Abstract
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Highlights
Conventional dynamics describes interactions with forces and fields; impulses are an afterthought
The divergent electrostatic self-energy of charges is avoided because there are no self-fields; impulse dynamics deals only with the interaction between particles
IV, the choice Eq (3) for impulse electrodynamics is in broad agreement with relativistic Møller and Mott cross sections [7]
Summary
Conventional dynamics describes interactions with forces and fields; impulses are an afterthought. Impulse dynamics does not use forces or fields or differential equations; it models interactions as a continual exchange of impulses. The familiar forces, fields, and potentials are not always a satisfactory foundation for dynamics. There are fundamental problems in classical electrodynamics that impulse dynamics successfully addresses or avoids. The divergent electrostatic self-energy of charges is avoided because there are no self-fields; impulse dynamics deals only with the interaction between particles. The calculation of two-particle trajectories does not involve hard to solve retarded differential equations; it is algebraic and straightforward, numerically challenging. The straightforward approach of impulse dynamics solves or avoids some of the problems at the foundations of classical electrodynamics. We are able to show how the classical action along a trajectory defines a Coulomb phase shift
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