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| {{Two other uses|hypothetical faster-than-light particles|quantum fields with imaginary mass|Tachyonic field|other uses}}
| | Hi at this time. Let me start by introducing the author, his name is Norris. [http://Data.Gov.uk/data/search?q=Alabama Alabama] has always been her the house. One of the things he loves most is ballet and is working to make it a task. After being out of his job in a great many he became a postal service worker. I'm not able at [https://Www.Flickr.com/search/?q=webdesign webdesign] but you might in order to check my website: http://archive.org/details/miley_cyrus_maxim<br><br>Feel free to surf to my web page :: [http://archive.org/details/miley_cyrus_maxim Miley Cyrus Maxim] |
| [[File:Tachyon04s.gif|thumb|250px|alt=Alt text|Because a tachyon would always move faster than light, it would not be possible to 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]], shown only in one moment of time. This double image effect is most prominent for an observer located directly in the path of a superluminal 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 sphere as it approaches. The left-hand reddish image is formed from red-shifted light that leaves the sphere after it passes the observer. Because 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 splits into two—one of the arriving sphere (to the right) and one of the departing sphere (to the left).]]
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| A '''tachyon''' {{IPAc-en|ˈ|t|æ|k|i|.|ɒ|n}} or '''tachyonic particle''' is a hypothetical [[particle]] that always moves [[faster-than-light|faster than light]].Theoretical propositions of Tachyons were done by [[George Sudarshan]] in his 1962 paper. He was the first to propose the existence of tachyons. The word comes from the {{lang-el|[[Wiktionary:ταχύς|ταχύς]]}} or ''tachys'', meaning "swift, quick, fast, rapid", and was coined by [[Gerald Feinberg]].<ref name="Feinberg67"/> Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.<ref name=Randall/><ref name=Tipler/> If such particles did exist, they could be used to build a [[tachyonic antitelephone]] and send signals faster than light, which (according to [[special relativity]]) would lead to violations of [[causality (physics)|causality]].<ref name=Tipler/> Potentially consistent theories that allow faster-than-light particles include those that break [[Lorentz invariance]], the symmetry underlying special relativity, so that the speed of light is not a barrier.
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| In the 1967 paper that coined the term,<ref name="Feinberg67"/> Feinberg proposed that tachyonic particles could be quanta of a [[Quantum field theory|quantum field]] with negative squared mass. However, it was soon realized that excitations of such [[Tachyonic field|imaginary mass fields]] do ''not'' in fact propagate faster than light,<ref name="susskind"/> and instead represent an instability known as [[tachyon condensation]].<ref name=Randall/> Nevertheless, negative squared mass fields are commonly referred to as "tachyons",<ref name=Sen/> and in fact have come to play an [[Tachyonic_field#Importance_in_physics|important role in modern physics]].
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| Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In 3 instances however (OPERA PROJECT, CERN, T2K) Neutrinos were measured traveling at speeds faster than that of light. The publications however were mostly met with doubt due to various possible errors in the measurements. It is important to note that many physicists do infer a possible link between the properties of neutrinos and theoretical tachyons. <ref name="Feinberg">{{cite book |last=Feinberg |first=G. |year=1997 |chapter=Tachyon |title=[[Encyclopedia Americana]] |publisher=[[Grolier]] |volume=26 |page=210 |isbn=}}</ref>
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| == Tachyons in relativistic theory ==
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| In [[special relativity]], a faster-than-light particle would have [[space-like]] [[four-momentum]],<ref name=Feinberg67 /> in contrast to ordinary particles that have [[time-like]] [[four-momentum]]. It would also have [[imaginary number|imaginary]] mass. Being constrained to the [[spacelike]] portion of the energy–momentum graph, it could not slow down to subluminal speeds.<ref name="Feinberg67"/>
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| === Mass ===
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| In a [[Lorentz invariant]] theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "[[bradyon]]s" in discussions of tachyons) must also apply to tachyons. In particular the [[energy–momentum relation]]:
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| :<math>E^2 = p^2c^2 + m^2c^4 \;</math>
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| (where '''p''' is the relativistic [[momentum]] of the bradyon and '''m''' is its [[rest mass]]) should still apply, along with the formula for the total energy of a particle:
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| :<math>E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}.</math>
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| This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest mass–energy") and a contribution from its motion, the kinetic energy.
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| When ''v'' is larger than ''c'', the denominator in the equation for the energy is [[imaginary number|"imaginary"]], as the value under the [[square root|radical]] is negative. Because the total [[energy]] must be [[real number|real]], the numerator must ''also'' be imaginary: i.e. the [[rest mass]] '''m''' must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.
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| === Speed ===
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| One curious effect is that, unlike ordinary particles, the speed of a tachyon ''increases'' as its energy decreases. In particular, <math> E </math> approaches zero when <math> v </math> approaches infinity. (For ordinary [[Bradyon|bradyonic matter]], ''E'' increases with increasing speed, 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'', because infinite energy is required to reach the barrier from either above or below. | |
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| As noted by [[Einstein]], [[Richard Chace Tolman|Tolman]], and others, [[special relativity]] implies that faster-than-light particles, if they existed, [[Tachyonic antitelephone|could be used to communicate backwards in time]].<ref name=Benford/>
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| === Neutrinos ===
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| In 1985 Chodos et al. proposed that [[neutrino]]s can have a tachyonic nature.<ref name=Chodos/> The possibility of standard model particles moving at superluminal speeds can be modeled using [[Lorentz invariance]] violating terms, for example in the [[Standard-Model Extension]].<ref name=Colladay/><ref>
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| {{cite journal
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| |last1=Colladay |first1=D.
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| |last2=Kostelecky |first2=V. A.
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| |year=1998
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| |title=Lorentz-Violating Extension of the Standard Model
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| |journal=[[Physical Review D]]
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| |volume=58 |issue=11 |pages=116002
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| |arxiv=hep-ph/9809521
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| |bibcode=1998PhRvD..58k6002C
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| |doi=10.1103/PhysRevD.58.116002
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| }}</ref><ref>
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| {{cite journal
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| |last=Kostelecky |first=V. A.
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| |year=2004
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| |title=Gravity, Lorentz Violation, and the Standard Model
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| |journal=[[Physical Review D]]
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| |volume=69 |issue=10 |pages=105009
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| |arxiv=hep-th/0312310
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| |bibcode=2004PhRvD..69j5009K
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| |doi=10.1103/PhysRevD.69.105009
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| }}</ref> In this framework, neutrinos experience [[Lorentz-violating neutrino oscillations|Lorentz-violating oscillations]] and can travel faster than light at high energies. This proposal was strongly criticized.<ref>
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| R. J. Hughes and G. J. Stephenson Jr., ''Against tachyonic neutrinos'', Phys. Lett. B 244, 95–100 (1990).
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| </ref>
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| === Cherenkov radiation ===
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| A tachyon with an electric charge would lose energy as [[Čerenkov radiation|Cherenkov radiation]]<ref>
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| {{cite web
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| |last1=Bock |first1=R. K.
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| |date=9 April 1998
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| |title=Cherenkov Radiation
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| |url=http://rd11.web.cern.ch/RD11/rkb/PH14pp/node26.html
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| |work=The Particle Detector BriefBook
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| |publisher=[[CERN]]
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| |accessdate=2011-09-23
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| }}</ref>—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 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 speed at the same place in space. (At infinite speed 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.)
