The Longest-Term Prediction in Cosmology and Fundamental Physics: The Evolution of the Proton-to-Electron Mass Ratio mp/me

One of the most persistent mysteries in physics is the origin and potential time evolution
of the proton-to-electron mass ratio mp/me ≈ 1836.15.

For nearly a century, this number has
resisted theoretical explanation and remains an arbitrary parameter in the Standard Model.
The anthropic principle explains why we observe a value compatible with life, but it does not
explain why it has exactly this value.

In the Theory of Hyperbolic Unity (THUI), we propose a different view: mp/me is not a
fixed constant but a dynamic quantity arising from the geometry of a dual vacuum. The local
cubic layer (finite, rigid) and the nonlocal hyperbolic layer {5, 3, 3} (infinite, expanding) are
linked by resonance 1729. The slow unfolding of the vacuum, governed by the cubic curvature
correction R3, leads to a gradual decrease in the mass ratio over cosmic time.

We derive the evolution equation for mp/me(t) and provide numerical predictions for the
next 10–1000 billion years. The change is extremely slow (on the order of 10−18 per year at
present), but directional and, in principle, testable with future ultra-precise laboratory and
astrophysical measurements.

This makes the evolution of mp/me one of the longest-term yet
potentially observable predictions in the history of cosmology and fundamental physics.

If confirmed, it would open a direct observational window into the dynamics of vacuum
duality and the geometric origin of particle masses.