Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-Clocks

Abstract

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.

Plain Tex, 109 pages. This version contains all refinements made since 26 Oct. 2010. arXiv admin note: text overlap with arXiv:physics/0005031, arXiv:0802.1809, arXiv:math-ph/0312007