Testing the Influence of the Gravitational Redshift on the Casimir Effect in Space

We show that the Casimir effect should be influenced by variations of the gravitational potential. This could be tested with a satellite in a highly elliptic orbit. Still significant technology development is required to achieve a relative accuracy of $<5\times {10}^{-10}$ necessary to detect the effect around Earth. That may be obtained in the future based on recent concepts for giant casimir forces. Such a space mission could evaluate both the laws of gravitation and quantum mechanics and their interaction. A dedicated mission, Gravity-Probe C, is proposed.