Speed of light
The speed of light in vacuum is exactly equal to 299,792,458 metres per second. This is approximately 300,000 kilometres per second, or 186,000 miles per second.At present, the speed of light is a definition, not a measurement, as the metre is defined in terms of the speed of light and not vice versa.
According to standard modern physical theory, all electromagnetic radiation, including light, propagates (or moves) at a constant speed in vacuum - the speed of light. It is a physical constant and denoted as (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. If information could travel faster than in one reference frame, causality would be violated, as in some other reference frame the information would be received before it had been sent. Such a violation of causality has never been observed.
According to the currently prevailing definition, adopted in 1983,
the speed of light is exactly
Overview
This is approximately 3 × 108 metres per second, that is, about thirty centimetres (12 inches) per nanosecond. The value of defines the
permittivity of free space () and the permeability of free space () in SI units as
- .
Since the speed of light in vacuum is constant, it is convenient to measure both time and distance in terms of . Both the SI unit of length and SI unit of time have been defined in terms of wavelengths and cycles of light. In 1983 the metre was redefined in terms of . In particular, one metre is defined as . This relies on the constancy of the velocity of light for all observers.
Astronomic distances are sometimes measured in light years, especially in popularized texts.
The speed of a light is of relevance to communications. For example, given the
equatorial circumference of the earth at 40,075 km and c, the shortest
amount of time for a piece of information to theoretically travel half the globe
is 0.067 seconds.
Given that the speed of light is slower in an Optical fiber and that straight lines rarely occur in communications situations, a typical time as of 2004 for an Australia or Japan to US computer-to-computer ping is 0.250 seconds. The speed of light additionally affects wireless communications design.
The speed of light can also be of concern on short distances. In supercomputers, the speed of light imposes a limit on how quickly data can be sent between nodes. If a processor operates at 1 GHz, a signal can only travel a maximum of 30 cm in a single cycle. Nodes 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 chipss.
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 will measure it moving away from him at the same speed as a stationary observer. This leads to some unusual 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:
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 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.
In passing through materials, light is slowed to less than , by the ratio called the refractive index of the material. 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 3/4 and 2/3 of .
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.
Recent experimental evidence shows that it 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 . However, it is not possible to use this technique to transfer information faster than ; the product of the group velocity and the velocity of information transfer 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 in a distantly spaced line of people, 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 last person shouting.
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 .
Although it may sound paradoxical, it is possible for shock waves to be formed with electromagnetic radiation. In such a situation, an object emitting light is travelling faster than the speed of light for the medium in which it is travelling. This forms the basis of Cherenkov radiation.
In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light beam to about 17 meters per second. In 2001, they were able to momentarily stop a beam. See Bose-Einstein condensate for more information.
In 2003, Mikhail Lukin, with scientists at Harvard University and the Lebedev Institute in Moscow, succeeded in completely halting light by directing it into a mass of hot rubidium gas, the atoms of which, in Lukin's words, "[behaved] like tiny mirrors", due to an interference pattern in two "control" beams.
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 is that light is emitted from the eye,
instead of being reflected into the eye from another source. On this theory,
Heron of Alexandria advanced the argument that the speed of light must be infinite, since distant objects such as stars appear immediately when one opens one's eyes.
The Islamic philosophers Avicenna and Alhazen believed that light has a finite speed, although most philosophers agreed with Aristotle on this point. 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 (e.g. a musket ball). Rene Descartes argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light is infinite. In fact, Descartes was convinced that if the speed of light were finite, his whole system of philosophy would be demolished. Isaac Beeckman, a friend of Descartes, proposed an experiment (1629) in which one would observe the flash of a cannon reflecting off a mirror about one mile away. Galileo proposed an experiment (1638) 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 of Descartes and Galileo by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great.
The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer, who was studying the motions of Jupiter's satellite Io. Rømer observed that eclipses of Io by Jupiter appeared sooner when Earth was approaching Jupiter and later when Earth was moving farther away. Rømer correctly deduced that this discrepancy was due to the time it took for light to cross the lesser or greater distance between the planets. 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 two results were combined by Christiaan Huygens, who estimated the speed of light to be 16 and 2/3 Earth diameters per second. This is about 220,000 kilometres per second, well below the currently accepted value, but still very much faster than any physical phenomenon then known.
The finite speed of light was not conclusively established by these observations, as it could be argued the differences in the times of eclipses were due to perturbations of the orbits of the satellites. However, 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 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.
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 meters 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.
Definition of the Metre
Communications
Physics
Constant in all reference frames
where and are the speeds of the spaceships relative to the observer, and is the speed perceived by each spaceship.Refraction
"Faster-than-light" experiments
"Slower-than-light" (i.e., slowing light) experiments
History
See also
References
Historical references
Modern references
External links