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

TL;DR

This paper applies modern infinitesimal analysis to the general relativity metric dS, rigorously exploring its physical implications and deriving gravitational time-dilation expressions based on photon-atom interactions influenced by gravity.

Contribution

It introduces a rigorous application of infinitesimal analysis to the dS metric and verifies a time-dilation conjecture through quantum and geometric methods.

Findings

Derived gravitational time-dilation expressions from photon interactions.

Confirmed the physical meaning of the dS metric using infinitesimal analysis.

Provided 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.