Quantum field theory

Feynman diagram

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A tachyon (from the Greek ταχυόνιον, takhyónion, from ταχύς, takhýs, i.e. swift, fast) is any hypothetical particle that travels at superluminal speed. The first description of tachyons is attributed to German physicist Arnold Sommerfeld; however, it was George Sudarshan, Olexa-Myron Bilaniuk^[1][2], Vijay Deshpande^[2] and Gerald Feinberg^[3] (who originally coined the term in the 1960s) that advanced a theoretical framework for their study. Tachyonic fields have appeared theoretically in a variety of contexts, such as the Bosonic string theory. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time. A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds. Even if tachyons were conventional, localisable particles, they would still preserve the basic tenets of causality in special relativity and not allow transmission of information faster than light^[3]. Quantum field theory (QFT) is the quantum theory of fields. ... Image File history File links Feynmann_Diagram_Gluon_Radiation. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... The history of quantum field theory starts with its creation by Dirac when he attempted to quantize the electromagnetic field in the late 1920s. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... It has been suggested that this article or section be merged with Poincaré group. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... This article or section does not cite its references or sources. ... In theoretical physics, crossing symmetry is a relation between the S-matrix that describe processes that can be obtained from each other by replacing incoming particles with outgoing antiparticles after taking the analytic continuation. ... C-symmetry means the symmetry of physical laws over a charge-inversion transformation. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ... Wikipedia does not have an article with this exact name. ... In physics, an anomaly is a classical symmetry — a symmetry of the Lagrangian — that is broken in quantum field theories. ... In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ... In quantum field theory the vacuum expectation value (also called condensate) of an operator is its average, expected value in the vacuum. ... In physics, Faddeev-Popov ghost ci is a field that violates the spin-statistics relation. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral: where S is the action functional. ... In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ... Figure 1. ... In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ... In physics the Wightman axioms are an attempt of mathematically stringent, axiomatic formulation of quantum field theory. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the Schrödinger equation. ... In field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. ... This box:      In theoretical physics, the Wheeler-DeWitt equation is a functional differential equation. ... This is a detailed description of the standard model (SM) of particle physics. ... This article or section does not cite its references or sources. ... 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Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... This box:      String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. ... This article or section is in need of attention from an expert on the subject. ... This page discusses Theories of Everything in physics. ... Steven Adler was part of the original line-up of the legendary Guns N Roses. ... Hans Albrecht Bethe (pronounced bay-tuh; July 2, 1906 – March 6, 2005), was a German-American physicist who won the Nobel Prize in Physics in 1967 for his work on the theory of stellar nucleosynthesis. ... Nikolai Nikolaevich Bogoliubov (21 August 1909 – 13 February 1992) was a Russian-Ukrainian mathematician and theoretical physicist known for his work in statistical field theory and dynamical systems. ... Curtis Callan is a physicist and a professor at Princeton University. ... Sidney Coleman at Harvard University Sidney Coleman is an eminent theoretical physicist. ... Dr. Bryce S. DeWitt (January 8, 1923—September 23, 2004) was a theoretical physicist best known for his role in formulating the fundamental Wheeler_deWitt equation. ... Freeman John Dyson FRS (born December 15, 1923) is an English-born American theoretical physicist and mathematician, famous for his work in quantum mechanics, solid-state physics, nuclear weapons design and policy, and for his serious theorizing in futurism and science fiction concepts, including the search for extraterrestrial intelligence. ... Fermi redirects here. ... This article is about the physicist. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... Jeffrey Goldstone is a theoretical physicist and an emeritus physics faculty at MIT. He was educated at the Cambridge University. ... David Jonathan Gross (born February 19, 1941 in Washington, D.C.) is an American particle physicist and string theorist (although hes stated to the Brazilian newspaper Folha de São Paulo, on 09/27/2006, that the second area is included in the first one). ... Gerard t Hooft at Harvard University Gerardus (Gerard) t Hooft (born July 5, 1946) is a professor in theoretical physics at Utrecht University, The Netherlands. ... Roman W. Jackiw is a theoretical physicist and Dirac Medallist. ... Oskar Klein (September 15, 1894 - February 5, 1977) was a Swedish theoretical physicist. ... Lev Davidovich Landau Lev Davidovich Landau (Russian language: Ле́в Дави́дович Ланда́у) (January 22, 1908 – April 1, 1968) was a prominent Soviet physicist, who made fundamental contributions to many areas of theoretical physics. ... Tsung-Dao Lee (T. D. Lee, 李政道 Pinyin: Lǐ Zhèngdào) (born November 24, 1926) is a Chinese American physicist, well known for parity violation, Lee Model, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons and soliton stars. ... Herbert Henry Lehman (March 28, 1878 - December 5, 1963) was a Governor and Senator from New York. ... Ettore Majorana (Catania, Sicily, 1906 – Tyrrhenian Sea, 27 March 1938 (presumed)) was an Italian physicist who began promising work on neutrino masses. ... Yoichiro Nambu (1921–) is a Japanese-born American physicist. ... Giorgio Parisi (Rome, August 4, 1948-) is an influential Italian theoretical physicist, . 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Steven Weinberg (born May 3, 1933) is an American physicist. ... External links National Academy of Sciences biography Categories: People stubs | 1908 births | 2002 deaths | Manhattan Project | Physicists ... Kenneth Geddes Wilson (born June 8, 1936) is an American physicist. ... Edward Witten (born August 26, 1951) is an American theoretical physicist and professor at the Institute for Advanced Study. ... Zhen-Ning Franklin Yang (Traditional Chinese: ; pinyin: ) (born 22 September[1], 1922) is a Chinese American physicist who worked on statistical mechanics and symmetry principles. ... Hideki Yukawa Hideki Yukawa FRSE (湯川 秀樹, January 23, 1907 - September 8, 1981) was a Japanese theoretical physicist and the first Japanese to win the Nobel prize. ... Thousands of 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. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... This article does not cite any references or sources. ... Arnold Johannes Wilhelm Sommerfeld (December 5, 1868 in Königsberg, East Prussia – April 26, 1951 in Munich, Germany) was a German physicist who introduced the fine-structure constant in 1919. ... Enchakkal Chandy George Sudarshan (September 16, 1931, Pallam, in Kottayam district of Kerala, India) is a prominent Indian-American physicist, author, and professor at the University of Texas at Austin. ... Gerald Feinberg, (b. ... Bosonic string theory is the original version of string theory, developed in the late 1960s. ... For a generally accessible and less technical introduction to the topic, see Introduction to special relativity. ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... In the context of special relativity, space-like separated points (or events) in spacetime have a spacetime interval less than 0 (see sign convention). ... Causality or causation denotes the relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first. ... For a generally accessible and less technical introduction to the topic, see Introduction to special relativity. ...

Today, in the framework of quantum field theory, tachyons are best understood as signifying an instability of the system and treated using tachyon condensation, rather than as real faster-than-light particles, and such instabilities are described by tachyonic fields. According to the contemporary and widely accepted understanding of the concept of a particle, tachyon particles are too unstable to be treated as existing^[4]. By that theory, faster than light information transmission and causality violation with tachyons are impossible on both grounds: they are non-existent in the first place (by tachyon condensation)^[4] and even if they existed (by Feinberg's analysis^[3]) they wouldn't be able to transmit information (also by Feinberg's analysis^[3]). Despite the theoretical arguments against the existence of tachyon particles, experimental searches have been conducted to test the assumption against their existence; however, no experimental evidence for or against the existence of tachyon particles has been found. ^[5] Quantum field theory (QFT) is the quantum theory of fields. ... 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. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... 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. ... 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. ... Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ...

Basic properties

Tachyon visualization, analogous to the sound made by a supersonic jet. Since a tachyon moves faster than the speed of light, we can not see it approaching. After a tachyon has passed nearby, we would be able to see two images of it, appearing and departing in opposite directions. The black line is the shock wave of Cherenkov radiation (analogous to a sonic boom), shown only in one moment of time. This double image effect is most dramatically illustrated for an observer located directly in the path of a faster-than-light object (in this example a sphere, shown in grey). The right hand bluish shape is the image formed by the blue-doppler shifted light arriving at the observer—who is located at the apex of the black Cherenkov lines—from the faster-than-light sphere as it approaches; it moves "backwards" as light arrives from earlier and earlier positions of the sphere before it arrived at the observer. The left-hand reddish image is formed from redshifted light that leaves the sphere after it passes the observer; it moves "forward" following the sphere. Since the object arrives before the light the observer sees nothing until the sphere starts to pass the observer, after which the image-as-seen-by-the-observer slowly splits into two—one of the arriving sphere (to the right) and one of the departing sphere (to the left).

Animation

From a special relativity dynamics perspective a tachyon is a particle with space-like four-momentum. There are two equivalent approaches to handling their kinematics: Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A United States Navy F/A-18E/F Super Hornet in transonic flight. ... A line showing the speed of light on a scale model of Earth and the Moon, taking about 1â…“ seconds to traverse that distance. ... 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 that medium. ... For other uses, see Sonic boom (disambiguation). ... A source of waves moving to the left. ... This article is about the physical phenomenon. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In the context of special relativity, space-like separated points (or events) in spacetime have a spacetime interval less than 0 (see sign convention). ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ...

• Requires that all the same formulas that apply to regular slower-than-light particles ("bradyons") also apply to tachyons. In particular the energy-momentum relation:

where p is the relativistic momentum of the bradyon and m is its rest mass still holds, along with the formula for the total energy of a particle:

which is interpreted to mean that the total energy of a particle (bradyon or tachyon) contains a contribution from the rest mass (the "rest mass-energy") and a contribution from the body's motion, the kinetic energy.

However the energy equation has, when v is larger than c, an "imaginary" denominator, since the value inside the square root is negative. Since the total energy must be real then the numerator must also be imaginary, i.e. the rest mass m must be imaginary, since a pure imaginary number divided by another pure imaginary number is a real number.

• A simple substitution for the mass yields an equivalent way of describing tachyons with real masses. Define m = i*z (where i² = − 1) and we get Einstein's energy-momentum relation to read:

With this approach the energy equation becomes:

And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a complex-valued mass may physically mean. Except, of course, when converting z back to m for interactions with non-tachyon particles

Both approaches are equivalent mathematically and have the same physical consequences. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. (For ordinary bradyonic matter, E increases with increasing velocity, becoming arbitrarily large as v approaches c, the speed of light.) Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, since to reach the barrier from either above or below requires infinite energy. A tardyon or bradyon is a particle that travels slower than light. ... In special relativity, the energy-momentum relation is an equation which relates energy, rest mass, and momentum of an object together: where c is the speed of light, E is total energy, m is rest mass, and p is momentum. ... This article is about momentum in physics. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... In mathematics, a square root (√) of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... In special relativity, the energy-momentum relation is an equation which relates energy, rest mass, and momentum of an object together: where c is the speed of light, E is total energy, m is rest mass, and p is momentum. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ... A line showing the speed of light on a scale model of Earth and the Moon, taking about 1⅓ seconds to traverse that distance. ...

Quantizing tachyons shows that they must be spinless particles which obey Fermi-Dirac statistics, i.e. tachyons are scalar fermions, a combination which is not permitted for ordinary particles.^[3] They also must be created and annihilated in pairs. In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... Fermi-Dirac distribution as a function of ε/μ plotted for 4 different temperatures. ... See scalar for an account of the broader concept also used in mathematics and computer science. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ...

The existence of such particles would pose intriguing problems in modern physics. For example, taking the formalisms of electromagnetic radiation and supposing a tachyon had an electric charge—as there is no reason to suppose a priori that tachyons must be either neutral or charged—then a charged tachyon must lose energy as Cherenkov radiation—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. However, as we have seen, reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite velocity at the same place in space. (At infinite velocity the two tachyons have no energy each and finite momentum of opposite direction, so no conservation laws are violated in their mutual annihilation. The time of annihilation is frame dependent.) Even an electrically neutral tachyon would be expected to lose energy via gravitational Cherenkov radiation, since it has a gravitational mass, and therefore increase in velocity as it travels, as described above. This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... The terms a priori and a posteriori are used in philosophy to distinguish between two different types of propositional knowledge. ... ÄŒerenkov radiation glowing in the core of a TRIGA reactor ÄŒerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... 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 that medium. ...

Modern interpretation

Quantum field theory

Causality

The property of causality is a fundamental principle of theoretical particle physics; tachyons, if they existed, would not violate causality, even if they interacted with ordinary (time-like) matter^[3]. Causality would be violated if a particle could send information into its own past, forming a so-called causal loop, leading to logical paradoxes such as the grandfather paradox. Tachyons are prevented from violating causality by the Feinberg reinterpretation principle^[3] which states that a negative-energy tachyon sent back in time in an attempt to violate causality can always be reinterpreted as a positive-energy tachyon travelling forward in time. This is because observers cannot distinguish between the emission and absorption of tachyons. For a tachyon, there is no distinction between the processes of emission and absorption, since there always exists a sub-light velocity reference frame shift that alters the temporal direction of the tachyon's world-line, which is not true for bradyons or photons. The attempt to detect a tachyon from the future (and violate causality) actually creates the same tachyon and sends it forward in time. (which is causal) A tachyon detector will seem to register tachyons in every possible detection model; in reality, the tachyon "detector" is spontaneously emitting tachyons. The effect of the reinterpretation principle on any tachyon "detector" is that any incoming tachyonic message would be lost against the tachyon background noise, which is an inevitable accompaniment of the uncontrollable emission. The counter-intuitive conclusion is that tachyons (if they existed) could be used to transmit energy-momentum, but they can't be used for communication. Thus there is no need to fall back on some quantum field theory form of the Novikov self-consistency principle to preserve causality. Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world. ... Quantum field theory (QFT) is the quantum theory of fields. ... In the context of special relativity, time-like separated points (or events) in spacetime have a spacetime interval greater than 0 (see sign convention). ... A predestination paradox, also called either a causal loop, or a causality loop and (less frequently) either a closed loop or closed time loop, is a paradox of time travel that is often used as a convention in science fiction. ... Look up paradox in Wiktionary, the free dictionary. ... The grandfather paradox is a paradox of time travel, first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (The Imprudent Traveller).[1] The paradox is this: Suppose a man traveled back in time and killed his biological grandfather before the latter met the... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... A tardyon or bradyon is a particle that travels slower than light. ... Spontaneous emission is the process by which a molecule in an excited state drops to the ground state, resulting in the creation of a photon. ... Quantum field theory (QFT) is the quantum theory of fields. ... This article or section does not cite its references or sources. ... Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ...

Other avenues of speculation involve parallel universes. One can imagine a scenario in which sending energy or information back in time causes history to diverge into two distinct tracks, one in which events reflect the altered information and one in which they do not. The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to every event to...

In the theory of general relativity, it is possible to construct spacetimes in which particles travel faster than the speed of light, relative to a distant observer. One example is the Alcubierre metric, another is of traversable wormholes. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally. For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ... This article is in need of attention from an expert on the subject. ... For other uses, see Wormhole (disambiguation). ... A line showing the speed of light on a scale model of Earth and the Moon, taking about 1â…“ seconds to traverse that distance. ...

Condensation

Main article: tachyon condensation

In quantum field theory, a tachyon is a quantum of a field—usually a scalar field—whose squared mass is negative, and is used to describe Spontaneous symmetry breaking: The existence of such a field implies the instability of the field vacuum; the field is at a local maximum rather than a local minimum of its potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to quantum fluctuations) will lead the field to roll down with exponentially increasing amplitudes: it will induce tachyon condensation. It is important to realize that once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons any more but rather have a positive mass-squared, such as the Higgs boson. 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. ... Quantum field theory (QFT) is the quantum theory of fields. ... It has been suggested that quartic interaction be merged into this article or section. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ... 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 Higgs boson, also known as the God particle, is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics. ...

Technically, the squared mass is the second derivative of the effective potential, at a point where the first derivative is zero. So for a tachyonic field the second derivative is negative, meaning that the effective potential is at a local maximum rather than a local minimum. Therefore this situation is unstable and the field will roll down to another point, stopping only at a local minimum, where its quanta have a non-negative squared mass, so that it is not tachyonic any longer ^[4]. This article does not cite any references or sources. ... This article does not cite any references or sources. ...

Since a tachyon's squared mass is negative, it formally has an imaginary mass. This is a special case of the general rule, where unstable massive particles are formally described as having a complex mass, with the real part being their mass in usual sense, and the imaginary part being the decay rate in natural units ^[4]. In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ... Many fundamental particles (including quarks and leptons) have finite lifetimes, after which they decay into lower-mass particles. ... In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ...

However, in quantum field theory, a particle (a "one-particle state") is roughly defined as a state which is constant over time, i.e. an eigenvalue of the Hamiltonian. An unstable particle is a state which is only approximately constant over time; However, it exists long enough to be measured. This means that if it is formally described as having a complex mass, then the real part of the mass must be greater than its imaginary part. If both parts are of the same magnitude, this is considered a resonance appearing in a scattering process rather than particle, since it does not exist long enough to be measured independently of the scattering process. In the case of a tachyon, the imaginary part of the mass is infinitely larger than the real part, and hence no concept of a particle can be attributed to it. Quantum field theory (QFT) is the quantum theory of fields. ... In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ... In physics, Hamiltonian has distinct but closely related meanings. ... Many fundamental particles (including quarks and leptons) have finite lifetimes, after which they decay into lower-mass particles. ... This article is about resonance in physics. ...

It is important to stress that even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality. Therefore information never moves faster than light.

Examples for tachyonic fields are all cases of spontaneous symmetry breaking. In condensed matter physics a notable example is Ferromagnetism; In particle physics the best known example is the Higgs mechanism in the standard model. Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. ... Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ... Thousands of 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. ... This box:      The Higgs mechanism, also called the Brout-Englert-Higgs mechanism, Higgs-Kibble mechanism or Anderson-Higgs mechanism, was proposed in 1964 by Robert Brout and Francois Englert [1], independently by Peter Higgs [2] and by Gerald Guralnik, C. R. Hagen, and Tom Kibble [3] following earlier work by... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ...

Tachyons in string theory

In string theory tachyons have the same interpretation as in quantum field theory. However, string theory can, at least in principle, not only describe the physics of tachyonic fields, but also predict whether such fields appear. This box:      String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. ... Quantum field theory (QFT) is the quantum theory of fields. ...

Tachyonic fields indeed arise in many versions of string theory. In general, string theory states that what we see as "particles"—electrons, photons, gravitons and so forth—are actually different vibrational states of the same underlying string. The mass of the particle can be deduced from the vibrations which the string exhibits; roughly speaking, the mass depends upon the "note" which the string sounds. Tachyons frequently appear in the spectrum of permissible string states, in the sense that some states have negative mass-squared, and therefore imaginary mass. If the tachyon appears as a vibrational mode of an open string, this signals an instability of the underlying D-brane system to which the string is attached. The system will then decay to a state of closed strings and/or stable D-branes. If the tachyon is a closed string vibrational mode, this indicates an instability in spacetime itself. Generally, it is not known what this system will decay to. However, if the closed string tachyon is localized around a spacetime singularity the endpoint of the decay process will often have the singularity resolved. This box:      String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. ... An open string is a one-dimensional fundamental object in string theory that has two end-points, and therefore is topologically equivalent to a line interval. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... A closed string is a one-dimensional fundamental object in string theory that has no end-points, and therefore is topologically equivalent to a circle. ...

Tachyons in fiction

Main article: Tachyons in fiction

Tachyons appear in many works of fiction. It has been used as a standby mechanism upon which many science fiction authors rely to establish faster-than-light communication, with or without reference to causality issues. The word tachyon has become widely recognized to such an extent that it can impart a science-fictional "sound" even if the subject in question has no particular relation to superluminal travel (compare positronic brain). Tachyons are exhibited in many novels of the late science fiction author, Frank Herbert. Primarily seen in the last installment of the Dune series, Chapterhouse Dune, as a tachyon net tries to enclose the no-ship. The hypothetical particles tachyons have inspired many occurrences of tachyons in fiction. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... A positronic brain is a fictional technological device, originally conceived by science fiction writer Isaac Asimov. ... Frank Patrick Herbert (October 8, 1920 – February 11, 1986) was a critically acclaimed and commercially successful American science fiction author. ... The fictional Dune universe, or Duniverse, is the political, scientific, and social setting of author Frank Herberts six-book Dune series of science fantasy novels. ... Chapterhouse Dune is a science fiction novel by Frank Herbert, last in his series of six Dune novels. ...

