Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

TL;DR

This review addresses the Casimir puzzle and conundrum by analyzing discrepancies between Lifshitz theory predictions and experimental data, focusing on thermodynamic violations and exploring nonlocal response functions as potential resolutions.

Contribution

It provides a comprehensive summary of the theoretical and experimental issues in Casimir force calculations and discusses novel nonlocal response models that reconcile theory with measurements and thermodynamics.

Findings

Lifshitz theory violates Nernst heat theorem with standard dielectric functions.

Experimental data exclude traditional Casimir force predictions.

Nonlocal Drude-like models align theory with experiments and thermodynamics.

Abstract

We review complicated problems in the Lifshitz theory describing the Casimir force between real material plates made of metals and dielectrics including different approaches to their resolution. It has been shown that both for metallic plates with perfect crystal lattices and for any dielectric plates the Casimir entropy calculated in the framework of the Lifshitz theory violates the Nernst heat theorem when the well approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature this situation received the names of the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. The review presents a summary of the main facts on this subject on both theoretical and experimental sides. Next, we discuss the main approaches proposed in the literature in order to bring the Lifshitz theory in agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions which take into account the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations off the mass shell. Further advances and trends in this field of research are discussed.