ABSTRACT
The CC relativity theory does not accept a priory any restriction on the values of speeds and on the scaling coefficients. It is completely relaxed of such constraints. It discovers the existence of the basic time scaling coefficients in the mathematical relativity theories including both Galilean - Newtonian relativity theory and Einsteinian relativity theory. It introduces them from the theory of dynamical systems with multiple time scales into the mathematical relativity theories. It overcomes the problems of inconsistencies and of paradoxes caused by Einstein’s a priory accepted sever constraints. The fundamentals of the CC relativity theory are established so that the
transformations obey the generalized distance preservation condition. Each of them forms the Poincaré group. The CC relativity theory uses consistently the values of all the variables rel-
ative to integral spaces. It does not accept a priory the invariance of any speed (e.g. of the light speed and/or of the temporal or spatial transfer speed). It establishes a great variety of the coordinate and of the velocity transformations. It presents the proofs of necessity and of sufficiency of their forms, structures and arguments. It provides also the proofs of complete both entire and pairwise compatibility of the transformations. They open various new directions for future developments of the mathematical relativity theories of time. Their common physical basis are the properties of time expressed in Axiom 47. The obtained results agree fully with this axiom. The transformations of the coordinates that do not obey Einstein’s a pri-
ory accepted constraints are permissible for correct applications. Consequently, the formulae valid in terms of such coordinates need not agree with those of Einsteinian relativity theory. It is not the form of a mathematical model that
provided the units are constant. The relationships among coordinates are essential for mathematical models related either to noninertial or to inertial frames. They should adequately express the modelled physical phenomena, process or system. The mathematical models should be mutually equivalent. The physical laws, the used coordinates and the relationships among them, determine the forms of the mathematical models. We may apply any coordinate transformation to every mathematical model.
Whether such application will be useful, we cannot always conclude a priory.
