http://en.wikipedia.org/wiki/Tachyon wrote:
<<A tachyon is a hypothetical subatomic particle that moves faster than light. A tachyon would be constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.
The first hypothesis about tachyons is attributed to German physicist Arnold Sommerfeld. However, it was George Sudarshan, Olexa-Myron Bilaniuk, Vijay Deshpande, and Gerald Feinberg (who originally coined the term in the 1960s) who advanced a theoretical framework for their study. The name comes from the Greek: ταχύς (tachus, “swift, quick, fast, rapid”).
No experimental evidence for the existence of tachyon particles had been found until the CERN laboratory in Geneva, Switzerland made public the results of an experiment with [muon] neutrinos that found them 1 part in 40,000 faster than light. The findings have yet to be independently duplicated. In 1985 it was proposed by Chodos et al. that neutrinos can have a tachyonic nature. Today, the possibility of having standard particles moving at superluminal speeds is a natural consequence of unconventional dispersion relations that appear in the Standard-Model Extension, a realistic description of the possible violation of Lorentz invariance in field theory. In this framework, neutrinos experience Lorentz-violating oscillations and can travel faster than light at high energies. IOn the other hand, the above-mentioned proposal by Chodos et al. was strongly criticized by some researchers, but this criticism was subsequently shown to be incorrect.
Quantizing tachyons shows that they must be spinless particles which obey Fermi-Dirac statistics; i.e., tachyons are scalar fermions, a combination which is not permitted for ordinary particles. They also must be created and annihilated in pairs.
Tachyonic fields have appeared theoretically in a variety of contexts, such as the bosonic string theory. According to the contemporary and widely accepted understanding of the concept of a particle, tachyon particles are too unstable to be treated as existent. According to that theory, faster than light information transmission and causality violation with tachyons are impossible.
Conventional massive particles that travel slower than the speed of light are sometimes termed "bradyons" or "tardyons" in contrast, although these terms are only used in the context of discussions about tachyons.
The Theory of Relativity requires that all the same formulas that apply to regular slower-than-light particles ("bradyons") also apply to tachyons since they too exist in spacetime. In particular the energy-momentum relation:
where p is the relativistic momentum of the bradyon and m is its rest mass still holds, along with the formula for the total energy of a particle:
which is interpreted to mean that the total energy of a particle (bradyon or tachyon) contains a contribution from the rest mass (the "rest mass-energy") and a contribution from the body's motion, the kinetic energy.
However the energy equation has, when v is larger than c, an "imaginary" denominator, as the value inside the square root is negative. Because the total energy must be real then the numerator must also be imaginary (i.e., the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number). In quantum field theory imaginary mass would induce tachyon condensation; essentially a mathematical treatment of the 'particle' which yields a real result.
One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, E approaches zero when v approaches infinity. Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.
As noted by Gregory Benford, among others, special relativity implies that tachyons, if they existed, could be used to communicate backwards in time.
It has been argued that we can avoid the notion of tachyons traveling into the past using the Feinberg reinterpretation principle which states that a negative-energy tachyon sent back in time in an attempt to challenge forward temporal causality can always be reinterpreted as a positive-energy tachyon traveling forward in time. This is because observers cannot distinguish between the emission and absorption of tachyons. For a tachyon, there is no distinction between the processes of emission and absorption, because there always exists a sub-light speed reference frame shift that alters the temporal direction of the tachyon's world-line, which is not true for bradyons or luxons. The attempt to detect a tachyon from the future (and challenge forward causality) can actually create the same tachyon and sends it forward in time (which is itself a causal event).
According to the Feinberg reinterpretation principle every tachyon detector will register tachyons in every possible detection mode; from the perspective of a frame where the registration by the "detector" preceded the activation of the "emitter", the "detector" in the past is actually spontaneously emitting tachyons, only some of which will be intercepted by the detector in the future. However, Feinberg's reinterpretation principle, treats events in a way that the earlier event is defined as the "emission" and the later one the "detection", and one critic claims that it does not, in itself, solve the causality problems associated with tachyon information transmission.[15] This criticism however is ill-conceived as it completely ignores the causal structure of reality. For example, suppose experimenter A could selectively influence the rate at which tachyons from her emitter traveled to the detector of experimenter B, and B could measure changes in the rate tachyons arrived at his detector, so that A could transmit a message to B in binary code. Then in a frame where B's detector went off at an earlier time than A influenced her emitter, relabeling B's device as a "spontaneous emitter" and A's as a "detector" would be necessary to make the experiment intelligible as it wouldn't change the fact that B, by observing the changing rates of tachyons being spontaneously emitted from his device, could gain information about A's interactions with her own device in the future. In fact, this experiment would solidify the principle of causality even more since B can follow the causal link and make preditions about A's action in the future. Although remote, the possibility of backward causality is not a real challenge to the principle of causality, but rather a novel way of understanding an additional aspect of it.
In quantum field theory, a tachyon is a quantum of a field—usually a scalar field—whose squared mass is negative, and is used to describe spontaneous symmetry breaking: The existence of such a field implies the instability of the field vacuum; the 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: it will induce tachyon condensation. It is important to realize that once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons any more but rather have a positive mass-squared, such as the Higgs boson.
Because a tachyon's squared mass is negative, it formally has an imaginary mass. This is a special case of the general rule, where unstable massive particles are formally described as having a complex mass, with the real part being their mass in usual sense, and the imaginary part being the decay rate in natural units. However, in quantum field theory, a particle (a "one-particle state") is roughly defined as a state which is constant over time; i.e., an eigenvalue of the Hamiltonian. An unstable particle is a state which is only approximately constant over time; However, it exists long enough to be measured. This means that if it is formally described as having a complex mass, then the real part of the mass must be greater than its imaginary part. If both parts are of the same magnitude, this is interpreted as a resonance appearing in a scattering process rather than particle, as it is considered not to exist long enough to be measured independently of the scattering process. In the case of a tachyon, the imaginary part of the mass is infinitely larger than the real part, and hence no concept of a particle can be attributed to it.
Examples for tachyonic fields are all cases of spontaneous symmetry breaking. In condensed matter physics a notable example is ferromagnetism; in particle physics the best known example is the Higgs mechanism in the standard model.
In string theory, tachyons have the same interpretation as in quantum field theory. However, string theory can, at least in principle, not only describe the physics of tachyonic fields, but also predict whether such fields appear.
Tachyonic fields indeed arise in many versions of string theory. In general, string theory states that what we see as "particles" —electrons, photons, gravitons and so forth—are actually different vibrational states of the same underlying string. The mass of the particle can be deduced from the vibrations which the string exhibits; roughly speaking, the mass depends upon the "note" which the string sounds. Tachyons frequently appear in the spectrum of permissible string states, in the sense that some states have negative mass-squared, and therefore imaginary mass. If the tachyon appears as a vibrational mode of an open string, this signals an instability of the underlying D-brane system to which the string is attached. The system will then decay to a state of closed strings and/or stable D-branes. If the tachyon is a closed string vibrational mode, this indicates an instability in spacetime itself. Generally, it is not known (or theorized) what this system will decay to. However, if the closed string tachyon is localized around a spacetime singularity the endpoint of the decay process will often have the singularity resolved.>>
HEAPOW: Light OPERA; or Faster? (2011 Sep 26)
