Definitions

# light

[lahyt]
light, visible electromagnetic radiation. Of the entire electromagnetic spectrum, the human eye is sensitive to only a tiny part, the part that is called light. The wavelengths of visible light range from about 350 or 400 nm to about 750 or 800 nm. The term "light" is often extended to adjacent wavelength ranges that the eye cannot detect—to infrared radiation, which has a frequency less than that of visible light, and to ultraviolet radiation and black light, which have a frequency greater than that of visible light.

If white light, which contains all visible wavelengths, is separated, or dispersed, into a spectrum, each wavelength is seen to correspond to a different color. Light that is all of the same wavelength and phase (all the waves are in step with one another) is called "coherent"; one of the most important modern applications of light has been the development of a source of coherent light—the laser.

## The Nature of Light

The scientific study of the behavior of light is called optics and covers reflection of light by a mirror or other object, refraction by a lens or prism, diffraction of light as it passes by the edge of an opaque object, and interference patterns resulting from diffraction. Also studied is the polarization of light. Any successful theory of the nature of light must be able to explain these and other optical phenomena.

The Wave, Particle, and Electromagnetic Theories of Light

The earliest scientific theories of the nature of light were proposed around the end of the 17th cent. In 1690, Christian Huygens proposed a theory that explained light as a wave phenomenon. However, a rival theory was offered by Sir Isaac Newton in 1704. Newton, who had discovered the visible spectrum in 1666, held that light is composed of tiny particles, or corpuscles, emitted by luminous bodies. By combining this corpuscular theory with his laws of mechanics, he was able to explain many optical phenomena.

For more than 100 years, Newton's corpuscular theory of light was favored over the wave theory, partly because of Newton's great prestige and partly because not enough experimental evidence existed to provide an adequate basis of comparison between the two theories. Finally, important experiments were done on the diffraction and interference of light by Thomas Young (1801) and A. J. Fresnel (1814-15) that could only be interpreted in terms of the wave theory. The polarization of light was still another phenomenon that could only be explained by the wave theory. Thus, in the 19th cent. the wave theory became the dominant theory of the nature of light.

The wave theory received additional support from the electromagnetic theory of James Clerk Maxwell (1864), who showed that electric and magnetic fields were propagated together and that their speed was identical with the speed of light. It thus became clear that visible light is a form of electromagnetic radiation, constituting only a small part of the electromagnetic spectrum. Maxwell's theory was confirmed experimentally with the discovery of radio waves by Heinrich Hertz in 1886.

Modern Theory of the Nature of Light

With the acceptance of the electromagnetic theory of light, only two general problems remained. One of these was that of the luminiferous ether, a hypothetical medium suggested as the carrier of light waves, just as air or water carries sound waves. The ether was assumed to have some very unusual properties, e.g., being massless but having high elasticity. A number of experiments performed to give evidence of the ether, most notably by A. A. Michelson in 1881 and by Michelson and E. W. Morley in 1887, failed to support the ether hypothesis. With the publication of the special theory of relativity in 1905 by Albert Einstein, the ether was shown to be unnecessary to the electromagnetic theory.

The second main problem, and the more serious of the two, was the explanation of various phenomena, such as the photoelectric effect, that involved the interaction of light with matter. Again the solution to the problem was proposed by Einstein, also in 1905. Einstein extended the quantum theory of thermal radiation proposed by Max Planck in 1900 to cover not only vibrations of the source of radiation but also vibrations of the radiation itself. He thus suggested that light, and other forms of electromagnetic radiation as well, travel as tiny bundles of energy called light quanta, or photons. The energy of each photon is directly proportional to its frequency.

With the development of the quantum theory of atomic and molecular structure by Niels Bohr and others, it became apparent that light and other forms of electromagnetic radiation are emitted and absorbed in connection with energy transitions of the particles of the substance radiating or absorbing the light. In these processes, the quantum, or particle, nature of light is more important than its wave nature. When the transmission of light is under consideration, however, the wave nature dominates over the particle nature. In 1924, Louis de Broglie showed that an analogous picture holds for particle behavior, with moving particles having certain wavelike properties that govern their motion, so that there exists a complementarity between particles and waves known as particle-wave duality (see also complementarity principle). The quantum theory of light has successfully explained all aspects of the behavior of light.

