Derivation of the Proton/Electron Mass Ratio: A Demonstration of Unified Dilation Theory

Description:

This paper derives the proton/electron mass ratio, m_p/m_e = 6π⁵ = 1836.118 (measured: 1836.153; discrepancy −0.002%), from a single geometric postulate added to General Relativity. Beginning from the Einstein field equations restricted to static spherical symmetry, we adjoin a positional time-dilation postulate — the structural completion of the special- and general-relativistic derivative hierarchy by its zeroth-order term — and show that the spacetime metric is then fixed uniquely (with Schwarzschild recovered as the vacuum limit). Treating the Dirac operator as a geometric probe of this metric, the angular structure of its mass spectrum is fixed by exact integrals on the two-sphere. The proton/electron ratio isolates the purely angular content of that spectrum, in which the cavity energy scale and all interior constants cancel identically.

The derivation uses no continuous fitted parameters and no quantity tuned to the measured masses, and it imports no element of the Standard Model, quantum field theory, or ΛCDM cosmology; standard values appear only for final numerical comparison. Its status is reported transparently: each step is labelled derived or open, and the chain is shown to rest on exactly one un-derived structural integer (the value 4), which is a single fixed integer shared across all three lepton/baryon ratios rather than an adjustable parameter. Two candidate first-principles derivations of that integer are tested and excluded. The same angular machinery independently reproduces m_μ/m_e = 20π³/3 (−0.03%) and m_p/m_μ = 9π²/10 (+0.03%), a consilience that distinguishes the result from numerical coincidence. Establishing the origin of the remaining integer from the metric is identified as the principal open problem.

This work is part of Unified Dilation Theory (UDT).

The tiny remaining fractional discrepancies leave an open question as to whether they point to a minor structural refinement needed in the UDT boundary conditions, or if they represent systematic limits in translating raw experimental observables through a non-geometric theoretical framework.

© 2026 Charles Rotter and Anthony Watts. The text of this work is licensed under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). This license applies to the written expression only and grants no patent rights. Patent pending; all patent rights are expressly reserved by the authors. Commercial use of the text requires prior written permission.

Contact: c.rotter@udtphysics.com