If a classical physicist had been informed that protons and neutrons were composed of three bound particles with charges of 2/3 and -1/3, could he have created a model of these things moving around that would explain the magnetic moments of the nucleons? I realize there would still be a classical problem that they should radiate electromagnetic energy due to acceleration, but ignoring that is there any way to fit the observations?
(I suppose the magnetic moments might not have been known until after quantum mechanics was developed, but ignore that please.)
Would the classical physicist be allowed to posit some potential well the particles are all sitting in to stop them from flying off (in the case of the proton) due to electrostatic repulsion? If so, he could probably figure out some way to arrange the quarks in orbits to make the magnetic moment come out to the observed value. It wouldn’t be very compelling, though, as it wouldn’t explain why those orbits never get disturbed so we never see protons with different magnetic moments.
He would also be at a loss to explain why an electron has a magnetic moment without imagining it as an extended body instead of a point particle.
Any classical model which got the magnetic moment right would get the angular momentum wrong, and vice-versa. You could make a fairly simple model for either, but not for both together.