Local Tidal Tension and Global Spatial Curvature: A Measurement-Oriented Framework for Quantum Gravity

This note presents a measurement-oriented clarification of gravitational observables within General Relativity. We distinguish between Local Tidal Tension (LTT), defined operationally via geodesic deviation as the relative acceleration between neighboring freely falling worldlines, and Global Spatial Curvature (GSC), describing the large-scale geometry of cosmological spatial hypersurfaces.

While gravitational acceleration at a point may be locally transformed away via the equivalence principle, tidal structure cannot. Thus, the physically measurable content of gravity is fundamentally relational and finite-separation dependent.

Building on this distinction, we outline a structured research trajectory toward quantum gravity grounded in curvature observables, including (i) operator-valued tidal observables, (ii) semiclassical curvature corrections via effective field theory, (iii) parameterized tidal-correlation signatures, and (iv) relational evolution of curvature observables addressing the problem of time.

This work does not modify Einstein’s equations nor propose new gravitational dynamics. It is intended as a conceptual foundation for future quantum gravity investigations.