It has been suggested that FTL Drive be merged into this article or section. (Discuss)

Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. This concept is a staple of the science fiction genre, and is also the subject of ongoing scientific study. Image File history File links Please see the file description page for further information. ... FTL Drive is a band from Omaha, Nebraska. ... Superluminal communication is the term used to describe the hypothetical process by which one might send information at faster-than-light (FTL) speeds. ... Interstellar space travel is unmanned or manned travel between stars, though the term usually denotes the latter. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... Matter is commonly defined as the substance of which physical objects are composed. ... The speed of light in a vacuum is denoted by the letter c. ... Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ...

Unsolved problems in physics: Is it possible to go faster than the speed of light? If so, would it violate the theoretical principles of the universe?

Image File history File links Question_dropshade. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Terminology

Faster than light travel

In the context of this article, FTL refers to transmitting information or matter faster than c, a constant equal to the speed of light in a vacuum, roughly 300,000 kilometres per second, or 186,000 miles per second. This is not quite the same as travelling faster than light, since: The speed of light in a vacuum is denoted by the letter c. ...

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

Neither of these phenomena violate special relativity or create problems with causality, and thus do not qualify as FTL as described here. The refractive index (or index of refraction) of a material is the factor by which the phase velocity of electromagnetic radiation is slowed in that material, relative to its velocity in a vacuum. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ... Cherenkov radiation glowing in the core of a TRIGA reactor Cherenkov radiation (also spelled Cerenkov or sometimes ÄŒerenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in the medium. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

Possibility of FTL

Faster-Than-Light travel or communication is problematic in a universe that is consistent with Einstein's theory of relativity. In a hypothetical universe where Newton's laws of motion and the Galilean transformations are exact, rather than approximate, the following would be true: Wikisource has original text related to this article: Relativity: The Special and General Theory Albert Einsteins theory of relativity, or simply relativity, refers specifically to two theories: special relativity and general relativity. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... The Galilean transformation is used to transform between the coordinates of two coordinate systems in a constant relative motion in Newtonian physics. ...

• The laws of physics are the same in every 'frame of reference', although some laws would have to include terms containing the velocity of the frame of reference
• Quantities measured in different reference frames are related by Galilean transformations, although for some quantities the transformation under the Galilean group is complicated
• Velocities add linearly
• A fixed point x in one reference frame corresponds to the trajectory x+vt in a frame moving with relative velocity v to the first.
• There is nothing fundamental about the wave velocity of light
• All observers agree on the time, up to an overall shift
• Simultaneity is a well-defined concept in that all observers agree on whether any two events are simultaneous

However, according to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their acceleration or relative velocity, will always measure zero-mass particles (e.g., gravitons as well as photons) naturally traveling at c. 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: Frame of reference - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... Wave velocity is a general concept, of various kinds of wave velocities, for an electromagnetic waves phase and speed concerning energy (and information) propagation. ... Absolute simultaneity is a hypothetical coincidence of two or more events in different points in space for all observers in the universe. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... The speed of light in a vacuum is denoted by the letter c. ... Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the slope of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or derivative with respect to time) of velocity. ... The velocity of an object is simply its speed in a particular direction. ... This article or section is in need of attention from an expert on the subject. ... In physics, the photon (from Greek φως, phōs, meaning light) is the quantum of the electromagnetic field; for instance, light. ... In physics and mathematics, the Poincaré group is the group of isometries of Minkowski spacetime. ...

• To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time
• Either way, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not a sensible notion.
• Observers with relative motion will disagree 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 in any inertial frame of reference will be travel backwards in time in other, equally valid, frames of reference.

Because of this, there appear to be only a limited number of ways to justify Faster-Than-Light behavior: The term mass in special relativity can be used in different ways, occasionally leading to confusion. ...

