Since we do not have a third kind of device to specify the spatio-temporal location of the devices measuring the spacetime geometry, we do not have any further operationally defined, maybe nondynamic background, just in accordance with the principle of equivalence. If there were some nondynamic background metric g0ab on M, then, by requiring g0ab = ϕ∗g0ab we could reduce the almost arbitrary diffeomorphism ϕ (essentially four arbitrary functions of four variables) to a transformation depending on at most ten parameters.