Electromagnetism
Charge is a winding number. Photons are traveling transverse waves. The coupling α = 1/137.042 is geometry.
Overview
In the elastic lattice, each node can be disturbed in two internal states: outward (⊕) or inward (⊖). These are the yin/yang of the medium — the + and − of charge.
What Is Charge?
Electric charge is a winding number: how many times the wave pattern wraps around the internal state space. Standing wave boundary conditions force this number to be an integer — which is why charge is quantized in units of e.
What Is a Photon?
A photon is a traveling transverse wave in the lattice, propagating at c = a√(k/η). It carries energy ℏω because the lattice is discrete — energy comes in lumps of one lattice quantum.
The Coupling α
α = 1/137.042 is not an input — it is the fraction of wave amplitude that couples between transverse modes, determined by the geometry of the 5D configuration space. Full derivation →
Energy Density
The electromagnetic energy density around a charge follows directly from wave mechanics:
The factor α appears because EM coupling is suppressed by the fine structure constant relative to the full lattice stiffness. The r−4 scaling is exact for all atoms. See the interactive plot →