The paper discusses limitations resulting from the laws of conservation of energy and momentum in the processes of elastic and quasi-elastic scattering of relativistic particles with the participation of tachyons, luxons, and bradyons. The obtained expressions for the particle energies are given in the center-of-mass system in the generally accepted Mandelstam variables. Using the laws of conservation of energy and momentum, several channels of reactions of ultrarelativistic particles of high energy in cosmic rays have been considered. It has been shown that on the basis of the expressions obtained, assuming the existence of particles with imaginary masses - tachyons, the effect of "red shift" can be explained. © Published under licence by IOP Publishing Ltd.