(and this will be the case for all ordinary velocities, such as those which occur in mechanics), the equations of transformation degenerate into:
This is the familiar Galilean transformation which holds for the "mechanical" principle of relativity. We see that the Lorentz-Einstein transformation covers both mechanical and radiational phenomena.
The special theory of relativity may now be enunciated as follows: All systems of reference which are in uniform rectilinear motion with regard to one another can be used for the description of physical events with equal justification. That is, if physical laws assume a particularly simple form when referred to any particular system of reference, they will preserve this form when they are transformed to any other co-ordinate system which is in uniform rectilinear motion relatively to the first system. The mathematical significance of the Lorentz-Einstein equations of transformation is that the expression for the infinitesimal length of arc
in the space-time[19] manifold
,