The proper mass of the universe

A modification of the covariant theory based on the concept of the proper mass (mass distribution) of the system is proposed. The proper mass is a special dynamic quantity that forms a fundamental frame of reference for measuring proper time and spatial shifts without violating the theory’s covariance. A simple model of an ingomogeneous system (universe, string) with two proper time parameters, whose constraint algebra is isomorphic to SL2, is considered.