A tachyon or a superluminal wave group appears as a spacelike structure through a region in the reference frame in which it is at rest. Such a structure can arise from residue left (a) by a particle or wave group traveling at fundamental speed c or less, or (b) in the creation or separation of particles. Thus, Maund's argument does not prove that tachyons cannot exist. Creation may include lepton-quark production as well as particle-antiparticle production.

The theory of relativity forbids the superluminal travel of ordinary matter. However, it is possible to amend the theory of relativity and to develop a theory permitting superluminal travel. The acceptability of the features needed for superluminal travel is discussed.