But physicists have given up on figuring out what it IS. They have decided that having math that can predict the outcome of experiments is enough. They're not wrong, but it feels rather unsatisfying. IMHO there have been a couple avenues worth exploring that are being largely ignored.
It depends on what you mean by that. What they've given up on is trying to find some sort of anthropocentric analogy. It's understandable that this is unsatisfying, since analogies are fundamental to how we understand things. Unfortunately, there's no reason to believe that a good analogy will exist.
That's no reason not to try. If there IS an objective reality I think it deserves a better description than just the math which characterizes its behavior.
Why should we assume that the contradictions in contemporary theories are of this special, inexplicable type? Every era has contradictions, before they are resolved... But they'll only ever be resolved if people are trying to resolve them, meaning that they haven't resigned themselves to the idea that our minds haven't been gifted with the capacity to make sense of our experience.
One of my favorite books is called "Architecture of Matter", it's a history of ideas about matter. One early idea was that matter is made of little tiny bits of stuff and that qualities of these little bits (such as being smooth or spikey) leads to macroscopic phenomenon (like spikey bits being acidic.)
The problem with this idea (and almost all others) is that it's just pushing the problem down a level: If matter is made out of little bits of matter, what are the little bits of matter made of?
FWIW, the wave-particle duality gets around this self-reflexive problem. Matter is made out of some other kind of stuff. But then, as you say, we still have the essential problem of "wtf is this stuff?" but we don't worry about that so much as long as our math describes the behavior of the stuff.
> They're not wrong, but it feels rather unsatisfying. IMHO there have been a couple avenues worth exploring that are being largely ignored.
What avenues? (Genuinely curious, not trolling.) It seems to me that the ultimate, existential question of what "stuff" actually is, is unanswerable (within the logical/scientific framework.)
Pilot wave theory is one. The other was a paper - forgive this explanation - the found equivalence between particle physics and fluid dynamics. Suggesting the objects in physics might be modeled as say vorticies in some kind of fluid (aether). The equivalence was IIRC only to first order, but the work to get there must have been a lot. I'm sure there are others.
And the criticism of mainstream thought in physics would be: its wrongfully dismissive of my question, and ignoring the important job of looking for the answer.
Electromagnetic filed is mathematical model of what?
Let's talk about nature of EM force.
Analogy: look at a typical tropical cyclone. It rotates. Is it rotating because a unknown property of an air molecule? No. It rotates because our planet rotates, while air molecules are just trying to keep their positions. I.e. it's rotation of planet + inertia of molecules.
Is it possible that EM force is happens because our local space is moving trough global space by non-linear trajectory, so it just non-linear trajectory of local space + inertia of rotating and vibrating particles?
Physical things are real. Mathematical abstractions are not. OpenGL is not real too, but it looks very real and accurately predicts reality. In OpenGL, field is array, e.g. "float[][][] field;".