This paper presents a finite, physical resolution of quantum tunneling within the Dual Regulator Framework, interpreting barrier penetration as a temporary excursion into the virtual domain rather than a paradoxical traversal of classically forbidden space. In this framework, particles encountering a potential barrier transition from the real domain (on-shell, position space, RG-regulated) into a virtual domain (off-shell, momentum space, Λφ-regulated), where position-space potentials are undefined. After traversing the barrier off-shell, particles re-emerge into the real domain on the opposite side. Energy conservation is preserved through finite energy–time uncertainty, without invoking nonphysical violations. The formalism yields a modified tunneling length scale and probability law, introducing a universal Λφ correction to standard WKB results. This leads to quantitative, testable predictions across multiple systems, including: alpha decay half-lives with sub-percent accuracy across the periodic table, scanning tunneling microscope current–distance relations with φ-harmonic structure, ammonia inversion frequency corrected by a (1 + Λφ/π) factor matching experiment, tunneling time saturation consistent with the Hartman effect and attosecond measurements. All results derive solely from the Trinity constants {π, φ, e} with zero adjustable parameters. The paper resolves the tunneling mystery by identifying tunneling as a finite, domain-limited physical process rather than a purely mathematical artifact. This work constitutes Paper IV in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement, wave–particle duality, and entanglement. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 Internationa
This paper presents a finite, physical resolution of quantum tunneling within the Dual Regulator Framework, interpreting barrier penetration as a temporary excursion into the virtual domain rather than a paradoxical traversal of classically forbidden space. In this framework, particles encountering a potential barrier transition from the real domain (on-shell, position space, RG-regulated) into a virtual domain (off-shell, momentum space, Λφ-regulated), where position-space potentials are undefined. After traversing the barrier off-shell, particles re-emerge into the real domain on the opposite side. Energy conservation is preserved through finite energy–time uncertainty, without invoking nonphysical violations. The formalism yields a modified tunneling length scale and probability law, introducing a universal Λφ correction to standard WKB results. This leads to quantitative, testable predictions across multiple systems, including: alpha decay half-lives with sub-percent accuracy across the periodic table, scanning tunneling microscope current–distance relations with φ-harmonic structure, ammonia inversion frequency corrected by a (1 + Λφ/π) factor matching experiment, tunneling time saturation consistent with the Hartman effect and attosecond measurements. All results derive solely from the Trinity constants {π, φ, e} with zero adjustable parameters. The paper resolves the tunneling mystery by identifying tunneling as a finite, domain-limited physical process rather than a purely mathematical artifact. This work constitutes Paper IV in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement, wave–particle duality, and entanglement. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 Internationa
This paper presents a finite, regulator-based resolution of wave–particle duality, showing that quantum duality is not a fundamental paradox but a natural consequence of domain separation. Within the Dual Regulator Framework, wave behavior is shown to arise exclusively in the virtual domain (momentum space, off-shell propagation), regulated by the finite invariant Λφ=ln(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while particle behavior arises exclusively in the real domain (position space, on-shell detection), regulated by the Resolution Gap RG=ln(φ)/ln(π).\mathrm{RG} = \ln(\varphi)/\ln(\pi).RG=ln(φ)/ln(π). The double-slit experiment is reinterpreted as a virtual-domain interference process followed by a real-domain localization event. Which-path detection is shown to force a premature virtual-to-real transition, preventing interference from forming. Partial which-path information produces a quantitative reduction in visibility governed by a finite exponential law. The framework yields explicit, testable predictions with zero adjustable parameters, including: a φ-harmonic correction to interference fringe spacing, a sharp detector-coupling threshold for which-path information, an exact functional form for visibility–distinguishability relations, and scale-dependent corrections for matter-wave interferometry (electrons, neutrons, molecules). All results derive solely from the Trinity constants {π, φ, e}. Complementarity is shown to be a consequence of domain incompatibility, not a primitive principle. Wave–particle duality dissolves into a physically interpretable, observer-independent mechanism. This paper forms Paper II in a planned sequence addressing foundational inconsistencies in quantum field theory, following the finite resolution of the measurement problem.
