Gaussian Techniques applied to Completeness in Optical Calculations

An interesting interpretation of Completeness and Group Theory can be found in using classical Gaussian Calculations that have been used previously in Mapping (from Gauss and Riemann) and Relativity. A simple reinterpretation of the observer and the meaning of the completeness of the observation yields some fascinating results that may have a Theoretical Significance and seems to yield some testable Optical and Atomic Effects. The most interesting part of this interpretation is that it is not a difficult deviation from the current theory.