Hydrogen Atom and Time Variation of Fine-Structure Constant

TL;DR

This paper investigates how the fine-structure constant, electron mass, and Planck constant vary over time within a de Sitter space-time framework, using the Dirac equation for hydrogen and an adiabatic approximation, aligning with current observations.

Contribution

It introduces a novel approach to analyze time variation of fundamental constants in de Sitter space-time using the Dirac equation and adiabatic approximation, providing a cosmological context.

Findings

Fine-structure constant varies with time.

Electron mass and Planck constant also show time variation.

Results align with current observational data.

Abstract

In this paper, we have solved the de Sitter special relativistic ($\mathcal{SR}_{cR}$-) Dirac equation of hydrogen in the earth-QSO(quasar) framework reference by means of the adiabatic approach. The aspects of geometry effects of de Sitter space-time described by Beltrami metric are explored and taken into account. It is found that the $\mathcal{SR}_{cR}$-Dirac equation of hydrogen is a time dependent quantum Hamiltonian system. We provide an explicit calculation to justify the adiabatic approach in dealing with this time-dependent system. Since the radius of de Sitter sphere $R$ is cosmologically large, the evolution of the system is very slow so that the adiabatic approximation legitimately works with high accuracy. We conclude that the electromagnetic fine-structure constant, the electron mass and the Planck constant are time variations. This prediction of fine-structure constant is consistent with the presently available observation data. For confirming it further, experiments/observations are required.