We introduce the Phase–Coupled Field (PCF) framework: a real scalar field theory in which physical coherence is elevated to a fundamental primitive. A single real phase field ϕ(x), together with its coherent energetics and an explicit dissipative coupling to a thermodynamic conjugate field Θ(x), generates wave-like coherence, decoherence, irreversibility, and the emergence of classical behaviour within one unified action principle.The formalism is variationally grounded in the revised Coherence–Action Principle (CAP v2) and incorporates dissipation through the Thermal Influence Term (TIT). The result is a fully relativistic, coherence-driven field theory capable of describing microscopic interference, macroscopic order, thermalisation, and classical emergence without recourse to Hilbert space.
We introduce the Phase–Coupled Field (PCF) framework: a real scalar field theory in which physical coherence is elevated to a fundamental primitive. A single real phase field ϕ(x), together with its coherent energetics and an explicit dissipative coupling to a thermodynamic conjugate field Θ(x), generates wave-like coherence, decoherence, irreversibility, and the emergence of classical behaviour within one unified action principle.The formalism is variationally grounded in the revised Coherence–Action Principle (CAP v2) and incorporates dissipation through the Thermal Influence Term (TIT). The result is a fully relativistic, coherence-driven field theory capable of describing microscopic interference, macroscopic order, thermalisation, and classical emergence without recourse to Hilbert space.
The Phase–Coupled Field (PCF) framework and its Coherence–Action Principle (CAP) describe quantum, gravitational, and macroscopic physical behavior through phase-coherent field structures. While CAP formalizes the coherent dynamics via phase gradients, twist interactions, and misalignment terms, it lacks the dissipative channel needed to model decoherence, entropy, and irreversibility. This work introduces the Thermal Influence Term (TIT), a dissipative conjugate field \Theta(x) coupled linearly to the coherence gradient \nabla\phi. Defined variationally through the dissipative Lagrangian contribution \mathcal{L}_{\mathrm{diss}} = -\gamma\,\Theta \cdot \nabla\phi, TIT provides the missing microscopic mechanism for coherence degradation and entropy production. This term completes CAP, establishes the coherent–dissipative dual structure required by the Nonlinear–Schwartz (N/S) operator, and links phase-field physics to thermodynamic and chemical behavior. TIT is a load-bearing component in the CAP/PCF/GMM framework, enabling a unified description of coherence, dissipation, and emergent classicality.
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.
Physical theory remains fragmented across classical, quantum, thermodynamic, and gravitational regimes despite deep mathematical overlap. This work proposes phase coherenceas a primitive organizing principle governing physical evolution. By formalizing dynamics as extremization of a global coherence functional over admissible phase states, classicalequations of motion, unitary quantum evolution, thermodynamic irreversibility, quantumnonlocal correlations, and probabilistic structure emerge without independent postulation.Gravitation is reinterpreted as curvature of a coherence metric rather than a fundamentalforce. The framework is explicitly falsifiable and forbids objective wavefunction collapse,fundamental time asymmetry, and point-like graviton degrees of freedom.
This paper introduces the Entropic I-Field Theory, a fundamental framework that establishes irreversibility as a physical principle rather than an emergent property. We propose a universal scalar field—the I-field—that couples dissipatively to all matter and radiation. By breaking time-reversal symmetry at the fundamental level through an extended Euler-Lagrange-Rayleigh variational principle, the theory preserves causality and conservation laws while introducing intrinsic directionality to physical evolution.The framework replaces purely unitary quantum evolution with non-conservative dynamics in which the I-field coupling introduces dissipative terms into the equations of motion. Through numerical validation across quantum, chaotic, and thermodynamic systems, we demonstrate that the theory provides unified solutions to foundational paradoxes: the quantum measurement problem is resolved through objective I-field-mediated collapse, thermodynamic irreversibility arises from fundamental symmetry breaking rather than statistical coarse-graining, and the arrow of time emerges from field dynamics rather than initial conditions. The theory makes testable predictions accessible with current technology: temperatureindependent decoherence at ultralow temperatures, universal noise floors violatingfluctuation-dissipation relations, modified atomic energy levels proportional to I-field strength, and measurable time variation of fundamental constants. These predictionsdistinguish the framework from standard physics and provide experimental pathways for falsification. If confirmed, this would establish irreversibility as a fundamental interaction encoded in the Lagrangian rather than an emergent statistical phenomenon.
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.
Abstract This work proposes a conceptual connection between phase coherence, the principle of least action, and entropy within a discrete spatial framework. Space is interpreted as a lattice of elementary phase-supporting units, where physical processes occur through phase propagation and closure. Coherent phase evolution corresponds to minimal action and stable transport, while the loss of phase coherence leads to an increase in accessible microscopic configurations and thus entropy. The framework suggests that macroscopic irreversibility may emerge from the progressive breakdown of microscopic phase alignment. Triadic phase propagation, characterized by three equivalent directions separated by 120°, naturally generates hexagonal spatial connectivity and enables phase-cycle closure. This provides a unified geometrical perspective linking quantum coherence, transport processes, and thermodynamic behavior.