Emergent Relational Time from Momentum-Space Phase Gradients in Entangled Quantum Systems

We propose a relational mechanism for the emergence of time based on the momentum-space phase gradient after a Space-to-Momentum Quantum Fourier Transform applied toentangled states. When tested on real experimental two-qubit polarization density matricesfrom spontaneous parametric down-conversion (SPDC), the metric yields positive values forentangled states (e.g., ⟨τ ⟩ ≈ 0.8709 on the maximum-likelihood reconstruction from James etal.) and exactly zero for separable references. This pattern is consistent across high-fidelitydatasets. A spherical-harmonic extension using real Planck polarization maps producesstable outputs with near-zero attenuation, consistent with the near-Gaussian character ofthe CMB. The framework is non-circular and gauge-guarded, providing an experimentallygrounded contribution toward understanding the quantum origin of time.