Coarse graining erases distinctions

Purpose

Demonstrate that distinctions are scale-relative but ontically real.

Links to claims

• Coarse graining determines which distinctions exist

System

Multiscale stochastic reaction network or coupled oscillators.

Setup

• Micro variables: individual state components
• Macro variables: averaged or projected observables
• Noise: intrinsic stochasticity

Distinction definition

• Fine partition: microstate pattern
• Coarse partition: macrostate equivalence class

Measurement / metric

• Predictive divergence of future ensembles
• Mutual information decay across scales

Expected outcomes

• If claim holds: predictive distinction disappears under coarse graining.
• If claim fails: distinction remains invariant.