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- Title
The Lorentz-Dirac equation in complex space-time.
- Authors
Davidson, Mark
- 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.
- Subjects
SPACETIME; LORENTZ spaces; EQUATIONS of motion; ELECTROMAGNETIC fields; RADIATION; QUANTUM theory; WAVE-particle duality
- Publication
General Relativity & Gravitation, 2012, Vol 44, Issue 11, p2939
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-012-1432-6