**Faster-than-light** communications and

travelInterstellar space travel is manned or unmanned travel between stars. The concept of interstellar travel in starships is a staple of science fiction. Interstellar travel is much more difficult than interplanetary travel. Intergalactic travel, or travel between different galaxies, is even more...

refer to the propagation of

informationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

or

matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

faster than the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

.

Under the special theory of relativity, a particle (that has

rest massMass in special relativity incorporates the general understandings from the concept of mass-energy equivalence. Added to this concept is an additional complication resulting from the fact that "mass" is defined in two different ways in special relativity: one way defines mass as an invariant...

) 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 (

tachyonA tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

s).

On the other hand, what some physicists refer to as "apparent" or "effective" FTL depends on the hypothesis that unusually distorted regions of

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime. Although according to current theories matter is still required to travel subluminally with respect to the locally distorted spacetime region,

*apparent* FTL is not excluded by

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

.

Examples of FTL proposals are changing the frequency of mass to a higher state by applying high-frequency waves of energy, the

Alcubierre driveThe Alcubierre drive, also known as the Alcubierre metric, is a speculative, but valid solution of the Einstein field equations. It is a mathematical model of a spacetime exhibiting features reminiscent of the fictional "warp drive" from Star Trek, which can travel "faster than light", although...

, and the traversable wormhole, although the physical plausibility of some of these solutions is uncertain.

## FTL travel of non-information

In the context of this article, FTL is the transmission of information or matter faster than

*c*, a constant equal to the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in a vacuum, which is 299,792,458 meters per second or about 186,282.4 miles per second. This is not quite the same as traveling faster than light, since:

- Some processes propagate faster than
*c*, but cannot carry information (see examples section immediately following).
- Light travels at speed
*c/n* when not in a vacuum but travellingTime of flight describes a variety of methods that measure the time that it takes for an object, particle or acoustic, electromagnetic or other wave to travel a distance through a medium...

through a medium with refractive indexIn optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

= *n* (causing refractionRefraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

), and in some materials other particles can travel faster than *c/n* (but still slower than *c*), leading to Cherenkov radiationCherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...

(see phase velocity below).

Neither of these phenomena violates

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

or creates problems with

causalityCausality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

, and thus neither qualifies as

*FTL* as described here.

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

### Daily sky motion

For an earthbound observer, objects in the sky complete one revolution around the Earth in 1 day.

Proxima CentauriProxima Centauri is a red dwarf star about 4.2 light-years distant in the constellation of Centaurus. It was discovered in 1915 by Robert Innes, the Director of the Union Observatory in South Africa, and is the nearest known star to the Sun, although it is too faint to be seen with the naked eye...

, which is the nearest star outside the

solar systemThe Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

, is about 4 light years away. On a geostationary view

Alpha CentauriAlpha Centauri is the brightest star in the southern constellation of Centaurus...

has a speed many times greater than

*c* as the rim speed of an object moving in a circle is a product of the radius and angular speed. It is also possible on a geostatic view for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000 AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic frame.

### Light spots and shadows

If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than

*c*. Similarly, a shadow projected onto a distant object can be made to move across the object faster than

*c*. In neither case does the light travel from the source to the object faster than

*c*, nor does any information travel faster than light.

### Apparent FTL propagation of static field effects

Since there is no "retardation" (or

aberrationThe aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...

) of the apparent position of the source of a

gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

al or electric static field when the source moves with constant velocity, the static field "effect" may seem at first glance to be "transmitted" faster than the speed of light. However, uniform motion of the static source may be removed with a change in reference frame, causing the direction of the static field to change immediately, at all distances. This is not a change of position which "propagates", and thus this change cannot be used to transmit information from the source. No information or matter can be FTL-transmitted or propagated from source to receiver/observer by an electromagnetic field.

### Closing speeds

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of a

particle acceleratorA particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

Special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

does not prohibit this. It tells us that it is wrong to use Galilean relativity to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the

right formulaIn physics, a velocity-addition formula is an equation that relates the velocities of moving objects in different reference frames.- Galilean addition of velocities :...

for computing such

relative velocityIn non-relativistic kinematics, relative velocity is the vector difference between the velocities of two objects, as evaluated in terms of a single coordinate system....

.

It is instructive to compute the relative velocity of particles moving at

*v* and -

*v* in accelerator frame, which corresponds to the closing speed of 2

*v* > c. Expressed the speeds in units of

*c*, β = v/c:

### Proper speeds

If a spaceship travels to a planet one light year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance traveled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a

proper velocityIn relativity, proper-velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured...

. There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. A light signal that left the Earth at the same time as the traveled would always get to the destination before the traveller.

### How far can one travel from the Earth?

Since one might not travel faster than light, one might conclude that a human can never travel further from the earth than 40 light years if the traveler is active between the age of 20 and 60. A traveler would then never be able to reach more than the very few star systems which exist within the limit of 20-40 light years from the Earth. This is a mistaken conclusion; due to

time dilationIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

, the traveler can travel thousands of light years during their 40 active years. If the spaceship accelerates at a constant 1G, they will, after 354 days, reach speeds a little under the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, and

time dilationIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

will increase their lifespan to thousands of years, seen from the reference system of the

Solar SystemThe Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

, but the traveler's subjective lifespan will not thereby change. If the traveler returns to the Earth, they will land thousands of years into the future. Their speed will not be seen as higher than the speed of light by observers on Earth, and the traveler will not measure their speed as being higher than the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, but will see a length contraction of the universe in their direction of travel. And as the traveler turns around to return, the Earth will seem to experience much more time than the traveler does. So, although their (ordinary) speed cannot exceed

*c*, the

four-velocityIn physics, in particular in special relativity and general relativity, the four-velocity of an object is a four-vector that replaces classicalvelocity...

(distance as seen by Earth divided by his proper (i.e. subjective) time) can be much greater than

*c*. This is similar to the fact that a muon can travel much further than

*c* times its

half-lifeHalf-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

(at rest), if it is traveling close to

*c*.

### Phase velocities above *c*

The

phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at 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-rayX-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

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*.

### Phase velocities below *c*

Contrarily, a subluminal phase velocity

may be corresponding to

>

*c* because there has a relation

in

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. For example, the phase velocity of a low frequency electromagnetic field in metals is extremely low and hence the velocity of motion in inverse proportion to

is probably faster than light

On the other hand,the

dispersion relationIn physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

of such a field is proportional to

energy-momentum relationIn special relativity, the energy-momentum relation is a relation between the energy, momentum and the mass of a body: E^2 = m^2 c^4 + p^2 c^2 , \;where c is the speed of light, E \; is total energy, m \; is invariant mass, and p = |\vec p|\; is momentum....

of a

tachyonA tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

where the coefficient is the square of reduced

Planck constantThe Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

. Therefore,

(

). Substituting the

penetration depthPenetration Depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to 1/e of its original value at the surface.When electromagnetic radiation is incident on...

of commercial power (

angular frequencyIn physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...

:

: ) in

copperCopper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

,the mechanical velocity

of this

quantumIn physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

is much greater than light speed

*c*= 299,792,458 m/s in vacuum. Interestingly, the value equals the energy flow speed

of the field given by classical electrodynamics.

is

Poynting vectorIn physics, the Poynting vector can be thought of as representing the directional energy flux density of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector...

and

is

energy densityEnergy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

. Don't misunderstand to be

drift velocityThe drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. It can also be referred to as Axial Drift Velocity since particles defined are assumed to be moving along a plane. In general, an electron will 'rattle around' in a conductor at the...

of the

charge carrierIn physics, a charge carrier is a free particle carrying an electric charge, especially the particles that carry electric currents in electrical conductors. Examples are electrons and ions...

which is too slow.

### Group velocities above *c*

The

group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

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 (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than c without this effect.

### Universal expansion

The expansion of the

universeThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

causes distant galaxies to recede from us faster than the speed of light, if

comoving distanceIn standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects...

and cosmological time are used to calculate the speeds of these galaxies. However, in

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally (see

*comoving distance* for a discussion of different notions of 'velocity' in cosmology). 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 epochIn physical cosmology the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion...

thought to have occurred in a tiny fraction of the second after the

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

(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 10

^{20} to 10

^{30}.

There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually. However, because

the expansion of the universe is acceleratingThe accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...

