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It has been known that the Lifshitz theory of the Casimir force comes intoconflict with the measurement data if the response of conduction electrons inmetals to electromagnetic fluctuations is described by the well testeddissipative Drude model. The same theory is in a very good agreement withmeasurements of the Casimir force from graphene whose spatially nonlocalelectromagnetic response is derived from the first principles of quantumelectrodynamics. Here, we propose the spatially nonlocal phenomenologicaldielectric functions of metals which lead to nearly the same response, as thestandard Drude model, to the propagating waves, but to a different response inthe case of evanescent waves. Unlike some previous suggestions of this type,the response functions considered here depend on all components of the wavevector as is most natural in the formalism of specular reflection used. It isshown that these response functions satisfy the Kramers-Kronig relations. Wederive respective expressions for the surface impedances and reflectioncoefficients. The obtained results are used to compute the effective Casimirpressure between two parallel plates, the Casimir force between a sphere and aplate, and its gradient in configurations of the most precise experimentsperformed with both nonmagnetic (Au) and magnetic (Ni) test bodies. It is shownthat in all cases (Au-Au, Au-Ni, and Ni-Ni test bodies) the predictions of theLifshitz theory found by using the dissipative nonlocal response functions arein as good agreement with the measurement data, as was reached previously withthe dissipationless plasma model. Possible developments and applications ofthese results are discussed.

Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response