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.
