Learning more from the Lorentz transformations

Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or dilation effects. Furthermore we quantify the simultaneity error occurring in the relativity theory. Having done this, we analyse the root cause of these effects and identify it with a finite phase velocity associated with the moving frame. We define this phase velocity by analogy to the de Broglie wave associated with a moving particle. Based on this construct we demonstrate that the phase of the de Broglie waves further extended for stationary particles is a relativistic invariant being the same for all corresponding observers. Also the phase of the electromagnetic waves transporting energy at light speed is a relativistic invariant. Therefore the universe and its matter / energy may be seen as a superposition of waves propagating such that their phase is the same for all corresponding observers. The wave phase may replace the time as an invariant and universal reference.