Einstein’s 1905 Paper rides on a Kinematical Mistake to get the Lorentz Transformation

Abstract

Einstein’s derivation of the Lorentz transformation in section 3 of his famous 1905 paper is based on kinematics of light rays in X, Y and Z directions. However, the velocity of light worked out in Y and Z directions, with respect to the frame moving in X direction, and as observed from the stationary frame, is found to be incorrect. This renders the entire derivation invalid.

It is further pointed out that even if the mistake was ignored, the relations are achieved by taking a time that is for travel of light from origin to a specific location (mirror). This limits the applicability of the relations only to events of light. Despite the restriction, however, Einstein extensively applied the relations to rigid bodies and moving clocks, even in the same paper.

It is also discussed as to how, in the derivation of his 1916 book, he used the relations derived for a moving light signal, on rigid bodies.

Further, a new objection-free method has been presented based on kinematics, using the principle of reciprocity of relative velocity between the two frames.