Speed of light
A line showing the speed of light on a scale model of Earth and the Moon, taking
about 1⅓ seconds to traverse that distance.
Light traveling through a medium such as air (for example, this laser)
travels slower than light through a vacuum.
The speed of light in the vacuum of free
space is an important physical constant usually denoted by the letter c.[1]
It is the speed of all electromagnetic radiation, including visible light, in
free space. It is the speed of anything having zero rest mass[2]. In metric
units, the speed of light in vacuum is defined to be exactly 299,792,458 metres
per second (1,079,252,849 km/h).[3] The speed of light can be assigned a
definite numerical value because 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;
in other words, any increase in the measurement precision of the speed of light
would refine the definition of the metre, but not alter the numerical value of
c. The approximate value of 3×108 m/s is commonly used in rough estimates (the
error is 0.07%). In imperial units, the speed of light is about 670,616,629.4
miles per hour or 983,571,056.4 feet per second, which is about 186,282.397
miles per second, or roughly one foot per nanosecond. See also the later section
of this article at "Speed of light set by definition".
The speed of light when it passes
through a transparent or translucent material medium, like glass or air, is less
than its speed in a vacuum. The ratio of the speed of light in the vacuum
to the observed phase velocity is called the refractive index of the medium. See
dispersion (optics). In general relativity c remains an important constant of
spacetime, however the concepts of 'distance', 'time', and therefore 'speed' are
not always unambiguously defined due to the curvature of spacetime caused by
gravitation. When measured locally, light in a vacuum always passes an observer
at c. [edit] Overview
The speed of light in vacuum is now viewed as a fundamental physical constant.
This postulate, together with the principle of relativity that all inertial
frames are equivalent, forms the basis of Einstein's theory of special
relativity. According to the currently prevailing definition, adopted in 1983,
the speed of light is exactly 299,792,458 metres per second (approximately 3×108
metres per second, or about 30
centimetres (1 foot) per nanosecond). See metre.
Experimental evidence has shown that the speed of light is independent of the
motion of the source. It has also been confirmed experimentally that the two-way
speed of light (for example from a source, to a mirror, and back again) is
constant. It is not, however, possible to measure the one-way speed of light
(for example from a source to a distant detector) without some convention as to
how clocks at the source and receiver should be synchronized[4]. Einstein (who
was aware of this fact) postulated that the speed of light should be taken as
constant in all cases, one-way and two-way.
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.
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. An observer moving with respect to a collection of light
sources would find that light from the sources ahead would be shifted toward the
violet end of the spectrum while light from those behind was redshifted.
[edit] Use of the symbol 'c' for the speed of light
The symbol 'c' for 'constant' or the Latin celeritas ("swiftness")[5] is
generally used for the speed of light. NIST and BIPM practice is to use c0 for
the speed of light in vacuum. Occasionally, some writers use c for the speed of
light in media other than vacuum. Throughout this article c is used exclusively
to denote the speed of light in a vacuum.
In branches of physics in which the speed of light plays an important part, for
example relativity, it is common to use a system of units in which c is 1, thus
no symbol for the speed of light is required.
[edit] Causality and information transfer
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". Such a violation of causality has never been recorded[6].
A light cone defines locations that are in causal contact and those that are
not.
[edit] Communications and GPS
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.
[edit] Physics
[edit] 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 measure the
other as approaching at a combined speed of 50 + 50 = 100 km/h to a very high
degree of accuracy.
However, as speeds increase this rule becomes less accurate. Two spaceships
approaching each other, each traveling at 90% the speed of light relative to
some third observer between them, do not measure each other as approaching at
90% + 90% = 180% the speed of light; instead they each measure the other as
approaching at slightly less than 99.5% the speed of light. This last result is
given by the Einstein velocity addition formula:[7]
where v and w are the (positive) velocities of the spaceships as measured by the
third observer, and u is the measured velocity of either space ship as observed
by the other.[8] This reduces to u = v + w for sufficiently small values of v
and w (such as those typically encountered in common daily experiences), as the
term vw / c2 approaches zero, reducing the denominator to 1.
If one of the velocities for the above formula (or both) are c, the final result
is c, as is expected if the speed of light is the same in all reference frames.
Another important result is that this formula always returns 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 one 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.
[edit] 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 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, that is, 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.
[edit] 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. 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
and of c. Through diamond, light is much slower—only about 124,000 kilometres
per second, less than of c.[9] 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 may depend on the frequency of the light, light at different
frequencies can travel at different speeds through the same material. This
effect is called dispersion.
Classically, considering electromagnetic
radiation to be a wave, the charges of each atom (primarily the electrons)
interact with the electric and magnetic fields of the radiation, slowing its
progress.
A more complete description of the passage of light through a medium is given by
quantum electrodynamics.
[edit] Accelerated frames of reference and general relativity
Since the early part of the 20th century lightspeed in vacuum has been
considered a property of our spacetime metric, i.e. an exchange rate between
seconds and meters and thus an effective "limit speed for energy" in
general[10].
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.
Main article: Faster-than-light
The blue glow in this "swimming pool" nuclear reactor is Čerenkov radiation,
emitted as a result of electrons traveling faster than the speed of light in
water.
It is generally considered that it is impossible for any information or matter
to travel faster than c. The equations of relativity show that, for an object
travelling faster than c, some physical quantities would be not represented by
real numbers. However, there are many physical situations in which speeds
greater than c are encountered.
[edit] Things which can travel faster than c
[edit] Wave velocities and synchronized events
It has long been known theoretically
that it is possible for the "group velocity" of light to exceed c.[11] 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.[12] 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.
[edit] Light spots and shadows
If a laser is swept across a distant
object, the spot of light can easily be made to move at greater than c[13].
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.
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.
[edit] Travel faster than the speed of light in a medium
[edit] General relativity
Some topics (such as the expansion of the universe, and wormholes) require the
application of general relativity and are covered in the main faster than light
article.
Main article: 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 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[15]; in 2001, they were able to
momentarily stop a beam.[16]
[edit] Measurement of the speed of light
[edit] 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.
Rømer's observations of the occultations of Io from Earth.
[edit] Astronomical techniques
The first quantitative estimate of the
speed of light was made in 1676 by Ole Christensen Rømer, who was studying the
motions of Jupiter's moon, Io, with a telescope. It is possible to time
the orbital revolution of Io because it enters and exits Jupiter's shadow at
regular intervals (at 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 about 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 1,000
Earth diameters per minute. This is about 220,000 kilometres per second (136,000
miles per second), 26% lower than the currently accepted value, but still very
much faster than any physical phenomenon then known.
Isaac Newton also accepted the finite speed. In his 1704 book Opticks he reports
the value of 16.6 Earth diameters per second (210,000 kilometres per second, 30%
less than the actual value), 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 (less than one percent). The aberration effect has been studied
extensively over the succeeding centuries, notably by Friedrich Georg Wilhelm
Struve and de:Magnus Nyrén.
Diagram of the Fizeau-Foucault apparatus.
[edit] Earth-bound techniques
The first successful measurement of the speed of light using an earthbound
apparatus was carried out by Hippolyte Fizeau in 1849. (This measures the speed
of light in air, which is slower than the speed of light in vacuum by a factor
of the refractive index of air, about 1.0003.) 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, a distance of about 22 miles (36 km). The
precise measurements yielded a speed of 186,285 miles per second (299,796
kilometres per second).
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 aether. 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
amounted to a disproof of the aether theory. Developments in theoretical physics
had already begun to provide an alternative 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.
The constant speed of light is one of the fundamental Postulates (together with
causality and the equivalence of inertial frames) of special relativity.