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Line 48: === 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]]: Line 81: 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.<ref name="Jarrell" /> 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 backward in time. Because one of the two fundamental [[postulates of special relativity]] says that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backward 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 in ''every'' frame and opening the door to severe logical paradoxes.<ref name="Gron" /> This is known as the [[tachyonic antitelephone]]. ==== Reinterpretation principle ==== <!-- "Reinterpretation principle" redirects here. --> The '''reinterpretation principle'''<ref name="Feinberg 1967-1969" /><ref name="sudarshan62" /><ref name="Gron" /> asserts that a tachyon sent ''back'' in time can always be ''reinterpreted'' as a tachyon traveling ''forward'' in time, because observers cannot distinguish between the emission and absorption of tachyons. The attempt to ''detect'' a tachyon ''from'' the future (and violate causality) would actually ''create'' the same tachyon and send it ''forward'' in time (which is causal). Line 91 ⟶ 92: === Fields with imaginary mass === {{ In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with [[imaginary mass]].<ref name="Feinberg 1967-1969" /> Because the [[group velocity]] for such a field is [[Superluminal motion|superluminal]], naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the [[negative mass]] represents an instability to [[tachyon condensation]], and all excitations of the field propagate subluminally and are consistent with causality.<ref name="susskind" /> Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.<ref name="Sen" /><ref name="Greene" /><ref name="Kutasov" /><ref name="Gibbons" /><ref name="Randall 2005 p286" /> | |||