Abstract
The total energy and momentum of a mechanical-electromagnetic system are regarded as key concepts. The usual theory for a continuous system may not be applied without some alteration to a system of point charges because the orthodox electromagnetic energy-momentum tensor for the field leads to infinite self energies. In the present paper the method adopted is to assume that Maxwell's equations hold for point charge sources but to regard the equations of motion of the charges as dependent on the energy-momentum tensor chosen. A class of modified energy-momentum tensors are constructed in such a way that the field singularities do not lead to difficulty and the corresponding equations of motion are derived. Thus a class of theories is obtained each of which is capable of describing the history of a point charge system in terms of energy and momentum flow. One member of the class gives the Lorentz-Dirac equation of motion with radiation reaction term and the energy-momentum flow picture provides an interpretation of the runaway solutions and of pre-acceleration. One other member of the class is of particular interest because it does not lead to such results. In this theory, named the interaction theory, the equations of motion do not contain radiation reaction terms and whereas a group of charges may radiate on account of their mutual interactions an isolated point charge cannot, whatever its motion. By considering a slowly moving periodic system it is shown in detail how in the interaction theory the forces maintaining the motion supply the energy for the radiation. When certain reasonable conditions are satisfied it is shown that the interaction theory leads to the same results as the orthodox theory for the dipole radiation involved in a wide range of processes including Thomson and Coulomb scattering. The differences are only significant when the number of point charges is small. There is a possibility that the interaction theory may lead to a clearer understanding of the methods of renormalization used in quantum electrodynamics.