The tachyon is a theoretical particle mathematically derived from Einstein's equations for General Relativity. Its possible existence can be described from a model called a light cone. The edges of this cone are where the velocity of a particle or wave is equal to the speed of light. Events on these edges are called, logically, lightlike. Within the cone, velocities are always less than the speed of light and are called timelike. Outside the cone, theoretical events must occur at speeds greater than the speed of light and are called spacelike. Also important to note is that mathematically as a particle approaches the speed of light its mass approaches zero. Light beams, or photons, have zero mass. The mathematical derivation for the tachyon shows that for its speed to be greater than that of light its mass must actually be imaginary! Oops. The other problem with the tachyon is that it disobeys a principle fundamental to general relativity--causality. This is simply that the cause of an event must not occur before the effect. For example, a photon cannot be absorbed before it is emitted. Within the light cone the past and the future are divided so that the past is behind now and the future is in front of now. Outside the light cone in the domain of the tachyon, however, there is no such division and therefore the tachyon can break the law of causality.

There are groups out there who are literally selling the idea of a "tachyon field" of energy that is infinite. This is not possible. First of all, there is a fundamental law of physics called The Law of Conservation of Energy. Energy must exist in some form for it to be converted into a useful state. It does not just appear. The theory that tachyonists are propagating can be worked out mathematically, but it relies on some very shaky foundations:

• In order to "exist", the tachyon has an imaginary rest energy. For you non-mathematicians, the imaginary number i is the square root of -1. The reason why it's called imaginary is because you cannot take the square root of a negative number. Any two numbers with identical signs always multiply to be positive. Proponents get around this issue by saying that imaginary rest mass is okay because the tachyon is never at rest! (see next point)

• There is what is called an invariant interval (ds) that is equal to the sum of the squares of the difference in position in all three directions as well as the time component (ds² = dx² + dy² + dz² + dt²). If the velocity is greater than the speed of light, the invariant interval still holds true. The complication, however, is that in "normal" spacetime this interval was the mathematical condition that explained that no object moves faster than the speed of light. When tachyons arise, however, this interval prevents them from ever slowing down to the speed of light! Hence one could claim that rest mass is not an issue.

• If one can get beyond the contradictions of the laws of physics inherent to an imaginary rest mass and an inability to slow down there is one more factor that greatly decreases the plausibility of the tachyon's existence. These miniscule particles disobey a huge law that is fundamental to General Relativity. That law is called Causality. Absorption cannot happen before emission, or, the cause of an event must happen before the effect. Looking back to the light cone image at the top of this page perhaps you can see why this is true. Within the cone the past is behind the now and the future is ahead. Outside the cone, however, there is no clear-cut line between the past and the future. We don't even know when "now" is. So perhaps tachyons exist. But based on their violation of the Law of Causality they probably disappeared before they even existed!

• Finally, to get back to this idea of infinite energy, in the quantum world (subatomic particles like protons, neutrons, electrons, and their subsidiaries) energy can be measured by Einstein's famous law, E=mc². If we take the imaginary energy of a tachyon to be mi, then E=mic². Oops! Looks like the energy is imaginary too! I cannot say with certainty that the tachyon does not exist. I will continue to remain skeptical, however.

As you may or may not be able to see at this point it is possible to deduce somethimg mathematically and get all wound up inside the beauty of mathematics and then decide that that's proof enough. I just want to remind you that sometimes it's important to go back to the very beginning and remind yourself what you already know. Exercise your powers of skepticism! (And don't get suckered into buying a Tachyon Energy Crystal...)

• Tachyons & Takionics
  A nice, debunking definition from The Skeptic's Dictionary.

• Ask A High-Energy Astronomer
  This guy explains in simple terms how to discover tachyons as well as a healthy dose of skepticism.