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

In part 1 of this paper, newly identified logical errors in the derivations that yield Einstein’s Special and General Theories of Relativity are discussed. These errors are much more significant than those identified by Fock. The basic philosophy of science used as a foundation for these theories is identified. The philosophy of the privileged observer is detailed. Part 1 concludes with a brief discussion of a new derivation for the Lorentz transformations that eliminates all the logical errors associated with previous derivations as well as eliminating the controversial concepts of “length contraction” and “time dilation.”