Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== 1. Momentum & conservation laws. A single free photon cannot create a free massive particle (e.g., create an electron out of nothing) because energy–momentum conservation forbids it: you need either two photons (photon–photon pair production) or a nearby third body (nucleus or field) to take recoil. So “building mass from photons” must be physically modelled as energy deposition on an existing bound system (raising stored energy), or as processes that have allowed kinematics (pair-production in a field, multi-photon interactions, etc.). QAT’s shell must provide the extra degree of freedom (boundary) to absorb recoil — that’s consistent with modeling mass as stored boundary energy rather than "creating matter from the void". ===
# Absorption vs scattering. Many photons scatter rather than deposit rest energy (e.g., Thomson scattering). Effective absorption fraction α\alphaα or η\etaη matters a lot. If most photons are scattered and re-emitted, net stored energy is near zero. The numbers above assume perfect retention (worst case optimistic). Real absorption probabilities and resonance cross sections (atomic lines, plasma emission/absorption lines) can change timescales dramatically.
# Binding / confinement required. To keep absorbed energy as rest mass, you must trap it: otherwise the absorber will re-radiate. The classical tension TTT (Poincaré stress) we calculated earlier is the phenomenological way to hold field energy together. QAT must include a mechanism (tension, surface modes, plasma double layers, quantum binding) that prevents immediate re-emission — otherwise the photon energy simply passes through or is scattered.
# Quantum field effects / renormalization. At the electron scale real QED effects (self-energy renormalization, vacuum polarization) appear; the classical thin-shell is only a toy. That said the toy gives robust geometric scaling and order-of-magnitude numbers that can be compared to QAT intuition.