tachyon - Basic properties, Causality, Field and string theories, Tachyons in fiction

A hypothetical elementary particle having imaginary mass (ie m² less than 0), and able to travel faster than the velocity of light without violating special relativity. Observable effects are predicted, but have not been seen.

Tachyons have recurred in a variety of contexts, such as string theory. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time.

Basic properties

From a special relativity perspective a tachyon is a particle with space-like four-momentum. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. This is a consequence of special relativity because the tachyon, in theory, has a negative squared mass. If m denotes the rest mass, then the total energy is given by the relation

We take this relation to be valid for either tachyons or regular particles ("bradyons"). The denominator will be imaginary if the quantity inside the square root is negative, which only happens if v is larger than c. Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below light speed 'c'.

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. 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 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. 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.

Causality

The property of causality, a fundamental principle of theoretical particle physics, does not pose a problem for the physical existence of tachyons. It is not generally realised that if a tachyon were to exist and were allowed to interact with ordinary (time-like) matter, causality would not be violated. This would lead to logical paradoxes such as the grandfather paradox, if it were not for the Feinberg reinterpretation principle 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 travelling forward in time. 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. However, these are not tachyons in the above sense, as they do not exceed the speed of light locally.

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. 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.

Tachyons arise in many versions of string theory. 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. If the tachyon is a closed string vibrational mode, this indicates an instability in spacetime itself. However, if the closed string tachyon is localized around a spacetime singularity the endpoint of the decay process will often have the singularity resolved.

Tachyons in fiction

Tachyons appear in many works of fiction. 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).