A study of the Lorentz-Dirac equation in complex space-time for clues to emergent quantum mechanics

A hypothetical equation of motion is proposed for Kerr-Newman particles. Obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time, the goal is to study the implications of this theory for emergent quantum mechanics. A new class of "runaway" solutions is found which bear similarity to the quantum phenomenon of Zitterbewegung. Other solutions incorporating external forces are also presented. The electromagnetic fields generated by these motions are studied. It is found that the retarded times are multi-sheeted functions of the field points. As a consequence, the solutions are not unique. A cloaking mechanism is found which inhibits electromagnetic radiation by combining the fields from several Riemann sheets for the retarded time. These results reinforce to some extent, but also pose additional conceptual questions for the idea that Kerr-Newman solutions provide insight into elementary particles and into emergent quantum mechanics.