Temperature dependent Casimir forces: recurring subtleties

The Casimir force between two ideal conducting surfaces is a special (zero temperature) limit of a more general theory due to Lifshitz. The temperature dependent theory includes correlations in coupled quantum and classical fluctuation modes for conducting, dielectric and magnetic media. If the surfaces are at different temperatures, it has been postulated that these modes might act as a coupling spring, transferring thermal energy from the hotter to the colder even through a vacuum. Recent experiments have appeared to confirm this prediction, but the data were compared with the predictions of Casimir's original expression, rather than those of the full temperature-dependent theory. This is a common error in the literature. Another error is to ignore the fact that real conducting surfaces (gold in this case) can be far from ideal, and that a correction factor of up to 25% may be required. Here we give numerical values for both of these corrections. It appears that they may not affect the basic conclusions from recent experiments, but the take-home message is that care is needed in the interpretation of extensions of Casimir (Lifshitz) effects, which are increasingly emerging across a wide range of scientific problems.