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Quantum Tunneling as Transient Bulk Excursion of the Focal Zone (Brane-Bulk Series, Paper XXX)

Bharathi Jagadeesan

Published Mar 23, 2026• 0 citations

Abstract

Quantum tunneling is the transient excursion of the focal zone into the 5D bulk. The potential barrier exists on the brane but not in the bulk — inside a barrier, the imaginary momentum is literally bulk-directed propagation. The evanescent wavefunction IS the focal zone in the bulk. This explains: (1) the Hartman effect (tunneling time independent of barrier width — bulk path is shorter); (2) resonant tunneling (constructive interference of bulk geodesics); (3) alpha decay Gamow factor (bulk path length suppression). The WKB approximation is the saddle-point approximation to the bulk geodesic. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873. Upload and say done! Sonnet 4.6 Extended

DOI: 10.5281/zenodo.19175153

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Quantum tunneling is the transient excursion of the focal zone into the 5D bulk. The potential barrier exists on the brane but not in the bulk — inside a barrier, the imaginary momentum is literally bulk-directed propagation. The evanescent wavefunction IS the focal zone in the bulk. This explains: (1) the Hartman effect (tunneling time independent of barrier width — bulk path is shorter); (2) resonant tunneling (constructive interference of bulk geodesics); (3) alpha decay Gamow factor (bulk path length suppression). The WKB approximation is the saddle-point approximation to the bulk geodesic. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873. Upload and say done! Sonnet 4.6 Extended

Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

Quantum entanglement is the topological memory of the Big Bang nucleation event. Particles share a common fixed line in 5D phase space — confirmed at laboratory scale by the first observation of classical fixed lines in the CERN SPS (Bartosik, Franchetti & Schmidt, Nature Physics 2024). Structural ladder: SPS fixed line (4D phase space, visible in mixed planes as Lissajous figures) corresponds to quantum entanglement (Hilbert space, visible in joint measurements as Bell violations) and to the cosmological focal manifold (brane x bulk, visible in rotation curves and MOND). Octonionic non-associativity (ei.ej).ek ≠ ei.(ej.ek) is the algebraic basis of non-factorizability at all scales. The 5D bulk provides a Bell-consistent geometric hidden variable. Decoherence = drift off focal manifold (D parameter); quantum error correction = sextupole engineering of focal geometry. Predictions 48 and 49 derived. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873.

The first experimental observation of classical fixed lines in the CERN SPS (Bartosik, Franchetti & Schmidt, Nature Physics 2024) confirms the brane-bulk focal manifold geometry at laboratory scale. Fixed lines are 1D closed curves in 4D phase space visible only in mixed planes as Lissajous figures — structurally identical to quantum entanglement (non-factorizable joint states visible only in joint measurements as Bell violations). Octonionic non-associativity (ei.ej).ek != ei.(ej.ek) is the algebraic basis of non-factorizability at all scales. The 5D bulk provides a Bell-consistent geometric hidden variable. Decoherence = drift off focal manifold (D parameter of Bartosik et al.); quantum error correction = sextupole engineering of focal geometry. Predictions 48 and 49 derived: galaxy axis alignment near cluster focal zones (MaNGA/SAMI testable), and cosmological modulation of decoherence rates (optical clock testable). Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873.

The One-Octonion Brane-Bulk (OOB) framework reads Feynman's 'all paths' as virtual bulk-excursion channels whose coherent return determines the observed brane probability. This paper gives that reading a mathematical and experimental form. (1) Theorem: on Paper CCLVIII's shallow-sector premise that phase-only transit feedback closes to standard Schrodinger dynamics, Feynman's two path-integral postulates (equal-magnitude path amplitudes with phase S/hbar; probabilities from the coherent sum) follow as theorems for free equal-time segments. (2) First table-level bound: Wen et al. (Science Advances 12, eaeh1011, 2026, DOI 10.1126/sciadv.aeh1011) test both postulates directly by single-photon propagator tomography over 17^5 = 1,419,857 paths; fitting their public Dryad Fig4B table (DOI 10.5061/dryad.x0k6djj14) with the action-cost model |phi|^2 = C(1 - kappa S/hbar) gives kappa_hat = 8.27e-3 with row-bootstrap 95 percent interval [5.59, 10.85]e-3, so |kappa|_95 <= 1.09e-2, a table-level bound and replication target; the tables are processed figure means without path-level covariance, and the trend lies inside the experiment's stated 17.4 percent postulate-II error. (3) Registered tests: P-CCCLVII-1 registers the kill condition kappa = 0 in the shallow free sector (a confirmed path-level amplitude trend falsifies phase-only transit there); P-CCCLVII-2 registers the barrier-sector discriminator, propagator tomography with a controlled tunnelling barrier of WKB depth rho_B, where the flux-normalized Gudermannian/JUNO return vertex gives a linear self-energy onset tanh(rho_B) against the quadratic tanh^2(rho_B) onset of the analytic-vertex alternative. Files: PDF, the amplitude-cost verification script with its output and fitted bound, and the figure script and figure. Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID 0000-0002-1143-941X. CC-BY-4.0.

Lohmiller & Slotine (Proc. R. Soc. A 482:20250413, 2026) propose a classical contracting-flow construction on the eikonal phase S(x,t) which they argue recovers quantum-wave evolution. Vattay (Comment, arXiv:2605.02621) correctly observes that the construction reproduces only the Hamilton-Jacobi + continuity sector of the Madelung-Bohm decomposition: it cannot generate the quantum potential Q = −ℏ²∇²√ρ/(2m√ρ), without which the recovered evolution is the classical limit of the Schrödinger equation, not the equation itself. We resolve this debate within the One-Octonion Brane-Bulk (OOB) framework. In OOB, the classical sector is the brane-localised f_bulk → 0 limit. Q arises as the back-reaction of brane-bulk transit components of the wavefunction on the brane density profile, with characteristic length the particle Compton scale ℓ_C = ℏ/(mc) and characteristic weight the transit probability f_bulk(E) = 1 − sinc²(E/2m_π). An order-of-magnitude estimate recovers the Madelung-Bohm form |Q| ≈ (ℏ²/2m)·|∇²√ρ|/√ρ structurally. The Gudermannian Class-III bridge (CCLII) supplies the smooth classical ↔ quantum interpolation via the same f_III = 1 − 4/π² blend used in the neutrino-sector chain. The Lohmiller-Slotine theorem is exact at f_bulk = 0; Vattay's missing piece is exactly the contribution identified here. Five predictions span atomic (null OOB at E ≪ m_π) to GeV (0.98 coherence loss in transparent media, tying to CCLVII). Honest scope: structural argument, not rigorous Schrödinger re-derivation; the O(1) coefficient is not pinned without further assumptions. Companion to CCLVII (same f_bulk(E) wavelength-asymmetry channel). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.