# Tachyon

Tachyons ( old Greek ταχύς tachýs , 'fast') are hypothetical particles that move faster than the speed of light . Such particles are called superluminar .

## Tardyons, Luxons, and Tachyons

Olexa-Myron Bilaniuk, VK Deshpande and ECG Sudarshan pointed out in 1962 that there are several possible solutions for the equations of the special theory of relativity (and independently in the early 1960s the Soviet physicist Jakow Petrovich Terlezki ). One of them corresponds to normal matter , which moves at sub-light speed. Another would allow particles that constantly move faster than light and can never be slowed down to the speed of light. However, the mere fact that there is this mathematical solution for the equations does not mean that tachyons must also exist in real life.

Gerald Feinberg (1967), who examined tachyons more closely, found the following word coining for this division of particles into three classes :

Tardyons
Particles that always move slower than the speed of light through space.
Luxons
Particles that always move through space at the speed of light.
Tachyons
Particles that always move faster than the speed of light through space.

Of these, only the name Tachyon has prevailed.

## Properties of tachyons

• Their speed is greater than the speed of light c.
• Their mass is imaginary . That is, the square of their mass is negative. This follows from the energy-momentum relation of the special theory of relativity:
${\ displaystyle E ^ {2} = p ^ {2} c ^ {2} + m ^ {2} c ^ {4} \;}$
if one assumes that both the energy and the momentum of the particle are real quantities and, in addition, the relativistic formula for the energy of a particle:
${\ displaystyle E = {\ frac {mc ^ {2}} {\ sqrt {1 - {\ frac {v ^ {2}} {c ^ {2}}}}}}}$
accepts. Is , the expression under the root sign becomes negative and thus the root becomes imaginary. In order for the energy to be positive, the mass m must also be imaginary.${\ displaystyle v> c}$
• As the speed of a tachyon increases, the energy decreases. If the energy approaches 0, its speed even becomes infinite (transcendent state) and, conversely, the energy diverges when v approaches c. In order to slow a tachyon and approach the speed of light, one must add energy. In the case of tardyons (that is, ordinary elementary particles with a positive mass other than zero), however, energy must be added in order to induce an increase in speed.
• An electrically charged tachyon should excite Cherenkov radiation in matter , since the tachyon moves at a higher speed than the speed of light of the medium it traversed. However, there are also theorists who restrict this and argue on the contrary that tachyons only have Cherenkov radiation for frequencies in the X-ray range and UV frequencies if the refractive index is less than 1 and the speed of the tachyon is below the phase speed of light in the medium.
• A charged tachyon would radiate when accelerated and lose energy and also lose energy in matter through Cherenkov radiation alone, which according to the relativistic formula for energy leads to an increase in speed (“runaway solution”). The same is true for gravitationally interacting tachyons or generally interacting tachyons, so that a theory of interacting tachyons is problematic.
• In contrast to particles below the speed of light, in which the events on the world line have the same time order for every observer, the chronological order of different events on the Tachyon world line depends on the reference system.

In quantum mechanics or quantum field theory of tachyons it can be shown that localized field excitations ("particles") cannot propagate at a speed greater than the speed of light.

### Theoretical appearance

If one could see tachyons, one assumes that the observer would only be able to see them after they had flown past him. Similar to aircraft, which fly faster than sound and overtake their own background noise, the tachyons move faster than light and thus overtake their optical image . Therefore, after the tachyon has flown past you, you would see twice. Once in the direction in which it flies and once in the direction from which it came. Both images would move away from the observer.

The image of the approaching particle experiences an enormous blue shift ; that of the retreating one redshift .

## Existence of tachyons

The experimental results can be used to exclude tachyons with electrical charge , since they would be very easily detectable by Cherenkov radiation . Tachyons with colored charges , which are subject to the strong interaction , can also be excluded . Weakly interacting tachyons, not interacting or only interacting gravitationally or by hypothetical other forces, cannot be excluded from the experimental point of view.

## Neutrinos

Since the 1980s, some physicists have been working on the thesis that neutrinos are tachyons. There are several ways to test this. One possibility to prove or disprove this thesis is the direct mass determination, e.g. B. by measuring the end point energy during tritium decay . In the past, tritium decay experiments sometimes measured apparently negative mass squares. This could be traced back to a (previously unnoticed) surface effect of the detector crystal.

At OPERA at CERN in 2011 it was believed to have found indications of faster than light neutrinos (i.e. as tachyon candidates), but later this turned out to be a measurement error (see measurements of neutrinos ).

The observation of neutrino oscillations shows that neutrinos have a mass other than zero. This means that they are moving slower than the speed of light, so they cannot be tachyons.

## Tachyons in quantum field theory and string theory

Fields with complex mass (mostly scalar fields, referred to as tachyonic fields ) appear in various quantum field theories, where they are signs of an instability of the vacuum and lead to a so-called tachyon condensation, i.e. the interacting tachyonic fields annihilate and form new particles ( with real mass). Tachyons are signs of instability and the tachyon condensation corresponds to a second order phase transition, such as a spontaneous break in symmetry or the Higgs mechanism .

In string theory, there are many models that contain tachyons, both in bosonic and superstring theory. Most specialists, however, take the position that realistic models are recommended as candidates for the physically correct model precisely because of the lack of free tachyons. The bosonic string theory with a tachyon ground state is therefore (and because it cannot describe any fermions) mostly excluded (or viewed as unstable due to the tachyon ground state) and the tachyonic sector in superstring theories is usually removed with a special so-called GSO projection. As in the quantum field theory of point particles, the role of tachyon condensation as a sign of instabilities is discussed here (in string field theories). For example, Ashoke Sen assumed in the 1990s from the occurrence of tachyons in the open strings attached to a D-brane that these reflect the instability of D-branes during pair creation (Sen conjecture).

## Consequences of the retrograde time

If interactions between the tachyons and the tardyons could be demonstrated, it would mean that messages from the future could be conveyed into the past. The consequences would be time paradoxes , for example through a hypothetical anti-telephone .

## Tachyons in esoteric and commercial applications

Many esoteric products are advertised and commercially marketed on the Internet that are interspersed with alleged "tachyon energy" (also sometimes called "primal energy") and that are said to have positive effects on the wearer (see tachyon treatment ). There is no description of how it works or how it is manufactured and no evidence of effectiveness.

## literature

• O. Bilaniuk, ECG Sudarshan: Tachyons . In: Physics Today. 22, 1969, H. 5 (May), , 1969, P. 43-51, as well as letter to the editor Discussion: ibid. H. 12 (Dec.).
• Gerald Feinberg : Possibility of faster than light particles. In: Physical Review. 159, 1967, , pp. 1089-1105.
• Jayant Vishnu Narlikar : Cosmic tachyons - an astrophysical approach. In: American Scientist. 66, 1978, 9, , pp. 587-593.
• Erasmo Recami (Ed.): Tachyons, Monopoles and related topics. Proceedings of the 1st Session of the Interdisciplinary Seminars on "Tachyons and Related Topics", Erice, September 1-15, 1976. North Holland, Amsterdam 1978, ISBN 0-444-85165-8 .
• Erasmo Recami: Special Relativity Extended to (antimatter and) Superluminal motions: A Review , Rivista del Nuovo Cimento, Volume 9, 1986, pp. 1-178
• Erasmo Recami: Tachyon kinematics and causality: A systematic thorough analysis of the tachyon causal paradoxes , Foundations of Physics, Volume 17, 1987, pp. 239-296.
• Lawrence Schulman : Tachyon Paradoxes. In: American Journal of Physics. 39, 1971, , pp. 481-484, online (PDF; 523 KB) .
• ECG Sudarshan: The theory of particles traveling faster than light 1. In: Lectures presented at the 1969 seventh anniversary symposium of the Institute of Mathematical Sciences, Madras, India . No. 7. Plenum Press, New York NY 1970, ISBN 0-306-37050-6 , ( Symposia on theoretical physics and mathematics 10), pp. 129-151.
• Yakov P. Terletskii: Paradoxes in the theory of relativity. Plenum Press, New York NY 1968, (2nd print: ibid 1970).
• Rüdiger Vaas : Tunnel through space and time. Einstein's legacy - black holes, time travel and faster than light. (How Hawking lost his bet). 2nd updated edition. Franckh-Kosmos, Stuttgart 2006, ISBN 3-440-09360-3 (with a detailed chapter on tachyons).

Wiktionary: Tachyon  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. Arnold Sommerfeld already pointed out the paradoxes of the faster than light speed in the early years of the theory of relativity. Another pioneer of the tachyon concept is the Soviet physicist JP Terletzki, z. B. J. Phys. et radium. Vol. 21, 1960, p. 681, Vol. 23, 1962, p. 910, Sov. Phys. Docl. Vol. 5, 1961, p. 782, and S. Tanaka in Japan: Theory of matter with superlight velocity , Progress Theor. Phys., Vol. 24, 1960, p. 171
2. John Baez Do tachyons exist?
3. H. Lemke Cerenkov radiation induced by tachyons , Nuovo Cimento 32 A, 1976, the 169th
4. ^ R. Folman, E. Recami, On the phenomenology of tachyon radiation, Found. Phys. Lett. 8, 1995, 127-134, Arxiv
5. See John Baez, loc. cit.
6. ^ Y. Aharonov, A. Komar, Leonard Susskind : Superluminal Behavior, Causality, and Instability , Phys. Rev., Vol. 182, 1969, pp. 1400-1403, abstract
7. ^ The ultimate neutrino page, CUPP, Finland
8. Sen, Tachyon condensation on the brane antibrane system , JHEP, 8, 1998, 9808: 012. Arxiv
9. Sen, Tachyon dynamics in open string theory, Int.J.Mod.Phys.A, Volume 20, 2005, pp. 5513-5656, Arxiv
10. Online with other works by Recami