A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists posit that faster-than-light particles cannot exist because they are inconsistent with the known laws of physics. If such particles did exist, they perhaps could be used to send signals faster than light and into the past. According to the theory of relativity, this would violate causality, leading to logical paradoxes such as the grandfather paradox. Tachyons would exhibit the unusual property of increasing in speed as their energy decreases and would require infinite energy to slow to the speed of light. No verifiable experimental evidence has been found to support the existence of such particles. The term "tachyon" is derived from from a 1967 paper by Gerald Feinberg about excitations of a quantum field with imaginary mass. Subsequent work has shown that the excitations are not faster-than-light particles, but particle physicists still discuss "tachyons", e.g., in tachyon condensation, when they are referring to tachyonic fields.
Etymology The term tachyon comes from the Greek: ταχύς, tachus, meaning swift. The complementary particle types are called luxons (which always move at the speed of light) and bradyons (which always move slower than light); both of these particle types are known to exist.
History Faster-than-light particles were discussed before the advent of relativity by such physicists as JJ Thomson and Arnold Sommerfeld. The possibility of existence of faster-than-light particles was also proposed by Lev Yakovlevich Shtrum in 1923. In 1962 and again in 1969 Oleksa-Myron Bilanuik, Vijay Deshpande and E. C. George Sudarshan discussed the possibility of a class of faster-than-light particles consistent with special relativity. As part of their discussion they point out that light particles are never accelerated but rather are created with the full velocity of light. Similarly they argue that while accelerating normal matter beyond the speed of light is inconsistent with special relativity, this does not prevent creation of faster than light particles. The term tachyon was coined by Gerald Feinberg in a 1967 paper titled "Possibility of faster-than-light particles". He proposed that tachyonic particles could be made from excitations of a quantum field with imaginary mass. 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. It was soon realized that Feinberg's model did not in fact allow for superluminal (faster than light) particles or signals and that tachyonic fields merely give rise to instabilities, not causality violations. The term tachyonic field refers to imaginary mass fields rather than to faster-than-light particles. In September 2011, it was reported that a tau neutrino had traveled faster than the speed of light; however, later updates from CERN on the OPERA experiment indicate that the faster-than-light readings were due to a faulty element of the experiment's fibre optic timing system.
Special relativity In special relativity, a faster-than-light particle would have spacelike four-momentum, unlike ordinary particles that have time-like four-momentum. While some theories suggest the mass of tachyons is imaginary, modern formulations often consider their mass to be real, with redefined formulas for momentum and energy. Additionally, since tachyons are confined to the spacelike portion of the energy–momentum graph, they cannot slow down to subluminal (slower-than-light) speeds.
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 c ) 2 + ( m c 2 ) 2 {\displaystyle E^{2}=(pc)^{2}+(mc^{2})^{2}\;}
(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 = m c 2 1 − v 2 c 2 . {\displaystyle 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 {\displaystyle v} (the particle's velocity) is larger than c {\displaystyle c} (the speed of light), the denominator in the equation for the energy is imaginary, as the value under the square root is negative. Because the total energy of the particle must be real (and not a complex or imaginary number) in order to have any practical meaning as a measurement, 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 some modern formulations of the theory, the mass of tachyons is regarded as real.
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