Tachyons: difficulties and hopes.

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Tachyon hypothesis intensively discussed in the 70s and in early 80s provokes now a significantly lesser interest because it results in acausal anomalies and in experimental nonobservable symmetries appearing by attempts of superluminal extension of the Lorentz transformations. Nevertheless, tachyons appear stubbornly in string and other generalizations of modern theory. Therefore, the question about conditions under which faster-than-light signals could be realized, does not forfeit their significance. The present state of the tachyon hypothesis is considered. Special attention is focused two main difficulties: acausal effects and contradictions arising by attempts of an extension of the Lorentz transformations in the region of superluminal velocities. Particularly, nonlinear transformations are considered which may be applied both to sub- and superluminal velocities. The analysis of the problem allows to contend that tachyons cannot occur in a macroscopic space-time region, however hope still remains to discover them at a level of ultrasmall intervals Δx, Δt where concepts "earlier", "later" acquire a relative meaning.

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