Quantum Tunneling Time, the Principle of Least Action, and the Causal Coherence Limit: A Unified Analysis with a UAT/UCP Perspective

This repository presents a two-part exploration of negative transit times in quantum tunneling, combining a pedagogical explanation rooted in standard physics with a speculative extension inspired by the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) frameworks. Part 1 — Path-Integral Analysis and Numerical Simulation:We explain the experimentally observed negative group delay of photons traversing an ultracold atomic cloud via the principle of least action in Feynman's path-integral formulation. The dominant contribution comes from non-classical trajectories that avoid the energetic cost of the barrier. A numerical simulation of a Gaussian wave packet tunneling through a rectangular potential barrier reproduces the negative transit time, confirming the interpretation within standard quantum mechanics. Part 2 — The Hartman Effect and the Causal Coherence Limit:We review the Hartman effect —the saturation of the tunneling (phase) time to a finite, negative value— and provide an analytical calculation for an electron incident on a rectangular barrier. The phase time saturates at a fraction of a femtosecond, regardless of barrier width, guaranteeing that local temporal fluctuations never accumulate to violate macroscopic causality. We then offer a speculative interpretation through the lens of the UAT/UCP frameworks (DOIs: 10.5281/zenodo.17729221, 10.5281/zenodo.17718670), suggesting that the saturation is a manifestation of a deeper causal coherence limit that protects the global causal structure. Contents of the repository: LaTeX source and compiled PDF of the unified article. Python script for the numerical wave-packet simulation (Part 1). Python script for the analytical phase-time calculation (Part 2). Generated figures. Note: This work is a curiosity-driven intellectual exercise. The UAT/UCP connection is presented as a speculative perspective and does not form part of mainstream physics. The standard quantum mechanical analysis, however, is rigorous and self-contained. Related DOIs: UAT: 10.5281/zenodo.17729221 UPC: 10.5281/zenodo.17718670 Antifrequency: 10.5281/zenodo.18809178 Author: Miguel Ángel Percudani (Puan, Buenos Aires, Argentina)License: Creative Commons Attribution 4.0 International (CC BY 4.0)