Hypothetical subatomic particle whose velocity is always greater than that of light. Its existence appears consistent with the theory of relativity. Just as an ordinary particle such as an electron can exist only at speeds less than that of light, a tachyon can exist only at speeds greater than that of light. At such speeds, its mass would be real and positive. On losing energy, a tachyon accelerates; the faster it travels, the less energy it has. The existence of tachyons has not been established experimentally.
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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 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. 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) and even if they existed (by Feinberg's analysis) they wouldn't be able to transmit information (also by Feinberg's analysis). 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 or against the existence of tachyon particles has been found.
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 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.
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 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 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.
Other avenues of speculation involve parallel universes. 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 traversable wormholes. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally.
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.
Since a tachyon's squared mass is negative, it formally has an imaginary mass. This is a special case of the general rule, where unstable massive particles are formally described as having a complex mass, with the real part being their mass in usual sense, and the imaginary part being the decay rate in natural units.
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 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.
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 strings 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 are also central in 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). Part of the story is set on the Columbia University campus in homage to Gerald Feinberg.
Tachyons were discussed in the NBC 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. The tachyon, however, is most extensively used in the later era of Star Trek (TNG, VOY and DS9'').
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