## The Speed of Light

An important question in the history of the study of light has been the determination of its speed and of the relationship of this speed to other physical phenomena. At one time it was thought that light travels with infinite speed—i.e., it is propagated instantaneously from its source to an observer. Olaus Rømer showed that it was finite, however, and in 1675 estimated its value from differences in the time of eclipse of certain of Jupiter's satellites when observed from different points in the earth's orbit. More accurate measurements were made during the 19th cent. by A. H. L. Fizeau (1849), using a toothed wheel to interrupt the light, and by J. B. L. Foucault (1850), using a rotating mirror. The most accurate measurements of this type were made by Michelson. Modern electronic methods have improved this accuracy, yielding a value of 2.99792458 × 108 m (c.186,000 mi) per sec for the speed of light in a vacuum, and less for its speed in other media. The theory of relativity predicts that the speed of light in a vacuum is the limiting velocity for material particles; no particle can be accelerated from rest to the speed of light, although it may approach it very closely. Particles moving at less than the speed of light in a vacuum but greater than that of light in some other medium will emit a faint blue light known as Cherenkov radiation when they pass through the other medium. This phenomenon has been used in various applications involving elementary particles.

## Luminous and Illuminated Bodies

In general, vision is due to the stimulation of the optic nerves in the eye by light either directly from its source or indirectly after reflection from other objects. A luminous body, such as the sun, another star, or a light bulb, is thus distinguished from an illuminated body, such as the moon and most of the other objects one sees. The amount and type of light given off by a luminous body or reflected by an illuminated body is of concern to the branch of physics known as photometry (see also lighting). Illuminated bodies not only reflect light but sometimes also transmit it. Transparent objects, such as glass, air, and some liquids, allow light to pass through them. Translucent objects, such as tissue paper and certain types of glass, also allow light to pass through them but diffuse (scatter) it in the process, so that an observer cannot see a clear image of whatever lies on the other side of the object. Opaque objects do not allow light to pass through them at all. Some transparent and translucent objects allow only light of certain wavelengths to pass through them and thus appear colored. The colors of opaque objects are caused by selective reflection of certain wavelengths and absorption of others.

## Bibliography

See W. L. Bragg, The Universe of Light (1959); J. Rublowsky, Light (1964); H. Haken, Light (1981).

Band of very faint light in the night sky. It is thought to be sunlight reflected from interplanetary dust grains lying mostly in the plane of the zodiac, or ecliptic. Seen in the west after twilight and in the east before dawn, it is most clearly visible in the tropics, where the ecliptic is approximately perpendicular to the horizon. In midnorthern latitudes it is best seen evenings in February and March and mornings in September and October (vice versa in midsouthern latitudes). The light can be followed visually to a point about 90° from the Sun. It continues to the region opposite the Sun, where a slight enhancement, the gegenschein, is visible.

Portion of the electromagnetic spectrum extending from the violet end of visible light to the X-ray region. Ultraviolet (UV) radiation lies between wavelengths of about 400 nanometres and 10 nanometres, corresponding to frequencies of 7.5 × 1014 Hz to 3 × 1016 Hz. Most UV rays from the Sun are absorbed by the Earth's ozone layer. UV has low penetrating power, so its effects on humans are limited to the skin. These effects include stimulation of production of vitamin D, sunburn, suntan, aging signs, and carcinogenic changes. UV radiation is also used to treat jaundice in newborns, to sterilize equipment, and to produce artificial light.

Distance traveled by light moving in a vacuum in one year, at its accepted speed of 186,282 mi/second (299,792 km/second). It equals about 5.9 trillion mi (9.5 trillion km), 63,240 astronomical units, or 0.307 parsec.

