What is Quantum Tunnelling: The Framework of Zulfia Mapping Z = η + ∆ : η meets ∆ (1973 Observable Magic Tunnelling to 2026 Information Tunnelling)

AbstractThis work re-examines the 1973 concept of quantum tunnelling, historically described asa Magic Tunnelling phenomenon where a particle crosses a barrier without a physicalmechanism. In conventional quantum mechanics, tunnelling is treated as barrier penetrationprobability based on wave leakage, T ∼ e−2kL, without defining what tunnelling is.We introduce a conceptual framework for quantum tunnelling denoted as Z = η + ∆, calledZulfia Mapping. Here η is defined as the discrete, quantal state carrying invariant identityI(η), which cannot travel alone, while ∆ represents the continuous, contextual field of natureand barrier. Wave does not travel alone; it must hold the finger of η.In Z-language, we convert the magic concept into a real concept. Tunnelling is re-definednot as crossing the barrier, but as the formation of a new state Z via η + ∆ → Z, underidentity conservation I(T (η)) = I(η). Thus, the barrier is not an obstacle to be crossed,but a context to meet.Consequently, Z → η1, η2 provides a built-in origin for entanglement, and the observableend-state is defined as the MI Communication State ZM I = ηmessage + ∆channel. This marksthe transition from 1973 Magic Tunnelling to 2026 MI Tunnelling — from magicsafar to MI safari. This formalism provides a foundation for analysing information transferacross physical and natural systems

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22089664
Primary Topic
Quantum Mechanics and Applications
Type
article
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article

What is Quantum Tunnelling: The Framework of Zulfia Mapping Z = η + ∆ : η meets ∆ (1973 Observable Magic Tunnelling to 2026 Information Tunnelling)

DR. ZULFIQAR ALI KHAN
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
article

What is Quantum Tunnelling: The Framework of Zulfia Mapping Z = η + ∆ : η meets ∆ (1973 Observable Magic Tunnelling to 2026 Information Tunnelling)

DR. ZULFIQAR ALI KHAN
article en

Abstract

AbstractThis work re-examines the 1973 concept of quantum tunnelling, historically described asa Magic Tunnelling phenomenon where a particle crosses a barrier without a physicalmechanism. In conventional quantum mechanics, tunnelling is treated as barrier penetrationprobability based on wave leakage, T ∼ e−2kL, without defining what tunnelling is.We introduce a conceptual framework for quantum tunnelling denoted as Z = η + ∆, calledZulfia Mapping. Here η is defined as the discrete, quantal state carrying invariant identityI(η), which cannot travel alone, while ∆ represents the continuous, contextual field of natureand barrier. Wave does not travel alone; it must hold the finger of η.In Z-language, we convert the magic concept into a real concept. Tunnelling is re-definednot as crossing the barrier, but as the formation of a new state Z via η + ∆ → Z, underidentity conservation I(T (η)) = I(η). Thus, the barrier is not an obstacle to be crossed,but a context to meet.Consequently, Z → η1, η2 provides a built-in origin for entanglement, and the observableend-state is defined as the MI Communication State ZM I = ηmessage + ∆channel. This marksthe transition from 1973 Magic Tunnelling to 2026 MI Tunnelling — from magicsafar to MI safari. This formalism provides a foundation for analysing information transferacross physical and natural systems

Zenodo (CERN European Organization for Nuclear Research)
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Quantum Mechanics and Applications
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What is Quantum Tunnelling: The Framework of Zulfia Mapping Z = η + ∆ : η meets ∆ (1973 Observable Magic Tunnelling to 2026 Information Tunnelling) — DR. ZULFIQAR ALI KHAN · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS