  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.
