Beyond Lorentz One Dimensional Approach: The General Expression of Its Transformation Equations

Abstract

Light propagates with the same velocity c in all directions of a 3D Reference Frame (RF), whether this is stationary or in motion with respect to its source. Analysing the omnidirectional propagation of a flash of light, we obtain a set of transformation equations between a stationary RF and one in motion that are the general expression of Lorentz’ equations.  According to them, the invariance of light speed in RFs in motion between them necessarily requires the existence of a 4-dimensions space-time. Motion, in fact, generates a spatial component normal to the velocity v and to the x, y, z coordinates, therefore an “imaginary” component transverse to the motion itself. This component reduces the “density” of the RF in motion with respect to that of the stationary RF, which means that both its space and time are reduced of the same quantity  . Motion only modifies the RF, that is, the space-time of an object. However, as objects cannot be separated from the space that contains them, inevitably they result modified according to the transformation equations.