A Novel Framework for Characterizing Spacetime Microstructure with Scaling

TL;DR

This paper introduces a scaling-based framework to analyze spacetime microstructure at the Planck scale, revealing new properties and potential explanations for quantum gravity phenomena.

Contribution

It develops a novel scaling approach to reformulate fundamental equations and uncover properties of spacetime microstructure, including the natural emergence of the golden ratio.

Findings

Golden ratio appears in linear scale measurements

Scale invariance restores classical geometric stability

New properties of local spacetime dynamics are revealed

Abstract

The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of spacetime as a smooth continuum, revealing a complex microstructure that defies traditional models. This study introduces a novel scaling-based framework to investigate the properties of spacetime microstructures. By deriving a scaling-characterized metric tensor and reformulating fundamental equations--including the geodesic, Einstein field, Klein-Gordon, and Dirac equation--into scaling forms, the research reveals new properties of local spacetime dynamics. Remarkably, the golden ratio emerges naturally in linear scale measurements, offering a potential explanation for the role of the Planck length in resolving ultraviolet (UV) divergence. Furthermore, the study demonstrates how scale invariance in spacetime can restore classical geometric stability through the renormalization group equations. These findings significantly revise classical geometric intuitions, providing a fresh lens for understanding quantum fluctuations and offering promising insights for advancing quantum gravity theories.