Option A: Ignore special relativity

This is the simplest solution, and is particularly popular in science fiction. Empirical evidence unanimously affirms that the universe obeys Einstein's laws rather than Newton's where they disagree. However general relativity is only an approximation due to its incompatibility with quantum mechanics. Special relativity is easily incorporated into nongravitational quantum field theories, however it only applies to a flat Minkowski universe.^{[citation needed]} In particular, our universe is expanding, contains stress-energy which curves the ambient space time and perhaps even has a cosmological constant and so is not Minkowski and in particular is not invariant under Poincaré transformations. However even in the broader context of general relativity, acceleration from subluminal to superluminal speeds does not appear to be possible.^{[citation needed]} Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... For a non-technical introduction to the topic, please see Introduction to Quantum mechanics. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

Option B: Get light to go faster (Casimir vacuum)

Einstein's equations of special relativity posit that the speed of light is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light itself. That is an experimentally determined quantity. For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

The experimental determination has been made in vacuum. However the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called the vacuum energy. This vacuum energy can be changed in certain cases. When vacuum energy is lowered, light itself can go faster than the standard value 'c'. 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 light will go faster in such a vacuum.^{[citation needed]} However, there has been no experimental verification, since the technology to detect the change isn't yet available. It has been suggested that this article or section be merged with Zero-point energy. ... In physics, the Casimir effect is a weak force exerted between separate objects, which is due to neither charge, gravity, nor the exchange of particles, but instead is due to resonance of all-pervasive energy fields in the intervening space between the objects. ...

Einstein's equations of special relativity have an implicit assumption of homogeneity. Space is assumed to be the same everywhere. In the case of the Casimir vacuum, this assumption is clearly violated. Inside the Casimir vacuum, we have homogeneous space, and outside it, we have homogeneous space as well. Inside the Casimir vacuum, the equations of special relativity will apply with the increased value of the speed of light. Outside it, the equations of special relativity will apply with the normal 'c'. However, when considering two frames of reference, one inside the vacuum, and one outside, the equations of special relativity can no longer be applied, since the assumption of homogeneity has been broken. In other words, the Casimir effect breaks up space into distinct homogeneous regions, each of which obey the special relativity laws separately. For a non-technical introduction to the topic, please see Introduction to Special relativity. ... In physics, the Casimir effect is a weak force exerted between separate objects, which is due to neither charge, gravity, nor the exchange of particles, but instead is due to resonance of all-pervasive energy fields in the intervening space between the objects. ...

While this may technically qualify as 'faster-than-light', that is only true relative to two disconnected regions of space. It is unclear whether (and unlikely that) a Casimir vacuum is stable under quantum mechanics, and whether non-trivial communication is possible between two such regions.

Option C: Give up causality

Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations.^{[citation needed]} Causality is not required by special or general relativity, but is nonetheless considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option. An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle. For a non-technical introduction to the topic, please see Introduction to Special relativity. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... 3D analogy to a wormhole. ... From the point of view of general relativity, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Dr. Igor D. Novikov in the mid-1980s to solve the problem of paradoxes in time travel. ...

Option D: Give up (absolute) relativity

Due to the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The most well-known attempt is doubly-special relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidence casts doubt on this theory, some physicists still consider it viable.^{[citation needed]} However, even if this theory is true, it is still very unclear that it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c. For a non-technical introduction to the topic, please see Introduction to Special relativity. ... Doubly-Special Relativity is a new theory of special relativity first postulated in a paper by Giovanni Amelino-Camelia. ... The Planck length, denoted by , is the unit of length in the system of units known as Planck units. ... Giovanni Amelino-Camelia is an astrophysicist of the University of Rome who works with gravity. ... João Magueijo at the journée de la Science at the EPFL, on the 11th of November 2005 João Magueijo is a cosmologist and lecturer in Theoretical Physics at Imperial College London. ... A variable speed of light (VSL) is the concept that the speed of light may not be constant over time. ...

There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis. This article is in need of attention from an expert on the subject. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

Option E: Go somewhere where special relativity does not apply

A very popular option taken in science fiction novels, movies, television programs, and computer games is to assume the existence of some other realm (typically called hyperspace or subspace) which is accessible from this universe, in which the laws of relativity are usually distorted, bent, or nonexistent, facilitating rapid transport between distant points in this universe, sometimes with acceleration differences - that is, not requiring as much energy or thrust to go faster. To accomplish rapid transport between points in hyperspace/subspace, special relativity is often assumed not to apply in this other realm. An alternative solution sometimes used is to posit that distant points in the mundane universe correspond to points that are close together in hyperspace. Scene from Star Wars depicting the inside of a starship entering hyperspace. ... Thrust is a reaction force described quantitatively by Newtons Second and Third Law. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

This method of faster-than-light travel does not correspond to anything seriously proposed by mainstream science, although there are also no arguments precluding its existence.

Option F: Become faster without acceleration

An often-implicit assumption about getting something past light speed is that one must get it to light speed as an intermediate step, thus encountering the infinite energy problem. Similarly to the idea of using wormholes to instantly change location, there might be a method to instantly change velocity, rather than having to accelerate through all intermediate velocities. The energy required for acceleration hits an asymptote as one approaches light speed. Thus, an object going much faster than light speed might only need energy comparable to an object going much slower than light; the difficulty lies in figuring out how to "convince" particles to move faster than light without resorting to acceleration. (This also gets around the problem of including a human being; inertia is caused by acceleration, not velocity, so it would not occur.)

As of yet, no method is known of instantly changing the velocity of matter.

Option G: Produce infinite energy

Almost every thought that says that something cannot be accelerated past lightspeed makes one major case: We cannot generate infinite energy. However, if infinite energy could be created, it would be quite possible to get past light speed.^{[citation needed]} Although this may at first thought violate the idea of conservation of energy, this is not completely the case. The idea of conservation of matter is the idea of a universal constant amount of energy, not necessarily a local. To put it simply, "To create infinite from 0, you need to also create negative infinite."^{[citation needed]} Conservation of energy states that the total amount of energy (including potential energy) in a closed system remains constant. ...

No known method yet exists to do this.

Tachyons

In special relativity, while it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light, it is not impossible for an object to exist which always moves faster than light. The hypothetical elementary particles that have this property are called tachyons. Their existence has neither been proven nor disproven. For a non-technical introduction to the topic, please see Introduction to Special relativity. ... The speed of light in a vacuum is denoted by the letter c. ... In particle physics, an elementary particle is one of a wide variety of particles simpler than atoms. ... A tachyon (from the Greek ταχύς takhús, meaning swift) is any hypothetical particle that travels at superluminal velocity. ...

While tachyons have never been observed, they are present in many physical theories. For example tachyons appear in the standard model of interactions in particle physics, in bosonic string theory and even in superstring theory in the presence of an unstable D-brane or in certain compactifications such as an eight-manifold times a discrete quotient of the complex plane.^{[citation needed]} In each of these examples one sees that the tachyon is best thought of not as a particle, but rather as an instability in the theory. In some cases one can demonstrate that this instability leads to a decay to a stable state, for example in the standard model at temperatures below the electroweak scale the instability implies that a condensate forms which is responsible for the mass of all matter. When one expands the theory about the condensed vacuum one finds no tachyons.^{[citation needed]} The open string tachyons attached to unstable D-branes also condense, after which the unstable D-branes disappear.^{[citation needed]} Allan Adams, Eva Silverstein and Joseph Polchinski have shown that the closed string tachyon in the forementioned unstable compactification also condenses, and as it condenses the space-time itself decays and it never reaches a stable state.^{[citation needed]} The fate of the bosonic string after closed string tachyon condensation is still unknown. In each of these cases it has not been useful to think of the propagation of a single tachyonic particle, as a flood of such particles is dynamically formed from the vacuum until a steady state is reached. See also tachyon condensation. The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Bosonic string theory is the original version of string theory, developed in the late 1960s. ... Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. ... In theoretical physics, D-branes are a special class of p-branes, named for the physicist Johann Dirichlet. ... In mathematics, the complex plane is a way of visualising the space of the complex numbers. ... A particle is Look up Particle in Wiktionary, the free dictionary In particle physics, a basic unit of matter or energy. ... In particle physics, the electroweak scale is the energy scale around 250 GeV, a typical energy of processes described by the electroweak theory. ... Natural Gas Condensate (usually just condensate) is a by-product of natural gas. ... Mass is a property of a physical object that quantifies the amount of matter and energy it contains. ... Eva Silverstein is a string theorist. ... Joe Polchinski in Santa Barbara Joseph Polchinski (b. ... In physics, tachyon condensation is a process in which a tachyonic field—usually a scalar field—of a negative squared mass acquires a vacuum expectation value and reaches the minimum of the potential energy. ...

