Relative motion in spacetime
arXiv:1309.4313 · doi:10.1016/S0034-4877(15)60003-9
Abstract
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The issue of an equivalent one-body description is discussed. We distinguish two different concepts: on the one hand an almost purely kinematic relative particle, on the other hand an effective particle which involves an explicit dynamical formulation; several versions of the latter are possible. Relative and effective particles have the same orbit, but may differ by their schedules.
26 pages, no figure. Several inadequacies and various misprints corrected. An example, an Appendix, one reference added; some obscure points clarified