Information Processing Complexity as Spacetime Curvature: A Formal Derivation and Physical Unification

We present a rigorous deductive proof demonstrating that information processing complexity, characterized by the geometric complexity Ω, necessarily and directly manifests as local spacetime curvature

We present a rigorous deductive proof demonstrating that information processing complexity, characterized by the geometric complexity Ω, necessarily and directly manifests as local spacetime curvature through established physical principles. Starting from Landauer’s principle and Fisher information geometry, as developed in foundational work on Geometric Information Theory (Spivack, 2025a), we derive a “Information Complexity Tensor,” CμνCμν​, representing the stress-energy contribution of information processing. This tensor is shown to be a necessary component of Einstein’s field equations. The framework establishes that Ω is not merely correlated with, but is a direct measure of, the spacetime curvature induced by information processing. This transforms the study of complex information systems and consciousness into a domain of applied general relativity, unifying information theory, thermodynamics, and gravity. We propose testable experimental predictions, including gravitational effects of large-scale computation and a potential information-geometric origin for dark energy.