The entirety of the field does not come directly from the magnet, but by a relatively small number of photons rubbing off their polarization onto neighbouring photons after first having passed through the magnet. This is visibly evident in ferro-fluids, with their peaks and troughs.
The fact that photons do not have to pass through a magnet to be polarized has been known since Faraday performed his famous experiment:
Polarization of light by magnet
Uncoordinated photons passing through a magnetic field comes out polarized. This happens to low energy photons present in the aether in the exact same way as it does for visible light.
By introducing a second magnet, we can now play around with the magnetic force that arises between magnets. This force is also due to particle collisions. However, in this case we're talking about photons, not neutrinos as was the case for the electric force and gravity. But the general mechanism is the same.
Photons passing through magnets come out well coordinated and spinning. In the case of two magnets facing each other with opposite polarity, we get abrasive head on collisions. This has the overall tendency of pushing photons out of the field. The density of the aether between the magnets is reduced. This in turn draws the magnets together.
Magnetic attraction due to photons vacating the field
Magnetic repulsion due to photons staying in the field
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