  The Lorentz force equations provide a partial description of the geodesic
motion of a charged particle on a four-manifold. Under the hypothesis that
Maxwell's equations express symmetry properties of the Ricci tensor, the full
electromagnetic connection is determined. From this connection, the fourth
equation of the geodesic is derived. The validity of this fourth equation can
be determined by studying the decay of charged particles in an electric field.
Time will accelerate or decelerate relative to the proper time of a charged
particle moving in an electric field. Unstable charged particles moving in
opposite directions parallel to an electric field should exhibit different
decay rates.