The equations of relativity do allow faster-than-light travel, however, any particle which is moving faster and faster, at velocities less than 'c', ends up with more and more kinetic energy. This is true even in the classical model, but with special relativity, as the velocity approaches 'c', the energy increases without limit. (Sometimes, incorrectly, stated as 'the energy goes to infinity'. Incorrect as the energy remains finite at all times, although it becomes arbitrarily large as the velocity approaches 'c'.) For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

If the velocity is greater than 'c', the energy has no place to go but down. In other words, a particle with mass moving at any speed above 'c' will lose energy when its velocity goes up even further. Put another way, such a particle will speed up when it loses energy.^{[citation needed]}

Everything that moves causes a change in the structure of the fabric of space. This change in the structure of the fabric of space causes the formation of gravitational waves that carry away energy. In most cases the change is negligible. However, for a particle with mass moving above 'c', even a tiny loss of energy is troublesome. As mentioned above, it actually increases the velocity, causing more energy loss, which increases the velocity further. This positive feedback loop causes the particle to soon reach infinite velocity.^{[citation needed]} In physics, gravitational radiation is energy that is transmitted through waves in the gravitational field of space-time, according to Albert Einsteins theory of general relativity: The Einstein field equations imply that any accelerated mass radiates energy this way, in the same way as the Maxwell equations that any...

General relativity

General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it. Another possible system is the wormhole, which connects two distant locations as though by a shortcut. To date there is no feasible way to construct any such special distortion; if such a distortion already exists, it will not last long enough for matter to traverse it unless one introduces exotic matter, enormous (though finite) amounts of energy, or both. For a non-technical introduction to the topic, please see Introduction to General relativity. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... Gravity is a force of attraction that acts between bodies that have mass. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... It has been suggested that this article or section be merged with Alcubierre metric. ... 3D analogy to a wormhole. ... Exotic matter is a hypothetical concept of particle physics. ...

General relativity also agrees that any technique for faster-than-light travel could also be used for time travel.^{[citation needed]} This raises problems with causality. Many physicists believe that the above phenomena are in fact impossible, and that future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In string theory Eric Gimon and Petr Horava have argued^[1] that in a supersymmetric five-dimensional Gödel universe quantum corrections to general relativity effectively cut off regions of spacetimes with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube. For a non-technical introduction to the topic, please see Introduction to General relativity. ... Time travel is a concept that has long fascinated humanity—whether it is Merlin experiencing time backwards, or religious traditions like Mohammeds trip to Jerusalem and ascent to heaven, returning before a glass knocked over had spilt its contents. ... The philosophical concept of causality, the principles of causes, or causation, the working of causes, refers to the set of all particular causal or cause-and-effect relations. ... Gravity is a force of attraction that acts between bodies that have mass. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles... Petr Horava is a Czech string theorist. ... In particle physics, supersymmetry is a hypothetical symmetry that relates bosons and fermions. ... The Gödel solution is an exact solution of the Einstein field equation 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 (see lambdavacuum solution). ...

Apparent FTL

Moving spot of light

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

This effect is believed to be responsible for supernova ejecta appearing to move faster than light as observed from Earth.^{[citation needed]} Multiwavelength X-ray image of the remnant of Keplers Supernova, SN 1604. ... Earth (often referred to as The Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth in order of size. ...

Relative motion

It is also possible for two objects to move faster than light relative to each other, but only from the point of view of an observer in a third frame of reference, who naively adds velocities according to Galilean relativity. An observer on either Object will see the other object moving slower than light. A velocity addition formula appears in the special theory of relativity as a consequence of the Lorentz transformations. ... Note: The principle of relativity should not be confused with the Theory of relativity. ...

For example, fast-moving particles on opposite sides of a circular particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator, and who naively adds velocities according to Galilean relativity. However, if the observer has a good intuition of special relativity, and makes a correct calculation, and the two particles are moving, for example, at velocities β and − β A 1960s single stage 2MeV linear Van de Graaff accelerator, here opened for maintenance A particle accelerator is a device that uses electric and/or magnetic fields to propel electrically charged particles to high speeds. ... Note: The principle of relativity should not be confused with the Theory of relativity. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... A velocity addition formula appears in the special theory of relativity as a consequence of the Lorentz transformations. ...

and

,

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

,

which is less than the speed of light.

Phase velocities above c

The phase velocity of a wave can easily exceed c, the vacuum velocity of light. In principle, this can occur even for simple mechanical waves, even without any object moving with velocities close to or above c. However, this does not imply the propagation of signals with a velocity above c.^[2] The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... A wave is a disturbance that propagates through space, often transferring energy. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ...

