Time as Information Rate Through Dimensional Apertures: Black Hole Phenomenology from Observer-Relative Channel Capacity

Black hole phenomenology emerges from dimensional accessibility constraints—no GR required. Time dilation is channel contraction: when an observer's aperture narrows, their information rate drops and time slows.

We demonstrate this computationally using coupled oscillators with observer-relative access weights. An external observer whose aperture closes at a horizon-analogue sees time freeze; an infalling observer with constant aperture sees nothing special. Same dynamics, different channels, different clocks.

Part 2 of the IPI Letters trilogy:

• Part 1: Thermodynamic Foundation — microscopic thermodynamics
• Part 3: Cosmic Relaxation — cosmological origins

The key equation is the effective dimension: $k_{\text{eff}} = (\sum_i w_i)^2 / \sum_i w_i^2$, where $w_i$ are aperture weights. As the aperture squeezes, $k_{\text{eff}} \to 2$, correlation rate drops, and time freezes for that observer.

This suggests spacetime geometry may be downstream of dimensional accessibility constraints, consistent with Jacobson's thermodynamic derivation of Einstein's equations.