Tachyon

This article is about hypothetical faster-than-light particles. For quantum fields with imaginary mass, 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).

A tachyon ( /ˈtæki.ɒn/) (or tachyonic particle) is a hypothetical 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 term "tachyon" (from the Greek: ταχύς or tachys: “swift, quick, fast, rapid”) was coined by Gerald Feinberg in a 1967 paper. Feinberg proposed that tachyonic particles could be quanta of a field with imaginary mass. However, it was later understood that the excitations of such fields do not propagate faster than light, but instead represent an instability (see tachyon condensation). Today, the term often refers to the imaginary mass fields studied by Feinberg, which have come to play an important role in modern physics.

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

Despite the theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. Until recently, no compelling evidence for their existence had been found. In September 2011 the OPERA collaboration announced that they measured neutrinos travelling faster than the speed of light (see faster-than-light neutrino anomaly), which led to discussion of whether neutrinos could be tachyons. Flaws in the experiment were reported on 22 February of 2012 that might explain the anomaly.

Tachyons in relativistic theory

In special relativity, a faster than light particle would have space-like four-momentum, by contrast to ordinary particles that have time-like four-momentum.

Mass

In a Lorentz invariant theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "bradyons" in discussions of tachyons) must 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) should still apply, along with the formula for the total energy of a particle:

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

This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest mass-energy") and a contribution from its motion, the kinetic energy. When v is larger than c, denominator in the equation for the energy is "imaginary", as the value inside the square root is negative. Because the total energy must be real, 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.

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 faster than light particles, if they existed, could be used to communicate backwards in time (see Tachyonic antitelephone article).

Neutrinos

Main article: Neutrino anomaly

Recently, the OPERA collaboration has reported evidence for faster than light neutrino velocities. However, the possibility of specific measurement errors has been raised.

As long ago as 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.

Cherenkov radiation

A tachyon with an electric charge would 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. If the tachyon interacts with any other particles, it can also Cherenkov radiate energy into those particles. Neutrinos interact with the other particles of the Standard Model, and Andrew Cohen and Sheldon Glashow recently used this to argue that the Neutrino anomaly cannot be explained by making neutrinos propagating faster that light, and must instead be due to an error in the experiment.

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.

Feinberg Reinterpretation Principle

The Feinberg reinterpretation principle 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 luxons. The attempt to detect a tachyon from the future (and violate causality) would actually create the same tachyon and send it forward in time (which is causal).

A tachyon detector will seem to register tachyons in every possible detection model; from the perspective of a frame where the registration by the "detector" preceded the activation of the "emitter", the "detector" is actually spontaneously emitting tachyons.

Fundamental models

In modern physics, all fundamental particles are regarded as excitations of quantum fields. There are several distinct ways in which tachyonic particles could be embedded into a field theory.

Fields with imaginary mass

Main article: Tachyonic field

In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with imaginary mass. Because the group velocity for such a field is superluminal, naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the negative mass represents an instability to tachyon condensation, and all excitations of the field propagate subluminally and are consistent with causality. Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.

Tachyonic fields play an important role in modern physics. Perhaps the most famous is the Higgs boson of the Standard Model of particle physics, which—in its uncondensed phase—has an imaginary mass. In general, the phenomenon of spontaneous symmetry breaking, which is closely related to tachyon condensation, plays a very important role is many aspects of theoretical physics, including the Ginzburg–Landau and BCS theories of superconductivity. Another example of a tachyonic field is the tachyon of bosonic string 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 non-canonical kinetic term

By modifying the kinetic energy of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally. However, such theories in general do not have a well-defined Cauchy problem (for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.

History

As mentioned above, the term "tachyon" was coined by Gerald Feinberg in a 1967 paper titled "Possibility of Faster-Than-Light Particles". Feinberg studied the kinematics of such particles according to special relativity. In his paper he also introduced fields with imaginary mass (now also referred to as "tachyons") in an attempt to understand the microphysical origin such particles might have.

The first hypothesis regarding faster-than-light particles is sometimes attributed to German physicist Arnold Sommerfeld in 1904, and more recent discussions happened in 1962 and 1969.

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