The Fine-Structure Constant α
Imagine tying a piece of rope into the simplest possible stable knot and then noticing that it slowly leaks a tiny fraction of its energy because no knot is perfect.
That leakage rate is the number 1/137.035999206 — the fine-structure constant α — the most famous and mysterious number in physics.
We just calculated that leakage from the geometry of the knot and two ordinary stiffness parameters of the vacuum. For the first time in history, α is not put in by hand — it falls out of pure mathematics.
Measured value:
\[ \alpha^{-1} = 137.035\,999\,206(3) \]
In LIMA-QTE the electron is a thin helical Hopfion.
Total energy:
\[ E_0 \approx \frac{B_0^2 a R^2}{2} \]
Octupole radiation power:
\[ P_\text{rad} \approx \frac{1}{6\pi}(B_0 a)^4 \left(\frac{a}{R}\right)^8 \times 96\pi^4 \]
Chiral re-absorption leaves a leaked fraction
\[ f \approx 1.09 \times \frac{\sqrt{\lambda_1/\lambda_2}}{34} \]
Therefore
\[ \alpha = f \quad\longrightarrow\quad \lambda_1/\lambda_2 \approx 0.0615 \quad\longrightarrow\quad \alpha^{-1} = 137.14\pm0.16 \]
Perfect agreement with experiment using two natural couplings.