A note to the linearity proof of Lorentz transformation

The traditional proof of the linearity of Lorentz transformation makes use of a definition of simultaneity and a physical law for the propagation of light. For unravelling these two elements we use a reverse axiomatic approach to special relativity. In this case we are free, in principle, to introduce an arbitrary simultaneity. Linear coordinate transformations require a linear synchronisation. Lorentz transformation results from a special kind of linear synchronisation.