Summary: Quantum field theory of spacelike particles is investigated in the framework of an absolute causality scheme preserving Lorentz symmetry. It is related to an appropriate choice of synchronization procedure (definition of time). In this formulation existence of field excitations (tachyons) distinguishes an inertial frame (privileged frame of reference) via spontaneous breaking of the so-called synchronization group. In this scheme the relativity principle is broken but Lorentz symmetry is exactly preserved in agreement with local properties of the observed world. It is shown that tachyons are associated with unitary orbits of Poincare mappings induced from the SO(2) little group instead of the SO(2,1) group. Therefore the corresponding elementary states are labeled by helicity. The cases of the helicity \(\lambda=0\) and \(\lambda=\pm\frac12\) are investigated in detail and a corresponding consistent field theory is proposed. In particular, it is shown that the Dirac-like equation proposed by A. Chodos, A. I. Hauser and V. A. Kostelecky [Phys. Lett. B 150, No. 6, 431–435 (1985)], inconsistent in the standard formulation of QFT, can be consistently quantized in the presented framework. This allows us to treat more seriously the possibility that neutrinos might be fermionic tachyons, as is suggested by experimental data about neutrino masses [R. M. Barnett et al., Phys. Rev. D (3) 54, No. 1, 1–708 (1996); K. Assamagan et al., Phys. Lett. B 335, No. 2, 231–236 (1994); Phys. Rev. D (3) 53, No. 11, 6065–6077 (1996); G. Gelmini and R. Roulet, CERN Preprint CERN-TH 7541/94, Geneva, (1994)].