Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-Clocks
Robert A. Herrmann
(Submitted on 9 Dec 2003 (v1), last revised 22 Aug 2009 (this version, v8))
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.
Comments: Plain Tex, 109 pages. This monograph has been modified in order to incorporate new research findings
Subjects: General Mathematics (math.GM)
MSC classes: 83A05, 83C99, 03H10
Cite as: arXiv:math/0312189v8 [math.GM]
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