Semiconductor diode that produces visible or infrared light when subjected to an electric current, as a result of electroluminescence. Visible-light LEDs are used in many electronic devices as indicator lamps (e.g., an on/off indicator) and, when arranged in a matrix, to spell out letters or numbers on alphanumeric displays. Infrared LEDs are used in optoelectronics (e.g., in auto-focus cameras and television remote controls) and as light sources in some long-range fibre-optic communications systems. LEDs are formed by the so-called III-V compound semiconductors related to gallium arsenide. They consume little power and are long-lasting and inexpensive.

or light quantum

Minute energy packet of electromagnetic radiation. In 1900 Max Planck found that heat radiation is emitted and absorbed in distinct units, which he called quanta. In 1905 Albert Einstein explained the photoelectric effect, proposing the existence of discrete energy packets in light. The term photon came into use for these packets in 1926. The energies of photons range from high-energy gamma rays and X rays to low-energy infrared and radio waves, though all travel at the same speed, the speed of light. Photons have no electric charge or rest mass and are the carriers of the electromagnetic field.

Device that produces an intense beam of coherent light (light composed of waves having a constant difference in phase). Its name, an acronym derived from “light amplification by stimulated emission of radiation,” describes how its beam is produced. The first laser, constructed in 1960 by Theodore Maiman (born 1927) based on earlier work by Charles H. Townes, used a rod of ruby. Light of a suitable wavelength from a flashlight excited (see excitation) the ruby atoms to higher energy levels. The excited atoms decayed swiftly to slightly lower energies (through phonon reactions) and then fell more slowly to the ground state, emitting light at a specific wavelength. The light tended to bounce back and forth between the polished ends of the rod, stimulating further emission. The laser has found valuable applications in microsurgery, compact-disc players, communications, and holography, as well as for drilling holes in hard materials, alignment in tunnel drilling, long-distance measurement, and mapping fine details.

That portion of the electromagnetic spectrum visible to the human eye. It ranges from the red end to the violet end of the spectrum, with wavelengths from 700 to 400 nanometres and frequencies from 4.3 × 1014 to 7.5 × 1014 Hz. Like all electromagnetic radiation, it travels through empty space at a speed of about 186,000 mi/sec (300,000 km/sec). In the mid-19th century, light was described by James Clerk Maxwell in terms of electromagnetic waves, but 20th-century physicists showed that it exhibits properties of particles as well; its carrier particle is the photon. Light is the basis for the sense of sight and for the perception of colour. Seealso optics; wave-particle duality.

Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. Science-fiction-style space travel, dubbed "true" FTL, defies known physics.

Under the special theory of relativity, a particle (that has mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons).

On the other hand, what some physicists refer to as "apparent" or "effective" FTL is the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations faster than what it would take light in the "normal" route (though still moving subluminally through the distorted region).

Apparent FTL is not excluded by general relativity. Examples of apparent FTL proposals are the Alcubierre drive and the traversable wormhole, although the physical plausibility of these solutions is uncertain.

Outside of mainstream physics, others (often without traditional physics training) have speculated on mechanisms that might allow FTL travel to be achieved, often relying on new conjectures of physics of their own invention, but their ideas have not gained significant acceptance in the physics research community. Fictional depictions of superluminal travel and the mechanisms of achieving it are also a staple of the science fiction genre.

## Faster than light travel

In the context of this article, FTL is transmitting information or matter faster than c, a constant equal to the speed of light in a vacuum, 299,792,458 meters per second, or about 186,282 miles per second. This is not quite the same as travelling faster than light, since:

• Some processes propagate faster than c, but cannot carry information (See below).
• Light travels at speed c/n when not in a vacuum but travelling through a medium with refractive index = n (causing refraction), and in some materials other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation.

Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here.

