Localization of Lorentz transformation and its induced local Lorentz invariance

Introducing the primed inertial coordinate system, for each inertial frame of reference, in addition to the usual inertial coordinate system, we assume that gravity-free space and time possess the Euclidean structures in the primed inertial coordinate system and the generalized Finslerian structures in the usual inertial coordinate system. We combine these assumptions with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, to derive the localized Lorentz transformation as a linear transformation between any two usual inertial coordinate systems. Based on this, it is proposed that all laws of physics are locally Lorentz-invariant in the usual inertial coordinate system. As a Lorentz-invariant law of physics must be locally Lorentz-invariant while a locally Lorentz-invariant law is not necessarily Lorentz-invariant, the change from the requirement of Lorentz invariance to that of the local Lorentz invariance on laws of physics provides with a larger acceptable scope to explore these laws.