Tachyon
31296
225947940
2008-07-16T04:03:12Z
WilliamKF
156790
MOS
{{quantum field theory}}
A '''tachyon''' (from the [[Greek language|Greek]] {{polytonic|ταχυόνιον}}, ''takhyónion'', from {{polytonic|ταχύς}}, ''takhýs'', i.e. swift, fast) is any hypothetical [[particle physics|particle]] that travels at [[Faster-than-light|superluminal]] [[speed]]. The first description of tachyons is attributed to German physicist [[Arnold Sommerfeld]]; however, it was [[George Sudarshan]], Olexa-Myron Bilaniuk <ref name="sudarshan69">{{cite journal | author = Bilaniuk | coauthors = [[George Sudarshan]] | title = Particles beyond the Light Barrier | journal = Physics Today | month = May | year = 1969}}</ref><ref name="sudarshan62">{{cite journal | author = Bilaniuk | coauthors = Deshpande, [[George Sudarshan]] | title = Meta Relativity | journal = American Journal of Physics | year = 1962 | pages = 718ff | volume = 30 | doi = 10.1119/1.1941773 <!--Retrieved from CrossRef by DOI bot-->}}</ref>, Vijay Deshpande <ref name="sudarshan62">{{cite journal | author = Bilaniuk | coauthors = Deshpande, [[George Sudarshan]] | title = Meta Relativity | journal = American Journal of Physics | year = 1962 | pages = 718ff | volume = 30 | doi = 10.1119/1.1941773 <!--Retrieved from CrossRef by DOI bot-->}}</ref> and [[Gerald Feinberg]]<ref name="feinberg67">{{cite journal | first = Gerald | last = Feinberg | authorlink = Gerald Feinberg | title = Possibility of Faster-Than-Light Particles | journal = Physical Review | volume = 159 | year = 1967 | pages = 1089–1105 | doi = 10.1103/PhysRev.159.1089}}</ref> (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 number|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 (physics)|causality]] in [[special relativity]] and not allow transmission of information faster than light,<ref name=feinberg67/> as has been written in many works of science fiction.
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 [[tachyon condensation|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.<ref name = "Peskin">Michael E. Peskin and Daniel V. Schroeder (1995). ''An Introduction to Quantum Field Theory''Perseus books publishing.</ref> 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]])<ref name = "Peskin"/> and even if they existed (by Feinberg's analysis<ref name="feinberg67"/>) they wouldn't be able to transmit information (also by Feinberg's analysis<ref name="feinberg67"/>). Despite the theoretical arguments against the existence of tachyon particles, experimental searches have been conducted to [[scientific method|test the assumption]] against their existence; however, no experimental evidence for or against the existence of tachyon particles has been found. <ref name="Feinberg">"Feinberg, Gerald (1997). "Tachyon" article in ''Encyclopedia Americana'', Grolier Incorporated, v. 26, p.210.</ref>
== Basic properties ==
[[Image:Tachion04b.jpg|thumb|200px|right| 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 effect|doppler shift]]ed 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 [[redshift]]ed 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).<br>
[[Image:Tachyon-200px.gif]]<br>
[[:Image:Tachyon04s.gif|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:
*Requires that all the same formulas that apply to regular slower-than-light particles ("[[bradyon]]s") also apply to tachyons. In particular the [[energy-momentum relation]]:
::<math>E^2 = p^2c^2 + m^2c^4 \;</math>
: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:
::<math>E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}.</math>
: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 number|"imaginary"]] denominator, since the value inside the [[square root]] is negative. Since the total [[energy]] must be [[real number|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 <math>i^2 = -1</math>) and we get Einstein's [[energy-momentum relation]] to read:
::<math>E^2 + z^2c^4 = p^2c^2 \;</math>
:With this approach the energy equation becomes:
::<math>E = \frac{zc^2}{\sqrt{\frac{v^2}{c^2} -1}}.</math>
:And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a [[complex number|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.
Quantizing tachyons shows that they must be [[Spin (physics)|spinless]] particles which obey [[Fermi-Dirac statistics]], i.e. tachyons are [[Scalar fermion]]s, a combination which is not permitted for ordinary particles.<ref name="feinberg67"/> They also must be created and annihilated in pairs.
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 and a posteriori (philosophy)|a priori]]'' that tachyons must be either neutral or charged—then a charged tachyon must lose energy as [[Čerenkov radiation|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.
==Modern interpretation==
===Quantum field theory===
====Causality====
The property of [[causality (physics)|causality]] is a fundamental principle of [[theoretical physics|theoretical]] [[quantum field theory|particle physics]]; tachyons, if they exist, would ''not'' violate causality, even if they interacted with ordinary ([[time-like]]) matter<ref name="feinberg67"/>. Causality ''would'' be violated ''if'' a particle could send information into its own past, forming a so-called [[Predestination paradox|causal loop]], leading to logical [[paradox]]es such as the [[grandfather paradox]]. Tachyons are prevented from violating causality by the '''Feinberg reinterpretation principle'''<ref name="feinberg67"/> 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 [[bradyon]]s 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 [[spontaneous emission|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 (physics)|causality]].
Other avenues of speculation involve [[Many-worlds interpretation|parallel universe]]s. 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.
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 [[Wormhole|traversable wormholes]]. However, these are not tachyons in the above sense, as they do not exceed the [[speed of light]] locally.
====Condensation====
{{main|tachyon condensation}}
In [[quantum field theory]], a tachyon is a quantum of a field—usually a [[Scalar field theory|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 [[exponential growth|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]].
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 <ref name = "Peskin"/>.
Since a tachyon's squared mass is negative, it formally has an [[Imaginary number|imaginary]] mass. This is a special case of the general rule, where unstable massive particles are formally described as having a [[complex number|complex]] mass, with the real part being their mass in usual sense, and the imaginary part being the [[Particle decay#Decay rate|decay rate]] in [[natural units]] <ref name = "Peskin"/>.
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 [[Particle decay|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.
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]].
==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.
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 string]]s 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.
==Tachyons in fiction==
{{main|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<!--Many? Which ones? --> novels of the late science fiction author, [[Frank Herbert]]. Primarily seen in the last installment of the ''[[Dune universe|Dune]]'' series, ''[[Sandworms of Dune]]'', as a tachyon net tries to enclose the no-ship.
Tachyons are also central in ''[[Gregory Benford|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).
Tachyons were discussed in the NBC series ''[[Journeyman (TV series)|Journeyman]]'' as an explanation of the protagonist's (Dan Vasser) ability to travel back in time.
Tachyons are extensively used in the television series ''[[Star Trek]]''. In Star Trek the tachyon is used mostly in situations regarding space-time anomalies but there is no real consistency to the use of the tachyon. An "inverted tachyon" is also quite common in Star Trek. Although the tachyon is most extensively used in the later era of Star Trek (''[[TNG]]'', ''[[VOY]] and ''[[DS9]]'').
Other places it's been used:
* ''[[Doctor Who]]'' "The Leisure Hive" - A tachyon regeneration generator was used.
* Tachyons are the only weakness of [[Doctor Manhattan]] in the [[Watchmen]] comic book series, as his precognitive abilities can be disrupted by them.
* Most powerful [[Directed-energy weapon|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.{{Fact|date=April 2008}}
* In the video game "[[Dino Stalker]]", each level must be completed before time runs out. The player can collect tachyons which temprarily stop the clock for either 5 (Purple) or 30 (Blue) seconds. Tachyons can be found floating above the ground or by destroying the in game environment.
* ''[[Red Dwarf]]'' "Holoship" - Kryten says that the holoship has no mass or volume and is able to travel as super-light particles (tachyons).
* In ''[[Fantastic Four]]'' "Rise of the Silver Surfer", Reed Richards suggests using a tachyon pulse to separate the Silver Surfer from his surf board.
== See also ==
* [[Tachyon condensation]]
* [[D-brane]]
* [[Poincaré group]]
* [[Superbradyon]], another class of hypothetical superluminal particles
* [[Tachyonic Antitelephone]]
* [[Massless particle]]
== References ==
{{reflist}}
== External links ==
* [http://web.archive.org/web/20001121064300/www.public.iastate.edu/~physics/sci.physics/faq/FTL.html The Faster Than Light (FTL) FAQ] (from the [[Internet Archive]])
* [http://scienceworld.wolfram.com/physics/Tachyon.html "Tachyon"] from [[Eric Weisstein]]'s ''World of Physics''
* [http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html Tachyon] entry from the ''Physics FAQ''
{{particles}}
[[Category:String theory]]
[[Category:Subatomic particles]]
[[Category:Time travel]]
[[Category:Faster-than-light travel]]
[[Category:Hypothetical particles]]
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