Speed of light

According to standard modern physical theory, light and all other
electromagnetic radiation propagates (or moves) at a constant speed in
vacuum, the speed of light. It is a physical constant and notated as c (from
the Latin celeritas, "speed"). Regardless of the reference frame of an
observer or the velocity of the object emitting the light, every observer
will obtain the same value for the speed of light upon measurement. No
information can travel faster than c without causing serious problems with
causality that have not been observed.

The value is precisely

     c = 2.997 924 58 × 108 metres per second,

or about thirty centimetres (12 inches) in a nanosecond. This is not an
empirical value. It is a solution to the wave equation, and can be
calculated from the permittivity of free space (ε0) and the
permeability of free space (μ0). In fact

     [c = \frac{1}{\sqrt{\epsilon_0 \, \mu_0}}]

It is important to realize that the speed of light is not a "speed limit" in
the conventional sense. As a consequence of the theory of special
relativity, all observers will measure the speed of light as being the same.
An observer chasing a beam of light well measure it moving away from him at
the same speed as a stationary observer. This leads to some unusually
consequences for velocities.

We are accustomed to the additive rule of velocities: if two cars approach
each other, each travelling at a speed of 50 miles per hour, we expect that
each car will perceive the other as approaching at a combined speed of 50 +
50 = 100 miles per hour (to a very high degree of accuracy).

At velocities approaching or at the speed of light, however, it becomes
clear from experimental results that this additive rule no longer applies.
Two spaceships approaching each other, each travelling 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:

     [u = {v + w \over 1 + v w / c^2}]

where v and w are the speeds of the spaceships relative to the observer, and
u is the speed perceived by each spaceship.

Contrary to our usual intuitions, regardless of the speed at which one
observer is moving relative to another observer, both will measure the speed
of an incoming light beam as the same constant value, the speed of light.

Albert Einstein developed the theory of relativity by applying the (somewhat
bizarre) consequences of the above to classical mechanics. Experimental
confirmations of the theory of relativity directly and indirectly confirm
that the velocity of light has a constant magnitude, independent of the
motion of the observer.

Since the speed of light in vacuum is constant, it is convenient to measure
both time and distance in terms of c. Both the SI unit of length and SI unit
of time have been defined in terms of wavelengths and cycles of light;
currently, the meter is defined as the distance travelled by light in a
certain amount of time: this relies on the constancy of the velocity of
light for all observers. Distances in physical experiment or astronomy are
commonly measured in light seconds, light minutes, or light years.

Refraction

In passing through materials, light is slowed to less than c, by the ratio
called the refractive index of the material. The speed of light in air is
only slightly less than c. Denser media such as water and glass can slow
light much more, to fractions such as 3/4 and 2/3 of c. On the microscopic
scale this is caused by continual absorption and re-emission of the photons
that compose the light by the atoms or molecules through which it is
passing.

"Faster-than-light" experiments

Recent experimental evidence shows that is is possible for the group
velocity of light to exceed c. One experiment made the group velocity of
laser beams travel for extremely short distances through caesium atoms at
300 times c. However, it is not possible to use this technique to transfer
information faster than c; the product of the group velocity and the
velocity of information transfer is equal to the normal speed of light in
the material squared.

The speed of light may also appear to be exceeded in some phenomena
involving evanescent waves. Again, it is not possible that information is
transmitted faster than c.

"Slower-Than-Light" (i.e. slowing light) Experiments

In 1999, scientists were able to slow the speed of a light beam to about 61
km/h. In 2001, they were able to momentarily stop a beam. See Bose-Einstein
condensate for more information.

History

Galileo Galilei as far as we know was the first person to suspect that light
might have a finite speed and attempt to measure it-but people before
Galileo probably thought of lights (i.e. stars, suns) as constants anyway.
He wrote about his unsuccessful attempt using lanterns flashed from hill to
hill outside Florence. The speed of light was first measured in 1676, some
decades after Galileo's attempt, by R¿mer, who was studying the motions of
Jupiter's moons. A plaque at the Observatory of Paris, where R¿mer happened
to be working, commemorates what was, in effect, the first measurement of a
universal quantity made on this planet. R¿mer published his result, which
had an error of 10-25%, in Journal des Scavans.

It is a bizarre coincidence that the average speed of the earth in its orbit
is very close to one ten-thousandth of this, actually within less than a
percent. This gives a hint as to how R¿mer measured light's speed. He was
recording eclipses of Jupiter's moon Io: every day or two Io would go into
Jupiter's shadow and later emerge from it. R¿mer could see Io blink off and
then later blink on, if Jupiter happened to be visible. Io's orbit seemed to
be a kind of distant clock, but one which R¿mer discovered ran fast while
Earth was approaching Jupiter and slow while it was receding from the giant
planet. Roemer measured the cumulative effect: by how much it eventually got
ahead and then eventually fell behind. He explained the measured variation
by positing a finite velocity for light.