>[!warning] >This content has not been peer reviewed. # Laws change when you change scale ## What it is (established result) The **Wilsonian renormalization group (RG)** formalises how the effective description of a system changes under **coarse-graining** (changing the scale of observation). As one integrates out short-distance degrees of freedom, the parameters (“couplings”) of the theory flow: - Systems near critical points exhibit **scale invariance** and universality: many microscopic models flow to the same **fixed point**, sharing critical exponents \([1–3]\). - RG explains why different scales can have different “effective laws” even when the underlying microphysics is unchanged: what matters is which degrees of freedom are relevant at the scale being probed. Wilson’s RG provides the modern foundation for critical phenomena and for the field-theoretic understanding of scale dependence \([1–3]\). --- ## How RRT / RST uses it RST uses RG as a **scale sensor** pattern: - Treat the exponent \(n\) (sharpness / topology parameter in the Resource Triangle) as an **effective parameter** that can depend on local relational density / scale. - In a simulator, compute a local density proxy (e.g. signal-to-noise per unit distance) and map it smoothly to an effective \(n_\mathrm{eff}\) that interpolates between regimes (gravity-like vs stiff). The `Reality Engine` demo implements this idea as a `WilsonRGSensor` mapping a local density proxy to \(n_\mathrm{eff} \in [1.25, 2]\). --- ## Links | Role | Link | |:---|:---| | Simulator application | [[further applications/Reality Engine/Reality Engine (RST)]] | | Simulator code | [[further applications/Reality Engine/Reality Engine - Code]] | --- ## References [1] K. G. Wilson, "Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture," *Physical Review B* **4**, 3174 (1971), `https://doi.org/10.1103/PhysRevB.4.3174`. [2] K. G. Wilson, "Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior," *Physical Review B* **4**, 3184 (1971), `https://doi.org/10.1103/PhysRevB.4.3184`. [3] K. G. Wilson and J. Kogut, "The renormalization group and the ε expansion," *Physics Reports* **12**, 75–199 (1974), `https://doi.org/10.1016/0370-1573(74)90023-4`.