The problem of two relativistically-moving pointlike particles of constant mass is undertaken in an arbitrary Lorentz frame using the classical Lagrangian mechanics of Stückelberg, Horwitz, and Piron. The particles are assumed to interact at events along their world lines at a common “world time,” an invariant dynamical parameter which is not in general synchronous with the particle proper time. The Lorentz-scalar interaction is assumed to be the Coulomb potential (i.e., the inverse square spacetime potential) of the spacetime event separation. The (...) classical orbit equations are found in 1 + 1 spacetime dimensions in the hyperbolic angle coordinates for the reduced problem. The solutions to the reduced motion in these coordinates are the spacetime generalizations of the nonrelativistic Kepler solutions. and they introduce an invariant eccentricity which is a function of other known constants of the motion for the reduced problem. Solutions compatible with physical scattering are obtained by the assumption that the eccentricity is a given function of the ratio of the particle masses. (shrink)

The classical two-body system with Lorentz-invariant Coulomb work function V = -k/ρ is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stückelberg. 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 semiclassical 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. (shrink)