In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass. Although tachyonic particles (particles that move faster than light) are a purely hypothetical concept that violate a number of essential physical principles, at least one field with imaginary mass, the Higgs field, is believed to exist. Under no circumstances do any excitations of tachyonic fields ever propagate faster than light—the presence or absence of a tachyonic (imaginary) mass has no effect on the maximum velocity of signals, and so unlike faster-than-light particles there is no violation of causality. Tachyonic fields play an important role in physics and are discussed in popular books. The term "tachyon" was coined by Gerald Feinberg in a 1967 paper that studied quantum fields with imaginary mass. Feinberg believed such fields permitted faster than light propagation, but it was soon realized that this was not the case. Instead, the imaginary mass creates an instability: any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the Standard Model of particle physics. 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.
Interpretation
Overview of tachyonic condensation
Although the notion of a tachyonic imaginary mass might seem troubling because there is no classical interpretation of an imaginary mass, the mass is not quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality. Therefore, information still does not propagate faster than light, and solutions grow exponentially, but not superluminally (there is no violation of causality). The "imaginary mass" really means that the system becomes unstable. The zero value field is at a local maximum rather than a local minimum of its potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to quantum fluctuations) will lead the field to roll down with exponentially increasing amplitudes toward the local minimum. In this way, tachyon condensation drives a physical system that has reached a local limit and might naively be expected to produce physical tachyons, to an alternative stable state where no physical tachyons exist. Once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons anymore but rather are ordinary particles with a positive mass-squared, such as the Higgs boson.
Physical interpretation of a tachyonic field and signal propagation 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 (the mass squared being negative). 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.
Importance in physics The phenomenon of spontaneous symmetry breaking, which is closely related to tachyon condensation, plays a central part in many aspects of theoretical physics, including the Ginzburg–Landau and BCS theories of superconductivity. Other examples include the inflaton field in certain models of cosmic inflation (such as new inflation), and the tachyon of bosonic string theory.
Condensation
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