Abstract This work presents a unified framework in which all physical fields and measurement outcomes emerge scale-dependently from the internal phase geometry of the Yugen wavefunction. Gauge, gravitational, and matter fields are described as components of a single operator-valued internal phase structure, whose dynamics naturally encode the transition between classical and quantum behavior depending on the observational scale (see Precursor Study A for the treatment of the measurement problem). We further show that interference among internal phase gradients generates suppressed corrections to the effective Hamiltonian. These fourth-order gradient terms, consistent with the internal algebraic structure, can manifest as a new long-range interaction—a “fifth force” arising purely from phase geometry. Building on previous work (Precursor Study B), the framework provides quantitative predictions for atomic isotope shifts and precision spectroscopy experiments, with characteristic frequency deviations on the order of for selected transitions. These results offer experimentally testable signatures connecting the emergence of classicality, quantum behavior, and novel interactions within a single unified internal phase structure.
Abstract This work presents a unified framework in which all physical fields and measurement outcomes emerge scale-dependently from the internal phase geometry of the Yugen wavefunction. Gauge, gravitational, and matter fields are described as components of a single operator-valued internal phase structure, whose dynamics naturally encode the transition between classical and quantum behavior depending on the observational scale (see Precursor Study A for the treatment of the measurement problem). We further show that interference among internal phase gradients generates suppressed corrections to the effective Hamiltonian. These fourth-order gradient terms, consistent with the internal algebraic structure, can manifest as a new long-range interaction—a “fifth force” arising purely from phase geometry. Building on previous work (Precursor Study B), the framework provides quantitative predictions for atomic isotope shifts and precision spectroscopy experiments, with characteristic frequency deviations on the order of for selected transitions. These results offer experimentally testable signatures connecting the emergence of classicality, quantum behavior, and novel interactions within a single unified internal phase structure.
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.
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.
Abstract Standard quantum mechanics encodes phase degrees of freedom through a single U(1) structure, implicitly assuming a flat phase geometry in which global phase transport is isometric and any curvature must be introduced externally, typically via spacetime metrics or interaction potentials. In this work, we show that replacing the U(1) phase algebra with the minimal cyclic algebra defined by j3=−1 (C₃) leads to an intrinsically curved phase space without invoking any external geometric input. The multi-carrier structure of C₃ generates nontrivial holonomy under closed phase evolution, producing residual phase components that cannot be eliminated by gauge transformations. This holonomy naturally defines an intrinsic connection whose curvature arises solely from the algebraic transition rules between phase carriers. Within this framework, we construct a C₃-generalized Laplace operator and analyze its Green function, demonstrating phase-mediated propagation that departs from flat-space behavior. When embedded into a C₃-generalized Schrödinger equation, curvature effects emerge dynamically through phase gradients, without the explicit introduction of gravitational or geometric potentials. In the weak-field limit, an effective Newtonian potential is recovered from hidden-phase gradients, providing a direct link to classical physics. The results reframe curvature as an emergent property of multi-carrier phase geometry and offer a unified perspective connecting quantum phase structure, measurement, and emergent spacetime features.
We propose a hidden U(1) gauge interaction that couples exclusively to quantum coherence in massive systems. The central innovation is a conserved coherence current operator constructed from the Noether mass current via operator-level coarse-graining. This current vanishes for classical matter distributions but is nonzero for spatial superpositions and entangled states, yielding a gauge interaction that is dormant in classical regimes but activated by quantum coherence. The framework predicts three distinctive signatures: (i) interferometric phase shifts scaling linearly with fringe visibility, (ii) decoherence rates with characteristic m^2 scaling and spatial dependence distinct from collapse models, and (iii) entanglement-selective forces between distant massive qubits. The theory maintains full gauge invariance, causality, and positive time evolution. We show that state-of-the-art atom interferometers and levitated nanoparticles can place first constraints on this interaction class, complementary to classical fifth-force searches. This approach provides a novel theoretical framework for probing coherence-selective fundamental interactions and their potential role in the quantum-classical transition. To make this more concrete, we also spell out a simple benchmark latent-field model and work out, in detail, how a representative large-momentum-transfer atom interferometer constrains the corresponding coupling strength.
A field-theoretic framework is developed in which a real scalar phase field serves as the fundamental object, and spacetime geometry, wave dynamics, and probabilistic structure emergefrom constraints on its gradients. The theory is defined by a scalar functional on momentumspace, leading to nonlinear equations of motion and an induced effective metric governing propagation. Under Lorentz invariance, the functional reduces to a single-variable dependence, andadditional assumptions on observability motivate a projective structure that constrains its form.In the weak-gradient regime, the theory reproduces linear relativistic wave equations andadmits a complex representation consistent with standard quantum wave behavior. Beyondthis regime, nonlinear effects lead to gradient steepening and caustic formation, resulting inmulti-branch phase structure. A detector model based on nonlinear coupling to the phase fieldis introduced, providing a dynamical mechanism for branch selection. A conserved current associated with phase transport yields a density that approximates the Born rule under controlledconditions.The framework unifies aspects of Hamilton–Jacobi theory, nonlinear scalar field dynamics, and emergent geometry, while providing a structured pathway from phase dynamics towave-like behavior and measurement-like phenomena. Possible phenomenological consequencesinclude background-dependent propagation, nonlinear deviations from superposition, and smallcorrections to standard probabilistic predictions.
We propose that the unobservability of absolute scale constitutes a foundational principle of physics. Starting from the requirement that physical predictions must be invariant under rescalings of the action, we show that only phase-based quantities remain well defined. This requirement uniquely selects a complex amplitude description, leading directly to the structure of quantum mechanics, including linear superposition, Hilbert space, and the Born rule. Within this framework, the classical notion of action loses absolute meaning, and physical observables arise from invariant phase relations. Quantum mechanics is therefore not postulated, but emerges as the minimal consistent description of systems in which scale cannot be directly observed. The formal structure of quantum theory is shown to follow from this principle without additional axioms. We further demonstrate that the same principle implies the existence of a dynamical scale field, which governs the effective quantum scale and connects naturally to cosmological models with a time- dependent Planck mass. In this way, the structure of quantum mechanics and the large-scale dynamics of the Universe are linked through a common origin. This framework provides a unified perspective in which quantum behavior and cosmological evolution arise from a single underlying principle, suggesting a new approach to the relationship between fundamental physics and cosmology.