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. We test this prediction by computing the informational complexity density around a Milky Way-like galaxy, convolving a Hernquist baryonic profile with quantum field theory-motivated correlation kernels; the resulting profile reproduces the Navarro–Frenk–White halo shape with R² = 0.99 across a broad plateau of kernel exponents consistent with the free scalar field scaling dimension Δ = 1. The coupling constant α relating baryonic density to informational complexity is shown to be determined by a steady-state balance between quantum correlation generation and observational destruction, predicting α ∝ M_bar^−0.491—in 2.0σ agreement with the measured scaling α ∝ M_bar^(−0.594 ± 0.052) across the SPARC galaxy database. Tested against stacked weak gravitational lensing profiles from KiDS-1000, the model outperforms NFW dark matter fits in all four stellar mass bins using 2 global parameters versus 8. The correlation kernel exhibits a consistent scale dependence—softer in dense inner halos, steeper in sparse outer regions—and the bare (sparse-regime) exponent is jointly measured at n_outer = 2.05 ± 0.04, placing the parameter-free free-scalar-field prediction n = 2 at 1.3σ. A two-zone model with the outer kernel fixed at this predicted value and a single fitted dressing depth improves the global lensing fit by Δχ² = −156 at equal parameter count (χ²_r ≈ 2.9 versus ≈ 8.9 for NFW). The framework's central exponent is thus a QFT prediction with measured environmental dressing; the dressing depth and one normalisation remain its fitted galactic-scale parameters, and we identify the derivation of the dressing—the dressed exponent and its ~300 kpc transition radius—as the framework's most important open calculation. The dressing itself survives a pre-registered robustness test: cold gas at measured amplitudes and a generous faint-satellite term close less than one fifth of the two-zone improvement, and a joint fit sets the satellite fraction to zero. Calibrated in physical units, the model predicts M(<100 kpc) = 7.6 × 10¹¹ M_⊙ for an isolated Milky-Way-stellar-mass galaxy, within 10–30% of Gaia-era Milky Way measurements; its distinctive rising outer circular-velocity profile is directly testable with stacked satellite kinematics around isolated analogues.