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The central concept of the theory of relativity is relative velocity. The velocity of a material body is not an intrinsic property of this body; it depends on the free choice of reference system. Relative velocity is thus reference-dependent; it is not an absolute concept. We stress that even zero-velocity must be relative. Every reference system possesses its own zero-velocity relative to exactly that one system. The theory of relativity formulated in terms of relative velocities, with many zero-velocities, does not imply the Lorentz isometry group. Moreover, we discuss a conceptual dichotomy: two different rival concepts of reference system: the Minkowski space-time observer-monad as time-like vector field, versus the Einstein space-time coordinate tetrad.

The central concept of the relativity theory is a relative velocity. Relativity of the velocity means that the velocity is not absolute concept. The velocity of positive-mass body is not an intrinsic property of this body; it depends on the free choice of the reference system, it is reference-dependent. We stress that the zero velocity must be relative. Every reference system possess the own zero-velocity relative to exactly this system. Many zeroth-velocities contradict to group structure, and therefore the relativity theory in terms of relative velocities must be formulated within the groupoid structure, which is not a group. There is a dichotomy: two di
erent concepts of a positive mass body, a tetrad versus a monad.