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# 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.

### Article Information

 Title Self-consistent translational motion of reference frames and sign-definiteness of time in universal kinematics Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 2, 107-119 MathSciNet MR3827123 Milestones Received 08/11/2017; Revised 11/01/2018 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

Grushka, Ya. I.
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine

### Citation Example

Ya. I. Grushka, Self-consistent translational motion of reference frames and sign-definiteness of time in universal kinematics, Methods Funct. Anal. Topology 24 (2018), no. 2, 107-119.

### BibTex

@article {MFAT1052,
AUTHOR = {Grushka, Ya. I.},
TITLE = {Self-consistent translational motion of reference
frames and sign-definiteness of time in universal
kinematics},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {2},
PAGES = {107-119},
ISSN = {1029-3531},
MRNUMBER = {MR3827123},
URL = {http://mfat.imath.kiev.ua/article/?id=1052},
}

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