ABSTRACT
After relaxing the a priory imposed conditions on the time scaling coefficients αji and α
i j to be equal, and on the space scaling coefficients λ
j i and λ
i j to be
also equal, we established various new forms of the time-invariant coordinate transformations in the general case. They are essentially different from Lorentz transformations. They do not contain either square roots or squared ratios of speed values. They are expressed in terms of relative values of speeds, including the relative values of the light speed and of the spatial transfer speed, with respect to the corresponding integral spaces. They enable a number of various consistent nonuniform and uniform coordinate transformations. The transformations are valid also for the particular case when the inertial
frames move in parallel, in the same sense and with the same speeds. Then they take the well known classical forms, which express the influence of a time scale and/or of a time unit change. Lorentz transformations do not express such influence. They are inapplicable in this case. Still in the special case we got new formulae different from Einsteinian. By starting with the features of time (Axiom 47) and by accepting a pri-
ory the same restrictions of Einsteinian relativity theory, we reproved Lorentz transformations as the singular case. There is not any contradiction between the time independence of the space and Lorentz transformations. This warns that Lorentz transformations, and from them deduced other results, do not and cannot prove time dependence of space, and may not be used to claim wrongly such time dependence. New velocity transformations resulted. We determined them for an arbi-
trary speed of the arbitrary point P by applying Einsteinian methodology to ignore the fact that the temporal and the spatial coordinate transformations were established exclusively either for the light speed or for another fixed reference speed used in the proofs as the speed of the arbitrary point P . Their or
μi general case, while the velocity transformations resulting from Lorentz transformations, i.e. the formulae of Einstein’s law of the composition of velocities, do not. Their partial compatibility is the consequence of the a priory accepted Lorentz - Einstein - Poincaré condition imposed on the scaling coefficients to be determined exclusively for the light speed of the arbitrary point P . The results show that the light speed is not invariant relative to all integral
spaces containing inertial frames. Lorentz - Einstein invariance of the light speed is the consequence of the property of the formula. It is not a property of light or of the light speed. The same holds for the spatial transfer speed v(.)ji . These facts explain why the a priory accepted invariance of both the light speed and the spatial transfer speed impose so sever restrictions on Einsteinian relativity theory that it represents a singular case. We considered only time-invariant coordinate transformations in order to
satisfy Einsteinian condition that the scaling coefficients are (positive) real numbers. Becoming aware of the above facts, we will continue studying the coor-
dinate transformations by omitting completely Lorentz - Einstein - Poincaré constraints.
