The Structural Necessity of Internal Time: The Two-Clock Projection Law Across Quantum, Classical, and Metrological Systems

Across atomic photoionization, solid-state attosecond spectroscopy, wave-chaotic scattering, and precision timekeeping, measured temporal observables systematically decompose into an intrinsic dynamical contribution and a measurement-dependent projection. We show that this structure is not technique-specific but operationally unavoidable: any temporal measurement whose outcome depends on the measurement configuration requires two temporally distinct variables. This result is formulated as the Two-Clock Projection Law, t = χτ + Δ_proj, and tested using a cross-domain collapse diagnostic Λ = Var(t) / Var(τ) − 1. Digitized datasets from atomic and symmetry-resolved solid-state attosecond measurements populate the same structural phase space, while wave and clock regimes define the remaining regions as explicitly labeled structural indicators. A universal experimental protocol is provided that allows any dynamical system to be tested for single-clock sufficiency or structural two-clock behavior. The result is interpretational rather than dynamical: the equations of motion remain unchanged, but the temporal variable governing evolution is identified with internal time τ, while laboratory time t appears as a measurement-dependent projection. Union Dipole Theory provides a candidate ontology for τ; however, the structural necessity derived here is independent of any specific model. All numerical values are documented in reproducible data-extraction tables, and all figures were generated using open Python workflows.