Group velocities above c

Under certain circumstances, even the group velocity of a wave (e.g. a light beam) can exceed c.^{[citation needed]} In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of a pulse may travel with a velocity above c. However, even this situation does not imply the propagation of signals with a velocity above c, even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind, the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than without this effect. The group velocity of a wave is the velocity with which the overall shape of the waves amplitude (known as the envelope of the wave) propagates through space. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ...

Universal expansion

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if Comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.^{[citation needed]} In other words, the galaxies (or more accurately, galaxy clusters) do not physically move away from each other. Rather, the fabric of spacetime between them expands. This also explains the Inflationary epoch during the Big Bang, when the universe expanded from a size a hundred billion times smaller than a proton to approximately one hundred million light years in diameter in just 10^-32 of a second. The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... The comoving distance or conformal distance of two objects in the universe is the distance divided by a time-varying scale factor representing the expansion of the universe. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... The inflationary epoch is the term used in cosmology to describe the brief time in the very early universe when, according to inflation theory, the universe was expanding exponentially. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ...

Astronomical observations

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed, and can be explained as an optical illusion caused by the object moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these object have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light.^{[citation needed]} Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds. In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, quasars and recently also in some galactic sources called microquasars. ... An active galaxy is a galaxy where a significant fraction of the energy output is not emitted by the normal components of a galaxy: stars, dust and interstellar gas. ... A blazar is a very compact and highly variable energy source associated with a supermassive black hole at the center of a galaxy. ... This view, taken with infrared light, is a false-color image of a quasar-starburst tandem with the most luminous starburst ever seen in such a combination. ... Microquasars are smaller cousins of quasars. ... An optical illusion is characterized by visually perceived images that, at least in common sense terms, are deceptive or misleading. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

Quantum mechanics

Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. These phenomena do not allow true communication; they only let two observers in different locations see the same event simultaneously, without any way of controlling what either sees.^{[citation needed]} The fact that the laws of physics seem to conspire to prevent superluminal communications via quantum mechanics is very interesting and somewhat poorly understood. For a non-technical introduction to the topic, please see Introduction to Quantum mechanics. ... Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. ...

The uncertainty principle implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than c, even in a vacuum; this possibility must be taken into account when enumerating Feynman diagrams for a particle interaction. To quote Richard Feynman: The Heisenberg uncertainty principle or just uncertainty principle (sometimes also the Heisenberg indeterminacy principle - a name given to it by N. Bohr) is one of the cornerstones of quantum mechanics. ... In this Feynman diagram, electrons annihilate and become a quark-antiquark pair. ... Richard Phillips Feynman (May 11, 1918 – February 15, 1988) (surname pronounced FINE-man; in IPA) was one of the most influential American physicists of the 20th century, expanding greatly on the theory of quantum electrodynamics, the quark theory, and the physics of the superfluidity of supercooled liquid helium. ...

"... there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c"^[3]

However, this does not imply the possibility of superluminal information transmission, as no photon can have an average speed in excess of the speed of light.

There have been various reports in the popular press of experimentally based of faster-than-light transmission in optics — most often in the context of a kind of quantum tunneling phenomenon. Usually, such reports deal with a phase velocity or group velocity faster than the vacuum velocity of light. But recall from above, that a superluminal phase velocity cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point. Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... The group velocity of a wave is the velocity with which the overall shape of the waves amplitude (known as the envelope of the wave) propagates through space. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...

As it is currently understood, quantum mechanics is completely consistent with special relativity, and doesn't allow for faster-than-light communication. For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

Variable speed of light

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

The speed of light is a dimensionful quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured.^[4] Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensionful 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. Our universe has three basic dimensionful quantities, which can be taken to be distance, time and energy, although in some fields one also includes charge and temperature (which are both forms of energy). One can then reduce all measurements to dimensionless quantities by constructing the ratios with respect to any 3 independent reference quantities, which can always be manipulated to construct a reference length, time and energy. For example, in quantum gravity one usually fixes Newton's constant, the speed of light and Planck's constant. By manipulating these basic constants one can construct the Planck time, Planck length and Planck energy which make a good system of units. The speed of light in a vacuum is denoted by the letter c. ... João Magueijo at the journée de la Science at the EPFL, on the 11th of November 2005 João Magueijo is a cosmologist and lecturer in Theoretical Physics at Imperial College London. ... The distance between two points is the length of a straight line segment between them. ... A pocket watch. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Temperature is also the name of a song by Sean Paul. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The speed of light in a vacuum is denoted by the letter c. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... In physics, the Planck time (tP), is the natural unit of time. ... The Planck length, denoted by , is the unit of length in the system of units known as Planck units. ... The Planck energy is the natural unit of energy, denoted by EP. 1. ...

