In the classical theory of electromagnesitm, as given by Maxwell, we know that by just looking at the four famous equations:
- An electric field has a source: there are charged particles (non-zero divergeance)
- Whereas there's no such equivalence for the magnetic field, i.e., there are no known magnetic charges.
- And roughly that, the change in time of either field generates the other.
Despite the difference in 1. and 2., it is nonetheless known that electric and magnetic fields are just different views of the same physical thing. That is, by considering the relative motion of charges, in different frames, we observe a magnetic field being generated or equivalently a static electric field.
Although I understand the reasoning behind this, as we are simply switching frames (once being at rest w.r.t. to the charge, once being in motion relative to it), it remains still a very confusing picture.
- To help clarify matters, are we saying that based on the classical Maxwellian theory of electromagnetism, magnetism has no fundamental physical meaning, instead it's all about the behaviour of charged particles?
On the other hand, in our modern theories, of QM and QFT, we quickly learn about a new fundamental physical property other than the charge, namely the spin, and how it is at the very core of everything in magnetism. Taking simple toy models such as all the Ising variants, we explain all sorts of magnetic behaviours (ferromagnetism, paramagnetism,...and phase transitions between them) based on the understanding of how spins interact, how they can be locked in blocks of same orientation, how they respond to an external field, and so on.
Moreover, unlike the concept of charge, spin extends to photons as well, where mathematically we assign half-integer spins to fermions (electrons e.g.) and integer ones to bosons (photons). Compared to the starting discussion of the classical theory, the contrasting feature here is the fact that magnetism deals with the spin properties of a system and not the charges, meaning that there does not seem to be a dual equivalence anymore between magnetic fields and electric fields based on QM.
Is there a way to meaningfully connect these two pictures? I.e., that of the classical theory of electromagnetism to the modern understanding of charges, spins in QM? For example, we know that part (1) is a macroscopic theory, so as a consistency check, is it possible to retrieve the results therein, but starting from the modern picture? (i.e., the collective behaviour of fermions)
In our modern understanding of the electromagnetic theory, considering relativistic and quantum mechanical corrections, do we still treat magnetic fields and electric fields as different views of the same thing?
This has been my attempt at claryfing what is confusing me, hopefully the questions are not too vague as they stand, please let me know if any additional details and clarification are required. Although this post is not necessarily a literature recommendation one, any books or papers that you think will help me better understand this whole matter, are perfectly welcome.