Beyond Time: A Relational Structure Framework for Quantum Interference and Cosmological Observations

We propose that physical observables traditionally attributed to time evolution arise from projection of an underlying timeless relational structure. Observations ranging from quantum interference to cosmological redshift are described as consequences of projecting this structure onto measurement apparatus. We introduce the ϕ-framework, where ϕ represents accumulated structural depth—defined operationally as logarithmic relational separation—along paths through hyperbolic relational geometry. This work extends the geometric ϕ-framework developed for gravity and light propagation [14] to a fully timeless formulation applicable to quantum and cosmological scales. Within this framework, (1) the Aharonov–Bohm effect emerges as path-dependent holonomy through multiply-connected structure, (2) cosmological redshift arises from accumulated structural separation ratherthan temporal expansion, and (3) the Hubble tension is explained as a projection artifact resulting from sampling different structural depths under implicit Euclidean assumptions. We present explicit calculations showing how hyperbolic structural geometry reproduces the observed ~9% discrepancy between local (H0 ≈ 73 km/s/Mpc) and CMB-derived (H0 ≈ 67 km/s/Mpc) measurements without introducing new dynamical degrees of freedom. The framework yields testable predictions distinguishing structural depth effects from genuine temporal evolution.