Explaining Electromagnetic Fields: Mass and Distance

Tim Edilation
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I have skimmed relevant links in wikipedia, and some external links regarding electromagnetic fields, but would like a simple (I'm no physicist) answer to the following question that I have.

When one, for example, takes two strong permanent magnets and aligns so that there is repulsive/or attractive force at sometimes a surprising large distance, is there really sub-atomic particles from one magnet flitting about so far away from the magnet that it interacts with the other magnet's flitting about 'particles'. Do all atoms have 'particles' flitting about that far from the atom ?
According to the current model/theory do these things/particles have mass ? Thanks
 
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Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...

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