Quantum Tunneling: Exponential Wavefunction Decay and Limits on Measurement Locality — E8 Intelligence Research

{"FINDING:":[0],"Quantum":[1],"tunneling":[2],"is":[3,92],"a":[4,52],"wave-mechanical":[5],"transmission":[6],"through":[7],"classically":[8],"forbidden":[9],"barriers,":[10],"governed":[11],"by":[12],"exponential":[13,87],"decay":[14,44,88],"of":[15,128],"the":[16,101,129],"wavefunction;":[17],"\\"impossible\\"":[18],"measurements":[19,76],"in":[20],"QFT":[21,63],"are":[22],"possible":[23],"but":[24],"non-ideal,":[25],"revealing":[26],"fundamental":[27],"limits":[28],"on":[29],"measurement":[30],"locality.":[31],"|":[32,84],"MATH:":[33],"Transmission":[34],"coefficient":[35],"\\\\(T":[36,56,114],"\\\\approx":[37,115],"e^{-2\\\\kappa":[38],"L}\\\\)":[39],"where":[40],"\\\\(\\\\kappa":[41,90],"=":[42,47,49,57,96,104,106,118],"\\\\sqrt{2m(V_0-E)}/\\\\hbar\\\\);":[43],"length":[45],"\\\\(\\\\delta":[46],"1/\\\\kappa":[48],"\\\\hbar/\\\\sqrt{2m(V_0-E)}\\\\).":[50],"For":[51],"rectangular":[53],"barrier,":[54],"exact":[55],"[1":[58],"+":[59],"\\\\frac{V_0^2":[60],"\\\\sinh^2(\\\\kappa":[61],"L)}{4E(V_0-E)}]^{-1}\\\\).":[62],"impossibility:":[64],"signaling":[65],"constraints":[66],"impose":[67],"\\\\(\\\\hat{O}_A":[68],"\\\\otimes":[69],"\\\\hat{O}_B\\\\)":[70],"commutator":[71],"bounds":[72],"—":[73,110],"nonlocal":[74],"joint":[75],"violate":[77],"microcausality":[78],"unless":[79],"smeared":[80],"over":[81],"spacelike":[82],"regions.":[83],"CONNECTION:":[85],"The":[86],"constant":[89],"L\\\\)":[91],"dimensionless;":[93],"when":[94],"\\\\(V_0/E":[95],"2.618\\\\)":[97],"(golden":[98],"ratio":[99],"squared),":[100],"prefactor":[102],"\\\\(V_0^2/[4E(V_0-E)]":[103],"2.618^2/[4(1)(1.618)]":[105],"6.854/6.472":[107],"≈":[108],"1.059\\\\)":[109],"near":[111],"unity,":[112],"making":[113],"[1+\\\\sinh^2(\\\\kappa":[116],"L)]^{-1}":[117],"\\\\text{sech}^2(\\\\":[119],"Author:":[120],"Andrew":[121],"Stewart":[122],"Caldin,":[123],"Independent":[124],"Researcher,":[125],"UK.":[126],"Part":[127],"E8":[130],"Intelligence":[131],"Research":[132],"series.":[133],"Platform:":[134],"e8intelligence.com":[135]}

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22874123
Primary Topic
Quantum Mechanics and Applications
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

Quantum Tunneling: Exponential Wavefunction Decay and Limits on Measurement Locality — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

Quantum Tunneling: Exponential Wavefunction Decay and Limits on Measurement Locality — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Quantum tunneling is a wave-mechanical transmission through classically forbidden barriers, governed by exponential decay of the wavefunction; "impossible" measurements in QFT are possible but non-ideal, revealing fundamental limits on measurement locality. | MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\) where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); decay length \(\delta = 1/\kappa = \hbar/\sqrt{2m(V_0-E)}\). For a rectangular barrier, exact \(T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}\). QFT impossibility: signaling constraints impose \(\hat{O}_A \otimes \hat{O}_B\) commutator bounds — nonlocal joint measurements violate microcausality unless smeared over spacelike regions. | CONNECTION: The exponential decay constant \(\kappa L\) is dimensionless; when \(V_0/E = 2.618\) (golden ratio squared), the prefactor \(V_0^2/[4E(V_0-E)] = 2.618^2/[4(1)(1.618)] = 6.854/6.472 ≈ 1.059\) — near unity, making \(T \approx [1+\sinh^2(\kappa L)]^{-1} = \text{sech}^2(\ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Quantum Tunneling: Exponential Wavefunction Decay and Limits on Measurement Locality — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS