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Tachyon (Greek: ταχύς, "swift" + English: -on "elementary particle") is a hypothetical subatomic particle that moves faster than light. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time. A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds. The first description of tachyons is attributed to German physicist Arnold Sommerfeld. However, it was George Sudarshan, Olexa-Myron Bilaniuk, Vijay Deshpande, and Gerald Feinberg (who originally coined the term in the 1960s) who advanced a theoretical framework for their study.
If tachyons were conventional, localizable particles that could be used to send signals faster than light, this would lead to violations of causality in special relativity. But in the framework of quantum field theory, tachyons are understood as signifying an instability of the system and treated using tachyon condensation, rather than as real faster-than-light particles, and such instabilities are described by tachyonic fields. Tachyonic fields have appeared theoretically in a variety of contexts, such as the bosonic string theory.
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Cherenkov radiation
Taking the formalisms of electromagnetic radiation and supposing a tachyon had an electric charge—as there is no reason to suppose a priori that tachyons must be either neutral or charged—then a charged tachyon must lose energy as Cherenkov radiation—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. However, as we have seen, reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite 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.) 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.
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Quantum field theory
Quantizing tachyons shows that they must be spinless particles which obey Fermi-Dirac statistics; i.e., tachyons are Scalar fermions, a combination which is not permitted for ordinary particles. They also must be created and annihilated in pairs.
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Causality
The property of causality is a fundamental principle of theoretical particle physics. If tachyons could be used to transmit information faster than light, then according to relativity they could also be used to violate causality using a scheme sometimes known as the "tachyon telephone paradox". This can be understood in terms of the relativity of simultaneity in special relativity, which says that in some cases different 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 interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).
It has been argued that we can avoid the notion of tachyons traveling into the past using the Feinberg reinterpretation principle 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 traveling 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, because there always exists a sub-light speed reference frame shift that alters the temporal direction of the tachyon's world-line. The attempt to detect a tachyon from the future (and violate causality) can actually create the same tachyon and sends it forward in time (which is causal).
In fact, there are arguments from quantum field theory suggesting that even if tachyons existed, they could not be used to transmit information faster than light at all, either because disturbances in the quantum field for a tachyon would not actually propagate faster than light, or because the tachyon is impossible to localize. Without the possibility of faster-than-light information transmission, the problem of backwards-in-time information transmission could be avoided as well.
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Despite the theoretical arguments against the existence of tachyon particles, experimental searches have been conducted to test the assumption against their existence; however, no experimental evidence for the existence of tachyon particles has been found.>>