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Solid State Communications

Traversal times for rectangular barriers within Bohm's causal interpretation of quantum mechanics

C. Richard Leavens

Published Oct 1, 1990• 57 citations
Publisher
DOI
10.1016/0038-1098(90)90833-w

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

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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)

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A Geometric formulation of the causal Interpretation of quantum mechanics

W. R. Wood, G. Papini

Foundations of Physics Letters•Jun 1, 1993•36 citations
In Bohm's causal or trajectory interpretation of quantum mechanics, it is straightforward to determine, from a sufficiently large number of calculated particle trajectories, probability distributions for time delays caused by a potential barrier, or for transmission times through a barrier. We show that these distributions can be calculated directly and more efficiently from probability currents, without the calculation of Bohm trajectories as an intermediate step. The ideas are illustrated for Gaussian wave packets incident on a square potential barrier and used to explain why average causal delay times differ from the average delay times calculated in other approaches.
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)