Since particles obey wave equations, in general one is not free to postulate
that particles move on the geodesics associated with test particles. Rather,
for this to be the case one has to be able to derive such behavior starting
from the equations of motion that the particles obey, and to do this for either
massless or massive particles one can employ the eikonal approximation. While
for massive particles one does obtain standard geodesic behavior this way, for
a conformally coupled massless scalar field the eikonal approximation only
leads to geodesic behavior if the Ricci scalar is zero. Similarly, for the
propagation of the light waves associated with the conformal invariant Maxwell
equations geodesic behavior only holds if the Ricci tensor is zero. While for
practical purposes such terms might only be of relevance in regions of high
curvature, the point of this paper is only to establish their presence in
principle. Thus in principle the standard null-geodesic-based gravitational
bending formula and the behavior of light rays in cosmology are in need of
modification in regions with high enough curvature. We show how to
appropriately modify the geodesic equations in such situations. We show that
relativistic eikonalization has an intrinsic light-front structure, and show
that eikonalization in a theory with local conformal symmetry leads to
trajectories that are only globally conformally symmetric. The modifications to
geodesics that we find lead to the propagation of massless particles off the
light cone. This is a curved space reflection of the fact that when light
travels through a refractive medium in flat spacetime its velocity is modified
from its free flat spacetime value. In the presence of gravity spacetime itself
acts as a medium, and this medium can then take light waves off the light cone.