Perihelion Precession in the Special Relativistic Two-Body Problem

Details Perihelion Precession in the Special Relativistic Two-Body Problem Perihelion Precession in the Special Relativistic Two-Body Problem

1998-05-24

arxiv.org/abs/physics/9805032v1

Physics

Classical Physics

9 pp., 1 GIF figure also viewable at http://order.ph.utexas.edu/mtrump/figures

Scientific paper

The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semi-classical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic two-body theory for the limit of no magnetic interaction.

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