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