  We performed measurements of the gradient of the Casimir force between
Au-coated surfaces of a sphere and a plate by means of significantly upgraded
dynamic atomic force microscope (AFM) based technique. By introducing combined
cleaning procedure of interior surfaces of the vacuum chamber and the test
bodies by means of UV light and Ar ions, we reached higher vacuum and
eliminated the role of electrostatic patches. Furthermore, the use of much
softer cantilever allowed a sixfold decrease of the systematic error in
measuring the force gradient. The experimental data are compared with
theoretical predictions of the Lifshitz theory taking into account corrections
due to the inaccuracy of the proximity force approximation and that due to
surface roughness. It is shown that the theoretical approach accounting for the
relaxation properties of free electrons is excluded by the data up to a larger
than previous sphere-plate separation of 820~nm, whereas an alternative
approach is found in a very good agreement with the data. Importance of these
results in connection with the foundations of quantum statistical physics is
discussed.
