Is diamagnetism really acausal?

Diamagnetism, in which the magnetisation in a medium opposes the direction of an applied magnetic field, is a weak but familiar effect in a wide class of materials. Being weak it is also a linear response to any applied field. The problem is that the existence of diamagnetism is in direct conflict with the requirements of causality as embodied in the familiar Kramers-Kronig relations. Nature doesn’t care about our confusion and diamagnetism exists and (as far as we are aware) physics is constrained by the requirements of causality (effect cannot precede cause).

This puzzle has received intermittent attention from time to time over the last hundred years, with a variety of arguments made to resolve the paradox. But none of these, no matter how plausible, reveal the mechanism that resolves the existence of diamagnetism without sacrificing causality. I shall present some of the previous proposals before revealing the resolution of this paradox.