An alternative response to the off-shell quantum fluctuations: a step forward in resolution of the Casimir puzzle

Abstract

© 2020, The Author(s). The spatially nonlocal response functions are proposed which nearly coincide with the commonly used local response for electromagnetic fields and fluctuations on the mass shell, but differ significantly for the off-shell fluctuating field. It is shown that the fundamental Lifshitz theory using the suggested response functions comes to an agreement with the measurement data for the Casimir force without neglecting the dissipation of free electrons. We demonstrate that reflectances of the on-shell electromagnetic waves calculated using the nonlocal and commonly employed local responses differ only slightly. The Kramers–Kronig relations for nonlocal response functions possessing the first- and second-order poles at zero frequency are derived, i.e., the proposed response satisfies the principle of causality. An application of these results to resolution of the Casimir puzzle, which lies in the fact that the Lifshitz theory is experimentally consistent only with discarded dissipation, is discussed.