Question: What are tachyons in string theory?

Jack Miller answered on 22 Jun 2013:

A tachyon is any (theoretical) particle that moves faster than the speed of light. It’s my understanding (perhaps flawed) that they were originally proposed as the quanta of field theories that had an imaginary mass term, which were important as they’d give rise to instabilities, and the spontaneous generation of properties as a result.

It was originally thought that ‘tachyonic’ field theories of this type, with an imaginary mass term, would give rise to faster-than-light particles. However, that believe has been subsequently disproven, and nobody believes that faster-than-light particles exist (as to have some would violate causality). It’s hence possible to have the pleasant mathematical trickery of having an imaginary mass without the difficulty of having them generate predictions that are violated by experiment.

The exact way that tachyonic fields give rise to emergent properties is really cool, and has lead to their inclusion in the standard model. To illustrate this, I’ve just copied the below from a good wikipedia article on the subject — http://en.wikipedia.org/wiki/Tachyonic_field.

Hope this helps!

— Jack

Due to the instability caused by the imaginary mass, any configuration in which one or more field excitations are tachyonic will spontaneously decay. In some cases this decay ends with another, stable configuration with no tachyons. A famous example is the condensation of the Higgs boson in the Standard Model of particle physics. Under no circumstances do any excitations ever propagate faster than light in such theories — the presence or absence of a tachyonic mass has no effect whatsoever on the maximum velocity of signals.
In modern physics, all fundamental particles are regarded as localized excitations of fields. Tachyons are unusual because the instability prevents any such localized excitations from existing. Any localized perturbation, no matter how small, starts an exponentially growing cascade that strongly affects physics everywhere inside the future light cone of the perturbation.

There is a simple mechanical analogy that illustrates that tachyonic fields do not propagate faster than light, why they represent instabilities, and helps explain the meaning of imaginary mass (negative squared mass).

Consider a long line of pendulums, all pointing straight down. The mass on the end of each pendulum is connected to the masses of its two neighbors by springs. Wiggling one of the pendulums will create two ripples that propagate in both directions down the line. As the ripple passes, each pendulum in its turn oscillates a few times about the straight down position. The speed of propagation of these ripples is determined in a simple way by the tension of the springs and the inertial mass of the pendulum weights. Formally, these parameters can be chosen so that the propagation speed is the speed of light. In the limit of an infinite density of closely spaced pendulums, this model becomes identical to a relativistic field theory, where the ripples are the analog of particles. Displacing the pendulums from pointing straight down requires positive energy, which indicates that the squared mass of those particles is positive.

Now consider an initial condition where at time t=0, all the pendulums are pointing straight up. Clearly this is unstable, but at least in classical physics one can imagine that they are so carefully balanced they will remain pointing straight up indefinitely so long as they are not perturbed. Wiggling one of the upside-down pendulums will have a very different effect from before. The speed of propagation of the effects of the wiggle is identical to what it was before, since neither the spring tension nor the inertial mass have changed. However, the effects on the pendulums affected by the perturbation are dramatically different. Those pendulums that feel the effects of the perturbation will begin to topple over, and will pick up speed exponentially. Indeed, it is easy to show that any localized perturbation kicks off an exponentially growing instability that affects everything within its future “ripple cone” (a region of size equal to time multiplied by the ripple propagation speed). In the limit of infinite pendulum density, this model is a tachyonic field theory.