2002/01/14 by Michael A. Graber, Graber, Michael A.
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0201027
10 pages, prepared with LaTeX2e
arxiv created 2002/01/14 · arxiv updated 2009/11/30
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.