"...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..."

"...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 'c'...."

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.

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.. . "