Relativistic Hydrodynamics of Rotating Fluid Masses

With the aid of the new notion of center of matter density, we give a relativistic treatment of the behavior of finite-size masses of rotating fluid. This treatment is based on an analysis of the relative motion of this center of matter density and the more familiar center of mass. In this way, we obtain a clear physical interpretation of the equations studied by Mathisson, Weysenhoff, and Möller. We also show that more general types of motions are possible, related to additional degrees of freedom of the relativistic fluid droplet. These degrees of freedom provide a framework for a theory of the quantum numbers of the elementary particles (isotopic spin, strangeness, etc.) which will be developed in a subsequent paper.