An important and crucial Law —‘Law of Light Propagation’— is firstly put forward by author, and a relevant Law —‘Law of Motion Observation’— is revealed. They are fundamental laws in Relativistic Theory for Motion Observation. Minkowski Space-time is the space-time where there is only one ‘Observer’, and could be imagined to be a ‘Single-Observer’s World’, and its ‘World-line’ is represented by a ‘single curve’ . The proposed equations for deriving Lorentz Transformation are defined in Minkowski Space-time, which makes Lorentz Transformation being ‘Identical Transformation’ i.e. ‘Null Transformation’. Lorentz Transformation describes observation process of either one single observer or two relatively rest observers. But, on the contrary, Galilean Space-time is the space-time where there are more than one ‘Observers’, and could be imagined to be a ‘Multi-Observer’s World’, and its ‘World-line’ is represented by a branch of similar curves. The logical relationship for Space-time and Transformation is as follows: Minkowski Space-time, which is the "Set of Identical Transformation", is subset of Galilean Space-time, and Galilean Space-time, which is the "Set of Galilean-Zhou Transformation", is subset of the "Newtonian Space-time" (the ‘Universe Space-time’). Lorentz Transformation in Minkowski Space-time is actually ‘Identical Transformation’ which is only fit for fibre-glass and wiring propagation without Doppler’s Effect, and Galilean-Zhou Transformation in Galilean Space-time is fit for all around wireless propagation with Doppler’s Effect. It is necessary to give crucial physical verification and evidence for predictions and mathematical conclusions made by STR and GTR, deduced in Minkowski Space-time (‘Single-Observer’s World’) by means of Galilean-Zhou Transformation in Galilean Space-time (‘Multi-Observer’s World’ ), otherwise any mathematical conclusion deduced in Minkowski Space-time won’t acquire real physical interpretation and, consequently, will not but just only be mathematical conjecture.