  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.