Tachyons are also central in Gregory Benford's seminal novel Timescape, where the main character tries to use them in order to warn people in his past about events that are in their future (but are past for him). Gregory Benford (born January 30, 1941 in Mobile, Alabama) is an American science fiction author and physicist who is on the faculty of the Department of Physics and Astronomy at the University of California, Irvine. ... For the Star Trek: The Next Generation episode, see Timescape (Star Trek). ...

Tachyons were discussed in the NBC series Journeyman as an explanation of the protagonist's (Dan Vasser) ability to travel back in time. For other uses, see Journeyman (disambiguation). ...

Other places it's been used:

• Doctor Who "The Leisure Hive" - A tachyon regeneration generator was used.
• Used in several episodes of Star Trek, in the 22nd century Starfleet vessels couldn't produce tachyon particles.
• Most powerful beam weapon in real-time strategy game Total Annihilation
• The X-Files "Synchrony" - An old man is capable of time travel through the use of tachyons.
• In the movie, Prince of Darkness (film) by John Carpenter, a tachyon beam is used to send communication of the world's impending danger from the future to characters of the movie in the form of dreams.
• K-PAX by Gene Brewer references tachyons in Prot's explanation of time travel.
• In Isaac Asimov's "Foundation" novels, the oft-used "Hyperspace-Jump" is explained to be a total conversion from normal matter to tachyons, allowing for instantaneous inter-spatial travel.^{[citation needed]}

This article is about the television series. ... This article is about the entire Star Trek franchise. ... A directed-energy weapon (DEW) is a type of weapon which emits energy in an aimed direction without the means of a projectile. ... Total Annihilation (abbr. ... The X-Files is an American Peabody, Golden Globe and Emmy Award-winning science fiction television series created by Chris Carter, which first aired on 10 September 1993, and ended on 19 May 2002. ... Prince of Darkness (also known as John Carpenters Prince of Darkness) is a 1987 American horror film directed, written and scored by John Carpenter. ... For other persons named John Carpenter, see John Carpenter (disambiguation). ... K-PAX is the name of the first novel in the K-PAX series by Gene Brewer and a film based on the series: K-PAX (1995) K-PAX (2001)— film K-PAX II: On a Beam of Light (2001) K-PAX III: Worlds of Prot (2002) K-PAX IV... Gene Brewer (b. ... Isaac Asimov (January 2?, 1920?[1] – April 6, 1992), pronounced , originally Исаак Озимов but now transcribed into Russian as Айзек Азимов [1], was a Russian-born American author and professor of biochemistry, a highly successful writer, best known for his works of science fiction and for his popular science books. ...

See also

• Tachyon condensation
• D-brane
• Poincaré group
• Superbradyon, another class of hypothetical superluminal particles
• Tachyonic Antitelephone
• Luxon

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. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... In physics and mathematics, the Poincaré group is the group of isometries of Minkowski spacetime. ... Superbradyons are a hypothetical class of superluminal particles. ... The tachyonic antitelephone is a hypothetical device that can be used to send signals into ones own past. ... A luxon is a particle that always travels at the speed of light. ...

References

Enchakkal Chandy George Sudarshan (September 16, 1931, Pallam, in Kottayam district of Kerala, India) is a prominent Indian-American physicist, author, and professor at the University of Texas at Austin. ... Enchakkal Chandy George Sudarshan (September 16, 1931, Pallam, in Kottayam district of Kerala, India) is a prominent Indian-American physicist, author, and professor at the University of Texas at Austin. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... Gerald Feinberg, (b. ...

External links

• The Faster Than Light (FTL) FAQ (from the Internet Archive)
• "Tachyon" from Eric Weisstein's World of Physics
• Tachyon entry from the Physics FAQ