According to wave mechanics, waves traveling in the same direction will add themselves constructively or destructively. On the contrary waves traveling in opposite direction will never cancel. Such waves will always produce standing waves. This means that when the particles position is inverted, two one-way systems as shown above produce plane standing waves systems along the axis.

Secondly, using aether waves' energy via the lens effect, standing waves always undergo an amplification phenomenon. Then this energy is radiated only along the axis because waves are out of phase for any transverse direction, in accordance with Huygens' Principle.

As a consequence, any system emitting waves in the opposite direction will emit waves toward another system, and the radiation pressure will push it.

This explains why two magnets repel themselves while the poles are inverted. On the other hand, there are no standing waves at all while the poles are on the same side. Then the shade effect, which is an attractive force, becomes stronger. The magnets will be attracted.

The Lorentz force.

The animated diagram below shows the same one-way waves (traveling upwards here) created by 2 electrons and 2 protons. It also shows very special wave patterns undulating on hyperboloids:  

Two shifted sets of hyperboloids produce magnetic lines of force.

Two concentric spherical wave systems produce interferences on hyperboloids and concentric ellipsoids. Neglecting the ellipsoids, one can easily superimpose two sets of hyperboloids:

Magnetic fields appear to be a rather complex phenomena, but it turns out that they can be explained by spherical standing waves. Moreover, both electrons and protons must be present, ruling out any traveling properties for magnetic fields.

Electromagnetic waves and Maxwell's equation.

This means that the so-called electromagnetic waves do not exist. The light and radio waves are just regular traveling waves, which nevertheless can induce electric and magnetic fields inside matter. 

This also means that Maxwell's equations just explain how electric and magnetic fields behave around any material device such as an antenna. Nobody can demonstrate that such fields are present everywhere else because a material device is needed to do so.