## Possibility of FTL

Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. According to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their relative velocity, will always measure zero-mass particles such as photons traveling at c in a vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by Poincaré transformations. These transformations have important implications:

• The relativistic momentum of a particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
• To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
• Either way, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not generally considered to be a sensible notion.
• Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a space-like interval. In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference, or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale). Therefore any theory which permits "true" FTL also has to cope with time travel and all its associated paradoxes, or else to assume the Lorentz invariance to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).

Albert Einstein elaborated that faster-than-light travel is impossible. Taking for granted the causality principle (causes happen before their consequences) this impossibility stems from the physical assumption that all physical phenomena satisfy, at any scale, the symmetries of the restricted Poincaré Group. This assumption has stood the test of time and has confirmed its efficiency with a high level of precision and reliability according to any presently known physics experiment.

## Justifications for FTL travel

Despite the established conclusion that relativity precludes FTL travel, some have proposed ways to justify FTL behavior:

### Ignore special relativity

This option is popular particularly in science fiction. However, empirical and theoretical evidence strongly supports Einstein's theory of special relativity as the correct description of high-speed motion, which generalizes the more familiar Galilean relativity, which is actually an approximation at conventional (much less than c) speeds. Similarly, general relativity is an overwhelmingly supported and experimentally verified theory of gravitation, except in the regime of very high energy densities over very short distances, where an as-yet-undeveloped theory of quantum gravity is necessary. Special relativity, however, is incorporated easily into quantum field theories. Therefore, even in the broader contexts of general relativity and quantum mechanics, conventional acceleration from subluminal to superluminal speeds is not possible.

### Get light to go faster (Casimir vacuum and quantum tunnelling)

Einstein's equations of special relativity postulate that the speed of light is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the unit of length (the meter) has been defined using the speed of light.

The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called the vacuum energy. This vacuum energy can perhaps be changed in certain cases. When vacuum energy is lowered, light itself has been predicted to go faster than the standard value 'c'. This is known as the Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon travelling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036. Accordingly there has as yet been no experimental verification of the prediction. A recent analysis argued out that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze (with the hope that such a theory would guarantee the impossibility of a true time machine ever forming). Other authors argue that Scharnhorst's original analysis which seemed to show the possibility of faster-than-c signals involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.

The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Koblenz, claim to have violated relativity experimentally by transmitting photons faster than the speed of light. They say they have conducted an experiment in which microwave photons - relatively low energy packets of light - travelled "instantaneously" between a pair of prisms that had been moved up to 3 ft apart, using a phenomenon known as quantum tunnelling. Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the train moves forward at each stop; in this way, the center of the train exceeds the speed of any of the individual cars.

### Give up causality

Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations. Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option. An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle.

An important point to note is that in general relativity it is possible for objects to be moving apart faster than light because of the expansion of the universe, in some reasonable choice of cosmological coordinates. This is understood to be due to the expansion of the space between the objects, and general relativity still reduces to special relativity in a "local" sense, meaning that two objects passing each other in a small local region of spacetime cannot have a relative velocity greater than c, and will move more slowly than a light beam passing through the region. (See Option F below)

### Give up (absolute) relativity

Because of the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is doubly-special relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidence casts doubt on this theory, some physicists still consider it viable. However, even if this theory is accurate, it is still very unclear whether it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c.

There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis.

### Go somewhere where the speed of light is not the limit

A very popular option in science fiction is to assume the existence of some other realm (typically called hyperspace, subspace, or slipspace) which is accessible from this universe, in which the laws of relativity are usually distorted, bent, or nonexistent, facilitating rapid transport between distant points in this universe, sometimes with acceleration differences - that is, not requiring as much energy or thrust to go faster. To accomplish rapid transport between points in hyperspace/subspace, special relativity is often assumed not to apply in this other realm, or that the speed of light is higher. Another solution is to posit that distant points in the mundane universe correspond to points that are close together in hyperspace.

This method of faster-than-light travel does not correspond to anything seriously proposed by mainstream science.

