A tachyon is a hypothetical particle that travels faster than the speed of light (and therefore also travels back in time). The existence of tachyons is allowed by the equations of Einstein's special theory of relativity. However, although searches have been carried out for tachyons, the results have so far proved negative. A tardyon, by contrast, is any elementary particle that travels more slowly than the speed of light – in other words, any normal (known) particle with non-zero rest mass.
Tachyons were first proposed in pre-relativistic times by the physicist Arnold Sommerfeld and named in the 1967 by Gerald Feinberg from the Greek tachys meaning "swift." By extension of this terminology, particles that travel slower than light are called tardyons (or bradyons in more modern usage) and particles, such as photons, that travel exactly at the speed of light are called luxons. The existence of tachyons is allowed by the mathematics of special relativity, one of the basic equations of which is
E = m /√(1 - v2/c2)
where E is the mass-energy of a particle, m its rest mass, and v its velocity, and is the speed of light. This shows that for tardyons (particles of ordinary matter), E increases as v increases and becomes infinite when v = c, thus preventing an initially slower-than-light particle from being accelerated up to the speed of light and beyond. What about a particle for which v is always greater than c? In this case, v2/c2 > 1, so that the denominator in the equation above is an imaginary number – the square root of a negative real number. If m has a real value, E is imaginary, which is hard for physicists to swallow because E is a measurable quantity. If m takes an imaginary value, however, then (because one imaginary number divided by another is real), E is real. Tachyons are allowed, therefore, providing (a) they never cross the light barrier and (b) they have an imaginary rest mass (which is physically more acceptable since the rest mass of an object that never stops is not directly measurable).
Bizarrely, tachyons would slow down if they gained energy, and accelerate if they lost energy. This leads to a problem in the case of charged tachyons because charged particles that move faster than the speed of light in the surrounding medium give off energy in the form of Cerenkov radiation. Charged tachyons would continuously lose energy, even in a vacuum, through Cerenkov emission. This would cause them to gain speed, thus lose energy at even greater rate, thus accelerate even more, and so on, leading to a runaway reaction and the release of an arbitrarily large amount of energy.
A tardyon is any elementary particle that travels more slowly than the speed of light – in other words, any normal (known) particle with non-zero rest mass.
More worryingly, as the physicist Gregory Benford and his colleagues first pointed out, tachyons seem to lead to a time paradox because of their ability to send messages into the past. Suppose Alice on Earth and Boole on a planet circling around Sirius can communicate using what has been called a tachyon "antitelephone." They agree in advance that when Boole receives a message from Alice, he will reply immediately. Alice promises to send a message to Boole at noon her time, if and only if she has not received a message from Boole by 10 a.m. The snag is that both messages, being superluminal, travel back in time. If Alice sends her message at noon, Boole's reply could not reach her before 10 a.m. "Then," as Benford and colleagues wrote in their 1970 paper called The Tachyonic Antitelephone, "the exchange of messages will take place if and only if it does not take place..."
Perhaps not surprisingly, despite numerous searches, no tachyon detection has so far been confirmed. The same is true of another hypothetical faster-than-light particle called a dybbuk (Hebrew for a "roving spirit"), which would have imaginary mass, energy, and momentum. Dybbuks, proposed by Raymond Fox of the Israel Institute of Technology, are so strange that some of their odd properties cancel out to an observer yet, interestingly, they avoid the causality problem of tachyons.