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I’m currently working on my PhD with a focus on electromagnetism. I know Maxwell’s equations by rote; I can derive the wave equations, vector potentials, equations governing resonant cavities and the interaction of electromagnetic waves with materials. But ask me what an electric or magnetic field actually is and I will tell you: I have no fucking clue. The physics answer is that fields arise due to the exchange of virtual photons, because the math behind that works. But what does that even mean? What is a virtual photon? And how does it actually produce a force that will attract or repel two parallel wires with current passing through them?
you could call the “little kicks” “differential changes”, and now you’re talking about an integral. If you wanted to talk about all of the loops individually, you’d write a system of differential equations. If you wanted to solve such a system, you could treat it like a control system with negative feedback. If you’re doing that, you’d almost HAVE to move into the laplace domain… which is literally complex in the sense of complex numbers.
Or you could use the simpler models in your average undergraduate physics textbook, and leave the systems of differential equations to computers that can do numeric approximations.