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| Our motivations for introducing a neoclassical field theory for electromagnetically interacting elementary charges were as follows. First, we wanted to have a theory which completely accounts for the relativistic dynamics of a system of charges interacting electromagnetically. Second, we wanted to have a theory which accounts for particle properties as well as for wave phenomena in a single mathematically sound Lagrangian relativistic theory. When constructing such a theory we also wanted: (i) to stay on the solid ground of the Lagrangian mechanics and the relativity principle; (ii) to recover all well established experimental facts described by the classical electromagnetic theory; (iii) to have all particle properties to naturally follow from the field equations as approximations.
We have constructed such a theory and demonstrated that it implies in the non-relativistic limit (i) the non-relativistic particle mechanics governed by the Newton equations with the Lorentz forces and (ii) the frequency spectrum for hydrogenic atoms. The relativistic version of our field theory implies, in particular, the relativistic point mechanics and the celebrated Einstein's energy-mass relation E=mc^2. |
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