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

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.