Problems with the Thermal Casimir Force Between Real Metals

Galina L. Klimchitskaya

Physics Department, Federal University of Paraiba, C.P.5008,
CEP 58059-970, Joao Pessoa, Pb-Brazil
(on leave from North-West Polytechnical University, St.Petersburg, Russia)

The energy of fluctuation electromagnetic field is investigated for the thermal Casimir force acting between parallel plates made of real metal. It is proved that for nondissipative media with temperature independent dielectric permittivity the energy at nonzero temperature comprises of the (renormalized) energies of the zero-point and thermal photons. If the dielectric permittivity depends on temperature the energy contains additional terms proportional to the derivatives of the dielectric permittivity with respect to temperature, and the quasiparticle interpretation fails. Previous computations of the Casimir energy in the framework of the Lifshitz formula at zero temperature and optical tabulated data supplemented by the Drude model at room temperature are analysed. It is demonstrated that this quantity does not serve as a good approximation neither to free energy nor to energy. The physical
interpretation of this hybrid quantity is suggested. The contradictory results in the recent literature on whether or not the zero-frequency term of the Lifshitz formula for the perpendicular polarized modes
contribute to physical quantities are discussed. Four main approaches to the resolution of this problem are specified. The precise expressions for entropy of the fluctuation field between plates made of real metal are obtained and this helps to decide between different approaches. The conclusion is that the Lifshitz formula supplemented by the plasma model and the surface impedance approach are best suited to describe the thermal Casimir force between real metals.