  Nonstandard analysis and electromagnetic propagation properties are used to
derive all of the fundamental results for the Special Theory of Relativity.
Infinitesimal modeling via infinitesimal light-clocks is used to derive two
general line-elements (metrics) without the use of Riemannian geometry. By
substituting potential velocities, the Schwarzschild, quasi and modified
Schwarzschild, de Sitter, Robertson-Walker and similar line-elements are
derived. New black hole and quasi-white hole investigations are presented. A
new fixed method using separating operators is used to obtain the major
predictions for the relativistic alterations in natural-system behavior. The
major conclusion is that all such changes are related to electromagnetic
properties and that Riemannian geometry is but an analogue model for
natural-system behavior.
