Geometric–Temporal Correspondence in the Local Classical Limit: A Structural Measure of the Transition between Relativistic and Classical Regimes v2

This work proposes a structural reformulation of the correspondence between geometry and time in the local classical limit of spacetime. The literal equality between geometric and temporal quantities is abandoned and replaced by a scale-mediated relation. The fundamental quantities are defined as well-established geometric invariants and physical observables: the residual derivative of geometry, denoted by Dᴳ, defined as the norm of the Riemann tensor, and the residual derivative of time, denoted by Dᵀ, defined as the normalized proper acceleration. A hypotenusal measure 𝒟 = √ (Dg² + Dt²) is introduced, which simultaneously quantifies the departure from Euclidean geometry and from absolute time in the local limit. It is shown that, in Schwarzschild spacetime, this measure reduces, to first order in the weak-field regime, to the dimensionless parameter GM / (c²·r), providing a unified interpretation of the transition between the relativistic and Newtonian regimes. Newtonian mechanics emerges as a regime of negligible structural loss, whereas general relativity describes regimes of relevant structural loss. The formalism remains open to generalizations to arbitrary metrics. The article "Geometric–Temporal Correspondence in the Local Classical Limit: A Structural Measure of the Transition between Relativistic and Classical Regimes" demonstrated that Riemannian geometry tends locally towards Euclidean geometry. Simultaneously, relativistic time tends towards the indistinguishable from the absolute locally. It is observed that the arrows of geometry and time point in the same direction... Therefore, is electron superposition emerging? The article "Emergent Superposition: The LFO Theory: A Complete Physical Formulation of Trajectory Instability as the Origin of the Wavefunction", aims to answer that question.