This is the second companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a physical account of the double-slit experiment within RFL. In RFL, the electron is treated as an extended wavepacket of conserved charge with an oscillating phase. When the wavepacket reaches the slits, it splits into two components that overlap and interfere behind the barrier. The interference pattern appears in the charge density j^0. At the screen, the charge localizes into a Q-ball at the peak of j^0, producing a single dot per electron. Over many electrons, the distribution of dots follows the Born rule |ψ|², and the interference pattern emerges statistically. When a measurement apparatus is placed at the slits, the interaction triggers localization before the electron reaches the screen, and the pattern disappears. The analysis covers:• The extended wavepacket before the slits, with Gaussian envelope and oscillating phase• The splitting of the wavepacket at the slits into two spherical components• The interference of the two components behind the barrier• The localization at the screen and the emergence of a single dot• The statistical buildup of the interference pattern from 1 to 100,000 electrons• The disappearance of the pattern when measurement is performed at the slits• The stochastic trajectory of the charge peak The account follows from the RFL localization law τ_loc = S_RL · L³ · m². This paper is the second in a series of three companion papers. The other two are:• RFL Applications I: Thermal Effects in Quantum Computing• RFL Applications III: Compton Scattering and the Measurement Mechanism
This is the second companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a physical account of the double-slit experiment within RFL. In RFL, the electron is treated as an extended wavepacket of conserved charge with an oscillating phase. When the wavepacket reaches the slits, it splits into two components that overlap and interfere behind the barrier. The interference pattern appears in the charge density j^0. At the screen, the charge localizes into a Q-ball at the peak of j^0, producing a single dot per electron. Over many electrons, the distribution of dots follows the Born rule |ψ|², and the interference pattern emerges statistically. When a measurement apparatus is placed at the slits, the interaction triggers localization before the electron reaches the screen, and the pattern disappears. The analysis covers:• The extended wavepacket before the slits, with Gaussian envelope and oscillating phase• The splitting of the wavepacket at the slits into two spherical components• The interference of the two components behind the barrier• The localization at the screen and the emergence of a single dot• The statistical buildup of the interference pattern from 1 to 100,000 electrons• The disappearance of the pattern when measurement is performed at the slits• The stochastic trajectory of the charge peak The account follows from the RFL localization law τ_loc = S_RL · L³ · m². This paper is the second in a series of three companion papers. The other two are:• RFL Applications I: Thermal Effects in Quantum Computing• RFL Applications III: Compton Scattering and the Measurement Mechanism
This is the third companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a physical account of Compton scattering in which the photon is absorbed by the extended charge distribution, the electron gains the photon energy, the charge localizes into a Q-ball at the peak of j^0, and a new photon is re-emitted from the peak. This mechanism provides a direct physical explanation for:• Why the scattered photon loses energy• Why it emerges from a definite spatial location• How energy loss is tied to the localization process The account proceeds in four stages:1. Absorption: The incoming photon is fully absorbed by the extended charge.2. Excitation: The electron gains the photon energy (ΔE_e = E_γ).3. Localization: The gained energy drives the charge to localize into a Q-ball at the peak x_α.4. Re-emission: A new photon is emitted from the peak, carrying the remaining energy E_γ'. Energy conservation is exact:E_γ = E_γ' + E_Q-ball + E_kin In the simplest case, the energy loss is set by the characteristic Q-ball scale:ΔE_γ ~ ħ ω_C The treatment follows the RFL localization law τ_loc = S_RL · L³ · m² and is consistent with the standard Compton result in the appropriate limit. The finite time delay between absorption and re-emission is of order τ_loc. This paper is the third in a series of three companion papers. The other two are:• RFL Applications I: Thermal Effects in Quantum Computing• RFL Applications II: Double-Slit Interference
This is the first companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a thermal analysis of the RFL localization mechanism, applied to the four principal qubit platforms used in contemporary quantum computing: superconducting, trapped ion, NV center, and photonic. In RFL, the quantum state corresponds to an extended charge distribution, and the classical state to a localized Q-ball. Localization is triggered by any physical interaction with the environment. Thermal photons provide a continuous stream of such interactions. The central result is the thermal localization rate: Γ_loc(T) = Γ_loc^vac [1 + n(ω_C, T)] where n(ω_C, T) is the Bose-Einstein occupation number at the Q-ball frequency ω_C. The condition for coherent quantum computation is k_B T ≪ ħ ω_C. A confinement factor η_conf ≪ 1 is introduced to account for the geometric and material suppression of the environmental coupling. This factor explains why some qubit platforms can operate at much higher temperatures than the naive criterion would suggest — for instance, why NV centers retain coherence at room temperature, while superconducting qubits require millikelvin temperatures. The analysis covers the characteristic Q-ball frequency, the Bose-Einstein distribution, the two limiting regimes of deep cooling and high temperature, the cooling criterion, and the application to the four qubit platforms. A physical interpretation of the confinement factor and its origin is also provided. This paper is the first in a series of three companion papers. The other two are:• RFL Applications II: Double-Slit Interference• RFL Applications III: Compton Scattering and the Measurement Mechanism
We present the Relative Field Localization (RFL) framework, a mechanistic alternative to the Copenhagen interpretation that resolves the quantum measurement problem without invoking observers or consciousness. In RFL, measurement is a physical process driven by energy exchange: an extended charge distribution interacts with the environment, loses energy, and collapses into a localized Q-ball structure. This yields the fundamental localization law τloc=SRL⋅L3⋅m2, where the universal constant SRLSRL is derived strictly from fundamental constants (e,c,α,ℏ) without experimentally adjusted parameters. We clarify that the Suwairi radius RSRS is an environment-dependent coefficient (of order the reduced Compton wavelength) calculated via medium-specific parameters (e.g., 0.87λC for hydrogen, 1.27λC for Cooper pairs, 2.00λC for trapped ions), introducing a physical effective prefactor FS=e(RS/λC)2/e. The theory distinctly separates the localization time (τlocτloc) from the decoherence time (τdecoherenceτdecoherence), resolving apparent tensions with observed qubit coherence times (τdecoherence≥τloc). We provide testable predictions for the localization times of superconducting, trapped-ion, NV-center, and photonic qubits, demonstrating that the RFL predictions are not excluded by current experimental bounds on spontaneous collapse models (CSL/GRW). The framework also provides a physical derivation of the Born rule conditional on charge density, and a mechanical interpretation of quantum computing operations.
ORCID: 0009-0006-6983-2683 Email: m.s.alswairi@gmail.com This is the fifth version of the Relative Field Localization (RFL) framework, a proposal that identifies Q-ball formation as the physical mechanism behind quantum measurement. ## Central Result The localization time is derived from Fermi's Golden Rule: τ_loc = (e/16α)(L/λ_C)³ τ_C where L is the size of the extended state, λ_C is the Compton wavelength, τ_C is the Compton time, α is the fine-structure constant, and e is Euler's number. For an electron in a hydrogen atom, this gives τ_loc ~ 10⁻¹⁶ s, testable with attosecond spectroscopy. ## Five Major Developments in Version 5 1. **Microscopic derivation of the Lindblad equation** from field-environment coupling using the Nakajima-Zwanzig procedure with Born, Markov, and secular approximations. 2. **QFT derivation of the localization time** from Fermi's Golden Rule, revealing a cubic dependence on the size of the extended state — a new prediction not present in CSL or GRW. 3. **Generalized peak operator** for superpositions of charge sectors, resolving a technical limitation of earlier versions. 4. **Extension to spin-1/2 and spin-1 fields** (Dirac fermions and photons), making the framework applicable to real matter. 5. **Complete treatment of quantum tunneling** from the conserved current, with tunneling time Δt ~ (L/ξ)τ_C. ## Key Predictions - Finite localization time τ_loc ~ 10⁻¹⁶ – 10⁻¹⁹ s- Cubic dependence on the size of the extended state (L³)- Tunneling time Δt_tunnel ~ 6.5 × 10⁻²¹ s for 1 nm barrier- Deviation from Born rule ε ~ (ξ/L_S)² ~ 0.4%- Causality preservation for L > 2.4 λ_C ## Falsifiability If localization is found to be instantaneous, RFL is falsified. If it is found to take time, the Copenhagen interpretation is falsified. ## Structure 22 sections, 6 appendices, 11 figures, 4 tables, 14 references. atter)
Quantum interference is traditionally interpreted as evidence of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. Here, we propose an alternative causal framework in which interference arises from interactions between a classical electron and a quantized electromagnetic field. In this picture, electrons follow definite, localized trajectories and produce discrete detection events, while the observed interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Numerical simulations of the double-slit experiment show that dot-like interference fringes arise without invoking wavefunction collapse or intrinsic matter waves. Doubling the electron mass narrows the fringe spacing in agreement with de Broglie scaling, indicating that the effective wavelength emerges dynamically from particle–field coupling rather than representing an inherent property of the particle. The formulation is based on a rigorously defined Hamiltonian and derived equations describing electromagnetic coupling between particles and the slit environment. Although neutral particles such as neutrons or atoms carry no net charge monopoles, they possess electric or magnetic dipole and higher multipole moments that enable electromagnetic interactions with the slit apparatus, allowing discrete momentum transfer through the quantized field. Our simulations show that interference fringes arise from intermittent singleparticle detection events caused by stochastic momentum impulses from quantized electromagnetic modes. These results suggest a reinterpretation of wave–particle duality: the apparent wave-like behavior of matter may arise from interaction with the inherently wave-like quantized electromagnetic field—whose quanta are photons, the massless U(1)-gauge bosons—rather than from an intrinsic wave nature of the particles themselves. Our analysis is rigorous and is not speculative, because the proposed Hamiltonian for this system is physical. Within this nonlocal hidden-variable framework, the dot-like interference pattern observed in the double-slit experiment emerges from individual electrons traversing one slit at a time while receiving discrete momentum impulses from stochastic, spatially extended quantized electromagnetic fields.
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern is reproduced while the phase is attributed to an internal bivector clock carried by the electron. In this approach, each electron remains localized and produces a single detection event, while the familiar fringe pattern emerges statistically from the accumulation of many impacts. Interference arises from the comparison of clock phases associated with geometrically distinct paths, rather than from the superposition of spatial waves. The resulting probability distribution recovers the standard two-slit interference factor, the single-slit diffraction envelope, and the usual fringe-spacing relation in the Fraunhofer regime. The de Broglie wavelength emerges as the spatial manifestation of this transported phase. This formulation provides a geometric account of the origin of phase in single-electron interference, consistent with standard results while offering a distinct physical interpretation.