Geometric Resolution of the Quantum Tunneling Paradox: Reinterpreting Barrier Penetration as Zero-Distance Relational Projection

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Authors: Filipe Bastos
Cited by: 0

Abstract

Quantum tunneling conventionally invokes "energy borrowing" via Heisenberg uncertainty and exhibits the Hartman effect (barrier-independent traversal time). Both are conceptual paradoxes. We demonstrate the particle doesn't traverse the barrier in physical space. Tunneling results from zero-distance projection along an invariant coherence axis (Axis 4.5), orthogonal to the material density gradient. Key mechanism: When coherence is maintained (phase locking), spatial topology folds along the coherence axis. Effective distance D_eff = L·sin(φ). Perfect alignment (φ→0) yields D_eff→0—the particle bypasses metric interval L via rotational displacement. Energy conservation preserved: Transition occurs along isopotential geodesic (W=0, "Yanieva Rail"). Transmission coefficient T is geometric projection factor, not survival probability. Attenuation reflects angular deviation maintaining coherence—signal rotated out of observable plane, not lost. Hartman effect necessary consequence: topological distance zero implies instantaneous traversal without relativity violation. The "mystery" is observing 3D rotation from 1D perspective.

Fields of Study & Subjects

Quantum Mechanics and Applications Relativity and Gravitational Theory Noncommutative and Quantum Gravity Theories

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
12 January 2026
Document type
Preprint