, it is projected that most galaxies will eventually cross a type of cosmological

event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving distance#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening

*at present* would eventually be able to reach us in the future if the event was less than 16 billion light years away, but the signal would never reach us if the event was more than 16 billion light years away.

### Astronomical observations

Apparent

superluminal motionIn astronomy, superluminal motion is the apparently faster-than-light motion seen in someradio galaxies, quasars and recently also in some galactic sources called microquasars...

is observed in many radio galaxies,

blazarA blazar is a very compact quasar associated with a presumed supermassive black hole at the center of an active, giant elliptical galaxy...

s,

quasarA quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s and recently also in microquasars. The effect was predicted before it was observed by Martin Rees and can be explained as an

optical illusionAn optical illusion is characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source...

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 relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

. 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 mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, such as

quantum entanglementQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

, appear to transmit information faster than light. According to the

no-communication theoremIn quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics such as the EPR paradox or...

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 collapseIn quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

can be viewed as an

epiphenomenonAn epiphenomenon is a secondary phenomenon that occurs alongside or in parallel to a primary phenomenon.-Medicine:...

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 principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

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 diagramFeynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...

s for a particle interaction. It has since been proven that not even a single photon may travel faster than "c". In quantum mechanics,

virtual particleIn physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

s may travel faster than light, and this phenomenon is related to the fact that static field effects (which are mediated by virtual particles in quantum terms) may travel faster than light (see section on static fields above). 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 tunnellingQuantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...

phenomenon. Usually, such reports deal with a

phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

or

group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

faster than the vacuum velocity of light. However, as stated above, a superluminal

*phase velocity* cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point. Additionally a channel that permits such propagation cannot be laid out faster than the speed of light.

Quantum teleportationQuantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...

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.

#### 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 nonzero 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". The evanescent waves in the Hartman effect are due to virtual particles and a non-propagating static field, as mentioned in the sections above for gravity and electromagnetism.

#### Casimir effect

In physics, the

Casimir effectIn quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...

or Casimir-Polder force is a physical force exerted between separate objects due to resonance of

vacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

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. Because the effect is due to virtual particles mediating a static field effect, it is subject to the comments about static fields discussed above.

#### EPR Paradox

We can also quote the spectacular case of the

thought experimentA thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

of Einstein, Podolski and Rosen (

EPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

) which could be realized in experiments for the first time by

Alain AspectAlain Aspect is a French physicist noted for his experimental work on quantum entanglement....

in 1981 and 1982 in the Aspect experiment. In this case, the measurement of the state on one of the quantum systems of an

entangledQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

pair forces the other system to be measured in the complementary state. Thus functions

quantum teleportationQuantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...

.

An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated nonlocal quantum correlations between particles separated by over 10 kilometres. 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 theoremIn quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics such as the EPR paradox or...

for further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues in Geneva, Switzerland has determined that in any hypothetical nonlocal hidden-variables theory the speed of the

*quantum non-local connection* (what Einstein called

*spooky action at a distance*) is at least 10,000 times the speed of light.

#### Delayed choice quantum eraser

Delayed choice quantum eraserA delayed choice quantum eraser, first performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlan O. Scully, is an elaboration on a quantum eraser experiment involving the concepts considered in Wheeler's delayed choice experiment...

(an experiment of

Marlan ScullyMarlan Orvil Scully is a physicist best known for his work in theoretical quantum optics. He is currently a professor at Texas A&M University and Princeton University. He has authored over 700 scientific articles, as well as standard textbooks such as “Laser Physics” and “Quantum Optics” ...

) is a version 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.

## FTL communication possibility

Faster-than-light communication is, by Einstein's

theory of relativityThe theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

, equivalent to

time travelTime travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

. According to Einstein's theory of

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, what we measure as the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in a vacuum is actually the fundamental physical constant

*c*. This means that all inertial observers, regardless of their relative

velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, will always measure zero-mass particles such as

photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s 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 mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

ive 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
Mass in special relativity incorporates the general understandings from the concept of mass-energy equivalence. Added to this concept is an additional complication resulting from the fact that "mass" is defined in two different ways in special relativity: one way defines mass as an invariant...

