Knotted Light: The Topological Origin of Matter

Abstract

There is one field --- the Hopf field $\mathbf{n}: \mathbb{R}^3 \to S^2$, a nonlinear sigma model whose linearized sector is the electromagnetic field. It has two manifestations: propagating waves ($H = 0$), which we call photons, and topological knots ($H = 1$), which we call matter. The difference between matter and light is not substance but topology --- geometry that cannot be undone. In this picture, an electron is not a point particle but a stable, self-sustaining knot in the electromagnetic field, a configuration where the field lines are linked with Hopf invariant $H = 1$, topologically forbidden from unraveling. We summarize evidence from a 43-paper programme (Papers I--XLII plus the present paper; spanning published, reviewed, and draft-stage work) showing that this single idea --- matter is knotted light --- reproduces the fine structure constant ($1/\alpha = 137.09$, 0.04% accuracy), all three charged lepton masses (0.001%), the Weinberg angle ($\sin^2\theta_W = 3/13$, 0.19%), the complete neutrino mixing matrix (all three angles within $1\sigma$), the Higgs boson mass ($m_H = 125.82$ GeV, 0.46%), and the cosmological constant (1.4%) --- with zero free parameters for all but one prediction (the neutrino mass sum has one conditional input). The framework predicts exactly three generations of fermions, a neutrino mass sum of $62 \pm 5$ meV testable by CMB-S4, identically zero neutron electric dipole moment, and no axion. Dark matter emerges as the electrically neutral sector of the same knotted field. You are made of frozen disorder from $10^{-35}$ seconds after the Big Bang.

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