On the non-uniqueness of the electromagnetic instantaneous response

The instantaneous response models the rapid part of the interaction between electromagnetic fields and materials. From a physical point of view the instantaneous response is non-observable and from a mathematical point of view it constitutes the principal part of the Maxwell equations. In this paper, it is shown that the instantaneous response is not uniquely determined from a given set of values of the constitutive map. The given values only give an upper bound on the size of the instantaneous response. A numerical example illustrates the non-uniqueness of the instantaneous response