I.V. Bezmenov, I.Yu. Blinov

Al’manac of Modern Metrology № 2 (7) 2016, pages 39–66

The alternative axioms of STR (without Einstein’s second postulate) given in [1] and in the one-space variable case are formulated for the case of three space variables. For two inertial frames of reference (IFR), one of which is moving in an arbitrary direction relative to the other, formulas are sought for the transformation of the space-time coordinates of the four-vectors of the same event recorded by observers in these frames. From the assumptions of the smoothness of the sought transformation (axiom 1) and the invariance of the speed of relative motion of two free particles in different IFR (axiom 2), linearity of the transformation for the 3D case is proved. From the axioms of the equality of all IFR (axiom 3) and the isotropy of space (axiom 4), which assume the invariance of the form of the transformation under consistent rotations of the space coordinates of both frames that belong to the group SO(3) and under total space inversion of both frames, Lorentz equations are derived. This work extends to the 3D case the methods set forth in [1], [4-7] where the Lorentz equations were derived in the one-dimensional case.

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