João's proposal use a different set of units, as one is always free to do, 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. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ...

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

• Category:Faster-than-light travel
• Category:Faster-than-light communication

References

1. ^ Gimon, Eric G.; Petr Horava (May 2004). Over-rotating black holes, Gödel holography and the hypertube. Retrieved on 2006-06-05.
2. ^ Egan, Greg (2000). Subluminal. Retrieved on 2006-06-05. - Example of phase velocity
3. ^ Feynman. “Chapter 3”, QED, 89.
4. ^ Magueijo, João (1999). A time varying speed of light as a solution to cosmological puzzles. Retrieved on 2006-06-05.

2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... June 5 is the 156th day of the year in the Gregorian calendar (157th in leap years), with 209 days remaining. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... June 5 is the 156th day of the year in the Gregorian calendar (157th in leap years), with 209 days remaining. ... João Magueijo at the journée de la Science at the EPFL, on the 11th of November 2005 João Magueijo is a cosmologist and lecturer in Theoretical Physics at Imperial College London. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... June 5 is the 156th day of the year in the Gregorian calendar (157th in leap years), with 209 days remaining. ...

Fictional

• Hyperspace
• Jump drive
• Jumpgate
• Warp drive
• Starburst
• Sub-Ether Drive

Scene from Star Wars depicting the inside of a starship entering hyperspace. ... Jump drive is a name given to a method of traveling faster than light in science fiction. ... In sci-fi, Jumpgate (or jump gate) refers to a device that allows fast travel between two points in space. ... This article or section is missing references or citation of sources. ... In the science fiction television series Farscape, Starburst is the primary means of superluminal propulsion - and sole defensive capability - of Leviathans, a race of sentient bio-mechanical ships. ...

External links

• Encyclopedia of laser physics and technology on "superluminal transmission", with more details on phase and group velocity, and on causality
• July 22, 1997, The New York Times Company: Signal Travels Farther and Faster Than Light Quote: "..."We find," Chiao said, "that a barrier placed in the path of a tunneling particle does not slow it down. In fact, we detect particles on the other side of the barrier that have made the trip in less time than it would take the particle to traverse an equal distance without a barrier -- in other words, the tunneling speed apparently greatly exceeds the speed of light. Moreover, if you increase the thickness of the barrier the tunneling speed increases, as high as you please..."
• Markus Pössel: Faster-than-light (FTL) speeds in tunneling experiments: an annotated bibliography Quote: "...An experiment of theirs, where a single photon tunnelled through a barrier and its tunneling speed (not a signal speed!) was 1.7 times light speed, is described in Steinberg, A.M., Kwiat, P.G. & R.Y. Chiao 1993: "Measurement of the Single-Photon Tunneling Time" in Physical Review Letter 71, S. 708--711..."
• Relativity and FTL (=Superluminal motion) Travel Homepage
• The Warp Drive: Hyper-Fast Travel Within General Relativity, Miguel Alcubierre Class. Quantum Grav. 11 (1994), L73-L77 Quote: "...It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed..."
• NASA: Status of "Warp Drive" Maturity - speculation
• Usenet Physics FAQ: is FTL travel or communication Possible?
• Critique of Geometro-Stochastic Theory
• Superluminal
• The Speed of Light: How Fast Can We Go?
• Relativity, FTL and causality
• Tachyon Theory - the mathematics of tachyon theory. Quote: "To send a message faster than light using tachyons, we would have to encode the message on a localised tachyon field, and then send it off at superluminal speed. But this is impossible as local tachyon disturbances are subluminal, and superluminal tachyon disturbances cannot be localised."
  • Subluminal - Java applet demonstrating group velocity information limits
• Not-so-constants? in Christian Science Monitor

The implications of changeable fundamental "constants" are so profound that any hint that this might be proved true makes news. But the real news is the dramatic increase in precision of the relevant measurements. That is going on in laboratories around the world right now.