Description This work introduces a structural framework for understanding the quantum–classical crossover using two internal quantities of the Thickness Structure Hypothesis (TSH): the spread deviation Δf and the shrink tension γT. These quantities characterize the competing tendencies of quantum spreading and classical or gravitational contraction. By organizing physical behaviors on the Δf–γT phase diagram, the framework provides a unified structural classification of quantum, classical, and gravitational regimes. A key result is that the sharp disappearance of quantum interference can be interpreted as a critical phenomenon. Near the boundary between the Stable (quantum) and Composite (classical) phases, the interference visibility follows a Landau‑type scaling law with critical exponent β = 1/2. This suggests that the abrupt switching observed in the quantum–classical transition arises from structural changes in Δf and γT rather than from external decoherence alone. Within this framework, wave‑packet collapse and the loss of interference visibility correspond to motion toward larger γT in the structural parameter space. The Δf–γT phase diagram thus provides a general, theory‑independent viewpoint for describing interference, localization, and the onset of classical behavior. The approach offers a structural mechanism for the sharpness of the quantum–classical crossover and connects quantum, classical, and gravitational behaviors within a single unified diagram.
Description This work introduces a structural framework for understanding the quantum–classical crossover using two internal quantities of the Thickness Structure Hypothesis (TSH): the spread deviation Δf and the shrink tension γT. These quantities characterize the competing tendencies of quantum spreading and classical or gravitational contraction. By organizing physical behaviors on the Δf–γT phase diagram, the framework provides a unified structural classification of quantum, classical, and gravitational regimes. A key result is that the sharp disappearance of quantum interference can be interpreted as a critical phenomenon. Near the boundary between the Stable (quantum) and Composite (classical) phases, the interference visibility follows a Landau‑type scaling law with critical exponent β = 1/2. This suggests that the abrupt switching observed in the quantum–classical transition arises from structural changes in Δf and γT rather than from external decoherence alone. Within this framework, wave‑packet collapse and the loss of interference visibility correspond to motion toward larger γT in the structural parameter space. The Δf–γT phase diagram thus provides a general, theory‑independent viewpoint for describing interference, localization, and the onset of classical behavior. The approach offers a structural mechanism for the sharpness of the quantum–classical crossover and connects quantum, classical, and gravitational behaviors within a single unified diagram.
This work presents a new theoretical and numerical framework for understanding the sharp quantum–classical crossover by introducing two internal structural degrees of freedom—the local spread S(x) and contraction C(x)—derived from the gradient and curvature of a probability distribution. These quantities form a two‑dimensional Spread–Contraction (SC) phase diagram that characterizes the transition between quantum‑dominated spreading and classical localization. A minimal covariant action motivated by information geometry is constructed, from which the SC Ordinary Differential Equation (SC‑ODE) is obtained via variational principles. The SC‑ODE integrates spreading and contracting contributions in a minimal form and provides a structural mechanism for the steep drop in interference visibility observed in experiments. To investigate the role of spatial structure, the study introduces a conservative SC Partial Differential Equation (SC‑PDE) incorporating degenerate mobility and backward diffusion. Numerical experiments under extreme initial conditions—where micro‑noise is superimposed on a uniform field—reveal a three‑phase structure consisting of stable, critical, and collapse regimes. This behavior contrasts with the always‑stable SC‑ODE and demonstrates that spatial degrees of freedom are essential for generating critical phenomena. A comparison with the Cahn–Hilliard equation shows that, within the scope of the numerical experiments, the SC‑PDE preserves non‑negativity and boundedness even under conditions where the Cahn–Hilliard model fails. This robustness arises from the automatic suppression of backward diffusion near the vacuum due to the degenerate mobility structure. Overall, this work provides a unified structural framework for describing the sharpness of the quantum–classical crossover and offers a numerically stable PDE formulation that may be relevant for surface evolution, thin‑film processes, and nonlinear field dynamics.
