Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
E. C. G. Stückelberg, Helv. Phys. Acta 14, 372, 588 (1941); 15, 23 (1942).
L. P. Horwitz and C. Piron, Helv. Phys. Acta 46, 316 (1973).
J. L. Cook, Aust. J Phys. 25, 117, 141 (1972).
C. Piron and F. Reuse, Helv. Phys. Acta 48, 631 (1975).
M. A. Trump and W. C. Schieve, Special Relativistic Hamiltonian Particle Dynamics (Kluwer, Dordrecht, 1998); see also M. A. Trump, Ph.D. dissertation, University of Texas at Austin, 1997.
M. A. Trump and W. C. Schieve, “Classical scattering in an invariant Coulomb potential,” Found. Phys., to be published, 1998.
See A. Sommerfeld, Atomic Structure and Spectral Lines, Vol. I, 3rd revised ed.; translated from the 5th German edn. by H. L. Brose (Methuen, London, 1934). See also J. L. Synge, Relativity: The Special Theory(North-Holland, Amsterdam, 1965).
J. R. Fanchi, Parameterized Relativistic Quantum Theory (Kluwer, Dordrecht, 1993).
L. P. Horwitz and W. C. Schieve, Phys. Rev. A 45, 743 (1992).
M. A. Trump and W. C. Schieve, Found. Phys. 27, 1, 389 (1997).
H. Goldstein, Classical Mechanics, 2nd edn. (Addison-Wesley, Reading, Massachusetts, 1980).
H. A. Bethe and E. E. Salpeter, The Quantum Mechanics of One-and Two-Electron Atoms (Academic Press, New York, 1957).
W. Pauli, Z. Physik 43, 601 (1927).
R. Arshansky and L. P. Horwitz, J. Math. Phys. 30, 66 (1989).
Rights and permissions
About this article
Cite this article
Trump, M.A., Schieve, W.C. Perihelion Precession in the Special Relativistic Two-Body Problem. Foundations of Physics 28, 1407–1416 (1998). https://doi.org/10.1023/A:1018848909864
Issue Date:
DOI: https://doi.org/10.1023/A:1018848909864