Do tachyons violate the causality principle?

Very early, A. EINSTEIN has shown that particles with velocities greater than the velocity of light in vacuum may produce causal anomalies. Later, in quantum mechanics CPT transformations have allowed causal loops at a microscopic scale. So the possibility of faster-than-light particles has been analyzed again. The Meta-Relativity has extended the special theory of Relativity to particles beyond the light barrier (tachyons), by using the relativist formula with complex values. It has assigned to any tachyon an imaginary proper mass which does not easily offer a physical interpretation. In the framework of that theory, tachyons may appear to travel backwards in time and have negative energies, but they have to be interpreted as travelling forwards in time with positive energies (reinterpretation principle). The Meta-Relativity allows a tachyon reflection or re-emission to produce a causal loop, but some authors rejects the objection by postulating the tachyon emission cannot be systematically repeated. So causal loops can only occur at a microscopic scale. The theory of Relativity in the spacelike region has been developed by R. DUTHEIL using the tensor formalism of the general theory of Relativity. He defined tachyonic referential frames (TRF) with an other metric tensor and he showed it leads to an other LORENTZ group of transformations—the superluminal LORENTZ group. In this theory, tachyons always have a positive energy and a real proper mass, but their behavior must be described with tachyonic referential frames. R. DUTHEIL argued from the isomorphism of the both LORENTZ groups to prove the ZEEMAN'S theorem is respected by tachyons; so a sequence order is always preserved by any superluminal transformation. In the present communication, I show that time coordinates of tachyonic referential frames do not preserve causal order and do not make sense for natural observers. Nevertheless I show that the causal order is preserved within the superluminal proper time of tachyons, which is to be related to the proper time of any natural observer.