Description A Compact Structural Simulator Based on the Thickness Structure Hypothesis (TSH) This repository provides an executable model based on the structural dynamics suggested by the Thickness Structure Hypothesis (TSH). The simulator implements a compact dynamical equation derived from a covariant action involving the structural quantities p(x), Δf, and γT, and explores the possibility of organizing quantum‑like, classical‑like, and gravitational‑like behaviors within a common structural framework. The implementation numerically reproduces key structural components of the TSH formulation, including: the Δf–γT phase diagram the structural potential Φstruct the structural force Fμ=−∇μΦstruct(Δf,γT) mass‑dependent boundary behavior irreversible transitions across phase boundaries the evolution of the thickness‑field p(x) The simulator directly integrates the dynamical terms appearing in the compact covariant action, providing a computational environment for examining the structural behavior encoded in the TSH framework. Interpretation of the Dynamics The dynamical equation implemented here can be viewed operationally as: **“Next‑step trajectory = spreading tendency from −∇μlnp structural force determined by Δf and γT.”** −∇μlnp: spreading tendency (Bohm‑type behavior) Δf: structural degree of freedom associated with interference and nonlocality γT: structural degree of freedom associated with contraction and localization Fμ: structural force determined by the Δf–γT phase diagram Through this balance, the simulator produces behaviors that may resemble: quantum‑like spreading (Stable region) classical‑like trajectories (Composite region) gravitational‑ or measurement‑like localization (Core region) What the Simulator Computes The code performs the structural feedback cycle: (p(x),Δf,γT)t→Fμ→uμ(t+δt)→(p(x),Δf,γT)t+δt This realizes the loop: phase → structural force → motion → update → phase as suggested by the structural formulation. Characteristics of the Implementation uses the structural potential defined in the TSH formulation reproduces the three structural regions from the same phase diagram exhibits irreversible transitions when crossing structural boundaries visualizes interference‑like, classical‑like, and collapse‑like behavior follows the compact covariant action used in the theoretical formulation The simulator is intended as a computational tool for exploring the structural dynamics implied by the TSH framework. TSH Physics Engine (Structural Interaction Framework) The repository includes a structural physics engine capable of handling a variety of behaviors—quantum‑like, classical‑like, relativistic, and interaction‑related—within a single structural field p(x) and the associated structural variables Δf and γT. Because the structural action depends only on these internal variables, standard interaction tensors can be incorporated in a compatible way without modifying the structural equations. This allows the engine to accommodate: Standard Model–type sectors GUT‑like sectors effective string‑theoretic fields fluid or condensed‑matter tensors within the same structural framework. Computational Properties The structural formulation reduces the need for multiple PDE solvers and enables efficient GPU execution: single O(N) update loop no Navier–Stokes, Schrödinger, or GR field equations phase‑diagram‑based force evaluation real‑time simulation for large systems These properties allow the simulator to explore regimes that are typically difficult to compute within conventional formulations. Physics Engine (simulation, games, research) & AI Physics Engine (learning, optimization, universe editing)https://github.com/ababphysics/TSH/ xhttps://x.com/abab162535
This record presents the quantum-theoretical component of the thickness‑structure hypothesis, an original physical framework developed by the author (ab_ab). The thickness‑structure hypothesis models physical reality as a continuous substrate characterized by a thickness field ϕ. The spatial extension, localization, and dynamical behavior of physical systems arise from structural variations in this field. Two structural variables define the state of the substrate:• thickness deviation Δf — the local structural alternative that determines potential localization sites • thickness fluctuation γT — the spatial spread of the structure responsible for wave-like behavior Depending on the combination of Δf and γT, the system exhibits three phases:• Wave phase (large γT) • Composite phase (intermediate γT) • Stable phase (γT below a critical threshold) Measurement is interpreted as a constraining operation that reduces γT, and the transition from wave-like to particle-like behavior is described as a structural phase transition satisfying γT ≤ γcrit(Δf). This document focuses specifically on the quantum aspects of the framework, including:• wave–particle duality as a phase-structural phenomenon • measurement-induced localization as a continuous transition • interference and tunneling as geometric consequences of the thickness field • entanglement as multi-region constraint coupling in γT • predictions such as continuous visibility