Photon Dynamics in External Gravitational Fields: Energy–Momentum Exchange Between Photons and Gravitational Fields in Extended Classical Mechanics

Extended Classical Mechanics (ECM) describes the photon as an energetic physical entity whose interaction with an external gravitational field proceeds by direct force- and energy–momentum exchange, rather than through the geometric curvature of spacetime. This paper develops the ECM account of photon dynamics in external gravitational fields, with gravitational redshift interpreted as the expenditure of an acquired gravitational interaction-energy component Eɢ rather than as a depletion of the photon’s inherent frequency-defined energy. The photon’s inherent state is fixed by Eᵢₙₕₑᵣₑₙₜ = hf_photon = −Mᵃᵖᵖc², where Mᵃᵖᵖ < 0 is the Negative Apparent Mass (NAM) associated with the energetic reduction of the emitting electron. A coordinate framework for the photon–field interaction is constructed in which successive interaction stages generate external-field momentum displacements through Δpₑₓₜ = h/Δλ and its reverse-branch counterpart Δpₑₓₜ = h/(−Δλ), organised as a symmetric blueshift–redshift trajectory about the inherent reference state. The complete state-generation chain x° → f → Δf → λ → Δλ → Δpₑₓₜ → ΔG is established together with the ECM phase transformation Tₓˆ = x°/360°f = Δt, providing a rigorous, data-driven basis for graphing the exchange without arbitrary coordinates. An explicit nine-point displacement data set is specified, the complete coordinate table is computed, and the exchange trajectory is graphed.