An alternative to relativistic transformation of special relativity   based on the first principles
  A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz transformation is via transforming physical quantities, instead of space-time coordinates, to make laws of nature form-invariant. The differential Lorentz transformation may provide a way to resolve the incompatibility of the theory of special relativity and the quantum theory. 
Young-Sea Huang