# Self-consistent translational motion of reference frames and sign-definiteness of time in universal kinematics

### Abstract

Universal kinematics as mathematical objects may be interesting for astrophysics, because there exists a hypothesis that, in the large scale of the Universe, physical laws (in particular, the laws of kinematics) may be different from the laws acting in a neighborhood of our solar System. The present paper is devoted to investigation of self-consistent translational motion of reference frames in abstract universal kinematics. In the case of self-consistent translational motion we can give a clear and unambiguous definition of displacement as well as the average and the instantaneous speed of the reference frame. Hence the uniform rectilinear motion is a particular case of self-consistent translational motion. So, the investigation of self-consistently translational motion is technically necessary for definition of classes of inertially-related reference frames (being in the state of uniform rectilinear mutual motion) in universal kinematics. In the paper we investigate the correlations between self-consistent translational motion and definiteness of time direction for reference frames in universal kinematics.

**Key words:** Theory of universal kinematic sets, unanimously-translational reference frames, inertial reference frames, separately continuous mappings.