Generalised transformation relations for (1+1) dimensional motion of superluminal particles

Abstract

Here, we have proposed new transformation relations between two inertial frames with relative velocity greater than speed of light and discussed the required conditions to detect the faster than light particles in physical realm. For this a novel theoretical formulation is conceptualized to uniquely depict the frame of references, valid for all ranges of velocities, in a complex plane. For the tachyonic regime, the super-relativistic gamma (SRG) factor is obtained by parameterizing the generalised gamma factor using the complementary frames of reference of superluminal and subluminal space. This generalised gamma factor can also be reduced in the form of Lorentz factor for subluminal frame of references. The formulation of transformation relations has been analysed in four different classes, i.e., two inter and two intra classes of frames, for subluminal and superluminal particles. Further, it is suggested that intra classes of frames encompass a real gamma factor, whilst, inter classes of frames involve imaginary gamma factor. Velocity addition relations have been deduced and discussed corresponding to each transformation relations. To the end of this work, a generalized gamma factor has been concluded and validated for both frames of references.