Tachyon

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A tachyon (from the Greek ταχύς (takhús), meaning "swift, fast") is any hypothetical particle that travels at superluminal velocity. The first description of tachyons is attributed to German physicist Arnold Sommerfeld, but it was George Sudarshan, Olexa-Myron Bilaniuk^[1]^[2] and Gerald Feinberg^[3] (who originally coined the term) in the 1960s who advanced a theoretical framework for their study. Tachyons have recurred in a variety of contexts, such as the Bosonic string theory. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time. A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it can never slow to light speed or below. To date, the existence of tachyons has been neither confirmed nor explicitly ruled out. Tachyon condensation is a procedure which can remove tachyons or tachyonic-like behaviour from a quantum field theory.

1 Basic properties
2 Causality
3 Field and string theories
4 Tachyons in fiction
5 References
6 See also
7 External links

[edit] Basic properties

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. The black line is the shock wave of Cherenkov radiation. It is shown only in one moment at time.

Animation

From a special relativity perspective a tachyon is a particle with space-like four-momentum. There are two equivalent approaches to handling their kinematics:

Require that all the same formulae that apply to regular slower-than-light particles ("bradyons") also apply to tachyons. In particular the energy-momentum relation:

$E^2 = p^2c^2 + m^2c^4 \;$

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:

$E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}.$

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, since the value inside the square root is negative. Since the total energy must be real then the numerator must also be imaginary, i.e. the rest mass m must be imaginary, since a pure imaginary number divided by another pure imaginary number is a real number.

A simple subsitution for the mass yields an equivalent way of describing tachyons with real masses. Define m = i*m' (where $i = \sqrt{-1}$ ) and we get Einstein's energy-momentum relation to read:

$E^2 + m'^2c^4 = p^2c^2 \;$

With this approach the energy equation becomes:

$E = \frac{m'c^2}{\sqrt{\frac{v^2}{c^2} -1}}.$

And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a complex-valued mass may physically mean.

Both approaches are equivalent mathematically and have the same physical consequences. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. (For ordinary bradyonic matter, E increases with increasing velocity, becoming arbitrarily large as v approaches c, the speed of light.) Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, since to reach the barrier from either above or below requires infinite energy.

Quantising 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.^[3] They also must be created and annihilated in pairs.

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 a charged tachyon must lose energy as Cherenkov radiation—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon travelling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in spacetime. However, as we have seen, reducing a tachyon's energy increases its speed, so that the hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite velocity. (At infinite velocity tachyons have no energy and finite momentum, so no conservation laws are violated in their mutual annihilation. The time of annihilation is frame dependent.) Even an electrically neutral tachyon would be expected to lose energy via gravitational Cherenkov radiation, since it has a gravitational mass, and therefore increase in velocity as it travels, as described above.

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.

[edit] Causality

The property of causality is a fundamental principle of theoretical particle physics; tachyons, if they existed, would not violate causality, even if they interacted with ordinary (time-like) matter^[3]. Causality would be violated if a particle could send information into its own past, forming a so-called causal loop, leading to logical paradoxes such as the grandfather paradox. Tachyons are prevented from violating causality by the Feinberg reinterpretation principle^[3] which states that a negative-energy tachyon sent back in time in an attempt to violate 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, since there always exists a sub-light velocity reference frame shift that alters the temporal direction of the tachyon's world-line, which is not true for bradyons or photons. The attempt to detect a tachyon from the future (and violate causality) actually creates the same tachyon and sends it forward in time (which is causal). A tachyon detector will seem to register tachyons in every possible detection model; in reality the tachyon "detector" is spontaneously emitting tachyons. The effect of the reinterpretation principle on any tachyon "detector" is that any incoming tachyonic message would be lost against the tachyon background noise, which is an inevitable accompaniment of the uncontrollable emission. The counter intuitive conclusion is that tachyons (if they existed) could be used to transmit energy-momentum, but they can't be used for communication. Thus there is no need to fall back on some quantum field theory form of the Novikov self-consistency principle to preserve causality.

Other avenues of speculation involve parallel universes. One can imagine a scenario in which sending energy or information back in time causes history to diverge into two distinct tracks, one in which events reflect the altered information and one in which they do not.

In the theory of general relativity, it is possible to construct spacetimes in which particles travel faster than the speed of light, relative to a distant observer. One example is the Alcubierre metric, another is of traversable wormholes. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally.

[edit] Field and string theories

In quantum field theory, a tachyon is a quantum of a field—usually a scalar field—whose squared mass is negative. The existence of such a particle 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 will lead the field to roll down with exponentially increasing amplitudes: it will induce tachyon condensation. The Higgs mechanism is an elementary example, but it is important to realize that once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons anymore but rather Higgs bosons that have a positive mass-squared.

Even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality.

Tachyons 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 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.

[edit] Tachyons in fiction

Main article: Tachyons in fiction

Tachyons appear in many works of fiction. It has been used as a standby mechanism upon which many science fiction authors rely to establish faster-than-light communication, with or without reference to causality issues. The word "tachyon" has become widely recognized to such an extent that it can impart a science-fictional "sound" even if the subject in question has no particular relation to superluminal travel (compare positronic brain). Tachyon Publications, a science fiction and fantasy publishing company has produced over 40 titles since their inception in 1995, including works by such well known authors as Peter S. Beagle, Tim Powers, and Michael Swanwick. It is also discussed in Alastair Reynolds' Revelation Space trilogy.

[edit] References

^ Bilaniuk; George Sudarshan (May 1969). "Particles beyond the Light Barrier". Physics Today.
^ Bilaniuk; Deshpande, George Sudarshan (1962). "Meta Relativity". American Journal of Physics: 718ff.
^ ^a ^b ^c ^d Feinberg, Gerald (1967). "Possibility of Faster-Than-Light Particles". Physical Review 159: 1089-1105.