{
  "$type": "com.whtwnd.blog.entry",
  "theme": "github-light",
  "title": "sPNP: Curvature, Not Computation",
  "content": "**From Bits to Landscapes**\nWheeler’s “It from Bit” treats a yes/no distinction as the atom of reality. sPNP goes further:\n\nDistinction = Geometry.\n\n\nSharp changes in the wave amplitude makes neighboring configurations more distinguishable. The gradient of that sharpness defines the Fisher Information metric—a real curvature on the full 3 N-dimensional configuration space (or on the 3 N − 6 shape-plus-scale sub-manifold when centre-of-mass and rotations are factored out).\n\nG_IJ(X) = (1 / Q0²) · ∂I ln R · ∂J ln R  +  Σ_k m_k · δ_IJ\n\nThe first term is pure information curvature; the second is the classical Jacobi mass term. Together they form the Fisher–Jacobi metric that sculpts motion.\n\nClarification: (Q0).\nQ0 has units of length. Fixing Q0² = ħ / m_ref makes the first term reproduce the standard Bohm quantum potential. Any fixed value simply sets the information length scale; it could run with scale in an RG treatment.\n\n\n\n**Entanglement: Curvature That Spans Systems**\nWhen two subsystems entangle, distinguishability is no longer local. Off-diagonal components appear in  G_IJ, so curvature is literally shared across the composite system. In sPNP, entanglement is a geometric agent: it reshapes the metric rather than just correlating measurement statistics.\n\nClarification: No preferred foliation.\nCurvature lives on timeless configuration space. Lorentz symmetry emerges only after projecting into 4-D spacetime, so no spatial slice is privileged.\n\n\n**Projection: From Configuration Curvature to Spacetime Gravity**\n\nsPNP projects curvature into spacetime with a Gaussian kernel. K(X,x) = (4πQ₀²)^(3N/2) e^(-D²(X,x)/4Q₀²) [1+O(Q₀²RF)]\n\nsPNP introduces a geometric projection tensor F_μν(X, x) that folds the high-dimensional down to a 4-D one:\n\ng_μν(x)  =  η_μν  +  κ ∫ dμ(X) • P(X) • F_μν(X, x)\n\nThe kernel K(X,x) localizes the projection, while F_μν(X,x) extracts the specific geometric contribution to the emergent spacetime metric. Gravity is therefore a shadow of information curvature. Large Fisher gradients project to large spacetime curvature; weak gradients recover near-flat Minkowski space. \n\nClarification:Test-able consequences\n• Tiny curvature corrections predict O(10⁻²⁸) shifts in the Lamb shift for hydrogen-like ions.\n• In entangled macroscopic masses, sPNP forecasts ~ femtometer-scale deviations from Newtonian trajectories—one experimental target for next-generation cold-atom interferometers.\n\n\n**Jacobi Dynamics: Motion as Shortest Distinctive Path**\nInstead of “force = mass × acceleration,” sPNP uses an action equal to the arc-length in the Fisher–Jacobi metric. The system moves along geodesics that minimise that arc-length. Free particles coast (uniform motion) where the amplitude is flat; they accelerate where the information landscape steepens (steep gradients).\n\nBecause the action is reparametrisation-invariant, there is no absolute time variable—only a relational parameter. This automatically avoids the preferred-time problem that plagues non-relativistic pilot-wave models.\n\n\n**Entropy and the Arrow of Time**\nDecoherence spreads amplitude gradients into the environment, flattening the local Fisher curvature. That flattening is what we call entropy increase. In sPNP the thermodynamic arrow of time is the one-way diffusion of information curvature from subsystem to bath.\n\n\n**Field Theory Re-imagined**\nIf curvature is the basic substance, then:\n\nGauge fields = infinitesimal changes in the Fisher–Jacobi metric.\n\nFermions = topological obstructions in that metric (non-trivial spinor bundles over configuration space).\n\nConservation laws = balance equations for total Fisher curvature flux.\n\nIn this Energy-momentum picture, energy is secondary—a bookkeeping device for how much curvature is stored or transferred; total Fisher curvature.\n\n\n**What Stays Real When No One Looks?**\nBecause R(X) is ontic, the curvature exists even when no agent queries it. The Moon follows a geodesic in configuration space whether or not we observe it; observation merely updates our Shannon entropy, not the underlying Fisher geometry.\n\n\n**Distinction: Take-aways**\nFisher Information is not a statistical afterthought. It is the curvature that structures reality.\n\nEntanglement = shared curvature, neatly explaining non-local correlations without superluminal signals in spacetime.\n\nJacobi geodesics encode dynamics, restoring determinism while remaining Lorentz-compatible after projection.\n\nEntropy is curvature flattening, providing an informational account of the arrow of time.\n\nsPNP unifies motion, gravity, and thermodynamics in one information geometric language. ",
  "createdAt": "2025-05-30T19:08:21.852Z",
  "visibility": "url"
}