Modern Infinitesimal Analysis Applied to the Physical Metric dS and a Theoretical Verification of a Time-dilation Conjecture

Abstract

In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the time-dependent Schrodinger equation, gravitational time-dilation expressions are obtained and are shown to be caused by gravitationally altered photon interactions with atomic structures.