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Speed of light

According to standard modern physical theory, light and all other electromagnetic radiation propagates at a constant speed in vacuum, the speed of light. It is a physical constant and notated as <math>c</math> (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 matter or information can travel faster than <math>c</math>.

The value is precisely

c = 2.997 924 58 × 108 metres per second,

or about thirty centimetres (12 inches) in a nanosecond.

It is important to realize that the speed of light is not a "speed limit" in the conventional sense. 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 <math>50 + 50 = 100</math> 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:

<math>u = {v + w \over 1 + v w / c^2}</math>

where <math>v</math> and <math>w</math> are the speeds of the spaceships relative to the observer, and <math>u</math> 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 <math>c</math>. 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.

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In passing through materials, light is slowed to less than <math>c</math>, by the ratio called the refractive index of the material. The speed of light in air is only slightly less than <math>c</math>. Denser media such as water and glass can slow light much more, to fractions such as 3/4 and 2/3 of <math>c</math>. 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 <math>c</math>. However, it is not possible to use this technique to transfer information faster than <math>c</math>; 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 <math>c</math>.

See also: tachyon


Galileo seems to have been the first person to suspect that light might have a finite speed and attempt to measure it. 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 the young Danish astronomer Ole RÝmer, who was studying the motions of Jupiter's moons. A plaque at the Observatory of Paris, where RÝmer happened to be working, commemorates what was, in effect, the first measurement of a universal quantity made on this planet. RÝmer published his result, which was within about ten percent of being correct, in Journal des Scavans of that year.

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 RÝmer 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. RÝmer 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 RÝmer 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.

See also

Fizeau-Foucault Apparatus, Galileo Galilei, Michelson Morley experiment

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