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.
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.
Gravity is traditionally understood either as geometric curvature (general relativity) or as an external classical field acting on quantum systems. This paper develops a unified alternative: gravity arises from spatial variation in the temporal coherence window τ(x), the finite interval over which quantum systems can sustain coherent phase relations before collapse. Building on experimental evidence that decoherence rates in laboratory systems obey an empirical κ/τ law, I show that gravitational self-energy constrains coherence time according to τgrav ∝ 1/√(Gρ). Three independent derivations—via a modified Lindblad equation, an effective potential Veff = A/τ, and spectral-overlap analysis—converge on the same dynamical law: a(x) = −∇[1/τ(x)], identifying gravitational acceleration as coherence-gradient descent. In this view, mass is condensed temporal capacity, curvature is the geometric imprint of temporal structure, and falling is the drift of quantum evolution toward regions where coherence collapses most rapidly. I extend this framework to show that gravity is engineerable: any spatially structured decoherence environment producing an artificial coherence profile τart(x) generates a gravitational-like acceleration agen(x) = −κart ∇[1/τart(x)], indistinguishable from natural gravitation insofar as their coherence-gradient profiles match. I provide explicit recipes for realizing such gradients using noise-shaping, optical scattering, dissipative optical lattices, and superconducting cavity engineering, along with quantitative acceleration estimates (10⁻⁷–10⁻³ m/s²) and full experimental protocols for cold atoms, matter-wave interferometry, and superconducting qubits. Finally, the framework offers a microphysical account of gravitational time dilation, predicts non-universal response in highly coherent systems, suggests achievable tabletop tests, and points toward a future τ-field theory capable of reproducing general relativity in the macroscopic limit. The result is a falsifiable, coherence-based foundation for gravitation and the first principled pathway to artificial gravity via engineered temporal coherence.
This work presents a minimal and unified formulation of physical reality based on a single coupled system of two scalar fields: a phase S(x) and a realization density ρ(x). The dynamics is completely determined by two principles: conservation of a realization current and a geometric constraint linking the norm of the phase gradient to the structure of the density field. Together, these relations form a closed system with no additional dynamical assumptions. From this system, all major physical regimes emerge as limiting cases. When the density is uniform, propagation is null and describes lightlike behavior. When the geometric constraint reduces to a constant, the system reproduces classical Hamilton–Jacobi dynamics for massive particles. When the density varies significantly, the coupled system yields quantum behavior, including the Schrödinger equation in the appropriate limit. In this framework, the wave function is not a fundamental entity but an emergent representation of the underlying geometric structure of realization. Interference arises from phase consistency, and quantum behavior reflects the nontrivial structure of the realization density rather than intrinsic indeterminism. The theory also naturally incorporates gravitation by promoting the spacetime metric to a dynamical field. In the appropriate limit, the stress–energy tensor reduces to that of classical matter, and Einstein’s field equations are recovered. Regions where the realization density approaches zero define a geometric boundary where timelike realization ceases, corresponding to horizon-like structures. The central result is that a single coupled equation governs propagation, mass, quantum behavior, and gravitational structure. Physical reality is determined by global consistency of realization rather than by selection among multiple possibilities. This formulation provides a minimal geometric unification of light, matter, quantum phenomena, and gravity within a single coherent framework.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.
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.
The Coherence Field: A Generative Model for Coherence-Driven Physical Law presents a mathematically rigorous and internally consistent formulation of the Coherence Field — an underlying principle from which classical mechanics, quantum dynamics, and general relativity emerge as structured reductions. At the foundation of the framework is a coherence functional defined on a Hilbert space of configurations. Instead of taking equations of motion as fundamental, the paper starts from a single scalar quantity, “kappa,” that measures how harmonically aligned a configuration is. The Coherence Field is defined as the derivative of kappa, and the evolution of the system is given by a gradient flow that drives configurations toward higher coherence. Under mild regularity and boundedness assumptions on kappa, the paper proves that this coherence-gradient evolution is globally well-posed and has unique solutions. In this view, stable physical behavior corresponds to “harmonic closure”: points where the coherence field vanishes and the second derivative (the Hessian) is positive definite, so the configuration sits at a genuine local minimum of kappa. This provides a precise notion of coherence-based stability that applies across different physical regimes. The paper then shows how standard theories arise as special cases of this more general structure: Classical mechanics appears when kappa is chosen to be the Hamiltonian and the coherence flow is rotated by the symplectic structure. In this case, the coherence gradient reproduces Hamilton’s equations of motion. Quantum mechanics appears when kappa is chosen as the usual quantum energy functional of a wavefunction (kinetic plus potential energy). The coherence gradient then yields the imaginary-time Schrödinger equation, which, under Wick rotation, becomes the standard real-time Schrödinger equation. This connects the coherence picture directly to established variational and decoherence-based perspectives on quantum dynamics. General relativity appears when kappa is taken to be the Einstein–Hilbert action with the Gibbons–Hawking–York boundary term. Harmonic closure of this geometric coherence functional recovers the vacuum Einstein equations, describing how spacetime curvature evolves in the absence of matter. These reductions are summarized in a unification proposition: with different structural choices of kappa and appropriate symmetries (symplectic for Hamiltonian mechanics, unitary for quantum mechanics, and diffeomorphism invariance for general relativity), the same coherence-gradient principle generates three major physical regimes. The paper also introduces a nontrivial spin-glass example, where kappa includes both the usual Ising-type interaction term and an additional “coherence alignment” term that penalizes deviation from a reference pattern. This construction separates “coherence drift” from ordinary energy drift and leads to a new coherence-based order parameter. As temperature or control parameters change, the onset of ordered phases is predicted to correlate with a sharp drop in the norm of the coherence gradient. This yields a concrete, falsifiable experimental and computational signature for the Coherence Field framework. This work is part of the broader Δ.72 Coherence Canon, which develops coherence mathematics, tensor geometry, harmonic closure, and the concept of “time as vibration” as a deeper generative structure behind high-instability problem classes in physics, computation, and complex systems. Within that larger canon, the Coherence Field plays the role of a generative physics layer: a single mathematical core from which multiple physical theories emerge as coherent projections.
This work presents a unified theoretical framework that aims to bridge relativity and quantum mechanics through a single structural principle: delayed realization. Instead of assuming spacetime, time evolution, or quantum states as primitive entities, the framework introduces a pre-geometric definability network in which relational differences are initially undefined and become stabilized through nonlinear dynamics. The emergence of spacetime is then reinterpreted as the stabilization of definable differences, while the present is not given a priori but selected via delayed consistency over histories. Within this formulation, quantum phenomena arise naturally when multiple realization candidates coexist, producing interference structures governed by a variational principle. In the low-defect limit, the framework recovers effective relativistic geometry and field-theoretic behavior, including emergent gravitational curvature and gauge structures. A central contribution of this work is the formulation of a unified definability action, combining stabilization, curvature minimization, delayed consistency, and informational structure into a single variational framework. Under appropriate coarse-graining, this action yields structures consistent with Einstein field equations, quantum amplitudes, and gauge invariance as different regimes of the same underlying mechanism. This paper does not claim a fully closed mathematical unification of all physical sectors. Instead, it provides a coherent structural framework in which spacetime emergence, present realization, quantum probability, and effective field dynamics are organized as manifestations of a single principle. The framework is intended as a foundational step toward a deeper unification of physics, where time, geometry, and probability are not assumed, but emerge from the stabilization and realization of definable relational structures.