Wikipedi: 'Weber soon discovered, however, that he lacked sufficient mathematical talent, and so he abandoned mathematics entirely.' Ha!Bob,
Maxwell's equations are based on 3 experiments.
1. Coulomb's law......the electrostatic force between 2 static charges........INCOMPLETE....if either of the charges move.......the equation fails.
2. Ampere's law.....the magnetic force between 2 moving current elements.....INCOMPLETE....does not consider electric field movement.
3. Faraday law...induction......fairly complete and understood by Faraday, but not by his mathematic friends. Faraday was an excellent experimenter and physicist, but a poor mather.
Faraday had a much renowned mathematical friend write his equations for him. These equations were expressed with the electrical and the magnetic from 2 different frames of reference. Of course Faraday's experiments were conducted with the electric and the magnetic in the same frame reference.
This is what Maxwell had to work with. And this is why Maxwell's equations were never correct.
And you are right......a particle would collapse if it followed Maxwell. And you are right.....that's what started us down the rabbit hole called QM.
There was another experimenter.....the greatest experimenter, who redid all these experiments together. Only his equations properly expressed the relationship between the electronic and angular momentum. His name was Weber. Study Weber to understand.
If Maxwell would have used Weber's equations....we might be living on several planets today.
And if Maxwell's equations fail on particles.........why does it not fail on electromagnetic waves thru space. IT DOES FAIL.
Weber’s corrected equations work on plasma in the fusion reactors while Maxwell’s do not.
This corrected field theory work was done in the early 90’s.
From these equations, the true structure of matter has been discerned. All particles are rotating charge rings.
And with this structure......the universal force law has been derived.
There is only one physical entity and force in the universe.........charge.