Tachyon

A tachyon (from the Greek ταχύς takhús, meaning "swift, fast") 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 and Gerald Feinberg (who originally coined the term) in the 1960s who advanced a theoretical framework for their study. Tachyons have recurred in a variety of contexts, such as string theory. 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)

Tachyon visualization. Since that object moves faster then speed of light we can not see it approaching. Only after a tachyon has passed nearby, we could see two images of the tachyon, appearing and departing in opposite directions.
Animation: Image:Tachyon03.gif

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, does not pose a problem for the physical existence of tachyons. It is not generally realised that if a tachyon were to exist and were allowed to interact with ordinary (time-like) matter, causality would not be violated; this despite that there would no longer be a way (relative to the tachyon) to tell the difference between the future and the past along the worldline of a given piece of ordinary matter. A particle could seemingly 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, if it were not for the Feinberg reinterpretation principle which states that a negative-energy tachyon sent back in time in an attempt to violate causality can be reinterpreted as a positive-energy tachyon travelling forward in time; for a tachyon there is no distinction between the processes of emission and absorption since a sub-light velocity reference frame shift can alter the temporal direction of its world-line, which is not true for tardons or photons. The attempt to detect a tachyon from the future actually creates the same tachyon and sends it forward in time. The effect of the reinterpretation principle on any tachyon "receiver" is that any incoming tachyonic message is lost against the tachyon background noise, which is an inevitable accompaniment of detection/emission; a tachyon detector will register tachyons in every possible detection mode. Tachyons (if they existed) could be used to transmit energy-momentum, but they can't be used for communication. Thus there is no need to fall back on the some quantum field theory form of the Novikov self-consistency principle to preserve causality.

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

Main article: Tachyons in fiction

Tachyons appear in many works of fiction. It has been used as a standby mechanism upon which many science fiction authors rely to establish faster-than-light communication, with or without reference to causality issues. 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).

See also

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

External links

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