Speed of light

Light travels through a vacuum at a speed of roughly 300 million metres per second.

Table of contents

1 Overview
2 Constant in all reference frames
3 Refraction
4 "Faster-than-light" experiments
5 "Slower-than-light" (i.e., slowing light) experiments
6 History
7 See also
8 External links and references

Overview

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 (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 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 nanosecondsecond. This is not an empirical value - it yields a solution to the wave equation, and can be calculated from the permittivity of free space () and the permeability of free space (). In particular:

The derivation can be found here

Constant in all reference frames

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 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 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:

where and are the speeds of the spaceships relative to the observer, and 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 . 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 term of c. In particular, one meter is defined as 299792458^-1c s. 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 , 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.

"Faster-than-light" experiments

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 .

"Slower-than-light" (i.e., slowing light) experiments

In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light beam to about 17 m/s. 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" (Dum�, 2003), due to an interference pattern in two "control" beams. (Dum�, 2003)

History

To the best that can be determined, Galileo Galilei was the first person to suspect light might have a finite speed, and to attempt to measure it—but people before Galileo probably thought of lights (i.e., stars and 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 moonss. A plaque at the Observatory of Paris, where the Danish astronomer 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.