Possibility of measuring thermal effects in the Casimir force

We analyze the possibility of measuring small thermal effects in the Casimir force between metal test bodies in configurations of a sphere above a plate and two parallel plates. For the sphere-plate geometry used in many experiments, we investigate the applicability of the proximity force approximation (PFA) to calculation of thermal effects in the Casimir force and its gradient. It is shown that for real metals the two formulations of the PFA used in the literature lead to relative differences in the results obtained being less than a small parameter equal to the ratio of separation distance to sphere radius. For ideal metals, PFA results for the thermal correction are obtained and compared with available exact results. It is emphasized that in the experimental region in the zeroth order of the small parameter already mentioned, the thermal Casimir force and its gradient calculated using the PFA (and thermal corrections in their own right) coincide with the respective exact results. For real metals, available exact results are outside the application region of the PFA. However, the exact results are shown to converge with the PFA results when the small parameter goes down to experimental values. We arrive at the conclusion that the large thermal effects predicted by the Drude-model approach, if they exist, could be measured in both static and dynamic experiments in sphere-plate and plate-plate configurations. As for the small thermal effects predicted by the plasma-model approach, the static experiment in the configuration of two parallel plates is found to be the best for their observation.