  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.
