Symmetry of Galactic Structure

A fully relativistic description of an atomic clock is achieved by applying the equivalence principle directly to the space-time coordinates of electron transitions. The resulting differential equation of motion is then reformulated by means of Hamilton's principle to obtain an equivalent integral equation. Generalized coordinates describe the electron in a configuration space consisting of three coordinates that define the origin, or nucleus, and three coordinates that define the manifold on which the electron is constrained to move (the electron shells). Following Dirac the particle model is transformed to a field model by describing energy quantization as the four-dimensional localization of radial and transverse electromagnetic fields. It can then be compared to the emission energy of galaxies in terms of the radial baryonic fields and transverse gravitomagnetic fields that emanate from black holes. The symmetry exhibited by these diverse forms of energy demonstrates that the properties of energy, when described four-dimensionally with time, are independent of the material system which supports them.