A model for a relativistic, many-particle Lagrangian with electromagnetic interactions

Abstract

It is shown that the Fokker–Wheeler–Feynman theory for the relativistic modelling of a system of massive, charged, point particles interacting via action-at-a-distance forces, electromagnetic in origin, can be reformulated and reinterpreted so that it retains all of its required physical attributes but is devoid of the absurdities originally ascribed to it. That is, Lorentz covariance, time-reversal symmetry, and particle-interchange symmetry are maintained, whereas lack of causality and the paradox of "discontinuous" forces are removed. The reformulated theory yields a physically acceptable relativistic, many-particle Lagrangian. The Euler–Lagrange equations of motion can be written down for either closed or open systems. For closed systems, a generalized Hamiltonian, linear momentum, and angular momentum are constants of the motion. The concept of an open system is used to show that radiation reaction follows straightforwardly from the Euler–Lagrange equations of motion and their past and present time solutions. It is concluded that the basis for this type of modelling of such systems is now established.