What is a magnetic field?

We know of magnetic fields in two ways:
  1. Measurements detect the effect of charged particle motions on each other's motion.
  2. Mathematics by such greats as Maxwell  model such effects.
I presume that there is (well, could be) a more satisfying Ethereal Mechanics model that explains both of the above, the measured effects and the existing models thereof.  I wonder what such an Ethereal Mechanics model might be.
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