Wikipedia

Tachyon

This article is about hypothetical faster-than-light particles. For quantum fields with imaginary mass, seeTachyonic field.For other uses, seeTachyon (disambiguation).

Atachyon(/ˈtækiɒn/) ortachyonic particleis a hypotheticalparticlethat always travelsfaster than light.Physicistsbelieve that faster-than-light particles cannot exist because they are inconsistent with the knownlaws of physics.[1][2]If such particles did exist they could be used to send signals faster than light and into the past. According to thetheory of relativitythis would violatecausality,leading tological paradoxessuch as thegrandfather paradox.[1]Tachyons would exhibit the unusual property of increasing in speed as their energy decreases, and would require infinite energy to slow to the speed of light. No verifiable experimental evidence for the existence of such particles has been found.

Tachyon
ClassificationElementary particle
StatusHypothetical
Theorized1967

In the 1967 paper that coined the term,Gerald Feinbergproposed that tachyonic particles could be made fromexcitationsof aquantum fieldwithimaginary mass.[3]However, it was soon realized that Feinberg's model did not in fact allow forsuperluminal(faster-than-light) particles or signals and that tachyonic fields merely give rise to instabilities, not causality violations.[4]The termtachyonic fieldrefers to imaginary mass fields rather than to faster-than-light particles.[2][5]

Etymology

edit

The termtachyoncomes from the Greek:ταχύς,tachus,meaningswift.[6]: 515 The complementary particle types are calledluxons(which always move at thespeed of light) andbradyons(which always move slower than light); both of these particle types are known to exist.

History

edit

The first hypothesis regarding faster-than-light particles is sometimes attributed to physicistArnold Sommerfeld,who, in 1904, named them "meta-particles".[7][8]The possibility of existence of faster-than-light particles was also proposed byLev Yakovlevich Shtrum[ru]in 1923.[9]

The termtachyonwas coined byGerald Feinbergin a 1967 paper titled "Possibility of faster-than-light particles".[3]He had been inspired by the science-fiction story "Beep" byJames Blish.[10]Feinberg studied the kinematics of such particles according tospecial relativity.In his paper, he also introducedfields with imaginary mass(now also referred to as tachyons) in an attempt to understand the microphysical origin such particles might have.

Oleksa-Myron Bilanuik, Vijay Deshpande andE. C. George Sudarshandiscussed this more recently in their 1962 paper on the topic[11]and in 1969.[12]

In September 2011, it was reported that atau neutrinohad traveled faster than the speed of light; however, later updates from CERN on theOPERA experimentindicate that thefaster-than-light readingswere due to a faulty element of the experiment's fibre optic timing system.[13]

Special relativity

edit

Inspecial relativity,a faster-than-light particle would havespacelikefour-momentum,[3]unlike ordinary particles that havetime-likefour-momentum.While some theories suggest the mass of tachyons isimaginary,modern formulations often consider their mass to be real,[14][15][16]with redefined formulas for momentum and energy. Additionally, since tachyons are confined to thespacelikeportion of the energy–momentum graph, they cannot slow down to subluminal (slower-than-light) speeds.[3]

Mass

edit
Main articles:Mass § Tachyonic particles and imaginary (complex) mass,andTachyonic field

In aLorentz invarianttheory, the same formulas that apply to ordinary slower-than-light particles (sometimes called bradyons in discussions of tachyons) must also apply to tachyons. In particular, theenergy–momentum relation:

(wherepis the relativisticmomentumof the bradyon andmis itsrest mass) should still apply, along with the formula for the total energy of a particle:

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. When(the particle's velocity) is larger than(the speed of light), thedenominatorin the equation for the energy isimaginary,as the value under the square root is negative. Because the totalenergyof the particle must bereal(and not acomplexor imaginary number) in order to have any practical meaning as a measurement, the numerator mustalsobe imaginary (i.e. the rest massmmust be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number).

In some modern formulations of the theory, the mass of tachyons is regarded as real.[14][15][16]

Speed

edit

One curious effect is that, unlike ordinary particles, the speed of a tachyonincreasesas its energy decreases. In particular,approaches zero whenapproaches infinity. (For ordinarybaryonicmatter,increases with increasing speed, becoming arbitrarily large asapproaches,thespeed of light.) Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to belowc,because infinite energy is required to reach the barrier from either above or below.

As noted byAlbert Einstein,Richard C. Tolman,and others,special relativityimplies that faster-than-light particles, if they existed,could be used to communicate backwards in time.[17]

Neutrinos

edit

In 1985, Chodos proposed thatneutrinoscan have a tachyonic nature.[18]The possibility of standard model particles moving at faster-than-light speeds can be modeled usingLorentz invarianceviolating terms, for example in theStandard-Model Extension.[19][20][21]In this framework, neutrinos experienceLorentz-violating oscillationsand can travel faster than light at high energies. This proposal was strongly criticized.[22]

Superluminal information

edit
Spacetime diagramshowing that moving faster than light implies time travel in the context of special relativity. A spaceship departs from Earth from A to C slower than light. At B, Earth emits a tachyon, which travels faster than light but forward in time in Earth's reference frame. It reaches the spaceship at C. The spaceship then sends another tachyon back to Earth from C to D. This tachyon also travels forward in time in the spaceship's reference frame. This effectively allows Earth to send a signal from B to D, back in time.

If tachyons can transmit information faster than light, then, according to relativity, they violate causality, leading to logical paradoxes of the"kill your own grandfather"type. This is often illustrated with thought experiments such as the "tachyon telephone paradox"[17]or "logically pernicious self-inhibitor."[23]

The problem can be understood in terms of therelativity of simultaneityin special relativity, which says that differentinertial reference frameswill 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 thespacetime intervalbetween the events is 'space-like', meaning that neither event lies in the futurelight coneof the other.)[24]

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.[24]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 backward in time. Because one of the two fundamentalpostulates of special relativitysays that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backward 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 ineveryframe and opening the door to severe logical paradoxes.[25]This is known as thetachyonic antitelephone.

Reinterpretation principle

edit

Thereinterpretation principle[3][11][25]asserts that a tachyon sentbackin time can always bereinterpretedas a tachyon travelingforwardin time, because observers cannot distinguish between the emission and absorption of tachyons. The attempt todetecta tachyonfromthe future (and violate causality) would actuallycreatethe same tachyon and send itforwardin time (which is causal).

However, this principle is not widely accepted as resolving the paradoxes.[17][25][26]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[17]or a "logically pernicious self-inhibitor".[23]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.[27][28]

Fundamental models

edit

In modern physics, all fundamental particles are regarded as excitations ofquantum fields.There are several distinct ways in which tachyonic particles could be embedded into a field theory.

Fields with imaginary mass

edit
Main article:Tachyonic field

In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields withimaginary mass.[3]Because thegroup velocityfor such a field issuperluminal,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, thenegative massrepresents an instability totachyon condensation,and all excitations of the field propagate subluminally and are consistent with causality.[29]Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.[5][30][31][32][2]

Tachyonic fields play an important role in modern physics. Perhaps the most famous is theHiggs bosonof theStandard Model of particle physics,which has an imaginary mass in its uncondensed phase. In general, the phenomenon ofspontaneous symmetry breaking,which is closely related to tachyon condensation, plays an important role in many aspects of theoretical physics, including theGinzburg–LandauandBCStheories of superconductivity. Another example of a tachyonic field is the tachyon ofbosonic string theory.[30][33]

Tachyons are predicted by bosonic string theory and also theNeveu-Schwarz(NS) andNS-NS sectors,which are respectively the open bosonic sector and closed bosonic sector, ofRNS superstring theoryprior to theGSO projection.However such tachyons are not possible due to theSen conjecture,also known astachyon condensation.This resulted in the necessity for theGSO projection.

Lorentz-violating theories

edit

In theories that do not respectLorentz 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.[27]A class of field theories of that type is the so-calledStandard Model extensions.However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.[34][35]

Fields with non-canonical kinetic term

edit

By modifying the kinetic energy of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally.[29][28]However, such theories, in general, do not have a well-definedCauchy problem(for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.

In fiction

edit
Main article:Tachyons in fiction

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 wordtachyonhas 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 oftechnobabble,akin topositronic brain).[36]

See also

edit

References

edit
  1. ^ab Tipler, Paul A.; Llewellyn, Ralph A. (2008).Modern Physics(5th ed.). New York, NY: W.H. Freeman & Co. p. 54.ISBN978-0-7167-7550-8.... so existence of particlesv>c... Calledtachyons... would present relativity with serious... problems of infinite creation energies and causality paradoxes.
  2. ^abcRandall, Lisa (2005).Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions.Harper Collins. p. 286.ISBN9780060531089.People initially thought of tachyons as particles traveling 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.
  3. ^abcdef Feinberg, G. (1967). "Possibility of faster-than-light particles".Physical Review.159(5): 1089–1105.Bibcode:1967PhRv..159.1089F.doi:10.1103/PhysRev.159.1089.
    Feinberg, G. (1978). "[no title cited]".Physical Review D.17:1651.doi:10.1103/physrevd.17.1651.
  4. ^ Aharonov, Y.; Komar, A.; Susskind, L. (25 June 1969)."Superluminal behavior, causality, and instability".Physical Review.182(5): 1400–1403.Bibcode:1969PhRv..182.1400A.doi:10.1103/PhysRev.182.1400.
  5. ^ab Sen, Ashoke (2002). "Rolling tachyon".Journal of High Energy Physics.2002(4): 048.arXiv:hep-th/0203211.Bibcode:2002JHEP...04..048S.doi:10.1088/1126-6708/2002/04/048.S2CID12023565.
  6. ^Fox, R.; Kuper, C. G.; Lipson, S. G. (1970)."Faster-Than-Light Group Velocities and Causality Violation".Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences.316(1527): 515–524.ISSN0080-4630.
  7. ^ Sommerfeld, A. (1904). "Simplified Deduction of the Field and the Forces of an Electron Moving in Any Given Way".KNKL. Acad. Wetensch.7:345–367.
  8. ^Davidson, Mark P. (2001). "Tachyons, Quanta, and Chaos".arXiv:quant-ph/0103143.
  9. ^Chashchina, Olga; Silagadze, Zurab (13 April 2022)."Relativity 4-ever?".Physics.4(2): 421–439.arXiv:2107.10739.doi:10.3390/physics4020028.ISSN2624-8174.
  10. ^ Benford, Gregory(6 July 2013).Old Legends.p. 276.He told me years later that he had begun thinking about tachyons because he was inspired by James Blish's [1954] short story, "Beep". In it, a faster-than-light communicator plays a crucial role in a future society but has an annoying finalbeepat the end of every message. The communicator necessarily allows sending of signals backward in time, even when that's not your intention. Eventually, the characters discover that all future messages are compressed into that beep, so the future is known, more or less by accident. Feinberg had set out to see if such a gadget was theoretically possible.
  11. ^ab Bilaniuk, O.-M.P.; Deshpande, V.K.; Sudarshan, E.C.G. (1962). "'Meta' Relativity ".American Journal of Physics.30(10): 718.Bibcode:1962AmJPh..30..718B.doi:10.1119/1.1941773.
  12. ^ Bilaniuk, O.-M.P.; Sudarshan, E.C.G. (1969). "Particles beyond the Light Barrier".Physics Today.22(5): 43–51.Bibcode:1969PhT....22e..43B.doi:10.1063/1.3035574.
  13. ^ "Neutrinos Sent from CERN to Gran Sasso Respect the Cosmic Speed Limit"(Press release).CERN.8 June 2012. Archived fromthe originalon 22 February 2014.Retrieved8 June2012.
  14. ^abRecami, E. (16 October 2007). "Classical tachyons and possible applications".Rivista del Nuovo Cimento.9(6): 1–178.Bibcode:1986NCimR...9e...1R.doi:10.1007/BF02724327.ISSN1826-9850.S2CID120041976.
  15. ^abVieira, R. S. (2011). "An introduction to the theory of tachyons".Rev. Bras. Ens. Fis.34(3).arXiv:1112.4187.Bibcode:2011arXiv1112.4187V.
  16. ^abHill, James M.; Cox, Barry J. (8 December 2012)."Einstein's special relativity beyond the speed of light".Proceedings of the Royal Society A.468(2148): 4174–4192.Bibcode:2012RSPSA.468.4174H.doi:10.1098/rspa.2012.0340.ISSN1364-5021.
  17. ^abcd Benford, G.;Book, D.; Newcomb, W. (1970). "The Tachyonic Antitelephone".Physical Review D.2(2): 263–265.Bibcode:1970PhRvD...2..263B.doi:10.1103/PhysRevD.2.263.
  18. ^ Chodos, A. (1985). "The neutrino as a tachyon".Physics Letters B.150(6): 431–435.Bibcode:1985PhLB..150..431C.doi:10.1016/0370-2693(85)90460-5.hdl:2022/20737.
  19. ^ Colladay, D.; Kostelecky, V.A. (1997). "CPT Violation and the Standard Model".Physical Review D.55(11): 6760–6774.arXiv:hep-ph/9703464.Bibcode:1997PhRvD..55.6760C.doi:10.1103/PhysRevD.55.6760.S2CID7651433.
  20. ^ Colladay, D.; Kostelecky, V. A. (1998). "Lorentz-Violating Extension of the Standard Model".Physical Review D.58(11): 116002.arXiv:hep-ph/9809521.Bibcode:1998PhRvD..58k6002C.doi:10.1103/PhysRevD.58.116002.S2CID4013391.
  21. ^ Kostelecky, V. A. (2004). "Gravity, Lorentz Violation, and the Standard Model".Physical Review D.69(10): 105009.arXiv:hep-th/0312310.Bibcode:2004PhRvD..69j5009K.doi:10.1103/PhysRevD.69.105009.S2CID55185765.
  22. ^ Hughes, Richard J.; Stephenson, G. J. (1990)."Against Tachyonic Neutrinos".Physics Letters B.244(1): 95–100.Bibcode:1990PhLB..244...95H.doi:10.1016/0370-2693(90)90275-B.
  23. ^ab Fitzgerald, P. (1970). "Tachyons, backwards causation, and freedom".Proceedings of the Biennial Meeting of the Philosophy of Science Association vol. 1970.The Philosophy of Science Association, 1970 Biennial Meeting. PSA. Vol. 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'...
  24. ^ab Jarrell, Mark."The Special Theory of Relativity"(PDF).Electrodynamics course, chapter 11.University of Cincinnati.pp. 7–11. Archived fromthe original(PDF)on 13 September 2006.Retrieved27 October2006.
  25. ^abc Grøn, Ø.; Hervik, S. (2007).Einstein's General Theory of Relativity: With Modern Applications in Cosmology.Springer.p. 39.ISBN978-0-387-69199-2.The tachyon telephone paradox cannot be resolved by means of the reinterpretation principle.
  26. ^ Recami, Erasmo; Fontana, Flavio; Garavaglia, Roberto (2000). "Special Relativity and Superluminal Motions: A Discussion of Some Recent Experiments".International Journal of Modern Physics A.15(18): 2793–2812.arXiv:0709.2453.doi:10.1142/S0217751X00001403.it is possible... to solve also the known causal paradoxes, devised for[refuting]'faster than light' motion, although this is not widely recognized yet.
  27. ^ab Barceló, Carlos; Finazzi, Stefano; Liberati, Stefano (2010). "On the impossibility of superluminal travel: The warp drive lesson".arXiv:1001.4960[gr-qc].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...
  28. ^ab Adams, Allan;Arkani-Hamed, Nima; Dubovsky, Sergei; Nicolis, Alberto; Rattazzi, Riccardo (2006). "Causality, analyticity and an IR obstruction to UV completion".Journal of High Energy Physics.2006(10): 014.arXiv:hep-th/0602178.Bibcode:2006JHEP...10..014A.doi:10.1088/1126-6708/2006/10/014.S2CID2956810.
  29. ^ab Aharonov, Y.; Komar, A.; Susskind, L. (1969). "Superluminal Behavior, Causality, and Instability".Phys. Rev.182(5): 1400–1403.Bibcode:1969PhRv..182.1400A.doi:10.1103/PhysRev.182.1400.
  30. ^ab Greene, Brian(2000).The Elegant Universe.Vintage Books.
  31. ^ Kutasov, David; Mariño, Marcos; Moore, Gregory (2000). "Some exact results on tachyon condensation in string field theory".Journal of High Energy Physics.2000(10): 045.arXiv:hep-th/0009148.Bibcode:2000JHEP...10..045K.doi:10.1088/1126-6708/2000/10/045.S2CID15664546.
  32. ^ Gibbons, G.W. (13 June 2002). "Cosmological evolution of the rolling tachyon".Physics Letters B.537(1–2): 1–4.arXiv:hep-th/0204008.Bibcode:2002PhLB..537....1G.doi:10.1016/S0370-2693(02)01881-6.S2CID119487619.
  33. ^ Polchinski, J. (1998)."String Theory".Proceedings of the National Academy of Sciences of the United States of America.95(19). Cambridge, UK:Cambridge University Press:11039–11040.Bibcode:1998PNAS...9511039G.doi:10.1073/pnas.95.19.11039.PMC33894.PMID9736684.
  34. ^Glashow, Sheldon Lee (2004). "Atmospheric Neutrino Constraints on Lorentz Violation".arXiv:hep-ph/0407087.
  35. ^ Coleman, Sidney R. & Glashow, Sheldon L. (1999). "High-energy tests of Lorentz invariance".Physical Review D.59(11): 116008.arXiv:hep-ph/9812418.Bibcode:1999PhRvD..59k6008C.doi:10.1103/PhysRevD.59.116008.S2CID1273409.
  36. ^Wagstaff, Keith (15 July 2018)."The Science BehindStar TrekTechnobabble ".Mashable.Retrieved12 February2021.
edit
Look uptachyonin Wiktionary, the free dictionary.
Wikimedia Commons has media related toTachyon.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Tachyon&oldid=1252717528"