Distinguishability as a Fundamental Quantity: A Candidate Framework for Emergent Spacetime, Gravity, and Quantum Behavior

We propose a framework in which distinguishability between physical states is treated as a fundamental quantity underlying physical reality. In this formulation, spacetime geometry, quantum probability, and entropy emerge from the dynamics of a scalar distinguishability field. Motivated by connections between spacetime geometry and quantum information, we introduce a variational principle coupling distinguishability to curvature and entropy. We derive modified gravitational dynamics featuring an effective gravitational coupling and demonstrate consistency with classical gravity in the weak-field limit. The framework predicts deviations from standard gravitational behavior in regimes of high distinguishability density.