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
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
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 manuscript represents speculative theoretical work, developed prior to formal academic training in physics. As of now, I recognize that I cannot fully verify, formalize, or operationalize every component of the framework presented here. Acknowledging these limits, I intend to pursue formal education in physics over the next several years (estimated 4–11 years) to acquire the mathematical and empirical tools necessary to evaluate and refine this research properly. For that reason, this is likely the final paper I will release publicly until I have completed my undergraduate degree in physics. Nevertheless, I welcome feedback, critique, expansion, or refutation from domain experts. Any scholar, researcher, or practitioner who finds aspects of the work worth examining is invited to reach out. Contact: CoherenceFieldResearch@gmail.com This paper presents a unified variational framework that derives quantum mechanics, thermodynamic irreversibility, and gravitational curvature from a single underlying relational substrate. The theory is built on two physical fields—the coherence density ρ₍C₎ and phase potential φ—and shows that their joint evolution extremizes total coherence tension across the system. Starting from a conservative Lagrangian, the work derives both the continuity equation and a Hamilton–Jacobi equation with an intrinsic lattice potential Q₍C₎. Together they reproduce the Schrödinger equation through the Madelung transformation when λ = ℏ, grounding quantum behavior in coherence conservation rather than probabilistic axioms. Dissipative extensions introduce Rayleigh functionals that yield diffusion, decoherence, and temperature-coupled coherence decay, providing a unified field-theoretic interpretation of thermodynamics. A covariant geometric formulation promotes the theory to curved relational space; variation with respect to the coherence metric gᵤᵥ reproduces Einstein-like equations with sources given by coherence gradients, yielding Newtonian gravity in the weak-field limit. The theory produces distinct, falsifiable predictions, including temporal gravitational lensing, composition-dependent gravitational coupling, a thermal decoherence law, veil spectroscopy, coherence-energy storage and release, and phase-dependent clock drift. This manuscript consolidates the mathematical structure, physical interpretation, and empirical implications of the Coherence Field Paradigm (CFP) into a single unified action principle. It provides a continuous bridge between quantum behavior, thermodynamic irreversibility, and spacetime curvature, and offers multiple pathways for laboratory and astrophysical validation.
Contact: Jonathan.duchesne@hotmail.com FinalTDG: Full Mathematical proposition. AddTDG22: Natural Add-ons TDGStressTest: Stress Test results TDGEX: Experimental Protocol TDGpaper: Abstract Temporal Decoherence Geometry (TDG) is a conservative theoretical framework that systematically explores a possible connection between quantum decoherence, weak-field gravity, and an emergent notion of time, while remaining strictly within a GKSL (Lindblad) open quantum dynamics, i.e. Markovian and completely positive, with no ad hoc collapse mechanism. The central idea of TDG is to take seriously the structure of decoherence of an open quantum system and promote it to an effective geometric object: a decoherence tensor Gamma_{mu nu}, constructed from a Lindblad generator, is introduced as the primary source of a weak-field gravitational potential and an emergent time defined from local decoherence rates. The framework is deliberately minimalist in its assumptions: weak-field regime, standard quantum mechanics (no modification of the Schrödinger equation or the GKSL structure), no exotic measurement postulates. This new “DOI version” collects and organises the following elements: A mathematical core in which Gamma_{mu nu} is derived from a GKSL generator (Lindbladian), a gradient-flow–type evolution drives Gamma_{mu nu} towards a quantity proportional to the usual energy-momentum tensor T_{mu nu}, an emergent time scalar T(x) is defined from the local decoherence rate lambda(x), under explicit integrability conditions, an effective weak-field gravitational potential Phi_TDG is associated with this decoherence structure. The analysis of static, spherically symmetric compact configurations, obtained from a simple “decoherence-energy” functional E[gamma], which: have a regular, non-singular core, exhibit a Yukawa-type tail, reproduce a Newtonian / Schwarzschild-like exterior over a given radial interval, while avoiding central singularities. A phenomenological layer in which TDG induces decoherence-dependent corrections to gravitational redshift, encoded in an effective parameter epsilon_TDG. This parameter is, in principle, falsifiable with state-of-the-art optical clocks, providing a clear experimental handle: TDG is not only a