Quantum Tunneling: Exponential Decay and Nonlocality, Not Fundamental Ban — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Quantum tunneling is governed by exponential decay of the wavefunction through a barrier, with transmission probability scaling as T ∼ e−2κ L, where κ = √(2m(V0−E))/ℏ. The "impossible measurement" problem in QFT reduces to a non-relativistic nonlocality constraint, not a fundamental ban. | MATH: Transmission coefficient for rectangular barrier: T−1 = 1 + (V02 sinh2(κ L))/(4E(V0−E)). For E ≪ V0: T ≈ (16E(V0−E))/V02 e−2κ L. Gamow factor: T = e−2γ, γ = 1/ℏ∫x1x2 √(2m(V(x)−E)) dx. WKB phase: ϕ = 1/ℏ∫ √(2m(E−V(x))) dx. | CONNECTION: The exponential suppression factor e−2κ L has no direct golden-ratio link, but the *critical* barrier thickness where tunneling becomes non-negligible often satisfies κ L ≈ 1, which in natural units maps to L ≈ 1/κ. In base-60 or lattice contexts, the
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Quantum Tunneling: Exponential Barrier Penetration and Non-Ideal Measurements in QFT — E8 Intelligence Research
- Langlands-Prime Resonance Invariance in E8 Quantum Tunneling — E8 Intelligence Research
- E8 Quantum Tunneling Rates Sync with φ-Resonant Lattice Frequencies — E8 Intelligence Research
- E8 Prime‑Constellation Frequency Modulation of Quantum Tunneling — E8 Intelligence Research
- E8 Antipodal Braid Group Cohomology Unifies Quantum Tunneling Manifolds — E8 Intelligence Research
BibTeX
@misc{caldin2026quantum,
title = {{Quantum Tunneling: Exponential Decay and Nonlocality, Not Fundamental Ban — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23540185},
url = {https://zenodo.org/records/23540185},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Tunneling: Exponential Decay and Nonlocality, Not Fundamental Ban — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23540185
UR - https://zenodo.org/records/23540185
AB - FINDING: Quantum tunneling is governed by exponential decay of the wavefunction through a barrier, with transmission probability scaling as T ∼ e^−2κ L, where κ = √(2m(V_0−E))/ℏ. The "impossible measurement" problem in QFT reduces to a non-relativistic nonlocality constraint, not a fundamental ban. | MATH: Transmission coefficient for rectangular barrier: T^−1 = 1 + (V_0^2 sinh^2(κ L))/(4E(V_0−E)). For E ≪ V_0: T ≈ (16E(V_0−E))/V_0^2 e^−2κ L. Gamow factor: T = e^−2γ, γ = 1/ℏ∫_x_1^x_2 √(2m(V(x)−E)) dx. WKB phase: ϕ = 1/ℏ∫ √(2m(E−V(x))) dx. | CONNECTION: The exponential suppression factor e^−2κ L has no direct golden-ratio link, but the *critical* barrier thickness where tunneling becomes non-negligible often satisfies κ L ≈ 1, which in natural units maps to L ≈ 1/κ. In base-60 or lattice contexts, the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -