  This paper defines the spacetime geometry attached with observor as vacuum
geometry (it defines the idea physical measurement geometry) and the spacetime
geometry attached with matter as spacetime geometry. The initial spacetime
geometry attached with matter is taken as refference geometry (named as initial
co-moving coordinator system), and the current spacetime geometry attached with
matter (named as current co-moving coordinator system) is determined by the
four-dimensional displacement field measured in initial spacetime geometry.
Matter motion is expressed by the motion transformation of basic vectors of
four-dimensional co-moving coordinator system. The transformation of motion
expressed by displacement describes the transient geometry form of matter
motion. In general relativity theory and in gauge field theory, the geometrical
invariant of word-line distance is used to define the geometry of space-time
continuum. However, based on this research, this is only true when the
time-shift is in special form. For more complicated matter motion, the gauge
field theory and general relativity will be failed. The paper shows that
traditional physical conservation laws and the geometrical invariant introduced
by the gauge field theory and general relativity are included in the finite
geometrical field theory as simple special cases.

General Physics