An Integration of General Relativity and Relativistic Quantum Theory

TL;DR

This paper proposes a novel algebraic framework integrating general relativity with relativistic quantum theory by making structure constants space-time dependent, leading to new uncertainty principles and spectral predictions in strong gravitational fields.

Contribution

It introduces a generalized Lie algebra with space-time dependent structure constants based on Einstein's metric, bridging quantum theory and gravity.

Findings

New uncertainty principle in strong gravitational fields

Altered hydrogen atom spectra due to gravity effects

Framework unifies aspects of general relativity and quantum mechanics

Abstract

In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those structure constants to be the Riemann metric as determined by Einstein's equations from the energy momentum tensor. This gives a new type of "Lie" algebra whose structure constants are space-time dependent. One obtains a new type of uncertainty principle in strong gravitational fields and an altered spectra for the hydrogen atom.