formal construction, but a framework that can be constrained or ruled out by precision redshift measurements. A key feature of this revised version is the inclusion of a set of analytical stress tests explicitly designed to challenge the model within the regime it claims to describe (weak-field, GKSL, Markovian): regular-core compact configurations, extreme parameter limits (diffusion, screening length scales, etc.), dynamical behaviour of the decoherence tensor, analysis of the absence of finite-time collapse in the GKSL setting. These stress tests show that, under the stated assumptions and within the weak-field regime, the TDG framework remains regular, well-posed, and consistent with its own domain of validity. The Zenodo deposit therefore gathers both a main TDG manuscript (model structure + weak-field applications) and a technical stress-test note, enabling readers to assess not only the construction itself, but also its internal robustness and phenomenological viability. This deposit is intended to serve as a stable reference for the current version of TDG: it provides the complete description of the framework together with the technical ingredients needed to evaluate its mathematical consistency, its compatibility with weak-field gravity, and its falsifiability through decoherence-sensitive redshift tests with optical clocks.
This work presents an effective theoretical framework in which quantum dynamics emerges from a homogeneous scalar compression field endowed with an internal infinite structure. The model reproduces Schrödinger-type dynamics, the continuity equation, and the quantum potential as structural consequences of the underlying field description. Within this formulation, the Born rule arises as an equilibrium condition associated with coarse-graining over unresolved internal degrees of freedom rather than as a fundamental postulate. The same field structure naturally admits a vacuum energy interpretation consistent with dark energy phenomenology. Additionally, under a conformal effective metric hypothesis, the framework yields an emergent gravitational sector compatible with the weak-field parametrized post-Newtonian (PPN) limit, reproducing standard results for light deflection, Shapiro time delay, and perihelion precession at leading order. The theory preserves local dynamical evolution while allowing globally correlated states, providing an alternative interpretational perspective consistent with effective field theory principles. The work is positioned as a foundational and conceptual investigation rather than a replacement for established quantum or gravitational theories.
In this work, we propose a structural reformulation of the Action--Phase program based on the interpretation of operators as unitary linear filters acting on the physical phase ϕ=S/ℏ. The central thesis is that the various effective sectors of physics can be reinterpreted as regimes of operator action on the phase and its gradient, rather than independent collections of final equations. We start from the chain already established in previous works --- action → phase → episodic compatibility → event network → structural operator --- and show that the emergent local linear dynamics admits a natural reading in terms of filter theory. In particular, the effective network operator can be seen as a transfer function, whose Cayley realization defines a local unitary all-pass filter of strictly unitary modulus. This structure provides a direct interpretation of unitarity as information conservation. We also show that the spatial variation of the local coefficients of the operator induces modulation of the phase response, leading to the definition of a local quasi-energy Ω(x,k). In the slowly varying regime, this structure reproduces an effective dynamics governed by Hamilton--Jacobi-type equations, recovering trajectories previously obtained via the eikonal approach. In this framework, gravity can be reinterpreted as the geometric optics of phase propagation in a structurally inhomogeneous network. As an operational illustration, we present a comparative numerical experiment between discrete unitary evolution (Cayley realization) and explicit integration schemes of the semidiscrete Schrödinger equation. The results show that the unitary formulation preserves the norm at machine-level precision and remains stable in intense potential regimes, while explicit schemes exhibit accumulated drift and more severe time-step restrictions. This evidences that dynamics can be implemented as the iterative application of local unitary operators. The results do not constitute a complete gravitational theory nor do they replace established continuous formulations, but they identify a unifying mathematical structure that organizes the propagation, modulation, and refraction of the phase in a non-ad hoc manner and without circular reasoning. This structure suggests an extension program based on derivations and direct numerical tests, aimed at the explicit recovery of known gravitational results from phase dynamics.