Differential Lorentz transformation from the principle of relativity with an assumption of invariant speed and impossibility of superluminal motion

Abstract

The differential Lorentz transformation compatible with the uncertainty principle of quantum mechanics is analyzed from the principle of relativity with an assumption of invariant speed. The linearity and the possible form of the transformation are determined by the principle of relativity. The principle of relativity allows the existence of an invariant speed, which is also the maximal speed. However, the specific value of the invariant speed can not be derived theoretically and so the existence of an invariant speed is treated as an assumption. The invariant speed should be determined by experiment, which is the light speed in vacuum as is well-known. As the invariant speed is the maximal speed, motion of micro particles can not be superluminal.