We treat a Lorentz-covariant two-body problem due to Fokker: One electric charge experiences the retarded field of a second, while the second experiences the advanced field of the first; this is pure action at a distance, with no self-action; conservation principles exist. We show that this (apparently generally soluble) time-asymmetric problem is exactly soluble for straight-line motion and admits solutions in which the charges move in circles about a common center. We briefly consider nonelectrodynamic time-asymmetric interactions and aspects of quantizing the motions.

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