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

G L Klimchitskaya,V M Mostepanenko

doi:10.1140/epjc/s10052-020-08465-y

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.

Highlights

Ary conditions where the frequency-dependent dielectric permittivity plays the role of a response function
The Lifshitz theory using the Drude response function for calculation of the Casimir force was excluded over the separation range from 200 to 700 nm, whereas the same theory using the plasma response was found to be in good agreement with the measurement data
In the foregoing, we have proposed the phenomenological spatially nonlocal response functions to the electromagnetic field which are alternative to the standard Drude function

Summary

Introduction

Over a protracted period of the last 20 years, the Lifshitz theory has been facing a challenge when calculating the Casimir force between metallic surfaces and when comparing the results obtained with the measurement data. Later it was shown that the same is true up to the 1.1 μm separation [19,20,21] This situation presents a puzzle [33] when it is considered that the Lifshitz theory is based on the first principles of quantum electrodynamics at nonzero temperature and the Drude response function takes proper account of the dissipation of conduction electrons, whereas the plasma response excludes this phenomenon from consideration and is, applicable only at high frequencies. We propose the spatially nonlocal phenomenological response functions, which demonstrate nearly the same response as the standard Drude function to the electromagnetic field on the mass shell, but lead to quantitative differences for the off-shell fluctuating field.

The Lifshitz theory with spatially local and nonlocal response functions

Conclusions and discussion