  Special relativity theory is well established and confirmed by experiments.
This research establishes an operational measurement way to express the great
theory in a geometrical form. This may be valuable for understanding the
underlying concepts of relativity theory. In four-dimensional spacetime
continuum, the displacement field of matter motion is measurable quantities.
Based on these measurements, a finite geometrical field can be established. On
this sense, the matter motion in physics is viewed as the deformation of
spacetime continuum. Suppose the spacetime continuum is isotropic, based on the
least action principle, the general motion equations can be established. In
this part, Newton motion and special relativity are discussed. Based on the
finite geometrical field theory of matter motion, the Newton motion equation
and the special relativity can be derived simply based on the isotropy of
spacetime continuum and the definition of inertial system. This research shows
that the Lorentz transformation is required by both of the inertial system
definition and the time gauge invariance for inertial systems. Hence, the
special relativity is the logic conclusion of time invariance in inertial
system. The source independent of light velocity supports the isotropy of
inertial system rather than the concept of proper time, which not only causes
many paradox, such as the twin-paradox, but also causes many misunderstanding
and controversial arguments. The singularity of Lorentz transformation is
removed in other parts of finite geometrical field theory, where the gravity
field, electromagnetic field, and quantum field will be discussed with the time
displacement field.
