  We give a critical analysis of projective relativity theory. Examining
Kaluza's own intention and the following development by Klein, Jordan, Pauli,
Thiry, Ludwig and others, we conclude that projective relativity was abused in
its own terms. Much more in the case of newer higher dimensional Kaluza--Klein
theories with non-Abelian gauge groups. Reviewing the projective formulation of
the Jordan isomorphy theorem yields some hints how one can proceed in a
different direction. We can interpret the condition R5_{\mu\nu}=0 not as a
field equation in a 5-dimensional Riemannian space, e.g. as vacuum
Einstein-Hilbert equation, but can (or should) interpret it as a geometrical
object, a null-quadric. Projective aspects of quantum (field) theory are
discussed under this viewpoint.
