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

TL;DR

This paper proposes nonlocal electromagnetic response functions that align with experimental Casimir force measurements and satisfy causality, offering a new approach to resolve the Casimir puzzle related to dissipation.

Contribution

It introduces nonlocal response functions that reconcile Lifshitz theory with experimental data without neglecting dissipation, advancing understanding of quantum fluctuations.

Findings

Nonlocal responses closely match local responses on-shell.

The proposed response functions satisfy Kramers-Kronig relations.

Application to the Casimir puzzle shows improved theoretical-experimental agreement.

Abstract

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.