Tachyons

A tachyon or tachyonic particle is a hypothetical particle that always moves faster than light. It was coined in 1967 by Gerald Feinberg. The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan in 1962, although the term they used for it was “meta-particle”.

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Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality. 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.

In the 1967 paper that coined the term,Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,and instead represent an instability known as tachyon condensation.Nevertheless, negative squared mass fields are commonly referred to as “tachyons”, and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from “a faulty element of the experiment’s fibre optic timing system”.

As mentioned above, the term “tachyon” was coined by Gerald Feinberg in a 1967 paper titled “Possibility of Faster-Than-Light Particles”.He had been inspired by the science-fiction story “Beep” by James Blish. 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.

In special relativity, a faster-than-light particle would have space-like four-momentum,in contrast to ordinary particles that have time-like four-momentum. It would also have imaginary mass and proper time. Being constrained to the spacelike portion of the energy–momentum graph, it could not slow down to subluminal speeds.

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, the denominator in the equation for the energy is “imaginary”, as the value under the radical 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.
One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when 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 Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time.

Causality is a fundamental principle of physics. If tachyons can transmit information faster than light, then according to relativity they violate causality, leading to logical paradoxes of the “kill your own grandfather” type. This is often illustrated with thought experiments such as the “tachyon telephone paradox” or “logically pernicious self-inhibitor.”

The problem 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 relativitysays 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, challenging causality inevery frame and opening the door to severe logical paradoxes. Mathematical details can be found in the tachyonic antitelephonearticle, and an illustration of such a scenario using spacetime diagrams can be found in Baker, R. (2003)

 

Tachyons have appeared in many works of fiction. They have 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 connotation even if the subject in question has no particular relation to superluminal travel (a form of technobabble, akin to positronic brain)

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