Description/Abstract: Four mysteries have persisted at the quantum scale for decades: the mechanism of wavefunction collapse, the structure of quantum entanglement, the origin of the matter-antimatter asymmetry, and the unexplained smallness of neutrino masses. Each has resisted resolution within existing frameworks. This paper presents answers to all four, derived from a single classification: the identification of the fundamental equations of physics as fractal geometric. No equation is modified. No new particle is proposed. Each answer generates specific, testable predictions against existing or near-future experimental data. This is a companion paper to "How to Break Resonance Theory" (DOI: 10.5281/zenodo.18750736), which addresses the large-scale mysteries. Together, they span the full range of physical reality from the Planck scale to the observable universe. The challenge is simple: solve these mysteries better, or test the solutions offered here. Keywords: wavefunction collapse, quantum entanglement, baryogenesis, neutrino mass, seesaw mechanism, fractal geometry, phase transition, Resonance Theory, falsification, testable predictions, Bell inequality, measurement problem
Description/Abstract: Four mysteries have persisted at the quantum scale for decades: the mechanism of wavefunction collapse, the structure of quantum entanglement, the origin of the matter-antimatter asymmetry, and the unexplained smallness of neutrino masses. Each has resisted resolution within existing frameworks. This paper presents answers to all four, derived from a single classification: the identification of the fundamental equations of physics as fractal geometric. No equation is modified. No new particle is proposed. Each answer generates specific, testable predictions against existing or near-future experimental data. This is a companion paper to "How to Break Resonance Theory" (DOI: 10.5281/zenodo.18750736), which addresses the large-scale mysteries. Together, they span the full range of physical reality from the Planck scale to the observable universe. The challenge is simple: solve these mysteries better, or test the solutions offered here. Keywords: wavefunction collapse, quantum entanglement, baryogenesis, neutrino mass, seesaw mechanism, fractal geometry, phase transition, Resonance Theory, falsification, testable predictions, Bell inequality, measurement problem
Title: Quantum Mechanics: The Interpretation of Barcelona Description: For a century, the Copenhagen interpretation has taught us that quantum mechanics is fundamentally probabilistic, that the wavefunction collapses upon measurement, and that there is no reality independent of observation. Einstein rejected this: "God does not play dice." This preprint presents a concrete, testable alternative: the Cosmic Mesh — a discrete, elastic, fractal tetrahedral lattice that constitutes spacetime itself. From this single physical substrate we recover all quantum phenomena without probability, without collapse, and without action at a distance: The wavefunction is a real vibration in the Mesh. Entanglement is the same vibration extended across space. Measurement is a local interaction that does not create reality; it only reveals it. Particles are standing waves trapped in topological knots; light is free vibration. We derive a single deterministic rule that governs all motion: At each discrete time step, a vibration migrates to the neighboring tetrahedron that maximizes the local entanglement gradient (Sk−Si). The fine-structure constant emerges geometrically as: α−1=135+2πϕ5≈137.034 where 135 is the ideal torsional-to-volumetric ratio emerging from the geometry of the tetrahedral lattice (90° + 45°), and 2πϕ/5 is the residual torsional stress from 120º cracks and fractal inheritance (golden ratio ϕ). The Mesh is local, deterministic, and testable. We predict that quantum entanglement decays with distance beyond a fundamental coherence length — a direct, falsifiable test of the Copenhagen interpretation. This concise summary is based on the full framework developed in "THE BREATHING UNIVERSE: A Torsional Solid Machine" (Zenodo, 2026). For complete mathematical derivations, including the mechanical origin of lepton masses and the emergence of general relativity, see that work. Keywords: quantum foundations, emergent quantum mechanics, discrete spacetime, topological defects, entanglement, Bell inequalities, Copenhagen interpretation, deterministic quantum theory, elastic lattice, tetrahedral mesh, Weyl curvature imprints, dark matter, cosmological constant, fine-structure constant, golden ratio License: Creative Commons Attribution 4.0 International (CC BY 4.0) Related works: Bertran, A. (2026). THE BREATHING UNIVERSE: A Torsional Solid Machine. Zenodo. Bertran, A., Jussà, E., Vila, M. (2025). The Universe's Geometric Inertia – The Jussà-Vila Ansatz. Zenodo.
Title of Works: Geometric Origin of Spontaneous Collapse from a Compactified Timelike Dimension Supplementary Material: Experimental Tests of Geometric Collapse Overview: This integrated body of work proposes a novel geometric resolution to the quantum measurement problem. By extending spacetime with a compactified timelike dimension on a Z2 orbifold, the author derives the phenomenological GRW collapse rate from first principles. The mechanism identifies the QCD confinement scale as the fundamental driver of wave-function localization via the Jackiw-Rebbi mechanism, bridging the gap between quantum foundations and high-energy physics. Key Contributions: Geometric Micro-physics: Provides the full derivation of the Lindblad Master Equation and the Continuous Spontaneous Localization (CSL) dynamics directly from 5D bulk-brane interactions. Chromatic Coupling: Introduces a unique "chromatic" mechanism where only color-charged particles (nucleons) undergo spontaneous collapse. This predicts that leptons and photons remain transparent to the mechanism, a feature that distinguishes it from standard mass-proportional models. Quantum Computing Scalability: Establishes a quantitative "effective mass budget" for qubit design, defining a geometric ceiling for the scalability of quantum architectures based on nucleon count. Experimental Predictions & Falsifiability: The accompanying supplementary material details a comprehensive roadmap for testing the model using next-generation matter-wave interferometers such as MAQRO and OTIMA. Key testable signatures include: Isotope Shifts: A per-mille level shift in the collapse rate between different isotopes (e.g., 87Rb vs. 133Cs). Thermal Corrections: A temperature-dependent correction to the collapse rate at the 10−5 level, detectable in cryogenic-to-room-temperature comparisons. Comparative Interferometry: A definitive test through electron vs. neutron interferometry at matched mass scales to verify lepton transparency. This research offers a mathematically rigorous and experimentally falsifiable framework that transforms the "mystery" of wave-function collapse into a concrete parameter of spacetime geometry and quantum engineering.
