Relational Kinetics in Generativity Theory: ΔC, Δ²C and Non‑Inertial Motion

Abstract

This paper introduces a coherence‑based framework for non‑inertial motion in GenerativityTheory (GT). The model is built on two fundamental operators: ΔC, describing instantaneous velocity reconfiguration, and Δ²C, describing instantaneous directional reconfiguration. These operators define discontinuities in motion that do not require inertial propagation, do not generate Cherenkov radiation, and do not rely on mass‑dependent acceleration. In GT, motion is interpreted as a reconfiguration of coherence constraints rather than a propagationof matter. ΔC and Δ²C formalize this principle mathematically, providing a relational kinetic structure where velocity and direction can change discontinuously through constraint reconfiguration.This framework extends classical mechanics by introducing coherence‑based dynamics applicableto systems where mass, inertia, and force are not the primary determinants of motion. The paper presents the mathematical definitions of ΔC and Δ²C, their physical interpretation,and the role of constraint reconfiguration as the upstream mechanism enabling non‑inertial transitions. The resulting relational kinetics model offers a new theoretical foundation for discontinuous trajectories, non‑Cherenkov transitions, and mass‑independent motion in coherent systems. Author: Waldemar Superson