On the Origin of the Lorentz Transformations and the Special Theory of Relativity

A brief review of the history of the establishment of the Lorentz transformations and the special theory of relativity is given. The properties of privileged systems in uniform motion with respect to each other are then studied under the assumptions that space and time are homogeneous, that space is isotropic and symmetric with respect to velocities, and that the superposition of two positive velocities will again be a positive velocity, but without any reference to the phenomenon of light or electromagnetic phenomena. It is shown that the space and time coordinates of two systems are connected by linear relations, which have exactly the same form as the Lorentz transformations but contain a parameter a, which has the character of a limit velocity and is a fundamental structure constant of space-time. Phenomena moving with limit velocity in one privileged system are going to move with limit velocity in all privileged systems, and it is then natural to assume that light moves with limit velocity. After introducing the concepts of a Minkowski space, the laws of dynamics are studied in greater detail and the relation E=mc² is derived without any reference to radiation or electromagnetic phenomena in general. The results are going to be used to study the behavior of classical waves in privileged systems as a preparation for the introduction of “wave mechanics”.