Gravity as the Invariant Remainder A Diagnostic Framework Grounded in Tidal Acceleration

This paper presents a conceptual diagnostic framework that reorganises established results in classical mechanics and General Relativity to clarify the operational distinction between gravity and acceleration. Although the equivalence principle renders uniform gravitational fields locally indistinguishable from accelerated frames, conceptual ambiguity persists regarding what uniquely characterises gravity. The framework resolves this ambiguity by identifying invariant differential (tidal) acceleration between neighbouring free-falling trajectories as gravity’s non-removable operational signature.

Rather than introducing new physical laws or modifying existing theory, the framework synthesises established elements: acceleration, inertial motion, fields, spacetime geometry, and geodesic deviation, into a closed relational structure. Within this structure, uniform acceleration and uniform gravitational fields are locally removable by coordinate transformation, whereas curvature-induced tidal acceleration is not. Gravity is therefore defined operationally as differential acceleration arising from spacetime curvature that persists across all smooth reference-frame transformations.

A structured procedural method is provided for applying this distinction to concrete physical scenarios. Worked examples including uniform acceleration in flat spacetime, free fall in a non-uniform gravitational field, and gravitational waves demonstrate how the framework consistently separates frame-dependent effects from invariant gravitational phenomena. A contrast case involving non-gravitational forces clarifies why differential acceleration alone is insufficient unless it is universal and geometric in origin.

This work functions as a conceptual and pedagogical synthesis fully consistent with General Relativity. It advances no novel dynamical claims or experimental predictions, but provides structural clarification of gravity’s invariant physical content.