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| Even an electrically neutral tachyon would be expected to lose energy via gravitational [[Cherenkov radiation]], because it has a gravitational mass, and therefore increase in speed as it travels, as described above. If the tachyon interacts with any other particles, it can also radiate Cherenkov energy into those particles. Neutrinos interact with the other particles of the [[Standard model of particle physics|Standard Model]], and Andrew Cohen and [[Sheldon Glashow]] recently used this to argue that the [[faster-than-light neutrino anomaly]] cannot be explained by making neutrinos propagate faster than light, and must instead be due to an error in the experiment.<ref name=Cohen>{{cite journal |author=Cohen, Andrew G. and Glashow, Sheldon L.|title= Pair Creation Constrains Superluminal Neutrino Propagation | journal= Phys.Rev.Lett.|
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| volume = "107",|
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| pages = "181803",|
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| doi = 10.1103/PhysRevLett.107.181803,|
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| year = "2011",|
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| eprint = "1109.6562",|
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| archiveprefix = "arXiv",|
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| primaryclass = "hep-ph",}}</ref>
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| === Causality ===
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| [[causality (physics)|Causality]] is a fundamental principle of physics. If tachyons can transmit information faster than light, then according to relativity they violate causality, leading to logical paradoxes of the [[Grandfather paradox|"kill your own grandfather"]] type. This is often illustrated with thought experiments such as the [[Tachyonic antitelephone|"tachyon telephone paradox"]]<ref name=Benford/> or "logically pernicious self-inhibitor."<ref name=Fitzgerald/>
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| The problem can be understood in terms of the [[relativity of simultaneity]] in special relativity, which says that different [[inertial frame of reference|inertial reference frames]] will disagree on whether two events at different locations happened "at the same time" or not, and they can also disagree on the order of the two events (technically, these disagreements occur when [[Spacetime#Spacetime intervals|spacetime interval]] between the events is 'space-like', meaning that neither event lies in the future [[light cone]] of the other).<ref name="Jarrell">
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| {{cite web
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| |last1=Mark |first1=J.
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| |date=
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| |title=The Special Theory of Relativity
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| |url=http://www.physics.uc.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap11/chap11.pdf
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| |work=
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| |pages=7–11
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| |publisher=[[University of Cincinnati]]
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| |accessdate=2006-10-27
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| |archiveurl=http://web.archive.org/web/20060913173236/http://www.physics.uc.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap11/chap11.pdf
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| |archivedate=2006-09-13
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| }}</ref>
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| If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event.<ref name="Jarrell"/> However, in the case of a hypothetical signal moving faster than light, there would always be some frames in which the signal was received before it was sent, so that the signal could be said to have moved backwards in time. Because one of the two fundamental [[postulates of special relativity]] says that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backwards in time in any one frame, it must be possible in all frames. This means that if observer A sends a signal to observer B which moves faster than light in A's frame but backwards in time in B's frame, and then B sends a reply which moves faster than light in B's frame but backwards in time in A's frame, it could work out that A receives the reply before sending the original signal, challenging causality in ''every'' frame and opening the door to severe logical paradoxes.<ref name=Gron/> Mathematical details can be found in the [[tachyonic antitelephone]] article, and an illustration of such a scenario using [[Minkowski diagram|spacetime diagrams]] can be found in ''Baker, R. (2003)''<ref>.
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| {{cite web
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| |last=Baker |first1=R.
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| |date=12 September 2003
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| |title=Relativity, FTL and causality
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| |url=http://www.theculture.org/rich/sharpblue/archives/000089.html
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| |work=Sharp Blue
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| |publisher=
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| |accessdate=2011-09-23
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| }}</ref>
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| ====Reinterpretation principle====
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| The '''reinterpretation principle'''<ref name="Feinberg67"/><ref name=Gron/><ref name="sudarshan62"/> asserts that a tachyon sent ''back'' in time can always be ''reinterpreted'' as a tachyon traveling ''forward'' in time, because observers cannot distinguish between the emission and absorption of tachyons. The attempt to ''detect'' a tachyon ''from'' the future (and violate causality) would actually ''create'' the same tachyon and send it ''forward'' in time (which is causal).
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| However, this principle is not widely accepted as resolving the paradoxes.<ref name=Benford/><ref name=Gron/><ref name=Recami/> Instead, what would be required to avoid paradoxes is that unlike any known particle, tachyons do not interact in any way and can never be detected or observed, because otherwise a tachyon beam could be modulated and used to create an anti-telephone<ref name=Benford/> or a "logically pernicious self-inhibitor".<ref name=Fitzgerald/> All forms of energy are believed to interact at least gravitationally, and many authors state that superluminal propagation in Lorentz invariant theories always leads to causal paradoxes.<ref name=Barcelo/><ref name=Arkani/>
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| == Fundamental models ==
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| In modern physics, all fundamental particles are regarded as excitations of [[quantum field theory|quantum fields]]. There are several distinct ways in which tachyonic particles could be embedded into a field theory.
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| === Fields with imaginary mass ===
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| {{main|Tachyonic field}}
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| In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with imaginary mass.<ref name="Feinberg67" /> Because the [[group velocity]] for such a field is superluminal, naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the negative mass represents an instability to [[tachyon condensation]], and all excitations of the field propagate subluminally and are consistent with [[Causality (physics)|causality]].<ref name="susskind"/> Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.<ref name=Randall/><ref name=Sen/><ref name=Greene/><ref name=Kutasov/><ref name=NOVA/><ref name=Gibbons/>
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| Tachyonic fields play an important role in modern physics. Perhaps the most famous is the [[Higgs boson]] of the [[Standard model of particle physics|Standard Model of particle physics]], which—in its [[Tachyon condensation|uncondensed]] phase—has an imaginary mass. In general, the phenomenon of [[spontaneous symmetry breaking]], which is closely related to [[tachyon condensation]], plays a very important role in many aspects of theoretical physics, including the [[Ginzburg–Landau theory|Ginzburg–Landau]] and [[BCS theory|BCS]] theories of superconductivity. Another example of a [[tachyonic field]] is the tachyon of [[bosonic string theory]].<ref name=Greene/><ref name=NOVA/><ref>J. Polchinski, ''String Theory'', Cambridge University Press, Cambridge, UK (1998)</ref>
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| === Lorentz violating theories ===
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| In theories that do not respect [[Lorentz invariance]] the speed of light is not (necessarily) a barrier, and particles can travel faster than the speed of light without infinite energy or causal paradoxes.<ref name=Barcelo/> A class of field theories of that type are the so-called [[Standard-Model Extension|Standard Model extensions]]. However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.<ref name=Glashow2>{{cite journal|
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| author = Glashow, Sheldon Lee|
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| title = Atmospheric neutrino constraints on Lorentz violation|
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| year = 2004|
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| eprint = "hep-ph/0407087"|
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| archiveprefix = "arXiv"|
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| primaryclass = "hep-ph"}}</ref><ref name=Coleman/>
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| === Fields with non-canonical kinetic term ===
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| By modifying the kinetic energy of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally.<ref name="susskind" /><ref name=Arkani/> However, such theories in general do not have a well-defined Cauchy problem (for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.
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| == History ==
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| As mentioned above, the term "tachyon" was coined by [[Gerald Feinberg]] in a 1967 paper titled "Possibility of Faster-Than-Light Particles".<ref name="Feinberg67"/> Feinberg studied the kinematics of such particles according to [[special relativity]]. In his paper he also introduced [[Tachyonic field|fields with imaginary mass]] (now also referred to as "tachyons") in an attempt to understand the microphysical origin such particles might have.
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| The first hypothesis regarding faster-than-light particles is sometimes attributed to German physicist [[Arnold Sommerfeld]] in 1904,<ref name=Sommerfeld/> and more recent discussions happened in 1962<ref name="sudarshan62"/> and 1969.<ref name="sudarshan69"/>
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| == In fiction ==
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| {{Main|Tachyons in fiction}}
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| Tachyons have appeared in many works of fiction. They have 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 connotation even if the subject in question has no particular relation to superluminal travel (a form of [[technobabble]], akin to ''[[positronic brain]]'').
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| == See also ==
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| * [[Lorentz-violating neutrino oscillations]]
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| * [[Massless particle]]
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| * [[Retrocausality]]
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| * [[Tachyonic antitelephone]]
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| * [[Wheeler-Feynman absorber theory]]
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| == References ==
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| {{Reflist|refs=
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| <ref name=Arkani>Allan Adams, Nima Arkani-Hamed, Sergei Dubovsky, Alberto Nicolis, Riccardo Rattazzi, "Causality, Analyticity and an
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| IR Obstruction to UV Completion," JHEP 0610 (2006) 014 [http://arxiv.org/abs/hep-th/0602178].</ref>
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| <ref name=Barcelo>Carlos Barceló, Stefano Finazzi, Stefano Liberati, "On the impossibility of superluminal travel: the warp drive lesson", Second prize of the 2009 FQXi essay contest "What is Ultimately Possible in Physics?", p.8: "As a matter of fact, any mechanism for superluminal travel can be easily turned into a time machine and hence lead to the typical causality paradoxes..." [http://arxiv.org/abs/1001.4960]</ref> | |
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| <ref name=Benford>
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| {{cite journal
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| |last1=Benford |first1=G.
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| |last2=Book |first2=D.
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| |last3=Newcomb |first3=W.
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| |year=1970
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| |title=The Tachyonic Antitelephone
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| |journal=[[Physical Review D]]
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| |volume=2 |issue=2 |pages=263
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| |bibcode=1970PhRvD...2..263B
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| |doi=10.1103/PhysRevD.2.263
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| }}</ref>
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| <ref name=Chodos>
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| {{cite journal
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| |last1=Chodos |first1=A.
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| |year=1985
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| |title=The Neutrino as a Tachyon
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| |journal=[[Physics Letters B]]
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| |volume=150 |issue=6 |page=431
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| |bibcode=1985PhLB..150..431C
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| |doi= 10.1016/0370-2693(85)90460-5
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| }}</ref>
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| <ref name=Coleman>{{cite journal|
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| author = Coleman, Sidney R. and Glashow, Sheldon L.|
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| title = High-energy tests of Lorentz invariance|
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| journal = Phys.Rev.|
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| volume = D59|
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| pages = 116008|
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| doi = 10.1103/PhysRevD.59.116008|
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| year = 1999|
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| arxiv = hep-ph/9812418|bibcode = 1999PhRvD..59k6008C }}</ref>
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| <ref name=Colladay>
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| {{cite journal
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| |last1=Colladay |first1=D.
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| |last2=Kostelecky |first2=V. A.
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| |year=1997
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| |title=CPT Violation and the Standard Model
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| |journal=[[Physical Review D]]
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| |volume=55 |issue=11 |pages=6760–6774
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| |arxiv=hep-ph/9703464
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| |bibcode=1997PhRvD..55.6760C
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| |doi=10.1103/PhysRevD.55.6760
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| }}</ref>
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| <ref name="Feinberg67">
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| {{cite journal
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| |last=Feinberg |first=G.
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| |year=1967
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| |title=Possibility of Faster-Than-Light Particles
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| |journal=[[Physical Review]]
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| |volume=159 |issue=5 |pages=1089–1105
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| |bibcode=1967PhRv..159.1089F
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| |doi=10.1103/PhysRev.159.1089
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| }} See also Feinberg's later paper: Phys. Rev. D 17, 1651 (1978)</ref>
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| <ref name=Fitzgerald>P. Fitzgerald, "Tachyons, Backward Casuation, and Freedom," PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1970 (1970), pp. 425–426: "A more powerful argument to show that retrocausal tachyons involve an intolerable conceptual difficulty is illustrated by the Case of the Logically Pernicious Self-Inhibitor..."</ref>
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| <ref name=Gibbons>G. W. Gibbons,
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| "Cosmological evolution of the rolling tachyon,"
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| Phys. Lett. B '''537''', 1 (2002)</ref>
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| <ref name=Greene>Brian Greene, ''The Elegant Universe'', Vintage Books (2000)</ref>
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| <ref name=Gron>
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| {{cite book
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| |last1=Grøn |first1=Ø.
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| |last2=Hervik |first2=S.
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| |year=2007
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| |title=Einstein's General Theory of Relativity: With Modern Applications in Cosmology
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| |url=http://books.google.com/?id=IyJhCHAryuUC&lpg=PR1&pg=PA39#v=onepage&q
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| |pages=39
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| |publisher=[[Springer (publisher)|Springer]]
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| |isbn=978-0-387-69199-2
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| |quote=The tachyon telephone paradox cannot be resolved by means of the reinterpretation principle.
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| }}</ref>
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| <ref name=NOVA>NOVA, "The Elegant Universe", PBS television special, http://www.pbs.org/wgbh/nova/elegant/</ref>
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| <ref name=Kutasov>{{cite journal |
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| author = Kutasov, David and Marino, Marcos and Moore, Gregory W. |
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| title = Some exact results on tachyon condensation in string
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| field theory |
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| journal = JHEP|
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| volume = 0010|
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| pages = 045|
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| year = 2000|
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| eprint = hep-th/0009148|
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| archiveprefix = arXiv|
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| primaryclass = hep-th|
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| reportnumber = "EFI-2000-32, RUNHETC-2000-34"}}</ref>
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| <ref name=Randall>Lisa Randall, ''Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions'', p.286: "People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature."</ref>
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| <ref name=Recami>Erasmo Recami, Flavio Fontana, Roberto Garavaglia, "About Superluminal motions and Special Relativity: A Discussion of some recent Experiments, and the solution of the Causal Paradoxes", International Journal of Modern Physics A15 (2000) 2793–2812, abstract: "it is possible...to solve also the known causal paradoxes, devised for "faster than light" motion, although '''this is not widely recognized yet'''." [emphasis added].</ref>
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| <ref name=Sen>A. Sen, "Rolling tachyon,"
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| JHEP '''0204''', 048 (2002). [http://inspirehep.net/search?ln=en&ln=en&p=t+tachyon&of=hb&action_search=Search&sf=&so=d&rm=citation&rg=25&sc=0 Cited 720 times as of 2/2012.]</ref>
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| <ref name=Sommerfeld>{{cite journal
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| |last=Sommerfeld |first=A.
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| |title=Simplified deduction of the field and the forces of an electron moving in any given way
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| |journal=Knkl. Acad. Wetensch
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| |volume=7
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| |pages=345–367
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| |year=1904
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| }}</ref>
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| <ref name="sudarshan62">
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| {{cite journal
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| |last1=Bilaniuk |first1=O.-M. P.
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| |last2=Deshpande |first2=V. K.
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| |last3=Sudarshan |first3=E. C. G.
| |
| |year=1962
| |
| |title='Meta' Relativity
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| |journal=[[American Journal of Physics]]
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| |volume=30 |issue=10 |pages=718
| |
| |bibcode=1962AmJPh..30..718B
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| |doi=10.1119/1.1941773
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| }}</ref>
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| | |
| <ref name="sudarshan69">
| |
| {{cite journal
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| |last=Bilaniuk |first=O.-M. P.
| |
| |last2=Sudarshan |first2=E. C. G.
| |
| |year=1969
| |
| |title=Particles beyond the Light Barrier
| |
| |journal=[[Physics Today]]
| |
| |volume=22 |issue=5 |pages=43–51
| |
| |bibcode= 1969PhT....22e..43B
| |
| |doi=10.1063/1.3035574
| |
| }}</ref>
| |
| | |
| <ref name="susskind">{{cite journal
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| |volume = 182
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| |journal = Phys. Rev.
| |
| |last1 = Aharonov |first1 = Y.
| |
| |last2 = Komar |first2 = A.
| |
| |last3= Susskind |first3 = L.
| |
| |title = Superluminal Behavior, Causality, and Instability
| |
| |year = 1969
| |
| |doi = 10.1103/PhysRev.182.1400
| |
| |issue = {5},
| |
| |publisher = American Physical Society
| |
| |pages = 1400–1403|bibcode = 1969PhRv..182.1400A }}</ref>
| |
| | |
| <ref name=Tipler>{{cite book| last1 = Tipler| first1 = Paul A.|last2 = Llewellyn| first1 = Ralph A.| title = Modern Physics| publisher = W.H. Freeman & Co.| year = 2008| edition = 5<sup>th</sup>| location = New York, NY | isbn = 978-0-7167-7550-8| page = 54|quote = ... so existence of particles v > c ... Called tachyons ... would present relativity with serious ... problems of infinite creation energies and causality paradoxes.}}</ref> Tachyons could be [[Tachyonic antitelephone|used to send signals faster than light]], and (according to [[special relativity]]) this leads to violations of [[causality (physics)|causality]].<ref name=Tipler/>
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| }}
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| == External links ==
| |
| {{Wiktionary}}
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| {{Commons category}}
| |
| * [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]])
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| * {{ScienceWorld|title=Tachyon|urlname= physics/Tachyon}}
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| * [http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html Tachyon] entry from the ''Physics FAQ''
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| {{particles}}
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| [[Category:Faster-than-light travel]]
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| [[Category:Hypothetical particles]]
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| [[Category:String theory]]
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| [[Category:Tachyons]]
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| [[Category:Time travel]]
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