Imaginary Mass
A hypothetical particle with imaginary rest mass would always travel faster than the speed of light. Such particles are called tachyons. There is no confirmed existence of tachyons.
If the rest mass is imaginary this implies that the denominator is imaginary since the total energy is an observable and thus must be real; therefore the quantity under the square root must be negative, which can only happen if v is greater than c. As noted by Gregory Benford et al., among others, special relativity implies that tachyons, if they existed, could be used to communicate backwards in time (see Tachyonic antitelephone article). Since time travel is considered to be non-physical, tachyons are believed by physicists either to not exist, or else to be incapable of interacting with normal matter.
In quantum field theory, imaginary mass would induce tachyon condensation.
Read more about this topic: Exotic Matter
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