### Distort the space-time fabric

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light years from us today have a recession velocity which is faster than light. Miguel Alcubierre theorized that it would be possible to create an Alcubierre drive, in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally travelling faster than light. However, several objections raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the traversable wormhole, which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not locally move faster than light which travels through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.

Dr. Gerald Cleaver, associate professor of physics at Baylor University, and Richard Obousy, a Baylor graduate student, theorize that by manipulating the extra spatial dimensions of string theory around a spaceship with an extremely large amount of energy, it would create a “bubble” that could cause the ship to travel faster than the speed of light. To create this bubble, the physicists believe manipulating the 10th spatial dimension would alter the dark energy in three large spatial dimensions: height, width and length. Cleaver said positive dark energy is currently responsible for speeding up the expansion rate of our universe as time moves on, just like it did after the Big Bang, when the universe expanded much faster than the speed of light for a very brief time.

### Make use of the fact that space and time are quantized

As given by the planck length, there is a minimum amount of 'space' that can exist in this universe (1.616×10−35 meters). This limit can be used to determine a minimum time quantisation of 1.078×10−43 seconds, which corresponds to a beam of light with a wavelength approaching the planck length. This means that there is a physical limit to how much blue shift a beam of light can endure. According to general relativity there is no limit to this shift, and an infinitesimally small space can exist, but according to well accepted quantum theory these limits do exist.

This is precisely what happens towards the center of a black hole; the incoming light becomes blue shifted past the planck length as it approaches the region of discontinuity within our universe. The argument is: if a black hole with finite mass can create such a discontinuity in the fabric of space and time, why would people be unable to do the same thing using a finite amount of energy and acceleration? (According to general relativity, the space-time distortions caused by gravity are fundamentally identical to space-time distortions caused simply by accelerating your reference frame).

## Tachyons

In special relativity, while it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light, it is not impossible for an object to exist which always moves faster than light. The hypothetical elementary particles that have this property are called tachyons. Their existence has neither been proven nor disproven, but even so, attempts to quantise them show that they may not be used for faster-than-light communication. Physicists sometimes regard the existence of mathematical structures similar to Tachyons arising from theoretical models and theories as signs of an inconsistency or that the theory needs further refining.

## General relativity

General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it. Another possible system is the wormhole, which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypothetical exotic matter or negative energy.

General relativity also agrees that any technique for faster-than-light travel could also be used for time travel. This raises problems with causality. Many physicists believe that the above phenomena are in fact impossible, and that future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In string theory Eric Gimon and Petr Hořava have argued that in a supersymmetric five-dimensional Gödel universe quantum corrections to general relativity effectively cut off regions of spacetimes with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.

## Superficially FTL phenomena which do not carry information

### Closing speeds

An observer may conclude that two objects are moving faster than the speed of light relative to each other, by adding their velocities according to the principle of Galilean relativity.

For example, two fast-moving particles approaching each other from opposite sides of a 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. This correctly reflects the rate at which the distance between the two particles is decreasing, from the observer's point of view and is called the closing speed. However, it is not the same as the velocity of one of the particles as would be measured by a hypothetical fast-moving observer travelling alongside the other particle. To obtain this, the calculation must be done according to the principle of special relativity. If the two particles are moving at velocities v and -v, or expressed in units of c, $beta$ and $-beta$, where

$beta equiv v/c ,!$
then this relative velocity (again in units of the speed of light c) is
$beta_\left\{rel\right\} = \left\{ beta - \left(-beta\right) over 1 + beta ^2 \right\} = \left\{ 2beta over 1 + beta^2 \right\}$,
which is less than the speed of light.

### Phase velocities above c

The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information. Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.

### Group velocities above c

The group velocity of a wave (e.g. a light beam) may also exceed c in some circumstances. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope 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.

### 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. Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10-36 seconds after the Big Bang to around 10-33 seconds), when the universe may have rapidly expanded by a factor of around 1020 - 1030.

### 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 by Martin Rees and can be explained as an optical illusion caused by the object partly 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 objects 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 small numbers of elementary particles to such speeds.

### Quantum mechanics

Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. According to the No-communication theorem 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. Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment. Since the underlying behaviour doesn't violate local causality or allow FTL it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.

The uncertainty principle implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than c, even in a vacuum; this possibility must be taken into account when enumerating Feynman diagrams for a particle interaction. To quote Richard Feynman:

However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e. non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.

There have been various reports in the popular press of experiments on 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 faster than the vacuum velocity of light. But, recall from above, that a superluminal phase velocity cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point.

Quantum teleportation transmits quantum information at whatever speed is used to transmit the same amount of classical information, likely the speed of light. This quantum information may theoretically be used in ways that classical information can not, such as in quantum computations involving quantum information only available to the recipient. In science fiction, quantum teleportation is either used as a basis for teleportation of physical objects at the speed of light, presumably preserving some important aspect of the entanglement between the particles of the object, or else is misrepresented as allowing faster-than-light communication.

#### Hartman effect

The Hartman effect is the tunnelling effect through a barrier where the tunnelling time tends to a constant for large barriers. This was first described by Thomas Hartman in 1962. This could, for instance, be the gap between two prisms. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted. There is a finite probability that the photon will tunnel across the gap rather than follow the refracted path. For large gaps between the prisms the tunnelling time approaches a constant and thus the photons appear to have crossed with a superluminal speed.

However, an analysis by Herbert Winful from the University of Michigan suggests that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than c, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate". Winful means by this that the photons crossing the barrier are virtual photons only existing in the interaction and could not be propagated into the outside world.

#### Casimir effect

In physics, the Casimir effect or Casimir-Polder force is a physical force exerted between separate objects due to resonance of vacuum energy in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, due to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Energy appears suddenly as if it came from the vacuum. See Option B above for a discussion of whether or not this effect could actually be used to send signals faster than c or violate causality.

We can also quote the spectacular case of the thought experiment of Einstein, Podolski and Rosen (EPR paradox) which could be realized in experiments for the first time by Alain Aspect in 1981 and 1982. In this case, the measurement of the state on one of the quantum systems of an entangled pair forces the other system to be measured in the complementary state. Thus functions quantum teleportation.

An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated nonlocal quantum correlations between particles separated by over 10 kilometers. But as noted earlier, the nonlocal correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved; see no-communication theorem for further information.

#### Delayed choice quantum eraser

Delayed choice quantum eraser (The experiment of Marlan Scully) is an alternative of the EPR paradox in which the observation or not of interference after the passage of a photon through a double slit experiment depends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon, which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it can't be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an FTL or backwards-in-time manner (see the delayed choice quantum eraser article for further information).

## Variable speed of light

In conventional physics, the speed of light in a vacuum is assumed to be a constant. There exist theories which postulate that the speed of light is not a constant. The interpretation of this statement is as follows.

The speed of light is a dimensionful quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured. Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when you measure the height of a mountain you really measure the ratio of its height to the length of a meterstick. The conventional SI system of units is based on seven basic dimensional quantities, namely distance, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. These units are defined to be independent and so cannot be described in terms of each other. As an alternative to using a particular system of units, one can reduce all measurements to dimensionless quantities expressed in terms of ratios between the quantities being measured and various fundamental constants such as Newton's constant, the speed of light and Planck's constant; physicists can define at least 26 dimensionless constants which can be expressed in terms of these sorts of ratios and which are currently thought to be independent of one another. By manipulating the basic dimensional constants one can also construct the Planck time, Planck length and Planck energy which make a good system of units for expressing dimensional measurements, known as Planck units.

Magueijo's proposal used a different set of units, a choice which he justifies with the claim that some equations will be simpler in these new units. In the new units he fixes the fine structure constant, a quantity which some people, using units in which the speed of light is fixed, have claimed is time dependent. Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.

While it may be mathematically possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.

## References

### Notations

• D F Falla and M J Floyd, "Superluminal motion in astronomy", Eur. J. Phys. 23 69-81, 2002