This preprint develops a Lorentz-invariant semi-relativistic framework in which massive particles are modeled as slowed-down photonic excitations described by a modified Dirac equation with a velocity-dependent d’Alembertian operator. The model provides a continuous interpolation between photon-like and massive regimes through a generalized energy–frequency relation and an extended Dirac Lagrangian.The framework is applied to Young’s double-slit experiment, where coherent propagation of the slowed-light field produces interference, while localized perturbations of the four-velocity field u^u by a which-path detector induce entanglement and decoherence without invoking wavefunction collapse.The theory predicts measurable energy-dependent fringe shifts and visibility changes in electron interferometry, offering a unified dynamical perspective on wave–particle duality.
This preprint develops a Lorentz-invariant semi-relativistic framework in which massive particles are modeled as slowed-down photonic excitations described by a modified Dirac equation with a velocity-dependent d’Alembertian operator. The model provides a continuous interpolation between photon-like and massive regimes through a generalized energy–frequency relation and an extended Dirac Lagrangian.The framework is applied to Young’s double-slit experiment, where coherent propagation of the slowed-light field produces interference, while localized perturbations of the four-velocity field u^u by a which-path detector induce entanglement and decoherence without invoking wavefunction collapse.The theory predicts measurable energy-dependent fringe shifts and visibility changes in electron interferometry, offering a unified dynamical perspective on wave–particle duality.
A Lorentz-invariant semi-relativistic formulation is developed to extend the de Broglie hypothesis and establish a unified connection between matter waves and their photonic limit. Beginning with the classical relation pc = hf, a relativistic momentum expansion p ≈ mv (1 + ½ v²/c² + 3/8 v⁴/c⁴) leads to a generalized energy–frequency relation hf = pc + (v/c) Ek + (1 − γ⁻¹) mc², where Ek = ½ mv² and γ = (1 − v²/c²)⁻½. This provides a continuous transition between the non-relativistic (v ≪ c) and photonic (v → c) domains, describing matter as “slowed-down light” in a Lorentz-consistent sense.To preserve both relativistic and quantum consistency, a modified Dirac equation is introduced:(iħ γ^μ ∂_μ + β_ν ħ² / (2m) γ^ν □) ψ = 0,where β_ν = u_ν / c and □ = ∂_μ ∂^μ.This formulation, derived from a variational Lagrangian, naturally reduces to the Schrödinger and Dirac equations in their respective limits while maintaining Lorentz covariance. Numerical analysis for electrons in the 1–100 keV range reveals wavelength deviations of approximately 0.001–1%, suitable for precision diffraction experiments, and fine-structure variations around 0.7% for light atoms. The model strengthens de Broglie’s original interpretation of matter as a localized manifestation of slowed light within a Lorentz-invariant semi-relativistic framework.
The double-slit experiment highlights quantum mechanics’ wave-particle duality, with interference patterns collapsing upon measurement. The Energy-Information Gradient (EiG) Light Behavior Framework (ELBF) proposes a mechanistic model, redefining photons as structured information packets governed by discernibility gradients. Unlike classical interpretations relying on wavefunction collapse or non-local variables, ELBF models light propagation and coherence loss as a phase transition. Simulations of classical and ELBF-based double-slit scenarios (50,000 photons, λ = 0.5 µm) show that discernibility decay produces a barcode-like pattern, resolving the paradox without invoking an observer. Supported by supernova data on variable light speed and entangled photon simulations, ELBF offers predictive insights for quantum optics, cosmology, and biophotonics. Testable predictions include coherence thresholds measurable via Mach-Zehnder interferometry. This work corrects a prior rejected submission and invites collaboration to validate ELBF’s implications.
This work presents a unified, interpretive account of quantum interference and delayed-choice experiments that applies equally to photons and massive particles. Rather than invoking spacetime trajectories, wave–particle duality, retrocausality, or collapse postulates, the paper locates quantum interference in the coherent evolution of internal, pre-geometric degrees of freedom defined over classical spacetime. Within this framework, “which-path” questions are not merely unanswered but fundamentally ill-posed: interference arises from global coherence of an internal field subject to experimental boundary conditions, while spacetime itself remains single-valued and classical at laboratory scales. The approach reproduces all standard quantum-mechanical predictions without modification and is explicitly interpretive rather than predictive. A central result is a unified explanation of why interference occurs across disparate physical systems—photons, electrons, atoms, and molecules—while decoherence manifests through system-dependent physical mechanisms. Photons and massive particles differ in how internal coherence is lost (e.g., electromagnetic absorption versus collisional and thermal interactions), but not in the underlying principle. Delayed-choice experiments are reinterpreted without paradox: changes to the apparatus modify boundary conditions for the internal field rather than retroactively altering particle histories. By removing spacetime paths from the fundamental ontology, the framework offers a consistent, path-free account of interference, decoherence, and localized detection that preserves the empirical success of quantum mechanics while clarifying its conceptual foundations.
The double‑slit experiment epitomizes the wave–particle duality of quantum mechanics. In standard treatments, the interference pattern follows from superposition, while measurement of “which path” destroys coherence. The precise mechanism that turns a coherent superposition into a localized detection event remains an open question. We propose an operator‑based model within the open‑quantum‑system framework that describes the entire process through seven effective Lindblad generators: fluctuating diffusion (initial wavepacket spreading), cyclic reset (quantum Zeno effect), spatial‑mode splitting (simultaneous excitation of both slits), free evolution (interference formation), liminal projection (threshold‑activated measurement), irreversible loss (detector inefficiency), and subspace mapping (projection onto a definite detection outcome). Unlike standard quantum mechanics, the model introduces a nonlinear decoherence rate that depends on the spatial spread of the wavefunction, capturing environment back‑action through a feedback‑controlled coupling. This dependence leads to a small but testable reduction of fringe visibility with increasing particle flux or wavepacket width, even in the absence of explicit which‑path measurement. The measurement activation is modeled as a smooth threshold function, giving a sharp transition in detection probability as the system reaches the screen. Analytical expressions for visibility and the critical Zeno frequency are derived, and numerical simulations are presented. The predictions are accessible with current experimental technology (weak measurements, controlled decoherence, cavity‑QED systems). The framework suggests that wave–particle duality can be understood as a dissipative phase transition, bridging foundational quantum theory with practical open‑system control.
This paper presents a continuous measurement (partial observation) model for Young’s Double Slit Experiment, addressing the limitations of the traditional binary interpretation of the observer effect. In standard quantum mechanics, observation is often treated as a discrete event that collapses the wave function, leading to particle-like behavior. However, this work proposes that observation is inherently continuous and can be quantified using a dimensionless parameter α (0 ≤ α ≤ 1), representing the strength of measurement interaction. Two functional models are introduced to describe the relationship between measurement strength and interference visibility: a linear model V = 1 − α and a more physically motivated exponential model V = e^{-α}. These models demonstrate a gradual transition from wave-like interference to particle-like behavior, consistent with decoherence theory and weak measurement concepts. Theoretical analysis is supported by graphical and tabular representations, illustrating how interference visibility decreases continuously as measurement strength increases. The model also aligns with the fundamental wave-particle duality relation between visibility and distinguishability. This work provides a simplified yet insightful framework for understanding the observer effect as a continuous process rather than an instantaneous collapse, with potential implications for quantum measurement theory, decoherence studies, and quantum information systems.
We present a new paradigm of quantum reality in which classical particles interact deterministically with quantized electromagnetic fields embedded in a causal lattice spacetime. These interactions induce discrete momentum transfers that account for the dot-like buildup of double-slit interference fringes, the bi-fringe outcomes of the Stern–Gerlach experiment, and the correlations observed in entanglement tests. Within this framework, which provides a non-local hidden variable mechanism, naturally leads to the emergence of Heisenberg uncertainty, de Broglie duality, and the Dirac equation as natural consequences of causal field dynamics, rather than as postulated axioms. The model further provides experimentally testable predictions—including momentum-transfer sidebands and the temperature dependence of the Casimir force—that distinguish it from both the Copenhagen interpretation and more recent alternatives. By grounding quantum phenomena in causal field–particle interactions, this paradigm reproduces the experimental dot-like features in double-slit interference and Stern-Gerlach fringes. Thus, it offers a transparent and physically consistent alternative to the Copenhagen interpretation, achieving the completeness that Einstein argued was missing from conventional theory.