Modified transformation laws of coordinates and composition of velocities

A new transformation law of coordinates is determined, which allows the inclusion of complex velocity vectors. It is found that in an isotropic universe which is filled with matter throughout, each frame can have references for its position of rest or of motion in a localized domain wherein a frame at rest does not change its position with time relative to surroundings. However, in the system, the moving frame sees only a reflection of its own motion in the rest-frame to appear it moving in antipodal direction. It is therefore, the relative motion cannot be said to be a just direction reversal with two real velocities having a single magnitude common between them; however, it is a synthesis of both real and imaginary motions. The proposed transformation laws are similar to that of Lorentz under which vector quantities be in cross product or in dot product remain invariant such as Maxwell equations. However, inherent scalar quantities such as mass, time etc. vary to distinguish rest-frame from the moving one. It is seen that the physical processes are exactly the same as Einstein predicted but without reciprocity effects and thus provide a justification of quantization of red-shift and particle decay. These considerations are useful in understanding the intricacies of the micro world such as short-lived particle, antimatter, subatomic particles, gamma rays, gamma-ray burst (GRBs), cosmic rays, dark matter, and asymmetry of Doppler’s shifting images.