Gravitational Interactions and Fine-Structure Constant

TL;DR

This paper explores the relationship between electromagnetic and gravitational interactions within relativistic quantum mechanics, proposing a gravitational fine-structure constant analogous to the electromagnetic one, based on spectral and variational analyses.

Contribution

It introduces a gravitational fine-structure constant and links it to the electromagnetic constant through a variational principle on curved space-time.

Findings

Identification of corrections to transition current

Proposal of a gravitational fine-structure constant

Functional relationship between alpha_QED and alpha_G

Abstract

Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and electromagnetic spectra suggest the definition of a gravitational fine-structure constant. The electromagnetic and gravitational coupling constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the variational principle holds with regard to a global dilation transformation of the space-time coordinates. The variation suggests is consistent with a functional relationship of the form alpha_QED being proportional to alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant, and alpha_G its gravitational analogue.