  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.

Classical Physics