This paper presents a finite, regulator-based resolution of the quantum measurement problem, establishing measurement as a physical, time-resolved domain transition rather than an instantaneous postulate or observer-dependent process. The framework introduces a two-domain structure: a virtual domain, governed by momentum-space dynamics and regulated by the finite invariant Λφ, and a real domain, governed by on-shell observables regulated by the Resolution Gap (RG). Measurement is shown to correspond to a finite transition between these domains, with a calculable characteristic timescale derived from first principles. This eliminates instantaneous wavefunction collapse, resolves the Zeno paradox, and restores physical causality without modifying standard quantum dynamics. The Born rule emerges naturally from equal coupling across the measurement interface, without additional axioms or interpretive assumptions. Decoherence is reinterpreted as a regulator-mediated rate process rather than a substitute for collapse. A companion computational validation script is provided, numerically confirming the derived constants, measurement timescales, and domain-regulator relationships. All results are reproducible using standard numerical libraries. This work serves as Paper I in a planned sequence addressing foundational inconsistencies in quantum field theory, beginning with measurement as the necessary entry point for restoring finiteness, causality, and physical interpretation. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
This paper presents a finite, regulator-based resolution of quantum entanglement, extending the Dual Regulator Framework to nonlocal correlations while preserving causality, locality of dynamics, and relativistic consistency. Entanglement is shown to arise entirely within the virtual domain, which lacks spatial topology and is regulated by the finite invariant Λφ=ln(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while decoherence and measurement occur exclusively in the real domain, regulated by the Resolution Gap (RG). Because entangled correlations never propagate through real spacetime, their strength is shown to be exactly independent of spatial separation, without invoking superluminal influence or observer-dependent collapse. Bell inequality violations are derived from domain structure alone. The framework predicts a finite correction to the standard Tsirelson bound arising from virtual-domain regulation, yielding a testable enhancement at high precision. No hidden variables, signaling mechanisms, or modifications to relativistic causality are introduced. Decoherence of entangled systems is shown to be additive across subsystems and governed by regulator ratios rather than ad hoc environmental postulates. The Born rule emerges from symmetric coupling across the virtual–real interface, consistent with prior papers in the series. A companion computational validation script numerically reproduces all constants and predicted correlation bounds using standard numerical libraries. All results are reproducible and contain zero adjustable parameters. This work constitutes Paper III in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement and wave–particle duality. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
This paper proposes a finite, mechanism-based account of quantum decoherence within the Dual Regulator / Trinity Framework. Decoherence is interpreted as environmental real-forcing: environmental coupling drives a premature transition from a coherent virtual-domain superposition into a real-domain mixture, thereby suppressing interference without invoking ad hoc collapse postulates. The framework defines two regulated domains: a virtual domain supporting superposition and off-shell structure governed by a finite invariant, and a real domain governing measured observables and classical mixtures. Decoherence is modeled as a rate process driven by the environment’s coupling strength, yielding a universal scaling relation between environmental interaction rate and coherence decay. The same mechanism predicts a simple factor-of-two scaling for entanglement decay relative to single-system coherence in symmetric environments. The paper also discusses pointer states as real-domain eigenstates, decoherence-free subspaces as regimes where effective environmental forcing vanishes, and a master-equation form in which standard open-system dynamics acquire regulator-dependent scaling. A set of explicit experimental predictions is provided, including temperature trends, entanglement-versus-single-system decoherence comparisons, and conditions for suppressing decoherence through engineered decoupling. This work forms part of a seven-paper sequence developing a finite, regulator-based resolution of core quantum foundations problems (measurement, duality, entanglement, tunneling, uncertainty, and decoherence) using a shared domain structure and constant set. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
This paper reinterprets the Heisenberg uncertainty principle as a consequence of domain incompatibility within the Dual Regulator Framework. Rather than treating uncertainty as measurement disturbance, wavefunction spread, or a purely formal commutation constraint, the framework assigns conjugate quantities to distinct physical domains: Real-domain observables (e.g., position and measured energy) regulated by the Resolution Gap RGRGRG, and Virtual-domain observables (e.g., momentum and evolution-time duration) regulated by the finite invariant Λφ\Lambda_\varphiΛφ. Because conjugate variables inhabit incompatible domains, they cannot be simultaneously definite in a single measurement context. The uncertainty principle is therefore treated as an ontological constraint arising from the structure of the measurement interface, not merely an epistemic limit. The paper explores regulator-dependent modifications to standard uncertainty relations for position–momentum and energy–time, and proposes experimentally testable implications for resolution limits, decay lifetimes, and atomic linewidths. Numerical prefactors are treated as a subject for further refinement, while the central result remains: complementarity follows naturally from domain separation, and “measurement disturbance” is reinterpreted as forced domain selection. This work forms part of a planned sequence addressing foundational inconsistencies in quantum field theory using finite regulator structure derived from {π,φ,e}\{\pi,\varphi,e\}{π,φ,e}. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
This paper presents a finite, mechanism-based resolution of the quantum Zeno and anti-Zeno effects within the Dual Regulator / Trinity Framework. The Zeno effect is interpreted as virtual domain inhibition: quantum evolution proceeds through virtual-domain phase accumulation, while measurement repeatedly forces projection into the real domain, resetting accumulated phase and preventing measurable evolution. A universal Zeno time τφ=ℏ/(ΛφE)\tau_\varphi = \hbar / (\Lambda_\varphi E)τφ=ℏ/(ΛφE) is derived, representing the minimum duration required for virtual-domain phase to become physically manifest. Measurements performed at intervals shorter than this threshold suppress evolution, while measurements near the threshold resonantly enhance decay, producing the anti-Zeno effect. The framework predicts: A universal Zeno threshold scaling exactly as 1/E1/E1/E, A sharp transition between frozen and decaying regimes, A finite anti-Zeno enhancement peak (~4%) at an optimal measurement interval, A fixed ratio between measurement completion time and Zeno time, explaining why Zeno freezing occurs well before full measurement is completed. All results follow from the finite regulator Λφ=ln(φ2)\Lambda_\varphi = \ln(\varphi^2)Λφ=ln(φ2) with zero adjustable parameters. The Zeno effect is shown not to halt time or dynamics, but to prevent virtual-domain evolution from reaching real-domain measurability. This work constitutes the seventh and final paper in a coordinated series resolving foundational quantum phenomena—measurement, duality, entanglement, tunneling, uncertainty, decoherence, and Zeno dynamics—within a single finite, regulator-based framework. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International