change under partial measurement The purpose of this release is to establish a citable, timestamped reference for the quantum sector of the thickness‑structure hypothesis. All terminology, definitions, and conceptual structures introduced here originate with the author. License: CC BY 4.0 only. Thickness Structure HypothesisThickness Structure Hypothesis — A Relativistic Extension of Proper‑Time Structure and Thickness Fluctuation Thickness Structure Hypothesis DynamicsThickness Structure Hypothesis Dynamics - Unified Equation of Motion Thickness Structure Hypothesis Cosmological ExtensionsThickness Structure Hypothesis Cosmological Extensions Thickness Structure Hypothesis FrameworkThickness Structure Hypothesis Framework Xhttps://x.com/abab162535 Please help arxiv endorsementRelativity and Quantum Cosmology (gr-qchttps://arxiv.org/auth/endorse?x=DITNNU
We develop an effective gravitational framework for the quantum–classical transition based on the dynamical stability of historical information. Building on previous analyses of gravitational temporal decoherence and the emergence of classical time, the present work addresses the subsequent problem of how classical histories become stable, persistent, and objectively accessible. The framework is formulated as a non-relativistic, semiclassical open-system dynamics in which gravity induces structurally constrained dissipative effects of Lindblad type. Within this setting, we introduce a stability functional that operationally characterizes which quantum states can support robust historical records and which are dynamically suppressed. The quantum–classical transition is described as a smooth, scale-dependent crossover controlled by physically meaningful parameters, rather than as a sharp boundary or interpretational postulate. The emergence of a unique classical past is shown to arise from dynamical selection: while multiple quantum histories are formally allowed, only those supported by stable physical records persist under gravitationally induced dissipation. The framework is explicitly effective in scope and does not rely on a microscopic derivation or full relativistic covariance. Instead, it identifies universal structural features that any viable fundamental theory must reproduce in the appropriate semiclassical regime. This work complements earlier studies on the emergence of classical time by providing a dynamical account of historical stability, thereby contributing to a coherent program for understanding the physical origin of classical reality.
Classical and quantum criticality In most cases the phases of quantum field theories, in particular those of interest in condensed matter physics, can be described in terms of the behavior of local observables, such as order parameters or currents that transform properly under the symmetries of the theory. Quantum and thermal phase transitions are characterized by the behavior of these observables as a function of temperature and of the coupling constants of the theory. The phase transitions themselves, quantum or thermal, are classified into universality classes, which are represented by the critical exponents which specify the scaling laws of the expectation values of the observables. Historically, the development of this approach to critical behavior goes back to the Landau theory of critical behavior. It acquired its most complete form with the development of the renormalization group (RG) in the late 1960s and early 1970s. It is the centerpiece of Wilson’s approach to quantum field theory, in which all local quantum field theories are defined by the scaling regime of a physical system near a continuous phase transition. From this point of view there is no fundamental difference between classical (or thermal) phase transitions, which are described by the theory of classical critical behavior, and quantum phase transitions. For example, the expectation value of a local order parameter M as the thermal phase transition is approached from below behaves as M ~ (Tc − T) β . Here T c is the critical temperature and β is a critical exponent that depends on the universality class of the thermal phase transition and on the dimensionality of space. While quantum mechanics can play a key role in the existence of the ordered phase, e.g. superfluidity and superconductivity are macroscopic manifestations of essentially quantum-mechanical phenomena, the thermal transition itself is governed entirely by classical statistical mechanics, and quantum mechanics plays a role in setting the value of non-universal quantities such as the critical temperature, etc. On the other hand, in the case of a quantum phase transition, the order parameter M has a similar scaling behavior as a function of the coupling constant, M~(gc−g)β˜, where g is the coupling constant, g c is the critical coupling constant, and β˜ is a critical exponent that depends on the universality class of the quantum phase transition. Here we assume that M has a non-vanishing expectation value only for g < g c .
The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom. From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.