Editing Exotic matter (section)

== Complex mass ==
{{Main|Tachyon#Mass}}

A hypothetical particle with complex rest mass would always travel faster than the [[speed of light]]. Such particles are called [[tachyon]]s. There is no confirmed existence of tachyons.

: <math>E = \frac{m\cdot c^2}{\sqrt{1 - \frac{\left|\mathbf{v}\right|^2}{c^2}}}</math>

If the rest mass <math>m</math> is complex this implies that the denominator is complex because the total energy is [[observable]] and thus must be [[real number|real]]. Therefore, the quantity under the square root must be negative, which can only happen if [[speed|''v'']] is greater than [[speed of light|''c'']]. As noted by [[Gregory Benford]] ''et al.,'' [[special relativity]] implies that tachyons, if they existed, could be used to communicate backwards in time<ref>{{cite journal|author1=G. A. Benford |author2=D. L. Book |author3=W. A. Newcomb |year=1970|title=The Tachyonic Antitelephone|journal=[[Physical Review D]]|volume=2 |issue=2 |page=263|doi=10.1103/PhysRevD.2.263|bibcode = 1970PhRvD...2..263B }}</ref> (see [[tachyonic antitelephone]]). Because [[time travel]] is considered to be non-physical, tachyons are believed by physicists either not to exist, or else to be incapable of interacting with normal matter.

In [[quantum field theory]], complex mass would induce [[tachyon condensation]].