Spacetime as an Emergent Informational Invariant: Deriving the Metric Tensor from the Volume-Event Inversion Principle (VEIP)

This publication presents a formal derivation of the spacetime metric tensor as an emergent phenomenon arising from a fundamental density of informational events. The work introduces the Volume-Event Inversion Principle (VEIP), based on the informational invariant V4⋅LI=ℏ, which defines the spacetime hypervolume as the geometric cost of quantum action. Within the presented formalism, it is demonstrated that classical General Relativity constitutes a low-energy, thermodynamic effective theory emerging through the process of coarse-graining discrete quantum events. This model offers novel solutions to key problems in modern physics: Dark Energy: It is interpreted as a geometric vacuum pressure resulting from the dilution of information in cosmic voids. Singularities: By integrating results from Loop Quantum Gravity regarding the discrete spectrum of the volume operator, the work proves the mathematical impossibility of physical singularities, replacing them with a Big Bounce model. Unification: The derivation of the field equations integrates Yang-Mills gauge theory with differential geometry, utilizing Zurek’s decoherence mechanism to recover the classical metric. The work concludes by formulating a testable observational prediction regarding the anomalous dispersion of high-frequency gravitational waves, which may serve as direct evidence of the informational graininess of the geometric background.