  We review the classical and quantum mechanics of Stueckelberg, and introduce
the compensation fields necessary for the gauge covariance of the Stueckelberg-
Schr\"odinger equation. To achieve this, one must introduce a fifth, Lorentz
scalar, compensation field, in addition to the four vector fields which
compensate the action of the space-time derivatives. A generalized Lorentz
force can be derived from the classical Hamilton equations associated with this
evolution function. We show that the fifth (scalar) field can be eliminated
through the introduction of a conformal metric on the spacetime manifold. The
geodesic equation associated with this metric coincides with the Lorentz force,
and is therefore dynamically equivalent. Since the generalized Maxwell
equations for the five dimensional fields provide an equation relating the
fifth field with the spacetime density of events, one can derive the spacetime
event density associated with the Friedmann-Robertson-Walker solution of the
Einstein equations. The resulting density, in the conformal coordinate space,
is isotropic and homogeneous, decreasing as the square of the Robertson-Walker
scale factor. Using the Einstein equations, one sees that both for the static
and matter dominated models, the conformal time slice in which the events which
generate the world lines are contained becomes progressively thinner as the
inverse square of the scale factor, establishing a simple correspondence
between the configurations predicted by the underlying
Friedmann-Robertson-Walker dynamical model and the configurations in the
conformal coordinates.
