Myo Min Aung Unified Theory (MUT) v7. 9 investigates the universal scaling relationship between two fundamental quantities that appear in different domains of physics: the Rydberg–MCR scaling factor Psi and the Planck–proton hierarchy ratio mₚ / MPlanck. Although these two quantities originate from atomic physics and quantum gravity respectively, both are numerically of order 10^-20, suggesting a deeper physical connection. In MUT v7. 7 and v7. 8, the Rydberg frequency was derived from the Mass Curvature Rate constant fMCR = c / mₚ through the scaling relation: fRyd = Psi × fMCRUsing the experimentally measured Rydberg frequency, the scaling factor is obtained as: Psi ≈ 1. 8355 × 10^-20 kg/m. Independently, MUT v7. 0 established the hierarchy ratio between the proton mass and the Planck mass: mₚ / MPlanck ≈ 7. 68 × 10^-20. This ratio is central to the hierarchy problem in modern physics and explains why gravity is extremely weak compared to other fundamental interactions. This work explores whether the numerical proximity between Psi and the hierarchy ratio is coincidental or reflects a deeper structural relationship. By introducing the Planck length as a dimensional bridge and analyzing combinations involving the fine-structure constant and particle mass ratios, the paper demonstrates that both quantities arise from the same underlying geometric scaling structure. Within the MUT framework, atomic constants, gravitational strength, and fundamental mass hierarchies are not independent parameters but emerge from the universal Mass Curvature Rate constant. The analysis shows that the stability of atoms and the weakness of gravity can be interpreted as consequences of a common curvature suppression mechanism embedded in spacetime geometry. The results presented in this work synthesize the findings of MUT v7. 7 and v7. 8 into a broader scaling interpretation that links Planck-scale physics to atomic structure. This connection suggests that quantum scales and cosmological scales are governed by a single geometric principle. MUT v7. 9 therefore strengthens the unification program initiated in MUT v7. 0 by demonstrating that the hierarchy problem and atomic spectral structure can be understood within the same spacetime curvature framework. This document serves as supplementary material to MUT v7. 0 and forms part of the continuing development of the Mass Curvature Rate theory as a unified description of fundamental physical constants.
Myomin Aung (Sat,) studied this question.