Mass Geometry: Unifying Gravity from Planck to General Relativity

 The unification of quantum mechanics and general relativity remains one of the most profound challenges in theoretical physics. Building on Planck-scale physics and Einstein’s general relativity, this work introduces “Mass Geometry,” a paradigm positing that mass-energy is inherently geometric, governed by a universal surface density constant. This resolves the proton radius anomaly and the nature of dark matter through shared geometric origins in spacetime curvature.

The goal is a scale-invariant framework bridging quantum and cosmic regimes. By analyzing mass-energy distributions from neutrinos and protons to the Milky Way, we show consistent spacetime curvatures. Newton’s G emerges as derived, while the universal surface density 𝒬 links radius r, time flow Δt, and surface gravity g.

Results: a single neutrino and the Milky Way exert identical surface gravity; a scale-invariant relation holds over 60 orders of magnitude; time dilation follows one law. 𝒬 defines cosmic horizons and maximum curvature, removes singularities, and unifies Planck and GR scales.

Unique contributions include scale-invariant lensing deflection angles, alignment with CMB data, CPT preservation, and a geometric reframe of dark matter, resolving the information paradox via non-singular horizons. The framework is falsifiable and offers testable predictions in particle physics and cosmology.

Keywords: quantum gravity, dark matter, black hole information paradox, scale invariance, gravitational lensing, general relativity, Planck scale.