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The Lorentz-Dirac equation in complex space-time

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Abstract

A hypothetical equation of motion is proposed for Kerr–Newman particles. It’s obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time. A new class of “runaway” solutions are found which are similar to zitterbewegung. Electromagnetic fields generated by these motions are studied, and it’s found that the retarded (and advanced) times are multi-sheeted functions of the field points. This leads to non-uniqueness for the fields. With fixed weighting factors for these multiple roots, the solutions radiate. However, position dependent weighting factors can suppress radiation and allow non-radiating solutions. Motion with external forces are also considered, and radiation suppression is possible there too. These results are relevant for the idea that Kerr–Newman solutions provide insight into elementary particles and into emergent quantum mechanics. They illustrate a type of nascent wave-particle duality and complementarity in a purely classical field theory. Metric curvature due to gravitation is ignored.

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Acknowledgments

The author acknowledges Alexander Burinskii for informative correspondence and the open source groups supporting the Octave and Maxima computer languages along with the Wolfram-Alpha website which have been used in the course of this work.

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    Mark Davidson

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Davidson, M. The Lorentz-Dirac equation in complex space-time. Gen Relativ Gravit 44, 2939–2964 (2012). https://doi.org/10.1007/s10714-012-1432-6

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