[en] The repeated analysis of spin precession phenomenon of relativistic charged particles was performed. The inevitability of the relativity principle violation on local measurements of spin precession was shown while particle moving along a curvilinear trajectory due to the Thomas precession. The simplest deduction of spin equations of motion has been received in the fixed and reference frames. The possibility to determine the Earth's absolute velocity by means of measuring the azimuthal asymmetry of spin precession was shown. Besides, Lorentz's etheric conception is being developed as a more fundamental theory, which establishes the limits of existing phenomenological method of the conventional isotropic description of the phenomena in moving reference frames within the limits of the special relativity theory. 9 refs.; 3 figs