What did Einstein learn in his university electricity and magnetism courses? Did he learn about such prominent results as Ampère's force law, Weber's force law derived from it (cf. Maxwell's Treatise §§846-851), and Helmholtz's theory?
Doing a search through Einstein's collected papers, I could not find him mentioning any of these things. Did he? If not, why?
Einstein's physics teacher, H. F. Weber, apparently did not teach him any Helmholtz, as Einstein wrote in a 10 August 1899 letter to Mileva Marić:
I returned the Helmholtz volume* and am at present studying again in depth Hertz's propagation of electric force.** The reason for it was that [I] didn't understand Helmholtz's treatise on the principle of least action in electrodynamics. I am more and more convinced that the electrodynamics of moving bodies, as presented today, is not correct, and that it should be possible to present it in a simpler way. The introduction of the term "ether" into the theories of electricity led to the notion of a medium of whose motion one can speak without being able, I believe, to associate a physical meaning with this statement. I think that the electric forces can be directly defined only for empty space, [which is] also emphasized by Hertz…
—Volume 1: The Early Years, 1879-1902 (English translation supplement) Page 131
*Helmholtz's 1882 Wissenschaftliche Abhandlungen (not translated into English)
**Hertz's Electric waves being researches on the propagation of electric action with finite velocity through space
It's surprising Einstein was not formally taught the 19th century's leading way of doing E&M: deriving electric potentials from energetics first principles. This was taught in, e.g., Duhem's 1891-92 Leçons sur l'électricité et le magnétisme course.
Einstein's collected papers nowhere mention the derivation of Wilhelm Weber's law from Ampère's force law, which by the time Einstein was a physics student was at least ⅓ century old. Perhaps 19th century physics instruction lagged behind cutting-edge research developments, much as today the vast majority of what is taught in physics courses were cutting-edge developments at least a century ago. Perhaps this is why Einstein was frustrated and rarely attended class.
According to one biography I read, Einstein didn't learn much from his university courses in Electromagnetism. Presumably this was simply because he was already looking through the works of Maxwell, Hertz and so on. Also, according to Freeman Dyson, mainstream physics didn't really take to Maxwell Equations - no matter how they are lauded today. There was a lapse of at least two decades before they really began to be appreciated. And presumably this would have shown in the curriculum.
This is understandable in a way. Maxwell notation is not as compact as we have today. When he wrote down his equations there twenty of them. It took the efforts of Heaviside and Gibbs to reduce them to the four vector equations we have now, plus the Lorentz force equation. Nowadays, using the Cartan formalism, aka differential forms, Maxwell equation has been reduced to a single equation (this doesn't include the Lorentz force law)! This might seem like a marvel of compactness, but here all the complications have been hidden away in the formalism (one has to learn about manifolds, bundles and so on).
One thing that he would have learnt from Hertz which I only learnt of recently, and which isn't emphasised enough, is that Hertz held it to be a defect of Newtonian physics that there were two basic notions - inertia and force. For philosophical reasons he wanted a force less mechanics and to that end introduced additional variables which refer to 'hidden' dimensions of space.
This is obviously interesting in two ways. The first, a forceless gravity, is what GR is. Hidden dimensions of space manifesting themselves as force is exactly what Kaluza-Klein showed. In fact, the latter notion goes back to Riemann, who spoke of the possibility of metrical change, not in the large as one might expect - but in the small, that is the infinitesimal.
