§1.7 — Photon Transport

Resolved Curvature Transport

Within the EOTU framework, a photon is the emitted transport packet of a resolved curvature transition. It forms when a coupled Region releases excess curvature through an admissible packet channel.

A photon is therefore not an independent carrier introduced apart from the lattice. It is the transport expression of curvature change, emitted when a Region transition exports \(\Delta\mu\) into the dormant corridor network.

\[ \gamma \equiv \Delta\mu_{\mathrm{transport}} \]

This relation defines photon transport as curvature transport. The emitted packet preserves the curvature-transfer identity of the transition that produced it.

Emission Condition

Photon emission occurs when a composite Region transitions from one admissible closure state to another and the difference between those states must be exported as resolved curvature.

\[ \mathcal{R}_i \rightarrow \mathcal{R}_f + \gamma \] \[ \Delta\mu = \mu_i-\mu_f \]

The emitted photon carries the resolved curvature difference between the initial and later Region states. The local Region re-closes after emission, while the exported curvature propagates through the dormant lattice.

Packet Geometry

The emitted photon packet inherits its geometry from the transition that produced it. Its transverse family width is denoted \(L_b\), while its axial extent is denoted \(L_a\).

\[ L_b = \text{transverse packet family width} \] \[ L_a = \text{axial packet extent} \]

The photon wavelength is identified directly with the axial packet length:

\[ \lambda_{\gamma} = L_a \]

Wavelength is therefore not introduced as an independent spectral assumption. It is the resolved packet length produced by the emitting transition.

Energy Mapping

Photon energy is the projected value of the emitted curvature-transfer packet. In native form, the photon begins as a resolved \(\Delta\mu\) transport event. When projected into measured energy units, the packet is evaluated through the EOTU energy bridge.

\[ E_{\gamma} = \Gamma\left(\Delta\mu\right)^2 \]

Here \(\Gamma\) is the energy projection bridge and \(\Delta\mu\) is the curvature-transfer value associated with the emitting transition. This preserves the distinction between the native curvature packet and the measured energy assigned to it.

Dormant Corridor Propagation

After Freeze-Out, Dormant Corridors no longer store formation-scale curvature. They transmit curvature adjustments between Regions. Photon transport uses these corridors as the propagation pathway for resolved curvature packets.

\[ \text{Dormant Corridor} \rightarrow \Delta\mu\ \text{transport pathway} \]

The packet advances through the corridor network while preserving the emitted transition identity. It does not become a new particle species inside the corridor. It remains a resolved transport packet of curvature.

Photon and Neutrino Separation

Photon transport and neutrino transport are distinct ledger mechanisms. A photon carries resolved curvature \(\Delta\mu\). A neutrino carries unresolved phase \(\Delta\phi\). Both propagate through Dormant Corridors, but they satisfy different conservation requirements.

\[ \gamma \equiv \Delta\mu_{\mathrm{transport}} \] \[ \nu \equiv \Delta\phi_{\mathrm{transport}} \]

This separation prevents curvature transport and phase transport from being treated as the same object. A photon is emitted by resolved curvature transition. A neutrino is emitted by unresolved phase resolution.

Absorption Constraint

Photon absorption is constrained by packet compatibility. A receiving Region must contain an admissible transition capable of accepting the transported \(\Delta\mu\) packet. Absorption occurs when the incoming packet matches the closure requirement of the receiving system.

\[ \Delta\mu_{\mathrm{available}} = \Delta\mu_{\gamma} \]

If the receiving structure does not contain a compatible curvature requirement, the photon remains weakly coupled to that structure and continues propagation. This gives photon absorption its packet-matched character within the EOTU framework.

Spectral Interpretation

Spectral lines arise when repeated Region transitions emit packets with the same resolved axial extent. The measured wavelength corresponds to the packet length \(L_a\), while the measured energy corresponds to the projected curvature transfer.

\[ \lambda_{\gamma}=L_a \qquad \text{and} \qquad E_{\gamma}=\Gamma\left(\Delta\mu\right)^2 \]

In this form, photon spectra are not treated as detached frequency labels. They are the observable record of repeated Region closure transitions producing matched curvature-packet geometry.

Summary

Photon transport is the resolved movement of curvature through the post Freeze-Out lattice. A photon is emitted when a Region transition exports \(\Delta\mu\) through an admissible packet channel.

The emitted packet has transverse family width \(L_b\) and axial extent \(L_a\), with \(\lambda_{\gamma}=L_a\). Its projected energy is \(E_{\gamma}=\Gamma(\Delta\mu)^2\). Photon absorption requires packet-compatible curvature demand in the receiving Region, keeping photon interaction tied to closure geometry rather than to an independent carrier assumption.