TL;DR: the proton is complicated; this is a high-level, phenomenological “maybe.”
I’m sharing a short result from my “Emergent Alpha” work. I treat α as the solution of one gauge-invariant equation F(α)=0, scan it over the complex-α plane, and map |F|. On the real axis, the positive branch lands on α ≈ 0.0072973525643 (~1/137.0359) with no tuning. More surprising: there’s also a clean real zero near α ≈ −4.9948. The maps look asymmetric, and while the negative branch began as a stress test, it might carry real structure.
In a 2-page note (“Alpha Branches and a Geometric Link to the Proton–Electron Mass Ratio”) I use the two branches (α⁺, α⁻) to write a single, simple relation that ties the locked frequency split (ω_C vs ω_R3) to g-factors, giving a parameter-free handle on m_p/m_e—about 4% off in this crude version. It’s deliberately compact and easy to read. If you’re curious about the electron’s pieces (ω_C for bare-mass part vs ω_R3 for self-field part), I list the numbers in “Emergent Electron Mass from Two-Space Boundary” (see pp. 59–60). Open to feedback, replication, and counter-examples.
pajuhaan•3h ago
I’m sharing a short result from my “Emergent Alpha” work. I treat α as the solution of one gauge-invariant equation F(α)=0, scan it over the complex-α plane, and map |F|. On the real axis, the positive branch lands on α ≈ 0.0072973525643 (~1/137.0359) with no tuning. More surprising: there’s also a clean real zero near α ≈ −4.9948. The maps look asymmetric, and while the negative branch began as a stress test, it might carry real structure.
In a 2-page note (“Alpha Branches and a Geometric Link to the Proton–Electron Mass Ratio”) I use the two branches (α⁺, α⁻) to write a single, simple relation that ties the locked frequency split (ω_C vs ω_R3) to g-factors, giving a parameter-free handle on m_p/m_e—about 4% off in this crude version. It’s deliberately compact and easy to read. If you’re curious about the electron’s pieces (ω_C for bare-mass part vs ω_R3 for self-field part), I list the numbers in “Emergent Electron Mass from Two-Space Boundary” (see pp. 59–60). Open to feedback, replication, and counter-examples.
Links:
Alpha Branches and mass-ratio note: https://doi.org/10.5281/zenodo.17348620
Alpha (background): https://doi.org/10.5281/zenodo.16944532
Emergent Electron Mass from Two-Space Boundary: https://doi.org/10.5281/zenodo.17219278