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[1][2] and Gerald Feinberg[3] (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. The existence of tachyons has not been shown.
From a special relativity perspective a tachyon is a particle with space-like four-momentum. There are two equivalent approaches to handling their kinematics:
* Require that all the same formulae that apply to regular slower-than-light particles ("bradyons") also apply to tachyons. In particular the energy-momentum relation:
where p is the relativistic momentum of the bradyon and m is its rest mass still holds, along with the formula for the total energy of a particle:
which is interpreted to mean that the total energy of a particle (bradyon or tachyon) contains a contribution from the rest mass (the "rest mass-energy") and a contribution from the body's motion, the kinetic energy.
However the energy equation has, when v is larger than c', an "imaginary" denominator, since the value inside the square root is negative. Since the total energy must be real then the numerator must also be imaginary, i.e. the rest mass m must be imaginary, since a pure imaginary number divided by another pure imaginary number is a real number.
* An equivalent way of describing tachyons with real masses is to adapt Einstein's energy-momentum relation to read:
With this approach the energy equation becomes:
And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a complex-valued mass may physically mean.
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 light speed 'c', since to reach the barrier from either above or below requires infinite energy.
Quantising 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.[3] 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 travelling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in spacetime. However, as we have seen, reducing a tachyon's energy increases its speed, so that the 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 infinite velocity tachyons have no energy and finite momentum, 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.
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.
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). Tachyon Publications, a science fiction and fantasy publishing company has produced over 40 titles since their inception in 1995, including works by such well known authors as Peter S. Beagle, Tim Powers, and Michael Swanwick.
Tachyon visualization. Since that object moves faster than the 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. The black line is the shock wave of Cherenkov radiation. It is shown only in one moment at time.