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.
- 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
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

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).
- In special relativity the coordinate speed of light is only guaranteed to be
*c* in an inertial frameIn physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

, in a non-inertial frame the coordinate speed may be different than *c*; in general relativity no coordinate system on a large region of curved spacetime is "inertial", so it's permissible to use a global coordinate system where objects travel faster than *c*, but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" and the local speed of light will be *c* in this frame, with massive objects moving through this local neighborhood always having a speed less than *c* in the local inertial frame.

### Faster light (Casimir vacuum and quantum tunnelling)

Raymond Y. ChiaoRaymond Y. Chiao is an American physicist best known for his experimental work in quantum optics. He is currently on the faculty of the University of California, Merced, where he is conducting research on gravitational radiation.-Biography:...

was first to measure the quantum tunnelling time, which was found to be between 1.5 to 1.7 times the speed of light.

Einstein's equations of

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

postulate that the speed of light in a vacuum 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

SIThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

unit of length (the meter) has been defined using the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

.

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 energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

. 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 effectThe Scharnhorst effect is a hypothetical phenomenon in which light signals travel faster than c between two closely spaced conducting plates. It was predicted by Klaus Scharnhorst of the Humboldt University of Berlin, Germany, and Gabriel Barton of the University of Sussex in Brighton, England...

. 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 traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 10

^{36}. Accordingly there has as yet been no experimental verification of the prediction. A recent analysis argued 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 conjectureThe chronology protection conjecture is a conjecture by the physicist Professor Stephen Hawking that the laws of physics are such as to prevent time travel on all but sub-microscopic scales. Mathematically, the permissibility of time travel is represented by the existence of closed timelike curves...

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. 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 NimtzGünter Nimtz is a German physicist, working at the 2nd Physics Institute at the University of Cologne in Germany. He has investigated narrow-gap semiconductors and liquid crystals and was engaged in several interdisciplinary studies on the effect of non-ionizing electromagnetic radiation in...

and Alfons Stahlhofen, of the

University of CologneThe University of Cologne is one of the oldest universities in Europe and, with over 44,000 students, one of the largest universities in Germany. The university is part of the Deutsche Forschungsgemeinschaft, an association of Germany's leading research universities...

, 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 (0.9144 m) apart. Their experiment involved an optical phenomenon known as

"evanescent modes"An evanescent wave is a nearfield standing wave with an intensity that exhibits exponential decay with distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies...

, and they claim that since evanescent modes have an imaginary wave number, they represent a "mathematical analogy" to

quantum tunnellingQuantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...

. Nimtz has also claimed that "evanescent modes are not fully describable by the

Maxwell equationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

and quantum mechanics have to be taken into consideration." Other scientists such as Herbert Winful and Robert Helling have argued that in fact there is nothing quantum-mechanical about Nimtz's experiments, and that the results can be fully predicted by the equations of

classical electromagnetismClassical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...

(Maxwell's equations).

Nimtz told

*New Scientist*New Scientist is a weekly non-peer-reviewed English-language international science magazine, which since 1996 has also run a website, covering recent developments in science and technology for a general audience. Founded in 1956, it is published by Reed Business Information Ltd, a subsidiary of...

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 ever shrinking main train moves forward at each stop; in this way, the speed of the center of the train exceeds the speed of any of the individual cars. Herbert Winful argues that the train analogy is a variant of the "reshaping argument" for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse. Instead, Winful argues that the

group delayThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

in tunneling is not actually the transit time for the pulse (whose spatial length must be greater than the barrier length in order for its spectrum to be narrow enough to allow tunneling), but is instead the lifetime of the energy stored in a

standing waveIn physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...

which forms inside the barrier. Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling. A number of authors have published papers disputing Nimtz's claim that Einstein causality is violated by his experiments, and there are many other papers in the literature discussing why quantum tunneling is not thought to violate causality.

It was later claimed by the Keller group in Switzerland that particle tunneling does indeed occur in zero real time. Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500-600 attoseconds (an attosecond is one quintillionth of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.

### Give up causality

Another approach is to accept

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, but to posit that mechanisms allowed by

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

(e.g.,

wormholeIn physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...

s) 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 curveIn mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...

s (i.e.,

time travelTime travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

) and

causalityCausality is the relationship between causes and effects. It is considered to be fundamental to all natural science, especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics....

violations. Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that cannot be sensibly dispensed with. Because of this, most physicists expect that

quantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

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 principleThe Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general...

