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This paper is dedicated to proving a mathematical result that is paradoxical to Special Relativity Theory (SRT). The conclusion is that the basic formulae of the theory, namely, the Lorentz transformation and its derived formulae for length contraction and time dilation are mathematically inconsistent with each other. From this, it immediately follows that the alleged invariance of Maxwell equations under the transformation has no mathematical significance. Another consequence is thus that the alleged experimental confirmations of SRT cannot be mathematically correct.

This work is dedicated to a detailed mathematical scrutiny of the foundations of Special Relativity Theory (SRT), resulting in severe criticisms against SRT. In this Part I, we investigate the schematic of the Michelson-Morley experiment to measure Earth's speed in ether. The main finding is that a mathematical formula for relative speed used in the experiment has a subtle mistake which was not realized by the next two or three generations of investigators. Surprisingly, correction of this error leads to the conclusion that (from the classical point of view) the Michelson-Morley interferometer is insensitive to its own motion in ether. This finding proves that the experiment is null, and cannot be taken either as evidence against the undulatory theory, or as a motivation for formulation of new natural laws, as were the case for Lorentz's length contraction and time dilation.