Present status of controversies regarding the thermal Casimir force

Abstract

It is well known that, beginning in 2000, the behaviour of the thermal correction to the Casimir force between real metals has been hotly debated. As was shown by several research groups, the Lifshitz theory, which provides the theoretical foundation for the calculation of both the van der Waals and Casimir forces, leads to different results depending on the model of metal conductivity used. To resolve these controversies, theoretical considerations based on the principles of thermodynamics and new experimental tests were invoked. We analyse the present status of the problem (in particular, the advantages and disadvantages of the approaches based on the surface impedance and on the Drude model dielectric function) using rigorous analytical calculations of the entropy of a fluctuating field. We also discuss the results of a new precise experiment on the determination of the Casimir pressure between two parallel plates by means of a micromechanical torsional oscillator.

Casimir force on real materials—the slab and cavity geometry

“…In recent years there have been lively discussions in the literature about the thermal corrections; for some statements of both sides of the controversy, see Refs. [16,22,23,24,25,26,27,28,29]. We hope that the consideration of planar multilayer systems may provide additional insight into the temperature problem.…”

Analytical and numerical verification of the Nernst theorem for metals

“…In a series of recent papers -cf., for instance, Refs. [18,19,20,21,22] -it is argued that the Drude dispersion relation runs into trouble explaining recent experiments, and moreover comes into conflict with the Nernst theorem. These authors favor, instead of the Drude relation, the plasma relation…”

Reduction of the Casimir force using aerogels

“…(1) as discussed recently by Piroshenko [50]. Although the use of the Drude model at finite temperature has been questioned due to the apparent violation of Nerst heat theorem, we will not elaborate in this issue since we are interested in the effect of the aerogel on the Casimir force [19].…”