.

### Give up (absolute) relativity

Because of the strong empirical support for

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, 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-CameliaGiovanni Amelino-Camelia is an Italian physicist of the University of Rome La Sapienza who works on quantum gravity.He is the first proposer of Doubly special relativity that is the idea of introducing the Planck length in physics as an observer-independent quantity, obtaining a relativistic theory...

and

João MagueijoJoão Magueijo is a Portuguese cosmologist and professor in Theoretical Physics at Imperial College London. He is a pioneer of the varying speed of light theory.- Career :...

. One consequence of this theory is a

variable speed of lightThe variable speed of light concept states that the speed of light in a vacuum, usually denoted by c, may not be constant in most cases. In most situations in condensed matter physics when light is traveling through a medium, it effectively has a slower speed...

, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than

*c*. 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 principleIn theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

), which implies that the rest frame of the universe might be

*preferred* by conventional measurements of natural law. If confirmed, this would imply

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the

observable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

, it is difficult to imagine (much less construct) experiments to test this hypothesis.

### Space-time distortion

Although the theory of

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

forbids objects to have a relative velocity greater than light speed, and

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

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 AlcubierreMiguel Alcubierre Moya is a Mexican theoretical physicist. Born in Mexico City, he obtained a degree in physics, and a Master of Science in theoretical physics at the School of Science of Universidad Nacional Autónoma de México ....

theorized that it would be possible to create an

Alcubierre driveThe Alcubierre drive, also known as the Alcubierre metric, is a speculative, but valid solution of the Einstein field equations. It is a mathematical model of a spacetime exhibiting features reminiscent of the fictional "warp drive" from Star Trek, which can travel "faster than light", although...

, 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 traveling 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 UniversityBaylor University is a private, Christian university located in Waco, Texas. Founded in 1845, Baylor is accredited by the Southern Association of Colleges and Schools.-History:...

, and Richard Obousy, a Baylor graduate student, theorize that by manipulating the extra spatial dimensions of

string theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

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 energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

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.

### Heim theory

In 1977, a paper on

Heim theoryHeim theory is a physics theory, initially proposed by a German physicist, the late Burkhard Heim, that attempts to develop a theory of everything. Heim theory's six dimensional model was later extended to eight and twelve dimensions, in collaboration with W. Dröscher...

theorized that it may be possible to travel faster than light by using magnetic fields to enter a higher-dimensional space.

### MiHsC/Quantised inertia

A new theory has been proposed that

**M**odifies

**i**nertia by assuming it is due to Unruh radiation subject to a

**H**ubble

**s**cale

**C**asimir effect (

**MiHsC**, or quantised inertia). MiHsC predicts a minimum possible acceleration even at light speed, implying that this speed can be exceeded.

### Lorentz symmetry violation

The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called

Standard-Model ExtensionStandard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...

. This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.

The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including

Lorentz-violating neutrino oscillationsLorentz-violating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance...

and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.

In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that

spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

of Lorentz invariance shortly after the

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field; however, there are also some models where Lorentz symmetry is broken in a more fundamental way. If Lorentz symmetry can cease to be a fundamental symmetry at Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.

In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized, existing low-energy bounds cannot be applied to high-energy phenomena; however, many searches for Lorentz violation at high energies have been carried out using the

Standard-Model ExtensionStandard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...

.

Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.

Another recent theory (see EPR paradox above

ibidIbid. is the term used to provide an endnote or footnote citation or reference for a source that was cited in the preceding endnote or footnote. It is similar in meaning to idem , abbreviated Id., which is commonly used in legal citation. To find the ibid...

) resulting from the analysis of an EPR communication set up, has the simple device based on removing the effective retarded time terms in the Lorentz transform to yield a preferred absolute reference frame. This frame cannot be used to do physics (i.e. compute the influence of light-speed limited signals) but it provides an objective, absolute frame all could agree upon, if

superluminal communication is possible. If this sounds indulgent, it allows simultaneity, absolute space and time and a deterministic universe (along with decoherence theory) whilst the status-quo permits time travel/causality paradoxes, subjectivity in the measurement process and multiple universes.

