Cumulative Temporal Relativity: A Complete Framework for Emergent Time-Dependent Dynamics in Hierarchical Physical Systems

This paper presents Cumulative Temporal Relativity (CTR), a complete theoretical framework proposing that the effective rate of time passage for physical systems depends inversely on their accumulated proper time since emergence as coherent entities. Key contributions: Introduces the Principle of Informational Coherence to define temporal emergence in hierarchical systems Derives the Logarithmic Time Law: τ_eff = ln(τ/τ₀) Determines τ₀ = 45.9 Gyr from observed Hubble tension (H₀: 67.4 vs 73.0 km/s/Mpc) Predicts age-dependent dynamical mass: M_eff = M × [(τ + τ₀)/τ₀]² Offers falsifiable alternative to dark matter hypothesis Proposes novel experimental tests using Bose-Einstein condensates The framework maintains compatibility with Special and General Relativity while extending physics to incorporate temporal memory effects. All predictions are quantitative and empirically testable with existing astronomical data (Gaia, JWST) and laboratory experiments.