Reference spaces in Special Relativity Theory: an intrinsic approach

Abstract

Starting from a suggestion of Einstein on the construction of the concept of space, we elaborate an intrinsic method to obtain space and time transformations between two inertial spaces of reference, mathematically modeled as affine euclidean spaces. The principal device introduced for relating the space readings in both spaces is the so-called tracer mapping, which makes a snapshot of a space onto the other. The general form of the space and time transformations is obtained as an affine--preserving mapping compatible with the principle of relativity, a cylindrical symmetry around the relative velocities between spaces and the group character of the transformations. After having obtained Galileo and Lorentz transformations, the same method has been applied to two classical problems: the Coriolis theorem of Newtonian Mechanics and the geometry of a rotating disk in Special Relativity. Even in the case of Newtonian Mechanics, the possibility of distinguishing the spaces of reference is found useful.