### Superfluid theories of physical vacuum

In this approach the physical

vacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

is viewed as the quantum

superfluidSuperfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...

which is essentially non-relativistic whereas the Lorentz symmetry is not an exact symmetry of Nature but rather the approximate description valid only for the small fluctuations of the superfluid background. Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be the quantum Bose liquid whose ground-state wavefunction is described by the

logarithmic Schrödinger equationIn theoretical physics, the logarithmic Schrödinger equation is one of the nonlinear modifications of Schrödinger's equation...

.

It was shown that the

relativistic gravitational interactionGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

arises as the small-amplitude collective excitation mode whereas relativistic elementary particles can be described by the particle-like modes in the limit of low momenta. The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the

relativisticThe theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

one - they can reach the speed of light limit at finite energy; also the faster-than-light propagation is possible without requiring moving objects to have imaginary mass.

### MINOS experiment

In 2007

MINOSMINOS is a particle physics experiment designed to study the phenomena of neutrino oscillations, first discovered by a Super-Kamiokande experiment in 1998...

collaboration reported results measuring the flight-time of 3-GeV neutrinos yielding a speed exceeding that of light by 1.8-sigma significance.

However, those measurements were considered to be statistically consistent with neutrinos traveling at the speed of light. Currently the detectors for the project are being upgraded, and new results are not expected until at least 2012.

### OPERA neutrino anomaly

On September 22, 2011, a paper from the

OPERA CollaborationThe Oscillation Project with Emulsion-tRacking Apparatus is a scientific experiment for detecting tau neutrinos from muon neutrino oscillations. It is a collaboration between CERN in Geneva, Switzerland, and the Laboratori Nazionali del Gran Sasso in Gran Sasso, Italy and uses the CERN Neutrinos...

indicated detection of 17-

GeVIn physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...

and 28-GeV muon neutrinos, sent 730 kilometers (454 miles) from

CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

near Geneva, Switzerland to the

Gran Sasso National LaboratoryLaboratori Nazionali del Gran Sasso is a particle physics laboratory of the INFN, situated near the Gran Sasso mountain in Italy, between the towns of L'Aquila and Teramo, about 120 km from Rome. In addition to a surface portion of the laboratory, there are extensive underground facilities...

in

ItalyItaly , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

, traveling faster than light by a factor of 2.48×10

^{−5} (approximately 1 in 40,322.58), a statistic with 6.0-sigma significance. On 18 November 2011, a second followup experiment by OPERA scientists was reported that confirmed its initial results.

## Tachyons

In special relativity, while it is impossible in an inertial frame to accelerate an object

*to* the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, 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 particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

s that have this property are called

tachyonA tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

s. Their existence has not been proven, but even so, attempts to

quantiseQuantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

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. Various theorists have suggested that the

neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

might have a

tachyonA tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

ic nature, while others have disputed the possibility.

## General relativity

General relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

was developed after

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

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

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

that allow an object to move faster than light from the point of view of a distant observer. One such

distortionA distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...

is the Alcubierre drive, which can be thought of as producing a ripple in

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

that carries an object along with it. Another possible system is the

wormholeIn physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...

, 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 matterIn physics, exotic matter is a term which refers to matter which would somehow deviate from the norm and have "exotic" properties. There are several uses of the term....

or negative energy.

General relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

also agrees that any technique for faster-than-light

travelTravel is the movement of people or objects between relatively distant geographical locations. 'Travel' can also include relatively short stays between successive movements.-Etymology:...

could also be used for

time travelTime travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

. This raises problems with

causalityCausality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

. 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 theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, Eric Gimon and

Petr HořavaPetr Hořava is a Czech string theorist. He is currently a professor of physics at the University of California, Berkeley, where he frequently teaches courses on quantum field theory and string theory...

have argued that in a supersymmetric five-dimensional

Gödel universeThe Gödel metric is an exact solution of the Einstein field equations in which the stress-energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second associated with a nonzero cosmological constant...

, quantum corrections to general relativity effectively cut off regions of spacetime 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.

## Variable speed of light

In conventional

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the speed of light in a

vacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

is assumed to be a constant. However, there exist theories which postulate that the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

is not a constant. The interpretation of this statement is as follows.

