# Tachyon

A tachyon (from the Greek ταχύς {takhús}, meaning "swift") is a hypothetical particle that travels at superluminal velocity. The first theoretical description of tachyons is attributed to physicist Arnold Sommerfeld; however, the concept has recurred in a variety of other contexts, such as string theory. Many strange properties have been attributed to tachyons, which also play a role in some popular science fiction. 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 can never slow to light speed or below. A theory of tachyons was first proposed in the 1960s by George Sudarshan.

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## Basic properties (from a Special Relativity perspective)

As mentioned above, a tachyon is a particle with space-like four-momentum. If its energy and momentum are real, its rest mass is imaginary. It is difficult, for instance, to interpret exactly what a complex-valued mass may physically mean. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. This is a consequence of special relativity because the tachyon, in theory, has a negative squared mass. According to Einstein, the total energy of a particle contains a contribution from the rest mass (the "rest mass-energy") and a contribution from the body's motion, the kinetic energy. If m denotes the rest mass, then the total energy is given by the relation

[itex]E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}.[itex]

We take this relation to be valid for either tachyons or regular particles ("tardyons"). For ordinary matter, this equation shows that E increases with increasing velocity, becoming infinite as v approaches c, the speed of light. If m is imaginary, on the other hand, the denominator of the fraction must also be imaginary to keep the energy a real number (since a pure imaginary divided by another pure imaginary is real). The denominator will be imaginary if the quantity inside the square root is negative (recall the problem imaginary numbers were invented to solve), which only happens if v is larger than c. Therefore, just as tardyons are dogmatically forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below light speed.

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 an accelerating tachyon must radiate electromagnetic waves, just like ordinary charged particles do. However, as we have seen, reducing a tachyon's energy increases its speed, and so in this regime a small acceleration would produce a larger one, leading to a run-away effect similar to an ultraviolet catastrophe.

Some modern presentations of tachyon theory have demonstrated the possibility of a tachyon with a real mass. In 1973, Philip Crough and Roger Clay reported a superluminal particle apparently produced in a cosmic ray shower (an observation which has not been confirmed or repeated) [1] (http://scienceworld.wolfram.com/physics/Tachyon.html). This possibility has prompted some to propose that each particle in space has its own relative timeline, allowing particles to travel back in time without violating causality. Under this model, such a particle would be a "tachyon" by virtue of its apparent superluminal velocity, even though its rest mass is a real number.

## Causality

The property of causality, a fundamental principle of theoretical particle physics, poses a problem for the physical existence of tachyons. If a tachyon were to exist and were allowed to interact with ordinary (time-like) matter, causality could be violated: roughly, there would no longer be a way to tell the difference between the future and the past along the worldline of a given piece of ordinary matter. A particle could send energy or information into its own past, forming a so-called causal loop. This would lead to logical paradoxes such as the grandfather paradox, unless the theory was set up in such a way as to prevent them. At present such a fix is not known: for example, the Novikov self-consistency principle has not been obtained within a quantum field theory, but has to be imposed by hand. At the very least the principle of special relativity would have to be discarded.

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. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally.

## Field and string theories

In quantum field theory, a tachyon is a quantum of a field—usually a scalar field—whose squared mass is negative. The existence of such a particle implies the instability of the spacetime vacuum because the energy of the vacuum has a maximum rather than a minimum (at least with respect to the tachyonic direction). A very small impulse will lead the field to roll down with exponentially increasing amplitudes: it will induce tachyon condensation. The Higgs mechanism is an elementary example, but it is important to realize that once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons anymore but rather Higgs bosons that have a positive mass.

It is important to realize even for tachyonic quantum fields, the field operators at spacelike separated points still commutes (or anticommutes).

Tachyons 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-squareds, and therefore imaginary masses.

## Tachyons in fiction

In the Star Trek fictional universe, tachyons are frequently invoked to explain some aspect of the Romulan cloaking device. Cloaked ships have been detected by watching them pass through a tachyon beam, essentially creating a faster-than-light burglar alarm. (Ships using imperfect cloaking devices are also implied to produce residual tachyon emissions, such as in the film Star Trek: Nemesis.) Tachyons are among the fictitious or hypothetical particles frequently invoked in treknobabble, often as a deus ex machina used to maintain the plot.

In general, tachyons are a standby mechanism upon which many science fiction authors rely to establish faster-than-light communication, with or without reference to causality issues. For example, in the Babylon 5 television series, tachyons are used for real-time communication over long distances. Another instance is Gregory Benford's novel Timescape, winner of the Nebula Award, which involves the use of tachyons to transmit a message of salvation back in time. Likewise, John Carpenter's horror film Prince of Darkness uses tachyons to explain how future humans send messages backward through time to warn the characters of their impending doom.

Tim Powers' novel The Anubis Gates, winner of the Apollo Award in 1987, involves the use of tachyons to initiate time travel.

Classic Anime fans may associate tachyons with the energy source for the wave-motion gun and wave-motion engine in Space Battleship Yamato (Starblazers in the United States).

The PC game Dark Reign, made by Auran and Activision, had fearsome Tachyon Tank units.

Alan Moore's classic graphic novel The Watchmen features a character who uses "a hail of tachyons" broadcasting from space to muddle the mind of the only person on Earth capable of seeing the future.

Isaac Asimov's novel Foundation's Edge brings tachyons into its discussion of faster-than-light travel, where they are particles which exist in hyperspace.

Mario Puzo's novel "The Fourth K" uses tachyons as an argument for the establishment of new scientific procedures.

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