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.
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.
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.
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.
The Quantum Blueprint Formalism (QBF) proposes that the coherence of living systems arises from dissipative quantum field dynamics projected onto a finite-dimensional manifold of biologically meaningful order parameters Θ = (θ1, θ2, …, θ12). In this paper we derive, step by step, the macroscopic evolution equation for Θ(t) starting from the doubled Liouvillevon Neumann equation of dissipative quantum field theory (DQFT) in the sense of Umezawa and Vitiello (Umezawa, 1967; Takahashi & Umezawa, 1975; Celeghini, Rasetti, & Vitiello, 1992). We show how the doubled Hamiltonian H_total = H − H̃ acting on the tensor product state |Ψ> = |ψ> ⊗ |ψ̃> generates non-Hermitian dynamics, unitarily inequivalent vacua, and a geometrical manifold of coherent states parameterized by Θ. By applying a Mori–Zwanzigtype projection (Mori, 1965; Zwanzig, 1961) onto this manifold, we derive a generalized Langevin-like equation for θk(t) with a drift term, a dissipation term, memory kernels, and a noise term, and we identify the contribution of the conjugate sector ψ̃ as an informational recursion term. The order-parameter manifold is endowed with a metric g(k,l)(Θ) and a curvature scalar R(Θ), obtained from the vacuum overlap structure, which together define a dynamic vacuum geometry in which biological adaptation, stress, and self-restoring coherence can be interpreted as geometric flows. The final macroscopic dynamical law defines the core of QBF and provides a rigorous bridge between microscopic dissipative quantum dynamics and the emergent coherence behavior of living organisms.
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.
The foundations of modern theoretical physics rest on the interplay between quantum dynamics, thermodynamics, and spacetime geometry. While quantum mechanics describes microscopic dynamics through unitary time evolution, thermodynamic phenomena introduce irreversibility and entropy production. In this work we propose a unified framework in which quantum evolution is formulated on a complex-time manifold that naturally incorporates both dynamical and thermodynamic structures. We introduce a complex-time coordinate combining physical time and thermal flow and derive a generalized evolution equation from a variational principle defined on a complex-time geometric manifold. The resulting equation contains both Hamiltonian dynamics and geometric diffusion terms governed by the Laplace–Beltrami operator. This formulation provides a geometric interpretation of thermodynamic irreversibility within quantum theory and establishes connections with Euclidean quantum field theory, geometric quantum mechanics, and thermal time hypotheses. Possible implications for quantum statistical mechanics and information flow in gravitational systems are discussed.
This preprint develops a unified coherence-based formulation of physical time grounded in the χ–η–I invariant structure of the Aletheia framework. Across quantum, thermodynamic, gravitational, and cosmological regimes, the paper introduces a scalar coherence potential Ψ constructed from purity, entropy, and structural persistence, and proposes that the physical time increment satisfies the differential law: dt = –κ dΨ In this formulation, time flow is the measurable rate at which coherence is depleted through decoherence, coarse-graining, or environmental coupling. When Ψ is constant—as in globally stationary, Page–Wootters–style quantum states—no internal time elapses. When coherence degrades, time emerges as the bookkeeping of informational loss. The paper demonstrates that this temporal-coupling law naturally reproduces: Thermodynamic time in the macroscopic limit (dt ∝ dS), Quantum decoherence arrows in open-system dynamics, Proper-time–like behavior in weakly decohering or isolated systems, Cosmological time flow via mode decoherence in an expanding FRW universe. Explicit models including qubit dephasing, Lindblad oscillators, and cosmological field modes illustrate how temporal coupling unifies arrows of time across domains traditionally treated with separate frameworks. This formulation provides a coherence-theoretic bridge between general relativity, quantum decoherence, and thermodynamic irreversibility, offering an empirically grounded alternative to conventional parameter-time, thermal time, and entanglement-clock approaches.