Velocity-Curvature Relation in Quantum Coherence: A Geometric Threshold for Decoherence.

This work proposes a geometric criterion for quantum coherence by linking the de Broglie wavelength of a particle to an effective spatial curvature R, defined by the experimental confinement scale. We derive a critical velocity v = h / (mR), where R = 1/L² and L is the characteristic length of the system (e.g., slit separation, trap size). This framework predicts coherence thresholds consistent with electron, fullerene, and Bose-Einstein condensate experiments. By redefining R as a measurable geometric parameter, we resolve prior ambiguities and provide testable predictions for quantum coherence in curved or confined systems.