Bateman On Light: Synchrotron Rays

For over a century physicists have sought a mathematical theory that unites the dual, wave and corpuscle, behaviors that light exhibits. In the early twentieth century H. Bateman was studying a solution that uses wave functions with singularities to mark light quanta location in space and time as potential singularities do for material particles. He published an incomplete, mathematically obtuse paper applying his scheme to presciently predict synchrotron rays well before they were experimentally observed. Here, I clarify the presentation in Bateman's paper and supply a missing demonstration that it does predict results observed nearly four decades later.