This work presents a comprehensive theoretical formulation of Quantum Fractal Geometry (QFG), a framework in which spacetime is fundamentally resolution-dependent. The apparent distinction between quantum and classical physics emerges from a single geometric principle: observer resolution as a structural parameter. The paper develops the formal mathematical foundations of QFG, including the definition of resolution-dependent metrics, a projection operator governing information accessibility, and the derivation of key physical results. These include the emergence of the Born rule from projection covariance, the recovery of the Einstein field equations as an infrared limit, and the Schrödinger equation as a dual flow correspondence. The framework provides a unified geometric interpretation of entanglement, black hole entropy, and gravitational structure, and introduces the Curvature Texture Index (CTI) as a measurable prediction linking multiscale geometric structure to astrophysical observables. A companion empirical study tests the CTI prediction using observational data from supermassive black hole host galaxies. All predictions are formulated with explicit falsifiability criteria, enabling experimental validation or refutation.
AbstractWe develop and apply the Yugen wavefunction framework, a phase-geometric reformulation of quantum theory in which the vacuum is treated as an active medium with intrinsic stiffness set by the Planck scale. In this approach, physical fields and particles emerge from internal phase geometry rather than from fundamental point-like interactions. By identifying the amplitude of the Yugen wavefunction with the Planck energy, the Planck scale becomes a physical parameter governing vacuum rigidity and nonlinear phase response.We present explicit numerical predictions across atomic, particle, and mesoscopic regimes. In the atomic sector, the framework predicts small but systematic nonlinear deviations in isotope-shift spectroscopy, arising from coherent vacuum phase effects and consistent with recent high-precision datasets. In the neutrino sector, neutrino masses emerge naturally from localized topological phase interference, yielding the observed mass scale without introducing additional heavy fields.We further address the quantum–classical transition by deriving a nonlinear phase-induced decoherence mechanism for macroscopic objects. The resulting mass- and size-dependent decoherence times place mesoscopic systems near the picogram scale at the threshold of sustained quantum superpositions, a regime accessible to current optomechanical experiments.These results suggest that precision spectroscopy, neutrino phenomenology, and mesoscopic quantum tests probe a common underlying phase structure of the vacuum. The Yugen wavefunction thus provides a unified and experimentally falsifiable framework linking quantum fields, particle properties, and the emergence of classicality.
This work introduces a resolution-dependent geometric framework—Quantum Fractal Geometry (QFG)—in which the effective physical description of systems depends explicitly on observational scale. Within this framework, entangled quantum systems are modelled as unified geometric structures at deep resolution, characterised by a scale-dependent metric g_{μν}(ℓ) and a geometric phase field φ(x,ℓ) valued on S¹. Measurement is interpreted as a resolution-dependent projection of this unified structure onto detector-scale observables. A symmetry-constrained coarse-graining map is introduced as the minimal fixed point of resolution flow, identifying antipodal phase configurations (S¹ → S¹/ℤ₂). Under isotropy, continuity, and convex-linearity, the quantum correlation function E(a,b) = −cos(θ_a − θ_b) is recovered as the unique rotationally invariant statistic compatible with the projection structure, saturating the Tsirelson bound. Within QFG, Bell inequality violation arises not from nonlocal signalling or measurement dependence, but from the failure of scale-independent separability. Locality (in the operational no-signalling sense) and measurement independence are preserved. The framework further outlines a programme for deriving the Born rule from resolution-induced measure structure and identifies falsifiable predictions, including resolution-dependent deviations from ideal cosine correlations. This work should be understood as establishing the minimal geometric structure required for the QFG interpretation of Bell correlations, with full dynamical derivations deferred to future work.
Abstract We develop and apply the Yugen wavefunction framework, a phase-geometric reformulation of quantum theory in which the vacuum is treated as an active medium with intrinsic stiffness set by the Planck scale. In this approach, physical fields and particles emerge from internal phase geometry rather than from fundamental point-like interactions. By identifying the amplitude of the Yugen wavefunction with the Planck energy, the Planck scale becomes a physical parameter governing vacuum rigidity and nonlinear phase response. We present explicit numerical predictions across atomic, particle, and mesoscopic regimes. In the atomic sector, the framework predicts small but systematic nonlinear deviations in isotope-shift spectroscopy, arising from coherent vacuum phase effects and consistent with recent high-precision datasets. In the neutrino sector, neutrino masses emerge naturally from localized topological phase interference, yielding the observed mass scale without introducing additional heavy fields. We further address the quantum–classical transition by deriving a nonlinear phase-induced decoherence mechanism for macroscopic objects. The resulting mass- and size-dependent decoherence times place mesoscopic systems near the picogram scale at the threshold of sustained quantum superpositions, a regime accessible to current optomechanical experiments. These results suggest that precision spectroscopy, neutrino phenomenology, and mesoscopic quantum tests probe a common underlying phase structure of the vacuum. The Yugen wavefunction thus provides a unified and experimentally falsifiable framework linking quantum fields, particle properties, and the emergence of classicality.