Casimir effect for curved geometries: proximity-force-approximation validity limits.

We compute Casimir interaction energies for the sphere-plate and cylinder-plate configuration induced by scalar-field fluctuations with Dirichlet boundary conditions. Based on a high-precision calculation using world-line numerics, we quantitatively determine the validity bounds of the proximity-force approximation (PFA) on which the comparison between all corresponding experiments and theory are based. We observe the quantitative failure of the PFA on the 1% level for a curvature parameter a/R>0.00755. Even qualitatively, the PFA fails to predict reliably the correct sign of genuine Casimir curvature effects. We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA.