We compute Casimir interaction energies for the sphere-plate andcylinder-plate configuration induced by scalar-field fluctuations withDirichlet boundary conditions. Based on a high-precision calculation usingworldline numerics, we quantitatively determine the validity bounds of theproximity force approximation (PFA) on which the comparison between allcorresponding experiments and theory are based. We observe the quantitativefailure 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 ofgenuine Casimir curvature effects. We conclude that data analysis of futureexperiments aiming at a precision of 0.1% must no longer be based on the PFA.
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