[[File:Sun to Earth.JPG|thumb|300px|
Sunlight takes approximately 8 minutes to reach
Earth.
The
speed of light (usually denoted
c) is a
physical constant. Its value is
299,792,458
metres per second.
It is the speed of electromagnetic radiation (such as radio waves, visible light, or gamma rays) in vacuum, where there are no atoms, molecules or other types of matter that can slow it down. It is often approximated as 300,000 kilometres per second or 186,000 miles per second.
For much of human history, it was not known whether light was
transmitted instantaneously or simply very quickly. In the 17th
century,
Ole Rømer demonstrated that
it travelled at a finite speed by studying the apparent motion of
Jupiter's moon
Io.
By 1975, the speed of light was known to be with a relative
measurement uncertainty of 4
parts per billion. In 1983, the
metre was
redefined in the
International System of Units
(SI) as the distance travelled by light in vacuum in of a
second. As a result, the numerical value of
c in metres per second is now fixed exactly by the
definition of the metre.
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). 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, and it is
believed to be the
speed of gravity
and of
gravitational waves. It is
an upper bound on the speed at which
energy,
matter, and
information can travel, as surpassing
it would be equivalent to travelling backwards in time; its finite
value is a limiting factor in the speed of operation of electronic
devices.
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 ; the
refractive index of air is about 1.0003, so the speed of light in
air is very close to
c.
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 of a second (see " ", below). The effect of this definition is
to fix the speed of light in vacuum at exactly .
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 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.
Some authors use
c for the speed of waves in
any
material medium, and
c0 for the speed of light
in vacuum. This subscripted notation, which is endorsed in official
SI literature, 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 . Thus, no symbol for
the speed of light is required.
Fundamental role in physics
The speed at which light propagates in vacuum is independent of
both the source of the light and the
frame of reference of the observer. This
was first postulated by Albert Einstein in 1905, motivated by
Maxwell's theory of
electromagnetism and the results of the
Michelson–Morley
experiment, and has since been confirmed by various
experiments. The theory of
special
relativity explores the consequences of the existence of such
an invariant speed
c and the assumption that the laws of
physics are the same in all
inertial frames of reference.
One particular immediate result is that all massless particles and
waves, such as light, must always travel with the speed
c,
which justifies calling
c the "speed of light".
Special relativity has many implications, which often are
counter-intuitive. These include the
equivalence of mass and
energy ,
length contraction
(moving objects are shorter),
time
dilation (moving clocks run slower) and the
relativity of simultaneity. The
last item states that, if the spatial distance between two events A
and B is greater than the time interval between them multiplied by
c, then there are frames of reference in which A precedes
B, others in which B precedes A, and others in which they are
simultaneous, with the consequence that such events cannot have a
causal relation. The predictions of special relativity have since
been verified in many experiments.
The results of special relativity can be summarized by treating
space and time as a unified structure known as
spacetime (with
c relating units of space
and time), and requiring that physical theories satisfy a special
symmetry called
Lorentz invariance, which depends on
c. Lorentz invariance has become an almost universal
assumption for modern physical theories, such as
quantum electrodynamics (QED),
quantum chromodynamics (QCD),
the
Standard Model of
particle physics, and
general relativity. As such, the
parameter
c has become ubiquitous in modern physics,
appearing in many contexts which may seem at first unrelated to
light. For example, general relativity predicts that
gravitational waves propagate with the
speed of light.
In
non-inertial frames
(gravitationally curved space or
accelerated frame), the
local speed of light is constant and equal to
c,
but the
speed of
light along a trajectory of finite length can differ from
c, depending on how distances and times are defined.
It is generally assumed in physics that fundamental constants such
as
c have the same value throughout spacetime, meaning
that they do not depend on location and do not vary with time.
However, various theories have suggested that the
speed of light has changed over
time.
Although no conclusive evidence for such theories has been found, they remain the subject of ongoing research.
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 .
In modern
quantum physics, the
electromagnetic field is described by the theory of
quantum electrodynamics (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, its speed would depend on its
frequency, and the invariant speed
c of special relativity
would then be the upper limit of the speed of light in vacuum. To
date no such effects have been observed
putting stringent limits on the photon mass. The limit obtained depends on the used model: if the massive photon is described by Proca theory, the experimental upper bound for its mass is about 10−57 grams. If photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, (roughly 2 × 10−47 g).
In a medium
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. 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. 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
- v_p = c\ n(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 ; in 2001, they were able to momentarily stop a
beam.
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.
It is also possible for the
group
velocity of light pulses to exceed
c. In an experiment
in 2000,
laser beams travelled for extremely
short distances through
caesium atoms with a
group velocity of 300 times
c. 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.
Faster-than-light observations and experiments
It is normally impossible for information or matter to travel
faster than
c. One reason is that according to the theory
of special relativity, 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, and
causality would be violated. In
such a frame of reference, an "effect" could be observed before its
"cause". Such a violation of causality has never been recorded, and
would lead to
paradoxes.
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, no matter, energy, or information
travels faster than the speed of light in a vacuum. For example, if
a laser beam is swept quickly across a distant object, the spot of
light can move faster than
c. Similarly, a shadow
projected onto a distant object can be made to move faster than
c. In neither case does any matter or information travel
faster than light.
In some
interpretations of quantum
mechanics, certain quantum effects may be transmitted not just
faster than
c, but instantaneously. 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
instantaneously (i.e., faster than light could travel from one
particle to the other). 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.
Another prediction of faster-than-light speeds occurs for
quantum tunnelling and is called the
Hartman effect. However, no
information can be sent using these effects.
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, 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 approaching Earth at a small
angle to the line of sight: since the light which was emitted when
the jet was farther away took longer to reach us, the time between
two successive observations on Earth corresponds to a longer time
between the instants at which the light rays were emitted.
Cherenkov radiation
It is possible for
shock waves to be
formed with electromagnetic radiation. 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.
Galaxies moving faster than light
In models of the expanding universe, the farther galaxies are from
each other, the faster they move apart. This movement is not
considered to be a straightforward travel, like a rocket for
example, but a movement due to the
expansion of space. For example,
this expansion moves distant galaxies away from Earth faster and
faster the further away they are. At a boundary called the
Hubble sphere, the recessional velocity is the
speed of light.
Practical effect of the finite speed of light
The speed of light plays an important part in many modern sciences
and technologies. In electronic systems, despite their small size,
the speed of light can become a limiting factor in their maximum
speed of operation.
Transit time
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 ) 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. 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.
Doppler effect
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.
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.
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.
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. This effect is known
as
Terrell rotation.
History
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".
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. This led Alhazen to propose that light must therefore
have a finite speed, and that the speed of light is variable,
decreasing in denser bodies. He argued that light is a "substantial
matter", the propagation of which requires time "even if this is
hidden to our senses".
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.
Roger Bacon argued that the speed of
light in air was not infinite, using philosophical arguments backed
by the writing of Alhazen and Aristotle. In the 1270s,
Witelo considered the possibility of light travelling
at infinite speed in a
vacuum but slowing
down in denser bodies. 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 "the most
astonishing 'blind hit' in the history of science!" 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.
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.
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.
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.
Early astronomical techniques
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 Christensen
Rømer, one of a group of astronomers of the
French Royal Academy of Sciences
who were studying the
motion of
Jupiter's moons.
Although Rømer read a report on his work to the French Academy of
Sciences in November 1676
, he does not
appear to have written the published account.
An electronic copy of the latter and
one of a 1677 English translation are available
online. From the observation that the periods of Jupiter's
innermost moon
Io appeared to be shorter
when the earth was approaching Jupiter than when receding from
Jupiter he concluded that light travels at a finite speed, and was
able to estimate that would take light 22 minutes to cross the
diameter of Earth's orbit.
Christiaan
Huygens combined this estimate with an estimate for the
diameter of the Earth's orbit to obtain an estimate of speed of
light of , 26% lower than the actual value.
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). 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, 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. Bradley
was able to predict the aberration for several other stars, and
confirm his predictions by observation. 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.
Earth-bound techniques
The first successful entirely earthbound measurement of the speed
of light was carried out by
Hippolyte
Fizeau in 1849. Fizeau's experiment was conceptually similar to
those proposed by Beeckman and Galileo. A beam of light was
directed at a mirror 8 km away. On the way from the source to
the mirror, the beam passed through a rotating cog wheel. At a
certain rate of rotation, the beam could pass through one gap on
the way out and another on the way back. But at slightly higher or
lower rates, the beam would strike a tooth and not pass through the
wheel. Knowing the distance to the mirror, the number of teeth on
the wheel, and the rate of rotation, the speed of light could be
calculated. Fizeau reported the speed of light as .
Léon Foucault improved on Fizeau's method
by replacing the cogwheel with a rotating mirror. Foucault's
estimate, published in 1862, was .
Cavity resonance
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, , 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 , which became the value adopted by the
12th General Assembly of the
Radio-Scientific Union in 1957.
Heterodyne laser measurements
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. 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. 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). Their results were
- f = 88. (50) THz
- λ = 3. (12) μm
- c = .2(1.1) m/s
nearly a hundred times more precise than previous measurements of
the speed of light.
Redefinition of the metre
The 1972 measurement of the speed of light, with a relative
uncertainty of , 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 length of the metre.
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,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
2
p10 and 5
d5 of the
krypton-86 atom." but it turned out that the
chosen spectral line was not perfectly symmetrical. 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 for "the speed of propagation of electromagnetic
waves in vacuum". 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 of a second".
The effect of this definition gives the speed of light the exact
value , which is nearly the same as the value obtained in the 1972
experiment. This number was chosen so that the change in the actual
length of the metre was minimised, being similar to the measurement
uncertainty. As a result, within the SI system of units, the speed
of light is now a defined constant and no longer something to be
measured. Improved experimental techniques do not affect the value
of the speed of light in SI units, but do result in a more precise
realisation of the SI metre.
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 .A list of the
resulting wavelengths based upon these frequencies and λ =
c/f is found at
BIPM mise-en-pratique, method
b.
Practical realisations 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.
Modern astronomical measurements
The overriding problem with any modern measurement of the speed of
light (
c) is the definition of a precise standard of
length. For practical length measurements on Earth,
c is
the length standard, through the 1983 definition of the metre, but
it is still possible to define other standards and hence to measure
c 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
c 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:
- light time per unit distance:
- c = =
The relative uncertainty in these measurements is 0.02 parts per
billion (0.02 ), equivalent to the uncertainty in Earth-based
measurements of length by interferometry.
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", slightly longer
than the currently accepted value of 8 minutes
19 seconds.
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.
See also
Notes
References
Citations
- The speed of light can also be expressed exactly in
imperial
units and US units, based on an inch of
exactly 2.54 cm, as 186,282 miles, 698 yards, 2 feet, and inches
per second. ( Archived version 2009-11-14.)
- Archived version 2009-11-17
- See for example: * * * *
- English translation:
- Strictly speaking, it is only possible to experimentally verify
that the two-way speed of light (for example from a source to a
mirror and back again) is frame-independent, since it is impossible
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. However, by adopting
Einstein synchronization for the
clocks, the one-way speed of light becomes equal to the two way
speed of light by definition.
- An overview can be found in the dissertation of
- archived version 2009-11-17
- See Relativity of simultaneity.
- 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.
- See Tachyonic antitelephone for an
example.
- Archived version 2009-11-17
- Reprinted in
- Further discussion can be found at
- (cf. )
- Besides Rømer, the group included Giovanni Domenico Cassini and
Jean
Picard.
- . The text of Prop. XI is identical between the first
(1704) and second (1719) editions.
- A detailed discussion of the interferometer and its use for
determining the speed of light can be found in
- also found in
Historical references
Modern references
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