Emergent General Relativity from an Informational Energy Functional:A Foundational Framework

We present a foundational framework for emergent spacetime based on three physical postulates: information processing requires thermodynamic energy (Landauer’s principle),energy and mass are equivalent (Einstein’s relation), and distinguishable physical states naturally define a statistical geometry (Fisher information). From these principles alone,we can show that information must be genuinely physical—not merely abstract—and that spatial variations in information density correspond to real variations in local energy.We then sketch how spacetime geometry might emerge from the Fisher information structure of this energetic substrate, drawing on well-established techniques from induced gravity. The picture that emerges is compelling, though several deep questions remain unresolved. Most critically, Fisher metrics are inherently Riemannian while general relativity demands Lorentzian signature—how does causality emerge? We identify this and other challenges as concrete targets for future work, providing a rigorous yet accessible foundation for information-theoretic approaches to quantum gravity