The report is devoted to the critical analysis of some aspects of the relativity theory (RT). The logical and physical inconsistency of RT can be shown on the basis of some paradoxes, such as the modified twins paradox, paradox of antipodes etc (see http://www.antidogma.ru). RT can hide contradictions in the case of two points moving along one straight line only, but it appears inconsistent for more than two objects, or for a three-dimensional movement even for two objects moving on crossed straight lines. The classical approach separates an object under investigation from other Universe. Newton introduced classical notions of kinematics to determine registration points and standards independent on process under investigation (the base for uniform description of various phenomena, for joining of different areas of knowledge and simplification of the description). The relativistic equation of charge movement with the Lorentz force is simply reduced to Newton's 2nd law. There are neither physical nor mathematical bases to claim, as if Lorentz transformations (received for emptiness) determine all properties in the Universe. Even the analysis of invariance of Maxwell equations shows, that the hypothesis about application of Lorentz transformations to all the physical phenomena is groundless. The analysis of modern electrodynamics also shows, that it cannot be considered as principally strict theory (but only as approximate one). The ultimate conclusion of work consists in necessity of return to the classical concepts of space, time and interpretation of the phenomena on the basis of a classical paradigm.
