{
  "$type": "com.whtwnd.blog.entry",
  "theme": "github-light",
  "title": "Fisher Information: Am I Fishing?",
  "content": "Fisher Information as the Fabric of Reality: A Natural Extension into sPNP\n\nIntroduction: From Measurement to Metaphysics\n\nFisher Information is often treated as a statistical tool—a way of quantifying how much information an observable carries about a parameter. But what if Fisher Information isn't just a tool for scientists, but something real, something that actually helps shape the physical world? This post explores the idea that Fisher Information isn't just about inference, but may also be a real, physical quantity, part of the very structure of the universe. And this connects directly to the sPaceNPilottime framework (sPNP), which sees the world as shaped not just by particles and forces, but by information and geometry.\n\nIt is plausible that I am understanding Fisher Information in physics like Newton understood gravity, I haven't been able to make the curvature tangible, only functional. From an observer in spacetime, tangibility may be difficult to see in configuration space and 3N dimensions would allow for more complex Fisher Information structures. Fisher Information is used to measure how sharp or sensitive something is and this is like how a curve bends when the situation changes. In physics, that bending with the Quantum Potential can describe a real landscape: the sharper the wave bends, the more it pushes or pulls on particles. Fisher Information doesn’t push like a force, but it sculpts the paths that particles naturally follow. So Fisher Information is like a detective in nature. It tells us how much we can learn from changes, and in some theories (like sPNP), it also helps shape the space particles move through. \n\n1. The Principle of Extreme Physical Information (EPI)\n\nRoy Frieden's idea, called the Extreme Physical Information principle, flips the usual view. Instead of using physics to calculate Fisher Information, he says that nature works the other way: the laws of physics come from minimizing or optimizing Fisher Information. If you follow this principle, you can actually recover famous physical laws like the Schrödinger’s equation, Einstein’s general relativity and Maxwell’s laws of electromagnetism. This suggests that the universe might be like a computer, constantly working to arrange things in the most distinguishable and efficient way.\n\n\n2. Quantum Mechanics as Information Geometry\n\nThe quantum wavefunction is usually thought of as a probability tool. But it also contains structure: places where the wave bends or sharpens tell you how sensitive a system is to change. That’s what Fisher Information tracks. In sPNP, the way the wavefunction curves in configuration space becomes a kind of geometry. Particles follow paths shaped by this geometry. Where the information is rich and detailed, the curvature is strong, and this changes how things move. Entanglement, where particles are connected over distance, also shows up as curvature in this space—curvature that isn’t tied to ordinary space, but to a deeper configuration space. This information is deeper in configuration space, like non-locality is in spacetime. Entanglement distributes Fisher Information across multiple degrees of freedom. As correlations grow, so too does the curvature of the configuration-space metric. In effect, entanglement reshapes the geometry—modifying distinguishability relations among subsystems. This leads to a deeper insight, curvature tracks all amplitude gradients, but the more entangled a system, the more curved its configuration-space structure becomes. In this way, entanglement is not merely a quantum resource—it is a geometric agent.\n\n\n3. Spacetime Curvature as Fisher Curvature\n\nEinstein said mass and energy tell spacetime how to bend. But what is mass and energy really? It’s a way of saying how different one physical state is from another. That’s information. In sPNP, the bending of spacetime—the curvature we see as gravity—is actually a projection of a deeper curvature: the curvature of information in configuration space. Black holes help illustrate this: Their event horizons are places where information is hidden. Hawking radiation lets information slowly leak out. The idea that everything inside a black hole is encoded on its surface is a statement about information geometry.\n\n4. The Role of Jacobi Dynamics \n\nIn sPNP, Jacobi’s principle is about motion (kinetic energy). It says that nature follows paths of least action—a kind of optimal trajectory. Combine this with Fisher Information, and you get a system where the geometry tells you how things move. In sPNP, particles follow curved paths in configuration space. These curves aren’t caused by forces in the usual sense, but by the shape of the information landscape—the curvature encoded in the wavefunction. Distinctions, encoded in the Fisher Information metric, define structure. In this way, motion becomes not just about absolute position, but about optimal changes in distinguishability. Relationships are distinctions and physically meaningful.\n\n\n5. Thermodynamics and the Arrow of Time\n\nThermodynamics tells us about heat, entropy, and why time seems to flow in one direction. Fisher Information plays a role here too: Systems tend to move toward states with less accessible information. This loss or hiding of information is what we call entropy. When quantum systems decohere—lose their quantum-ness—it’s because information is leaking into the environment. In this view, measurement isn’t mysterious. It’s just a shift in how information is distributed. I have explored the concept of Fisher Information and Entropy in configuration space and how it could lead to an emergent gravity in spacetime (like Erik Verlinde's theory); but Moron doesn't want to add More-on now.\n\n\n6. A Fisher-Based Field Theory?\n\nIf Fisher Information is truly fundamental, then we can rethink the universe this way: Fields are places where information flows. Particles are where that information gets concentrated. Conservation laws are just statements that the total information stays balanced. Quantum field theory becomes a theory about how information is arranged and moves—not just particles bouncing around, but the dynamics of distinguishability.\n\n\n7. sPNP as the Einsteinian Upgrade to Information Geometry\n\nEinstein took Newton’s idea of force and turned it into geometry—gravity is the shape of spacetime. sPNP does something similar, but with information: It shows how entanglement creates real geometric structure. It lets particles move through this structure using Jacobi dynamics. It turns probability and information into actual curvature, not just math. This isn’t just a new interpretation—it’s a new kind of physical explanation.\n\n\nConclusion: Toward a Unified Informational Physics\n\nFisher Information may be the language of the universe, the thing that tells reality how to take shape. In spacetime, language is not just symbolic but physical, encoded in sound waves, written symbols, and neural patterns in the brain. It can create physical objects that materialize in the exact way our words describe. \n\nsPNP isn’t just another version of quantum mechanics. It’s a deeper vision, where: Geometry encodes information. Motion follows the most informative paths. Reality itself is shaped by how distinguishable one thing is from another. The next revolution in physics may not come from new particles, but from understanding how the universe organizes information—how it bends, flows, and evolves in ways we’re only beginning to grasp.\n",
  "createdAt": "2025-05-30T15:24:21.707Z",
  "visibility": "url"
}