Time as Observation-Limited Entropy Conversion: Emergent Temporality, Relativistic Time Dilation, and Dark Matter from Information Thermodynamics

We propose a framework in which time is not a fundamental background parameter but an emergent physical process: the irreversible conversion of informational entropy into thermodynamic entropy through observation. Informational entropy is formally defined as the von Neumann entropy of the reduced density matrix of unobserved degrees of freedom. The present moment is modelled as a local "now-horizon" — a boundary in possibility space where unobserved possibilities become irreversible records. Because Landauer's principle ties the minimum cost of each irreversible bit commitment to the local temperature, the now-horizon advances at different rates across spacetime. We show this observation-cost asymmetry reproduces the structure of relativistic time dilation via the Tolman–Ehrenfest relation: time runs slower where energy density is high, not as a geometric postulate, but as a thermodynamic consequence. We further argue that mass is the informational complexity of a region's unresolved possibility space — a measure of observation resistance — and that gravity emerges as the spatial gradient of observation cost. This reinterpretation predicts that dark matter is the gravitational signature of informationally complex regions of possibility space without baryonic substrate. Convolving a Hernquist baryonic profile with a QFT-motivated correlation kernel (scaling dimension Δ = 1. 09, near the free scalar field value) reproduces the Navarro–Frenk–White halo profile with R² = 0. 993 and scale radius Rs = 20. 8 kpc, consistent with observations. The coupling constant α relating baryonic density to informational complexity is determined by a steady-state balance between quantum correlation generation and observational destruction, predicting α ∝ M^ (−0. 491) — in 2. 0σ agreement with the measured scaling α ∝ M^ (−0. 594 ± 0. 052) across the SPARC galaxy database. Tested against stacked weak gravitational lensing profiles from KiDS-1000 (Brouwer et al. 2021), the model outperforms NFW dark matter fits in all four stellar mass bins (χ²ᵣ = 5. 65 vs 8. 93) using 2 global parameters versus 8. The correlation kernel exhibits a consistent scale dependence — softer in dense inner halos (n ≈ 1. 25), steeper in sparse outer regions (n ≈ 2. 0–2. 5) — confirmed in 12 out of 12 independent tests (p < 0. 02%), with the outer value converging on the bare theoretical prediction, consistent with propagator dressing in quantum field theory. The framework presents 18 testable predictions spanning time dilation, dark matter halo profiles, galaxy rotation curves, weak gravitational lensing, gravitational collapse, black hole thermodynamics, and the equivalence principle, and approaches zero truly free parameters.