Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant

TL;DR

This paper proposes that interpreting Planck's constant as a variable leads to a natural emergence of a running fine structure constant, offering insights into fundamental physics, cosmology, and potential explanations for recent dark energy observations.

Contribution

It introduces a model where Planck's constant varies effectively, connecting quantum, gravitational, and cosmological phenomena, and explains recent experimental findings.

Findings

A natural emergence of a running fine structure constant.

Resolution of the cosmological constant problem.

Identification of a phase transition-like behaviour in mass-radius relations.

Abstract

This letter explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck's constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass-radius relation for both quantum and classical systems reveals a phase transition-like behaviour similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe.