Tachyon

This article is about hypothetical faster-than-light particles. For another common usage of "tachyon" in high energy physics, see Tachyonic field. For other uses, see Tachyon (disambiguation).

Because a tachyon always moves faster than light, we cannot see it approaching. After a tachyon has passed nearby, we would be able to see two images of it, appearing and departing in opposite directions. The black line is the shock wave of Cherenkov radiation, shown only in one moment of time. This double image effect is most prominent for an observer located directly in the path of a superluminal object (in this example a sphere, shown in grey). The right hand bluish shape is the image formed by the blue-doppler shifted light arriving at the observer—who is located at the apex of the black Cherenkov lines—from the sphere as it approaches. The left-hand reddish image is formed from red-shifted light that leaves the sphere after it passes the observer. Because the object arrives before the light, the observer sees nothing until the sphere starts to pass the observer, after which the image-as-seen-by-the-observer splits into two—one of the arriving sphere (to the right) and one of the departing sphere (to the left).

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A tachyonic particle, or simply tachyon ( /ˈtæki.ɒn/), is a hypothetical subatomic particle that always moves faster than light. Most physicists do not believe that such particles exist or are consistent with the known laws of physics. Tachyons could be used to send signals faster than light, and (according to special relativity) this leads to violations of causality.

The first hypothesis regarding tachyons is sometimes attributed to German physicist Arnold Sommerfeld, and more recent discussions include. In modern physics, particles are excitations of quantum fields, and Gerald Feinberg coined the term "tachyon" in a paper in 1967 that studied a quantum field with imaginary mass. Today, such fields are still routinely referred to as "tachyons" in the physics literature, although the fact that imaginary mass field excitations do not propagate superluminally (instead, the imaginary mass represents an instability) has been clearly understood at least since the late 1960s. Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

The name comes from the Greek: ταχύς (tachys, “swift, quick, fast, rapid”). 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.

In the language of special relativity, a tachyon would have space-like four-momentum and imaginary proper time, and would be constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.

Despite the theoretical arguments against the existence of tachyon particles, experimental searches have been conducted to test the assumption against their existence; however, until recently no experimental evidence for the existence of tachyon particles has been found.

Following the results of the September 2011 observation of faster-than-light neutrino velocities, the faster-than-light neutrino anomaly, the value of the neutrino velocity is now a subject of theoretical and experimental studies.

Tachyons in relativistic theory

In special relativity, a tachyon would be a particle with space-like four-momentum, by contrast to ordinary particles that have time-like four-momentum.

Mass

There are two equivalent approaches to handling their kinematics^{[citation needed]}:

• 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:

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

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, 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 good way of illustrating this is by thinking of simple harmonic motion and the use of Euler's Formula to dissociate the 'imaginary' part of the motion which is of no meaning in the physical universe, although this is only a loose analogy.

• A simple substitution for the mass yields an equivalent way of describing tachyons with real masses. Define m = iz (where i² = −1) and we get Einstein's energy–momentum relation to read:

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

With this approach the energy equation becomes:

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

And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a complex-valued mass may physically mean. Except, of course, when converting z back to m for interactions with non-tachyon particles. Both approaches are equivalent mathematically and have the same physical consequences.

Speed

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. (For ordinary bradyonic matter, E increases with increasing speed, 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, 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 (see Tachyonic antitelephone article).

In 1985 it was proposed by Chodos et al. that neutrinos can have a tachyonic nature. The possibility of standard model particles moving at superluminal speeds can be modelled using Lorentz invariance violating terms, for example in the Standard-Model Extension. In this framework, neutrinos experience Lorentz-violating oscillations and can travel faster than light at high energies. On 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. Since then, the idea has been studied by other researchers.

In 1979 a new approach to study tachyon was proposed by Tsao Chang,in which a generalized Galilean transformation (GGT) is introduced. It has been shown that GGT is a non-standard form of the Lorentz transformation. When describing superluminal particles, the time of GGT always goes to positive direction.

In 1986 Chang suggested that the neutrino would be the most possible candidate of a free tachyon. To explain the experiment of parity non-conservation, the two-component neutrino theory was introduced. The neutrino has a left-hand spin and anti-neutrino has a right-hand spin. That means the velocity of an observer in any frame must be less than the velocity of neutrinos, otherwise the direction of the neutrino’s spin will be changed. In other words, the neutrino must be a particle with the velocity of light or faster than light.

Cherenkov radiation

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 traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. However, as we have seen, reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite speed at the same place in space. (At infinite speed the two tachyons have no energy each and finite momentum of opposite direction, 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, because it has a gravitational mass, and therefore increase in speed as it travels, as described above.

Causality

Causality is a fundamental principle of theoretical particle physics. If tachyons can be used to transmit information faster than light, then according to relativity, they can also be used to violate certain simple understandings of the causality principle using a scheme sometimes known as the "tachyon telephone paradox". This can be understood in terms of the relativity of simultaneity in special relativity, which says that different inertial reference frames will disagree on whether two events at different locations happened "at the same time" or not, and they can also disagree on the order of the two events (technically, these disagreements occur when spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).

If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event. However, in the case of a hypothetical signal moving faster than light, there would always be some frames in which the signal was received before it was sent, so that the signal could be said to have moved backwards in time. Because one of the two fundamental postulates of special relativity says that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backwards in time in any one frame, it must be possible in all frames. This means that if observer A sends a signal to observer B which moves faster than light in A's frame but backwards in time in B's frame, and then B sends a reply which moves faster than light in B's frame but backwards in time in A's frame, it could work out that A receives the reply before sending the original signal, a seeming challenge to temporal causality in every frame. Nonetheless, the event cannot be said to lack causal structure as the events are still connected, albeit in this case in a backwards relationship. Mathematical details can be found in the tachyonic antitelephone article, and an illustration of such a scenario using spacetime diagrams can be found here.

Microphysical models

There are several distinct ways in which tachyons could be embedded into physical theory:

• Lorentz violating theories: In theories that do not respect Lorentz invariance the speed of light is not (necessarily) a barrier, and particles can travel faster than c without infinite energy or causal paradoxes. A class of field theories of that type are the so-called Standard Model extensions. However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.
• Fields with imaginary mass: The paper that coined the term "tachyon" was concerned with Lorentz invariant quantum fields with imaginary mass.. Because the group velocity for such a field is superluminal, at first it appears that its excitations propagate faster than c. However, it was quickly understood that the superluminal group velocity does not represent the speed of propagation of any localized excitation (like a particle). Instead, the negative mass represents an instability to Tachyon condensation, and all excitations propagate subluminally.
• Fields with non-canonical kinetic term: By modifying the kinetic energy of the field (typically in a Lorentz-violating way), it is possible to produce theories with localized superluminal excitations. However, such theories are probably inconsistent quantum mechanically.

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 (a form of technobabble, akin to positronic brain).

See also

• Massless particle
• Lorentz-violating neutrino oscillations
• Tachyonic antitelephone

External links

• The Faster Than Light (FTL) FAQ (from the Internet Archive)
• Weisstein, Eric W., Tachyon from ScienceWorld.
• Tachyon entry from the Physics FAQ