The speed of light is a dimensional quantity and so, as has been emphasized in this context by

João MagueijoJoão Magueijo is a Portuguese cosmologist and professor in Theoretical Physics at Imperial College London. He is a pioneer of the varying speed of light theory.- Career :...

, 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

SIThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

system of units is based on seven basic dimensional quantities, namely

distanceDistance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

,

massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

,

timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

,

electric currentElectric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

,

thermodynamic temperatureThermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...

,

amount of substanceAmount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

, and

luminous intensityIn photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye...

. These

unitsA unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

are defined to be

independentThe terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

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 lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

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 timeIn physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...

,

Planck length and

Planck energy which make a good system of units for expressing dimensional measurements, known as

Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...

.

Magueijo's proposal used a different set of

unitsA unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

, 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.

## See also

- Intergalactic travel
Intergalactic travel is space travel between galaxies. Due to the relatively enormous distances between our own galaxy and even its closest neighbors, any such venture would be far more technologically demanding than even interstellar travel...

- Krasnikov tube
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole with the endpoints displaced in time as well as space...

- Wheeler–Feynman absorber theory
- OPERA experiment#Faster-than-light results

Fiction

- Jump drive
A jump drive is one of the speculative inventions in science fiction, a method of traveling faster than light .Related concepts are hyperdrive, warp drive and interstellar teleporter. The key characteristic of a jump drive is that it allows a starship to be instantaneously teleported between two...

- Jumpgate
In science fiction, a jump gate is a fictional device able to create a wormhole or portal, allowing fast travel between two points in space...

- Warp drive (Star Trek)
Warp drive is a faster-than-light propulsion system in the setting of many science fiction works, most notably Star Trek. A spacecraft equipped with a warp drive may travel at velocities greater than that of light by many orders of magnitude, while circumventing the relativistic problem of time...

- Starburst (Farscape)
- Slipstream (science fiction)
"Slipstream" is a science fiction term for a fictional method of faster-than-light space travel, similar to hyperspace travel, warp drive, or "transfer points" from David Brin's Uplift series.-Usage in Star Trek:...

- Skip drive
Skip drive is a common generic name for an FTL drive, used by various Science Fiction authors.* faster-than-light drive* Old Man's War#Skip Drive - John Scalzi's Old Man's War universe uses an FTL drive referred to as a skip drive* F. M...

- Infinite Improbability Drive
- Inertialess drive
The inertialess drive is a fictional means of accelerating to close to the speed of light or faster-than-light travel, originally used in Triplanetary and the Lensman series by E.E. "Doc" Smith, and later by Robert A...

- Stargate (device)
A Stargate is a portal device within the Stargate fictional universe that allows practical, rapid travel between two distant locations. The devices first appear in the 1994 Roland Emmerich film Stargate, and thereafter in the television series Stargate SG-1 and its spin-offs...

- Ansible
An ansible is a hypothetical machine capable of instantaneous or superluminal communication. Ansibles occur as plot devices in science fiction literature.- Origin :The word ansible was coined by Ursula K. Le Guin in her 1966 novel, Rocannon's World...

- Mass Effect
Mass Effect is an action role-playing game developed by BioWare for the Xbox 360 and Microsoft Windows by Demiurge Studios. The Xbox 360 version was released worldwide in November 2007 published by Microsoft Game Studios...

Relay
- Macross Space Fold
- FTL:2448
FTL:2448 is a science fiction role playing game, created by Richard Tucholka, and published by Tri Tac Games in 1982, about faster-than-light travel with alien races. In 1985, there was an expanded edition, and in 1990, a two-volume version of the game was released. Book One covered character...

by Tri Tac GamesTri Tac Games is a publisher of role-playing games based in Pontiac, Michigan. The company is built primarily on the work of Richard Tucholka, its founder and president.-Company history:Tri Tac Games was founded in 1978 as "Tacky Tack Games"...

- Interdimensional Drive (Earth Final Conflict)
- Kearny-Fuchida jump drive (BattleTech)
- Ultrawave
Ultrawaves are a concept used in science fiction to represent transmissions or signals that may propagate faster than light through either normal space, or alternate space, such as hyperspace or subspace...

### Scientific links

### Proposed FTL Methods links