Tachyons Without Causal Loops in One Dimension

Abstract

It is shown that, for the case of one spatial dimension, it is possible to formulate a theory of tachyons which is consistent with the special theory of relativity and involves no violation of causality. The preservation of causality requires the assumption that tachyons exist only with one sign of momentum. Although this assumption is not invariant under space inversion, it is consistent with the principle of relativity. In addition to the preservation of causality, a possible rationale for such an assumption is discussed briefly.