Abstract

This article introduces a mathematical model for a Complementary Special Relativity Theory (CSRT) in relation to Einstein?s Special Relativity Theory (SRT). The CSRT is derived following criterion of the logical independence of the Einstein?s postulates. The term "complementary" was selected in order to distinguish CSRT from alternative theories. The mission of the CSRT is not to replace the Einstein's SRT. Both of them must coexist and must have physical applications. Forasmuch as the CSRT postulates do not embody constant velocity of the light, the CSRT need not have four-dimensional symmetry of the Lorentz and Poincare group. The principal parts of the article are: new postulates, transformation equations, frequency transformations, law of the addition of velocities, proposal for the one-way velocity experiment. The existence of the CSRT transverse Doppler effect formula, which is different from Einstein's, is the crucial point of the new theory. Moreover, the article demonstrates some physical applications of the CSRT on John D. Anderson's discovery of a quasi acceleration of the Pioneer 10 spacecraft. It will be shown that the Pioneer 10 does not accelerate, but it moves with predicted velocity, and that the Deep Space Network (DSN) data remarkably well fit the predictions of the CSRT theory in range, Doppler, annual, and diurnal periodicity of the phenomenon. The CSRT needs to develop an adequate electrodynamics. Einstein's SRT, the present CSRT, and another still missing complementary theory need to develop into a complex system.