Faster-than-light: Encyclopedia II - Faster-than-light - Apparent FTL

Faster-than-light - Apparent FTL

Faster-than-light - Moving spot of light

Processes which do not transmit information may move faster than light. A good example is a beam of light projected onto a distant surface, such as the Moon. The spot which the beam strikes is not a physical object, just a point of light. Moving it (by reorienting the beam) does not carry information between locations on the surface. To put it another way, the beam can be considered as a stream of photons; where each photon strikes the surface is determined only by the orientation of the beam (assuming that the surface is stationary). If the distance between the beam projector and the surface is sufficiently far, a small change of angle could cause successive photons to strike at widely separated locations, and the spot would appear to move faster than light. If the surface is at the distance of the moon, a light source mounted on a phonograph is changing angle rapidly enough to create this effect. This effect is believed to be responsible for supernova ejecta appearing to move faster than light as observed from Earth.

Faster-than-light - Relative motion

It is also possible for two objects to move faster than light relative to each other, but only from the point of view of an observer in a third frame of reference, who naively adds velocities according to Galilean relativity. An observer on either object will see the other object moving slower than light.

For example, fast-moving particles on opposite sides of a circular particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator, and who naively adds velocities according to Galilean relativity. However, if the observer has a good intuition of special relativity, and makes a correct calculation, and the two particles are moving, for example, at velocities β and − β

and

then from the observer's point of view, the relative velocity Δβ (again in units of the speed of light c) is

which is less than the speed of light.

Faster-than-light - Phase velocities above c

The phase velocity of a wave can easily exceed c, the vacuum velocity of light. In principle, this can occur even for simple mechanical waves, even without any object moving with velocities close to or above c. However, this does not imply the propagation of signals with a velocity above c.

Faster-than-light - Group velocities above c

Under certain circumstances, even the group velocity of a wave (e.g. a light beam) can exceed c. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of a pulse may travel with a velocity above c. However, even this situation does not imply the propagation of signals with a velocity above c, even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind, the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than without this effect.

Faster-than-light - Universal expansion

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.

Faster-than-light - Astronomical observations

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed, and can be explained as an optical illusion caused by the object moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these object have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light. Earth-bound laboratories have only been able to accelerate elementary particles to such speeds.

Faster-than-light - Quantum mechanics

Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. These phenomena do not allow true communication; they only let two observers in different locations see the same event simultaneously, without any way of controlling what either sees. The fact that the laws of physics seem to conspire to prevent superluminal communications via quantum mechanics is very interesting and somewhat poorly understood.

The speed of light can have any value within the limits of the uncertainty principle as demonstrated in any Feynman diagram that draws a photon at any angle other than 45 degrees. To quote Richard Feynman, "...there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c" (Chapter 3, page 89 of Feynman's book QED). However, this does not imply the possibility of superluminal information transmission, as no photon can have an average speed in excess of the speed of light.

There have been various experimentally based reports of faster-than-light transmission in optics—most often in the context of a kind of quantum tunneling phenomenon. Usually, such reports deal with a phase velocity or group velocity above the vacuum velocity of light, but not with faster-than-light transmission of information, although there has sometimes been a degree of confusion concerning the latter point.

As it is currently understood, quantum mechanics is completely consistent with special relativity, and doesn't allow for faster-than-light communication.

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