Hydrogen 1s Orbital from Stochastic Collapse Testing the Quantum Measurement Problem via the Fine-Structure Constant

Abstract

We test a recently proposed algebraic resolution of the quantum measurement problem by deriving the fine-structure constant from the same dissipative collapse dynamics, and by verifying that the resulting stochastic collapse reproduces the Schrödinger distribution for the hydrogen 1s orbital. Working within the Jordan-Clifford immersive framework on the 14-dimensional operational subspace $\mathcal{H} = \mathbb{C}^{14}$ associated with the Fano incidence geometry, we show that the stochastic collapse equation $$dc_i = -\frac{1}{2}\gamma c_i(1 - 2p_i + \sum_j p_j^2)dt + \sqrt{\gamma}c_i(dW_i - \sum_j p_j dW_j)$$ contains the decoherence rate $\gamma = \sqrt{\lambda_{\text{graphon}}}$, where $\lambda_{\text{graphon}} = \Lambda_1/\Lambda_0 \approx 1.99765$ is the spectral gap of the graphon kernel emerging from the Fano 2-22 moduli space. The immersion of the measurement apparatus in the continuum flow identifies $\gamma$ with the spatial coupling coefficients of the MPS transfer operator. In the asymptotic limit $k \to \infty$, $\lambda_{\text{graphon}} \to 2$, hence $\gamma \to \sqrt{2}$. Substituting into the MPS duality $\alpha^{-1} = \ln\lambda_{\max} - \pi$ yields: $$\alpha^{-1} = \ln\lambda_{\max}(\sqrt{2}) - \pi = 137.0359991678.$$ This value is consistent with Rubidium atom interferometry (2020), the revised $g-2$ determination (2024-2025), and CODATA 2022 within $1\sigma$. As a further test of the collapse dynamics, we simulate the positional collapse of the hydrogen 1s orbital on a radial grid with $10{,}000$ stochastic trajectories. The ensemble mean $\langle r \rangle_{\mathrm{model}} = 1.49868\,a_0$ reproduces the Schrödinger expectation value $\langle r \rangle_{\mathrm{Sch}} = 1.50012\,a_0$ to within $1.44\times 10^{-3}\,a_0$. A Kolmogorov-Smirnov test ($p = 0.131$) and a bootstrap 95\% confidence interval confirm that the ensemble distribution is statistically indistinguishable from the quantum mechanical prediction. The construction contains no free parameters and is falsifiable via the bound $q \le 45$ on continued fraction quotients. The derivation and the hydrogen benchmark together provide an experimental test of the proposed resolution of the measurement problem.