100 km/h to a very high degree of accuracy.
However, at velocities at or approaching the speed of light, this rule does not apply. Two spaceships approaching each other, each traveling at 90% the speed of light relative to some third observer between them, do not perceive each other as approaching at 90% + 90% = 180% the speed of light; instead they each perceive the other as approaching at slightly less than 99.5% the speed of light. This last result is given by the
Einstein velocity addition formula:
:
where
and
are the (positive) speeds of the spaceships as observed by the third observer, and
is the speed of either space ship as observed by the other.
[4] From this, we can see how this reduces to
for sufficiently small values of
and
(such as those typically encountered in common daily experiences), as the term
approaches zero, reducing the denominator to 1.
If one of the velocities for the above formula (or both) are ''c'', the final result is ''c'', as is expected if the speed of light is the same in all reference frames. Another important result comes from this formula always returning a value which is less than ''c'' whenever ''v'' and ''w'' are less than ''c'': This shows that no acceleration in any frame of reference can cause you to exceed the speed of light with respect to another observer. Thus ''c'' acts as a speed limit for all objects with respect to all other objects in special relativity.
Luminiferous aether (discredited)
Interference pattern produced with a Michelson interferometer
Before the advent of special relativity, it was believed that light travels through a medium called the
luminiferous aether. Maxwell’s equations predict a given speed of light, in much the same way as is the speed of
sound in
air. The speed of sound in air is actually relative to the movement of the air itself, and the speed of sound in air with respect to an observer may be changed if the observer is moving with respect to the air (or
vice versa). The speed of light was believed to be relative to a medium of transmission for light that acted as air does for the transmission of sound—the luminiferous aether.
The
Michelson–Morley experiment, arguably the most famous and useful failed experiment in the history of physics, was designed to detect the motion of the Earth through the luminiferous aether. It could not find any trace of this kind of motion, suggesting, as a result, that it is impossible to detect one's presumed absolute motion, i.e., motion with respect to the hypothesized luminiferous aether. The Michelson–Morley experiment said little about the speed of light relative to the light’s source and observer’s velocity, as both the source and observer in this experiment were traveling at the same velocity together in space.
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).
In passing through materials, the observed speed of light can differ from ''c''. The ratio of ''c'' to the
phase velocity of light in the material is called the
refractive index. This apparent contradiction to the universality of the constant ''c'' is a consequence of sloppy (but universally practiced) nomenclature: what is referred to as light in a medium is really a light-like hybrid of electromagnetic waves and mechanical oscillations of charged or magnetic particles such as
electrons or
ions, whereas light in the strict sense is a pure
electromagnetic wave (see further discussion below). The speed of light in
air is only slightly less than
. Denser media, such as
water and
glass, can slow light much more, to fractions such as
¾ and
⅔ of ''c''. Through diamond, light is much slower—only about 124,000 kilometres per second, less than
½ of ''c''.
[5] 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, an effect 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 traveling 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 different from light.
Accelerated frames of reference and general relativity
Although it is constant in inertial frames of reference in special relativity, the speed of light can vary based on its position for accelerated frames of reference in special relativity and in general relativity. Before heading into this discussion, it must first be noted that in all cases the speed of light locally remains ''c'' in these cases. So when an observer measures the speed of light at his own position, the constancy of its speed holds. The issue arises at positions distant from the observer in these situations.
The cause of this change is
gravitational time dilation. As clocks at lower gravitational potentials tick slower, a beam of light will take longer to move along a rod at a lower gravitational potential than it would take to move along an identical rod at ones own potential. This light is considered to be moving more slowly at lower potentials. This slowdown becomes extreme as the light approaches the
event horizon of a
black hole, where both time and light will appear to stop. Similarly, light will appear to go faster at higher gravitational potentials.
In general relativity, the curvature of spacetime can also affect the number of rods between certain positions. This will add another factor to magnitude of the apparent speed change.
"Faster-than-light" observations and experiments
Main articles: Faster-than-light
It has long been known theoretically that it is possible for the "
group velocity" of light to exceed ''c''.
[6] One recent experiment made the group velocity of
laser beams travel for extremely short distances through
caesium atoms at 300 times ''c''. In 2002, at the
Université de Moncton, physicist Alain Haché made history by sending pulses at a group velocity of three times light speed over a long distance for the first time, transmitted through a 120-metre cable made from a coaxial photonic crystal.
[7]
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 waves' length much faster than the waves' 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 and the group velocity of evanescent waves may exceed ''c''; however, it would appear that the front velocity does not exceed ''c'', so, again, it is not possible for information to be transmitted faster than ''c''.
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 equilibrium can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves travel, as when a charged particle exceeds the speed of light in that medium, the photons constructively interfere and intensify the observed radiation. The result (analogous to a
sonic boom) is known as
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, and would potentially violate
causality if they were.
Some physicists, notably
João Magueijo and
John Moffat, have proposed that in the past light traveled much faster than the current speed of light. This theory is called
variable speed of light (VSL) and its supporters claim that it has the ability to explain many
cosmological puzzles better than its rival, the
inflation model of the
universe. However, it has not gained wide acceptance.
"Slow light" experiments
Main articles: Slow light
Refractive phenomena, such as this
rainbow, are due to the slower speed of light in a medium (water, in this case).
Light traveling through a medium other than a vacuum travels below
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;
[8] in
2001, they were able to momentarily stop a beam.
[9]
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 bec (
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.
[10]
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 traveling.
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 was that light was emitted from the eye, instead of entering the eye from another source. Using this theory,
Heron of Alexandria advanced the argument that the speed of light must be
infinite, since distant objects such as stars appear immediately upon opening the eyes.
Medieval and early modern theories
Early Muslim philosophers initially agreed with
Aristotle's view that light has an infinite speed. In the
11th century, however,
Muslim scientists realized that light has a finite speed. The
Iraqi
Arab scientist
Ibn al-Haytham (Alhacen), the father of
optics, using an early
experimental
scientific method in his ''
Book of Optics'', discovered that light has a finite speed. Some of his contemporaries, notably the
Persian scientists
Avicenna and
al-Biruni, also agreed with Alhacen that light has a finite speed. Avicenna "observed that if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite."
[11] Al-Biruni further discovered that the speed of light is much faster than the
speed of sound.
[12]
The 14th century
Indian scholar
Sayana wrote in a comment on verse
Rigveda 1.50.4 (1700–1100 BCE—the early Vedic period): "Thus it is remembered: [O Sun] you who traverse 2202
yojanas [ca. 14,000 to 30,000 km] in half a
nimesa [ca. 0.1 to 0.2 s]", corresponding to between 65,000 and 300,000 km/s, for high values of ''yojana'' and low values of ''nimesa'' consistent with the actual speed of light.
[13]
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 was finite, his whole system of philosophy would be demolished.
[14]
Measurement of the speed of light
Early attempts
Isaac Beeckman proposed an experiment (
1629) in which a person would observe the flash of a
cannon reflecting off a
mirror about one mile away.
Galileo proposed an experiment (1638), with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a
lantern and its perception some distance away. This experiment was carried out by the
Accademia del Cimento of
Florence in
1667, with the lanterns separated by about one mile. No delay was observed.
Robert Hooke explained the negative results as Galileo had: by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great.
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.
Astronomical techniques
The first quantitative estimate of the speed of light was made in
1676 by
Ole Rømer, who was studying the
motions of
Jupiter's moon,
Io, with a
telescope. It is possible to time the
orbital revolution of Io because it enters and exits Jupiter's shadow at regular
intervals (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5
hours when
Earth was closest to Jupiter (at H). He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. This was as a result of the extra time it took for light to cross the extra distance between the planets, time which had accumulated in the interval between one signal and the next. The opposite is the case when they are approaching (as from F to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the
astronomical unit); the modern estimate is 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), 26 per cent lower than the currently accepted value, but still very much faster than any physical phenomenon then known.
Isaac Newton also accepted the finite speed. In his 1704 book "
Opticks" he, in fact, reports the 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.
Earth-bound techniques
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).
Laboratory-based methods
During
World War II, the development of the
cavity resonance wavemeter for use in
radar, together with precision timing methods, opened the way to laboratory-based measurements of the speed of light. In
1946,
Louis Essen in collaboration with
A.C. Gordon-Smith
used a
microwave cavity of precisely known dimensions to establish the
frequency for a variety of
normal modes of microwaves—which, in common with all electromagnetic radiation, travels at the speed of light in vacuum. As the
wavelength of the modes was known from the geometry of the cavity and from
electromagnetic theory, knowledge of the associated frequencies enabled a calculation of the speed of light. Their result, 299,792±3 km/s, was substantially greater than those found by optical techniques, and prompted much controversy. However, by
1950 repeated measurements by
Essen established a result of 299,792.5±1 km/s; this became the value adopted by the 12th General Assembly of the
Radio-Scientific Union in
1957. Most subsequent measurements have been consistent with this value.
Speed of light set by definition
In
1983, the 17th
Conférence Générale des Poids et Mesures adopted a standard value, 299,792,458
m/s for the speed of light. This in turn defines the length of a meter in terms of the speed of light, so that further refinements in the current experimental value of the speed of light actually would just refine the definition of a meter.
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).
