Radial Uncertainty Expansion and Measurement Collapse: A Geometric Interpretation of Schrödinger Evolution

EUGENE CATRAMBONE

Published Dec 11, 2025• 0 citations

Abstract

Quantum mechanics precisely describes how a wavefunction evolves, yet standard interpretations provide little geometric intuition for how a delocalized state suddenly localizes when measured.This work introduces a visualizable interpretation in which quantum uncertainty forms a radially expanding region of potential presence, growing in time according to the Schrödinger equation.Measurement is modeled as a geometric reset: the expanding radius collapses to a sharply localized region determined by detector resolution, after which the radius resumes its growth under ordinary unitary evolution. This expansion–collapse cycle offers a simple and physically grounded narrative for quantum measurement without adding hidden variables or modifying the dynamics.The paper explores: Free wavepacket dispersion interpreted as radial uncertainty growth Collapse as a spatial origin reset Relations to decoherence, GRW, Bohmian mechanics, and QBism Experimentally testable consequences involving post-measurement dispersion, collapse timing, and detector geometry The framework is fully compatible with standard quantum mechanics while providing an intuitive geometric structure for uncertainty evolution.

DOI: 10.5281/zenodo.17895687

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