Huge problem with classical and quantum electrodynamics

I was thinking to myself today about a variety of ideas not related to my research. One problem which came up is in consideration of a charged particle and the electromagnetic field it generates. I suppose the problem I considered is from a classical sense. Imagine a charged particle such as a proton or electron. Neither particle decays according to theory, and no one has experimentally seen this occur. These particles may exist forever if left alone. There is energy stored in the mass of the particle, of course, but this is certainly finite. The problem I considered is how can a finite energy source give rise to fields which carry energy with them, but do so forever? I think this problem is very similar to some problems outlined in undergraduate and graduate books as well as in many published articles even as recent as 1998 (John David Jackson cites a paper from 1998 which discusses this problem, but the latest edition of his book was published in 1999). 

One problem, which I'm not yet sure deals with the same problem I'm considering, is the problem of a self-force. A radiation force from a moving electron with some decent degree of accuracy, perturbs the trajectory of an electron. The mathematics come in the form of the Abraham-Lorentz formula which describes the radiation reaction force. This approximation only works for certain regimes since it can mathematically have multiple, unrealistic solutions. The force works by considering the fields of the source particle exert a force on the particle while the particle is in motion. Since the fields are generated by the particle, this is in effect like the particle exerting a force on itself. This perturbation term is actually a useful correction despite the physical meaning being awkward and, I think, ridiculous.

Another problem, which I think is related to the self-force problem but is closer to the problem I'm considering, is mentioned in David J. Griffiths undergrad E&M textbook.

  "...the point charges (electrons, say) are given to us ready-made; all we do is move them around. Since we did not put them together, and we cannot take them apart, it is immaterial how much work the process would involve. (Still, the infinite energy of a point charge is a recurring source of embarrassment for electromagnetic theory, afflicting the quantum version as well as the classical. ... Where is the energy, then? Is it stored in the field, ..., or is it stored in the charge...? At the present level, this is simply an unanswerable question: I can tell you what the total energy is, and I can provide you with several different ways to compute it, but it is unnecessary to worry about where the energy is located. In the context of radiation theory (Chapter 11) it is useful (and in General Relativity it is essential) to regard the energy as being stored in the field, ... But in electrostatics one could just as well say it is stored in the charge... The difference is purely a matter of bookkeeping."

To me, his directions to the matter of bookkeeping seem like a cop out. There have been many that have attempted to "fix" the Abraham-Lorentz self-force problem with considerations of relativistic effects, but according to a paper by Rohrlich in 1997, the "pathological" solutions can be made to vanish (but sitll in special regimes). So there is still a problem with the matter of infinite energy, wherever it may be...I think. No one sounds entirely convincing even if you ask the experts.

So, what gives?

Adam D Scott

Center for Neurodynamics
Department of Physics & Astronomy
University of Missouri at St. Louis
http://www.umsl.edu/~neurodyn/students/scott.html