We measured the time decay of the electric field in two dielectric non-crystalline solids and the data were analyzed in the framework of a new theoretical approach. It is observed that the application of this approach allows identifying different regimes in the relaxation process. At long times the dynamics end up by following a power law decay, which suggests the existence of a scale property in the interaction that defines the state of the materials and also the possibility of defining an invariant. We check the stability of this invariant under different time intervals, which means also a low dependence of it on noisy data.