  Besides two fundamental postulates, (i) the principle of relativity and (ii)
the constancy of the one-way speed of light in all inertial frames of
reference, the special theory of relativity uses the assumption about the
Euclidean structure of gravity-free space and the homogeneity of gravity-free
time in the usual inertial coordinate system. Introducing the so-called primed
inertial coordinate system, in addition to the usual inertial coordinate
system, for each inertial frame of reference, we assume the flat structures of
gravity-free space and time in the primed inertial coordinate system and,
hence, their generalized Finslerian structures in the usual inertial coordinate
system. We further modify the special theory of relativity by combining the
alternative assumption with the two postulates (i) and (ii). The modified
special relativity theory involves two versions of the light speed, infinite
speed c-prime in the primed inertial coordinate system and finite speed c in
the usual inertial coordinate system. It involves the c-prime-type Galilean
transformation between any two primed inertial coordinate systems and the
localized Lorentz transformation between any two usual inertial coordinate
systems. The physical principle in the modified special relativity theory is:
the c-prime-type Galilean invariance in the primed inertial coordinate system
plus the transformation from the primed to the usual inertial coordinate
systems. It combines with the quantum mechanics theory to found a convergent
and invariant quantum field theory. We produce corrections to the Maxwellian
velocity and velocity rate distributions for free particles. The detection of
velocity and velocity rate distributions for free particles can serve as the
tests to investigate the local structures of gravity-free space and time.
