In a study of classical electrodynamics the dynamics of an electron appears to be an open question - on which a lot of interesting work has been completed, for example Hendrick Lorentz and Paul Drude, some of it very recent. This is also related to the Abraham-Minkowski controversy, which some claim is resolved and some claim is not. The crucial problem seems to be in all cases that the response of matter to a power flux is hard to determine.
This is an example of recent work: Gralla, Samuel E., Harte, Abraham I., Wald, and Robert M. "A Rigorous Derivation of Electromagnetic Self-force." There have been some very good advances, but they have taken 100 years to come to fruition.
I had heard, in passing, a statement that general relativity resolves this problem, determining the dynamics. However, I have not been able to find any work that seems to shed much light on the question. And my own thinking on it right now is that GR inherits the same problems as CEM (Maxwell-Lorentz electrodynamics) and SR.
I asked this question in a positive sense The path of an electron in general relativity
But, the answers suggest that there is no real answer.
So, I ask the question now in an explicit negative sense - is there no known answer?