Atomic Absorption and Emission as Vortex Mode Coupling: Photon–Electron Interaction, Emergent Bohr Quantisation, and Chemical Bonding as Amplitude Superposition in the PEW Framework (Article 6)

The Primordial Energy Wave (PEW) framework models all physical entities as topological vortex configurations of a single complex scalar field Ψ = ÷exp (iθ). The present article establishes that the complete cycle of atomic physics — photon absorption by an electron, electron binding to a proton, and photon emission — arises from a single mechanism: the coupling of amplitude profiles à between adjacent PEW vortices, without additional postulates. A photon is a free propagating fluctuation of the phase field θ (massless, Hopf invariant zero). It is guided toward the electron vortex by the geodesic curvature of the electron's amplitude field Ãₑ, with an effective gate cross-section σ = αₑm·λ² where αₑm = 1/137. 018 is the geometric gate ratio derived in Article 3. Absorption occurs when the photon frequency matches the difference between two internal mode frequencies of the electron vortex — the Bohr frequency rule ℏω = ΔE, derived here as a vortex mode-matching condition, not postulated. The binding of the electron to the proton is the superposition of their two amplitude profiles: the system minimises its total energy at the Bohr radius a₀ = ℏ/ (mₑ·c·αₑm) ≈ 0. 529 Å, where the amplitude gradients of the two vortices partially cancel. The Bohr radius is the distance of optimal gradient energy sharing between two PEW vortices. Chemical bonds — covalent, ionic — are superpositions of vortex amplitude profiles: bonding corresponds to constructive superposition (negative overlap energy), antibonding to destructive superposition. Emission occurs when the excited electron vortex returns to its ground mode: the beating of the excited gate oscillation with the vacuum fluctuations of the Mother Wave generates an outgoing θ-fluctuation at the transition frequency through the upper gate. The emitted photon is not released from storage inside the electron; it is generated by the gate oscillation itself. The selection rule Δℓ = ±1 emerges from the dipole radiation pattern of the gate oscillation. The complete Rydberg formula and all spectral series of hydrogen emerge from vortex mode transitions quantised by the Bohr radius condition, with αₑm, ℏ, mₑ, and c all derived from the PEW Lagrangian. Standard quantum mechanics — the Schrödinger equation, the Born rule, selection rules — emerges as the low-energy, small-vortex limit of PEW. The measurement collapse is reinterpreted as the irreversible entry of a θ-fluctuation through the electron gate.