A pre-metric generalization of the Lorentz transformation (2002.09500v1)

Abstract: The concept of an observer and their associated rest space is defined in a pre-metric (i.e., projective-geometric) context that relates to time+space decompositions of the tangent bundle to space-time. The transformation from one observer to another when the two are in a state of relative motion is then defined, and its relationship to the Lorentz transformation is discussed. The group of all linear transformations that preserve the observer quadric, which generalizes the proper-time hyperboloid in Minkowski space, is defined and the reductions to some of its subgroups are described, as well as its extension to the group that preserves the fundamental quadric, which generalizes the light cone.