Speed of light: Encyclopedia II - Speed of light - Physics

Speed of light - Physics

Speed of light - Constant velocity from all reference frames

It is important to realise that the speed of light is not a "speed limit" in the conventional sense. 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.

Most individuals are accustomed to the addition rule of velocities: if two cars approach each other from opposite directions, each travelling at a speed of 50 kilometres per hour (31 miles per hour), one expects that each car will perceive the other as approaching at a combined speed of 50 + 50 = 100 km/h (62 mph) to a very high degree of accuracy.

At velocities at or approaching the speed of light, however, it becomes clear from experimental results that this rule does not apply. 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 v and w are the speeds of the spaceships as observed by the third observer, and u is the speed of either space ship as observed by the other.

Contrary to one's 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.

The above equation was derived by Albert Einstein from his theory of special relativity, which takes the principle of relativity as a main premise. This principle (originally proposed by Galileo Galilei) requires physical laws to act in the same way in all reference frames. As Maxwell's equations directly give a speed of light, it should be the same for every observer—a consequence which sounded obviously wrong to the 19th century physicists, who assumed that the speed of light given by Maxwell's theory is valid relative to the luminiferous aether. But the Michelson-Morley experiment, arguably the most famous and useful failed experiment in the history of physics, could not find this aether, suggesting instead that the speed of light is constant in all frames of reference.

Although it is uncertain whether Einstein knew the results of the Michelson-Morley experiment, he took the speed of light being constant as a given fact, understood it as reaffirming Galilei's principle of relativity, and deduced the consequences, now known as the theory of special relativity which includes the counter-intuitive addition formula above.

Speed of light - Interaction with transparent materials

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. 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 depends on the frequency of the light, light at different frequencies travels at different speeds through the same material. This can cause distortion of electromagnetic waves that consist of multiple frequencies, called dispersion.

Note that the speed of light referred to is the observed or measured speed in some medium and not the true speed of light (as observed in vacuum). On the microscopic scale, considering electromagnetic radiation to be like a particle, refraction is caused by continual absorption and re-emission (not necessarily in quite the same direction) of the photons that compose the light by the atoms or molecules through which it is passing. In some sense, the light itself travels only through the vacuum existing between these atoms, and is impeded by the atoms. The process of absorption and re-emission itself takes time thereby creating the impression that the light itself has undergone delay (i.e. loss of speed) between entry and exit from the medium in question. It may be noted, that once the light has emerged from the medium it changes back to its original speed and this is without gaining any energy. This can mean only one thing - that the light's speed itself was never altered in the first place. Alternatively, considering electromagnetic radiation to be like a wave, the charges of each atom (primarily the electrons) interfere with the electric and magnetic fields of the radiation, slowing its progress.

Speed of light - Faster-than-light observations and experiments

It has long been known theoretically that it is possible for the group velocity of light to exceed c. One recent 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 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 in a distantly spaced 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 wave's length much faster than the wave's movement inland.

The speed of light may also appear to be exceeded in some phenomena involving evanescent waves, such as tunnelling. Experiments indicate that the phase velocity of evanescent waves may exceed c; however, it would appear that neither the group velocity nor the front velocity exceed c, so, again, it is not possible for information to be transmitted faster than c.

In some interpretations of quantum mechanics, quantum effects may be transmitted at speeds greater than c (indeed, action at a distance has long been perceived as a problem with quantum mechanics: see EPR paradox). 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.

So-called superluminal motion is also seen in certain astronomical objects, such as the jets of radio galaxies and quasars. However, these jets are not actually moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and at a small angle to the line of sight.

Although it may sound paradoxical, it is possible for shock waves to be formed with electromagnetic radiation. As a charged particle travels through an insulating medium, it disrupts the local electromagnetic field in the medium. Electrons in the atoms of the medium will be displaced and polarised by the passing field of the charged particle, and photons are emitted as the electrons in the medium restore themselves to equilibrium after the disruption has passed. (In a conductor, the disruption can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves travel, the photons constructively interfere and intensify the observed radiation. The result (analogous to a sonic boom) is known as Cherenkov radiation.

The ability to communicate or travel faster-than-light is a popular topic in science fiction. Particles that travel faster than light, dubbed tachyons, have been proposed by particle physicists but have yet to be observed.

Some physicists, notably João Magueijo and John Moffat, have proposed that in the past light travelled much faster than the current speed of light. This theory is called variable speed of light (VSL) and its supporters claim that it has the ability to explain many cosmological puzzles better than its rival, the inflation model of the universe. However, it has yet to gain wide acceptance.

Speed of light - Light-slowing experiments

In a sense, any light travelling through a medium other than a vacuum travels below c as a result of refraction. However, certain materials have an exceptionally high refractive index: in particular, the optical density of a Bose-Einstein condensate can be very high. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light beam to about 17 metres per second, and, in 2001, they were able to momentarily stop a beam.

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.

Adapted from the Wikipedia article "Physics", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki