We present a technical validation of Geometric Quantum Tunneling (GQT) within the MMA-DMF framework. In this approach, barrier penetration is not postulated: it emerges as a deterministic, noise-assisted escape process generated by a scalar-field generalized Langevin dynamics whose stochastic sector is thermodynamically closed by a strict fluctuation--dissipation relation [1, 2] and regulated by a finite ultraviolet (UV) cutoff at a fundamental scale M≃1.00×102 TeVM \simeq 1.00 \times 10^{2}\,\mathrm{TeV}M≃1.00×102TeV. We report 1D benchmark results showing (i) Schrödinger-like dispersion calibration at Nelson equilibrium, (ii) WKB recovery via exponential transmission scaling with barrier width (linear lnT\ln TlnT vs width with R2>0.99R^{2} > 0.99R2>0.99 and a consolidated WKB recovery error of 1.2%), (iii) quantitative isomorphism against transfer-matrix quantum mechanics across energy regimes (deep-tunneling RMSE 0.042, resonant RMSE 0.085, classical-transport RMSE 0.011), and (iv) the distinctive “geometric wall” prediction that tunneling collapses as V0/M→1V_{0}/M \to 1V0/M→1 (rapid suppression already near V0≈0.95MV_{0} \approx 0.95MV0≈0.95M and an inferred cutoff near 0.98M0.98M0.98M in the consolidated summary). We include mandatory ablations via the geometric toggle αgeo\alpha_{\mathrm{geo}}αgeo (tunneling vanishes as αgeo→0\alpha_{\mathrm{geo}} \to 0αgeo→0), and stability/convergence constraints requiring Δt≲0.01 M−1\Delta t \lesssim 0.01\,M^{-1}Δt≲0.01M−1 with validated production operation at Δt=0.005 M−1\Delta t = 0.005\,M^{-1}Δt=0.005M−1 and an energy drift slope 3.4×10−63.4 \times 10^{-6}3.4×10−6 over tmax=1000t_{\max}=1000tmax=1000. Finally, we specify a reproducibility and integrity layer (bit-exact seed replay across hardware targets, deterministic checkpointing, and SHA-256 manifesting) intended to make the full pipeline externally auditable. The consolidated evidence supports that MMA-DMF reproduces standard low-energy tunneling phenomenology while making a falsifiable high-energy prediction tied to UV regulation.
We present a technical validation of Geometric Quantum Tunneling (GQT) within the MMA-DMF framework. In this approach, barrier penetration is not postulated: it emerges as a deterministic, noise-assisted escape process generated by a scalar-field generalized Langevin dynamics whose stochastic sector is thermodynamically closed by a strict fluctuation--dissipation relation [1, 2] and regulated by a finite ultraviolet (UV) cutoff at a fundamental scale M≃1.00×102 TeVM \simeq 1.00 \times 10^{2},\mathrm{TeV}M≃1.00×102TeV. We report 1D benchmark results showing (i) Schrödinger-like dispersion calibration at Nelson equilibrium, (ii) WKB recovery via exponential transmission scaling with barrier width (linear lnT\ln TlnT vs width with R2>0.99R^{2} > 0.99R2>0.99 and a consolidated WKB recovery error of 1.2%), (iii) quantitative isomorphism against transfer-matrix quantum mechanics across energy regimes (deep-tunneling RMSE 0.042, resonant RMSE 0.085, classical-transport RMSE 0.011), and (iv) the distinctive “geometric wall” prediction that tunneling collapses as V0/M→1V_{0}/M \to 1V0/M→1 (rapid suppression already near V0≈0.95MV_{0} \approx 0.95MV0≈0.95M and an inferred cutoff near 0.98M0.98M0.98M in the consolidated summary). We include mandatory ablations via the geometric toggle αgeo\alpha_{\mathrm{geo}}αgeo (tunneling vanishes as αgeo→0\alpha_{\mathrm{geo}} \to 0αgeo→0), and stability/convergence constraints requiring Δt≲0.01 M−1\Delta t \lesssim 0.01,M^{-1}Δt≲0.01M−1 with validated production operation at Δt=0.005 M−1\Delta t = 0.005,M^{-1}Δt=0.005M−1 and an energy drift slope 3.4×10−63.4 \times 10^{-6}3.4×10−6 over tmax=1000t_{\max}=1000tmax=1000. Finally, we specify a reproducibility and integrity layer (bit-exact seed replay across hardware targets, deterministic checkpointing, and SHA-256 manifesting) intended to make the full pipeline externally auditable. The consolidated evidence supports that MMA-DMF reproduces standard low-energy tunneling phenomenology while making a falsifiable high-energy prediction tied to UV regulation.
Abstract We validate Geometric Quantum Tunneling (GQT) within the MMA–DMF framework, where barrier transmission is not imposed as a postulate but arises as a rare, noise-assisted escape process generated by deterministic scalar-field dynamics coupled to a structured vacuum sector. The stochastic forcing is thermodynamically constrained by a strict fluctuation–dissipation closure and regulated by a finite ultraviolet (UV) cutoff at a fundamental scale 𝑀 ≃ 1.00 × 102 TeV. Using a one-dimensional rectangular barrier as a controlled benchmark, we report: (i) Schrödinger-like wavepacket dispersion at Nelson equilibrium; (ii) recovery of semiclassical WKB scaling through an exponential dependence of transmission on barrier width (linear ln 𝑇 vs. width with 𝑅2 > 0.99 and a consolidated WKB recovery error of 1.2%); (iii) quantitative agreement with transfer-matrix quantum mechanics across deep-tunneling, resonant, and classical-transport regimes (RMSE 0.042, 0.085, and 0.011, respectively); and (iv) a distinctive near-cutoff prediction in which transmission is strongly suppressed as 𝑉0/𝑀 → 1 (rapid suppression already near 𝑉0 ≈ 0.95𝑀, with an inferred cutoff near 0.98𝑀 in the consolidated summary). Control tests include ablations that disable the geometric coupling, for which tunneling vanishes as expected. Numerical stability and convergence are verified with a step-size constraint 𝑑𝑡 ≲ 0.01𝑀−1; validated runs use 𝑑𝑡 = 0.005𝑀−1 with a small measured energy-drift slope (3.4 × 10−6) over 𝑇max = 1000. Data, scripts, and numerical artifacts required to reproduce the reported benchmarks are provided in the accompanying replication package.
The MMA–DMF framework connects cosmological “dark sector” phenomenology with quantum-foundational phenomena by treating a single screened scalar field as both a mediator of large-scale modified gravity and a stochastic vacuum bath responsible for gravitational decoherence. This paper consolidates the full, dated MMA–DMF validation record contained in the project materials (with an audited, frozen parameter set) and reports the complete test suite relevant to uncertainty and decoherence: (i) a strict Fluctuation–Dissipation Theorem (FDT) stability test for the Generalized Langevin Equation (GLE) memory kernel, which passes an energy-drift criterion of |slope| < 10−5 in long integrations; (ii) a dynamic contextuality roll-off test in which the CHSH Bell parameter transitions from the Tsirelson value S ≈ 2.828 at quasi-static settings to the classical bound S → 2 under fast modulation, quantified by explicit frequency-dependent suppression formulas; and (iii) a T-MAGIS atom-interferometry campaign prediction in which a density-modulated environment produces a detectable contrast loss ∆V ≈ 3.4 × 10−3 to 4 × 10−3 under representative configurations, with a tabulated scaling versus distance and interrogation time and a shot-noise sensitivity forecast yielding high signal-to-noise for hour-scale integration. We also summarize MMA–DMF-linked phenomenology across scales, including a joint cosmological likelihood structure with cross-covariance correction and representative reported values (H0, S8) ≈ (72.1 km s−1 Mpc−1, 0.761), plus a gravitational-wave echo delay estimate of ∆techo ≈ 32 ms for stellar-mass systems. The combined record constrains MMA–DMF by demanding simultaneous thermodynamic consistency of the stochastic sector, a controlled transition from contextual to classical correlations under finite response time, and a falsifiable laboratory decoherence signature under controlled density modulation
Abstract: Quantum tunneling is conventionally described through semiclassical WKB methods and imaginary-time formulations of the Feynman Path Integral, which successfully reproduce transmission probabilities but leave the local kinematic structure of the barrier transition largely implicit. In this work, we introduce a finite-rate temporal integration framework in which localized quantum states evolve through successive stochastic re-integrations over a characteristic interval . Within this picture, a macroscopic potential barrier acts as an open fluctuating electromagnetic environment rather than a rigid static boundary. As a localized state partially penetrates the barrier, transient geometric interlocking suppresses forward integration and prolongs the effective interaction window. The under-barrier configuration is modeled not as a single coherent leap across the forbidden region, but as a metastable sequence of stochastic local re-integrations continuously driven by environmental fluctuations. Transmission through thick barriers therefore emerges as a rare cumulative process requiring repeated successful geometric alignments across many finite integration intervals, naturally producing exponential suppression with barrier thickness. To formalize this mechanism, the tunneling process is represented as a coupled stochastic escape problem governed by bipartite Langevin dynamics and an associated Fokker–Planck description. The transition probability acquires a bilinear structure arising from simultaneous compatibility conditions between particle-side and environment-side fluctuations. In the self-consistent limit, this naturally produces the quadratic probability weighting characteristic of the Born measure, while remaining compatible with normalized Hilbert-space amplitudes. Within this framework, the Euclidean-time contribution appearing in standard tunneling theory admits a local kinematic interpretation as the extended stochastic integration interval required for compatible transition geometries to accumulate across the barrier. The formalism further predicts enhanced sensitivity of tunneling dynamics to high-frequency external probing, potentially relevant to attoclock tunneling-delay experiments and strong-field manifestations of the Quantum Zeno effect.
The MMA–DMF framework connects cosmological “dark sector” phenomenology with quantum-foundational phenomena by treating a single screened scalar field as both a mediator of large-scale modified gravity and a stochastic vacuum bath responsible for gravitational decoherence. This paper consolidates the full, dated MMA–DMF validation record contained in the project materials (with an audited, frozen parameter set) and reports the complete test suite relevant to uncertainty and decoherence: (i) a strict Fluctuation–Dissipation Theorem (FDT) stability test for the Generalized Langevin Equation (GLE) memory kernel, which passes an energy-drift criterion of |slope| < 10−5 in long integrations; (ii) a dynamic contextuality roll-off test in which the CHSH Bell parameter transitions from the Tsirelson value S ≈ 2.828 at quasi-static settings to the classical bound S → 2 under fast modulation, quantified by explicit frequency-dependent suppression formulas; and (iii) a T-MAGIS atom-interferometry campaign prediction in which a density-modulated environment produces a detectable contrast loss ∆V ≈ 3.4 × 10−3 to 4 × 10−3 under representative configurations, with a tabulated scaling versus distance and interrogation time and a shot-noise sensitivity forecast yielding high signal-to-noise for hour-scale integration. We also summarize MMA–DMF-linked phenomenology across scales, including a joint cosmological likelihood structure with cross-covariance correction and representative reported values (H0, S8) ≈ (72.1 km s−1 Mpc−1, 0.761), plus a gravitational-wave echo delay estimate of ∆techo ≈ 32 ms for stellar-mass systems. The combined record constrains MMA–DMF by demanding simultaneous thermodynamic consistency of the stochastic sector, a controlled transition from contextual to classical correlations under finite response time, and a falsifiable laboratory decoherence signature under controlled density modulation.
This research paper explores the theoretical foundations of quantum tunneling, explaining how particles can pass through potential barriers despite lacking the classical energy to do so. It develops the mathematical framework using the Schrödinger equation, derives the transmission coefficient for a rectangular potential barrier, introduces the WKB approximation for more realistic barriers, and examines key applications such as alpha decay, scanning tunneling microscopy (STM), and the Josephson effect. The paper also reviews the historical development, experimental verification, and limitations of quantum tunneling, highlighting its significance as one of the most fundamental and experimentally validated predictions of quantum mechanics.
FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, governed by exponential decay of the wavefunction inside the barrier; "impossible" QFT measurements are possible but non-ideal, with relativistic causality constraints. MATH: Transmission coefficient T≈e−2κL, where κ=2m(V0−E)/ℏ; barrier penetration probability P∝e−2∫κ(x)dx. For a rectangular barrier: T=[1+4E(V0−E)V02sinh2(κL)]−1. In the WKB limit, T∼exp(−ℏ2∫x1x22m(V(x)−E)dx). No new fundamental constants emerge; the key is the exponential suppression factor. CONNECTION: The exponential decay e−κL has no direct golden-ratio link. However, the *critical* barrier opacity κL=ln(2) (for 50% transmission) and κL=ln(ϕ)≈0.4812 (where ϕ=1.618...) appear as natural thresholds — but t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com