Tachyon

A tachyon (from the Greek ταχύς takhús, meaning "swift") is any hypothetical particle that travels at superluminal velocity. The first description of tachyons is attributed to German physicist Arnold Sommerfeld, but it was George Sudarshan in the 1960s who advanced a theoretical framework for their study. Tachyons have recurred in a variety of contexts, such as string theory, and in 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.

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. 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

$E={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}.$

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 arbitrarily large 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, which only happens if v is larger than c. Therefore, just as tardyons are 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]. 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 were 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.

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. 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.

Even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute).

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 among the fictitious or hypothetical particles frequently invoked in treknobabble, often as a deus ex machina used to maintain the plot. 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. Finally, in the film Star Trek: Insurrection, ships fire "tachyon pulses" at one another, disrupting the targets' "shield harmonics" and thereby allowing transport through the shields.

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

Robert J. Sawyer's novel Flashforward features the invention of a Tachyon-Tardyon Collider, allowing experiments which previously required large particle accelerators to be performed in a machine about the size of a microwave. Additionally, a space probe is launched with a tachyon transmitter, allowing it to send information to earth at faster-than-light speeds.

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

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. Similarly, Troy Denning's novel Star By Star, part of the "New Jedi Order" Star Wars series, has a method of following a ship's path through hyperspace by stripping tachyons from it and thereby leaving a superluminal "trail". In the third season Star Trek: Deep Space Nine episode "Explorers", a tachyon stream was used as an (accidental) means to propel a sailing ship to warp speed. In Jack Williamson's novel The Humanoid Touch, the humanoids are said to have tachyonic ships propelled by "rhodomagnetic" science.

The word "tachyon" has become widely recognized to such an extent that it can impart a science-fictional "sound" even if the subject in question has no particular relation to superluminal travel (compare positronic brain). 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). Further examples include the "Tachyon Tanks" of the PC game Dark Reign and the "tachyon beam" of the game Master of Orion. The space-combat sim Tachyon: The Fringe utilizes "tachyon gates" for superluminal travel but gives no exact explanation for the technology, and the MMORPG Eve Online features six types of "Large Tachyon Lasers", technically a contradiction since by definition, lasers emit light—photons, not any kind of hypothetical tachyon.

The Tom Baker-era Doctor Who story "The Leisure Hive" features a race called the Argolins who utlise tachyons for a cloning-like procedure and for "illusions" as such. The Argolin Pangol explains, "Tachyons travel faster than light. A tachyon field can therefore be made to reach point B—that visidome, say—before its departure from point A, the Generator." Romana says that the Time Lords "abandoned tachyonics when we developed warp matrix engineering".

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

In the Korean version of MapleStory, items called tachyons are required to complete a certain high-level quest.

In Red Dwarf, a reference to tachyons is made to describe the form in which a holoship is able to travel as super-light particles through wormholes and stargates.

In the children's series Andrew Lost by J. C. Greenburg, tachyons are said to power the Time-a-tron in books 9-12.

See also

• Superbradyon, another class of hypothetical superluminal particles
• Poincaré group
• D-brane

External links

• The Faster Than Light (FTL) FAQ (from the Internet Archive)
• "Tachyon" from Eric Weisstein's World of Physics
• Tachyon at Memory Alpha