Current status of the problem of thermal Casimir force

TL;DR

This paper reviews the ongoing debate over the thermal Casimir force, highlighting discrepancies between theory and experiment, and discusses recent approaches involving nonlocal permittivities that may resolve these issues.

Contribution

It provides a comprehensive review of approaches to resolve the thermal Casimir force problem, emphasizing the role of spatial dispersion and nonlocal permittivities.

Findings

Nonlocal Drude-like permittivities align theory with experiments.

Spatial dispersion effects are crucial in understanding the thermal Casimir force.

Recent models improve thermodynamic consistency of Lifshitz theory.

Abstract

The problem of thermal Casimir force, which consists in disagreement of theoretical predictions of the fundamental Lifshitz theory with the measurement data of high precision experiments and some peculiar properties of the Casimir entropy, is reviewed. We discuss different approaches to the resolution of this problem proposed in the literature during the last twenty years. Particular attention is given to the role of the effects of spatial dispersion. The recently suggested nonlocal Drude-like permittivities which take proper account of the dissipation of conduction electrons and bring the predictions of the Lifshitz theory in agreement with experiment and requirements of thermodynamics are considered. The prospects of this approach in the ultimate resolution of the problem of thermal Casimir force are evaluated.