Departamento de Matemática, Universidade Federal de Santa Catarina

We present two models combining some aspects of the Galilei and the Special Relativity that leads to a unification of both relativities. This unification is founded on a reinterpreta-tion of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low veloc-ity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, e.g. the Lorentz transformation and the velocity law, follows from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a second model that leads to a gen-eralization of the Lorentz transformation, which includes, as particular cases, the standard Lorentz transformation and transformations that apply to the case of superluminal frames.