Tachyon
Particle Faster Than Light!
What Is Tachyons?
A tachyon (/ˈtækiɒn/) or tachyonic particle is a hypothetical particle that always travels faster than light. Most physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. Tachyon is the name given to the supposed "fast particle" which would move with v > c. Tachyons were first introduced into physics by Gerald Feinberg, in his seminal paper "On the possibility of faster-than-light particles"
[Phys. Rev. 159, 1089—1105 (1967)].
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={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}.}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 {\displaystyle v}v (the particle's velocity) is larger than {\displaystyle c}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)[why?] 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.
One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, {\displaystyle E}E approaches zero when {\displaystyle v}v approaches infinity. (For ordinary bradyonic matter, {\displaystyle E}E increases with increasing speed, becoming arbitrarily large as {\displaystyle v}v approaches {\displaystyle c}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
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 the spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other)
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