Summary: A frame is characterized by a hermitic operator with independent of direction eigenvalues. For a particular type of frames (El Naschie’s frame), the hermitic operator eigenvalues may be put in correspondence with a Cantor set. This is the situation when the used coordinates, could be some values directly measurable for instance, via the mass spectrum of high energy particle physics. By using the Cayleyene metric associated to the hermitic operator and to Ernst’s equations, the generalized hyperbolic stationary metrics is obtained. When imposing on the metrics the conform Minkowskian character, we obtain both the inertial nature of the Universe expansion and, by the gravitational coupling constant, the correspondence with \({\mathcal E}^{(\infty)}\) space-time. The quantum mechanics in the form of a Schrödinger type equation with complex eigenvalues appears in the process of frames synchronization.