A primary winding induces a current in a moving copper mass and the current in the copper mass induces a current in a secondary winding. As copper moves from primary to secondary, the effect of secondary on primary will not be the same as that of primary on secondary, due to the copper induced currents that always move away from primary. So in terms of mutual induction, M12 ≠ M21.
I had looked closely at this paper when it came out. Non-reciprocity M12 ≠ M21 does not imply a victory against Lenz's law. Indeed, if copper were static and secondary open, the primary would behave as a purely reactive inductance, and no energy would be dissipated except for the usual losses in the resistance of the winding and the copper mass. But as copper moves away, part of the induced currents cannot return to the primary winding, the system is no longer purely reactive, it is as if it radiated. Seen from the primary, energy is consumed. The part of the energy carried away can be used by the secondary, and if it is not, it will be dissipated in the copper or will return after one turn if the copper dissipates little, for example because it is at superconducting temperature.
The best model seems to me to be radiation. The energy is mechanically carried away in the form of current loops in the copper mass. This could lead to interesting applications. I also wondered how to apply the same principle by replacing the association of currents/magnetic fields with voltages/electrical fields. I think that an insulating disc rotating as a common dielectric under two plates side by side, and another common plate on the other side of the dielectric, could give an identical non-reciprocal effect between the two capacitors, but with less losses.
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"Open your mind, but not like a trash bin"
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