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 traveling at
right angles to one another. After leaving the splitter, each beam was reflected back and forth between
mirrors several times (the same number for each beam to give a long but equal path length; the actual Michelson-Morley experiment used more
mirrors than shown) then recombined to produce a pattern of constructive and destructive
interference. Any slight change in speed of light along each arm of the interferometer (because the apparatus was moving with the Earth through the proposed "aether") would change the amount of time that the beam spent in transit, which would then be observed as a change in the pattern of interference. In the event, the experiment gave a
null result.
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.
See also
★
Fizeau-Foucault apparatus
★
Michelson-Morley experiment
★
Variable speed of light
References
Footnotes
1. Why is c the symbol for the speed of light?
2. Speed of light in vacuum CODATA
3. It is worth noting that it is the constant speed ''c'', rather than light itself, that is fundamental to special relativity; thus if light is somehow manipulated to travel at less than ''c'', this manipulation will not directly affect the theory of special relativity.
4. Francis Weston Sears, ''Introduction to the Theory of Relativity'', p. 24, footnote: Except in giving a name to [this equation], the term "velocity" is used in this book to mean the speed and direction of motion. Velocity is a vector quantity, whereas speed refers only to the magnitude of the velocity. Since we have restricted motion to a single dimension (along the x-axis), we have not needed to introduce the concept of velocity here.
5. Refraction, Snell's law, and total internal reflection
6. Applets Gallery / Subluminal
References Gain-assisted superluminal light propagation, LJ Wang, , , Nature, ''
7. Electrical pulses break light speed record, physicsweb, 22 January 2002; see also A Haché and L Poirier (2002), Appl. Phys. Lett. v.80 p.518.
8. Light speed reduction to 17 metres per second in an ultracold atomic gas, L.V. Hau, S.E. Harris, Z. Dutton, and C.H. Behroozi, , , Nature,
9. Observation of coherent optical information storage in an atomic medium using halted light pulses, C. Liu, Z. Dutton, C.H. Behroozi, and L.V. Hau, , , Nature,
10. Stationary pulses of light in an atomic medium, M. Bajcsy1, A.S. Zibrov, and M.D. Lukin, , , Nature,
11. George Sarton, ''Introduction to the History of Science'', Vol. 1, p. 710.
12.
13. Light or Coincidence Subhash Kak ; Bengali Calendar
14. Historical Background, footnote 5
Historical references
★ Ole Rømer. "Démonstration touchant le mouvement de la lumière", ''
Journal des sçavans'', 7 Décembre 1676, pp. 223–236. Translated as "A Demonstration concerning the Motion of Light", ''Philosophical Transactions of the
Royal Society'' no. 136, pp. 893–894; June 25, 1677. ''(Rømer's 1676 paper, in English and French, as
bitmap images, and
in French as plain text)''
★ Edmund Halley. "Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London", ''Philosophical Transactions'' XVIII, No. 214, pp 237–256, Nov.–Dec., 1694.
★ H.L. Fizeau. "Sur une expérience relative à la vitesse de propogation de la lumière", ''Comptes Rendus'' 29, 90–92, 132, 1849.
★ J.L. Foucault. "Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil", ''Comptes Rendus'' 55, 501–503, 792–796, 1862.
★ A.A. Michelson. "Experimental Determination of the Velocity of Light", ''Proceedings of the American Association for the Advancement of Science'' 27, 71–77, 1878. (
Project Gutenberg Etext version)
★ Simon Newcomb. "The Velocity of Light", ''Nature'', pp 29–32, May 13, 1886.
★ Joseph Perrotin. "Sur la vitesse de la lumière", ''Comptes Rendus'' 131, 731–734, 1900.
★ A.A. Michelson, F.G. Pease, and F. Pearson. "Measurement Of The Velocity Of Light In A Partial Vacuum", ''Astrophysical Journal'' 82, 26–61, 1935.
Modern references
★ Léon Brillouin. ''Wave propagation and group velocity''. Academic Press Inc., 1960.
★ John David Jackson. ''Classical electrodynamics''. John Wiley & Sons, 2nd edition, 1975; 3rd edition, 1998. ISBN 0-471-30932-X
★ R.J. MacKay and R.W. Oldford.
"Scientific Method, Statistical Method and the Speed of Light", ''Statistical Science'' 15(3):254–278, 2000.
External links
★
Speed of light in vacuum ''(at
NIST)''
★
Data Gallery: Michelson Speed of Light (Univariate Location Estimation) ''(download data gathered by
A.A. Michelson)''
★
Switching light on and off ''(news article on stopping light)''
★
Beam smashes light barrier ''(news article on group velocity experiment)''
★
Subluminal ''(Java applet demonstrating group velocity information limits)''
★
Light discussion on adding velocities
★
Discussion on binary stars and adding of velocities
★
Surpassing speed of light
★
We have broken speed of light
.PNG)
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