Quantum Tenson Field Theory: Probabilistic Geometry, Emergent Time, and Unified Quantum Gravity

We develop the Quantum Tenson Field Theory (QTFT), a unified framework that merges probabilistic geometry, relativity, and quantum theory through an ex- tended tensor field formalism. Starting from the geometric quantization of probabil- ity space, we introduce an augmented manifold combining spacetime coordinates xµ with informational coordinates θi, on which a complex tensor field Φ(x,θ) is defined. The resulting action S= d4xdnθ|g|L(Φ,∂µΦ,∂iΦ) naturally connects classical gravitation and quantum fields. The derived field equa- tion generalizes the Klein–Gordon equation into an informational–gravitational cou- pled form. We further demonstrate that this framework provides a natural pathway toward a covariant quantum gravity theory, with an emergent notion of time as a probabilistic flow.