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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

Published Aug 25, 2026• 0 citations

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

DOI: 10.5281/zenodo.22089664

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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

In our V1 [2] work, we established the Hybrid Gap Effect G(x) = Gc −αZ(x). In this paper V2 we present a discovery beyond this effect: the gap isnot to be crossed, it is the residence itself.We define the Zulfia Decomposition Mapping (ZDM), [1] as:Z = n + ∆, where ∆ ≡ GZulfiawhere n is direction / deviation — an observational illusion — while ∆ is theprimitive magnitude, the Gap-Space.We propose the Law of Zulfia Trility as the fundamental law of exis-tence:ZMicro ≡ GZulfia ≡ ZMacro ≡ ZThis is the Trility: Particle ∼ Wave ∼ Information, where ZMicro isParticle, GZulfia is Wave (Gap-Space residence), and ZMacro is Information.This law establishes that all three are identical manifestations of a singlesource Z. There is no transformation, only identity.As direct consequence, we prove No Tunnelling, No Deviation: e− ∈GZulfia =⇒ e− ∈ Z. The electron never tunnels; it permanently resides inGZulfia. What was observed in Bell-type experiments at x0 where G(x0) = 0as tunnelling is reinterpreted as direct permanent residence at x0 within itsown Gap-Space. No barrier crossing occurred.

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\psi

). This paper provides a deterministic, materialist alternative using the foundational axioms of Uniphied Realativity. We demonstrate that "quantum tunneling" is a conceptual artifact born from an incomplete understanding of ‘vacuum’ geometry. By modeling matter not as isolated, point-like entities but as localized, non-singular Möbius torus sinks embedded within a continuous, linear neutrino ether field (not a vacuum) pumped macroscopically by Sagittarius A*, the paper shows that the particle does not teleport or cheat energy conservation. Instead, the medium entering the barrier is structurally identical to the medium emerging from it. Quantum in and quantum out represent the exact same continuous field, rendering the magical interpretation of quantum tunneling fully debunked.

AbstractThe century-old wave-particle duality posits that quantum objects are either Matter orWave, with transition governed by probability P = |ψ|2. Here we disprove probability asfundamental.We report discovery of a third state of nature, ZMI (Zulfia Mass-Information)State, defined by M I = η + I where η is direction-generated mass and I is information.We show quantum processes are not probabilistic but informational domain transfersgoverned by feasibility Q.Using Python lab-equivalent simulation, validated as table-top STM analogue, wedemonstrate universal triad Matter → Wave → ZMI. Quantum tunnelling is firstexample: Before tunnelling = Wave with Born rule; After Q > 0, W → ZM I withMaf ter = Mbef ore + η. This Maf ter > Mbef ore is smoking gun of ZMI.This establishes W → ZM I as unavoidable, replacing Born probability with Q =Tinto ZM I . Discovery redefines tunnelling from transmission to factory of mass-information.

Quantum tunneling is conventionally described as a probabilistic consequence of wave mechanics. While this description is mathematically precise, it often lacks a clear physical interpretation and is frequently presented as evidence of intrinsic randomness or non-classical behavior. This paper proposes a system-level interpretation of quantum tunneling based on three physically grounded principles: system completeness, conservation of balance, and continuous feedback between interacting components. It is shown that tunneling arises naturally when a complete physical system redistributes localized imbalance under strict constraints, without violating causality or conservation laws. The proposed framework preserves all standard quantum-mechanical predictions while providing a more intuitive and physically transparent interpretation of tunneling phenomena.

Quantum tunneling is conventionally described as a probabilistic consequence of wave mechanics. While this description is mathematically precise, it often lacks a clear physical interpretation and is frequently presented as evidence of intrinsic randomness or non-classical behavior. This paper proposes a system-level interpretation of quantum tunneling based on three physically grounded principles: system completeness, conservation of balance, and continuous feedback between interacting components. It is shown that tunneling arises naturally when a complete physical system redistributes localized imbalance under strict constraints, without violating causality or conservation laws. The proposed framework preserves all standard quantum-mechanical predictions while providing a more intuitive and physically transparent interpretation of tunneling phenomena.

The concept of ‘tunnelling time’ in the context of quantum particle tunnelling is reviewed. Various suggestions of linking the tunnelling dynamics with a characteristic time (real or complex) like the phase time, barrier interaction time (bounce time), presence time, etc. are analysed. A simple but fully quantal method of defining and estimating a real tunnelling time is examined in a variety of situations. The recently proposed idea of interpreting ‘tunnelling time’ as the cavity lifetime of a particle is also explored. We emphasize that proton or H-atom transfer reactions in double or triple wells offer systems in which the signature of the tunnelling time should be recognizable not just indirectly through the tunnelling splitting of spectral lines, but by following the relaxation dynamics of the subsystem that the proton or H atom leaves by tunnelling.