Relativity: A Matter of Causality

Abstract We take causality and uniqueness of events observation as our driving forces. They are embedded in the way we define distinct observers, which then require a finite time to communicate between each other. This inevitably leads to the existence of a maximal transfer-information velocity between arbitrary (not necessarily inertial) reference frames. Inertial reference frames are defined by fixing the geometrical properties of (spatial) distance without any reference to relativity, electromagnetism, or laws of physics in general. For these inertial reference frames, the causality condition fixes the causal group to be the orthochronous inhomogeneous Lorentz group times dilatations. The mathematics we will use are quite basic.