Wave Dynamics and Unified Mathematical Description of Graviton Fluid Medium Based on FQ Theory

General relativity interprets gravitational waves as geometric perturbations of spacetime metric, electromagnetic phenomena are described by Maxwell’s field equations, and matter waves in quantum mechanics are defined as probability amplitudes. These three categories of wave phenomena belong to mutually incompatible ontological paradigms. As the tenth sub-paper of the FQ Unified Field Theory series, this paper establishes a unified medium wave dynamic framework by postulating that vacuum is a compressible graviton fluid with intrinsic background pressure P_0 and intrinsic number density ρ_0. All wave effects are essentially pressure-density perturbations formed by momentum transfer between microelements of the graviton fluid, in which fluid microelements only oscillate locally without macroscopic long-distance migration. In this paper, the continuity equation and momentum equation of fluid mechanics are linearized under small perturbations around the equilibrium state, and the three-dimensional d’Alembert wave equation is derived. The intrinsic wave speed relation c=√P_0/ρ_0 is directly emergent from the medium constitutive relation. This paper distinguishes the energy attenuation laws between two-dimensional interfacial waves I∝ 1/r and three-dimensional spherical body waves I∝ 1/r^2. Gravitational waves, electromagnetic waves, and matter waves are not fundamentally independent physical entities, but three types of perturbation modes of the same graviton fluid under different excitation scales and boundary scattering conditions. In the weak-field limit, this model reproduces multiple well-verified observational results including the constancy of vacuum light speed, the consistent propagation velocity of gravitational and electromagnetic waves verified by GW170817, the inverse-square attenuation of spherical wave flux, interference and diffraction effects, and gravitational light refraction. Meanwhile, three falsifiable physical predictions are proposed to distinguish the FQ fluid model from mainstream theories under strong-field and strong medium perturbation conditions. This work completes the dynamic branch of the FQ Unified Field Theory and forms a closed logical system with previous studies including the metric equivalence proof, magnetic scattering mechanism, and primitive orbital solution. 摘要 广义相对论将引力波诠释为时空度规的几何扰动,电磁现象依托麦克斯韦场方程描述,量子力学中物质波被解释为概率幅,三类波动现象分属互不兼容的本体范式。本文作为FQ统一场论系列第十篇子论文,以真空为具备本底压强P_0、本底数密度ρ_0的可压缩引力子流体作为基础公设,建立统一的介质波动动力学图像:一切波动效应,本质是引力子流体内部微元之间动量接力所形成的压强‑密度扰动,介质微元只做局域振荡,不发生宏观长程输运。 本文对流体连续性方程、动量方程做平衡态附近的小扰动线性化,推导出三维达朗贝尔波动方程;由介质本构关系直接涌现波速关系 c=√P_0/ρ_0。区分二维界面波能流I∝ 1/r与三维体球面波能流I∝ 1/r^2衰减规律。引力波、电磁波、物质波并非三种完全独立的本体,而是同一引力子流体在不同激发源尺度、不同边界散射条件下的三类扰动模式。 本模型在弱场条件下可以复现光速不变、GW170817观测得到引力波‑电磁波传播速度一致、球面波流量平方反比衰减、干涉衍射、引力介质折射偏折等已被证实的观测结果;同时提出三组可证伪物理预言,用以在强场、强介质扰动条件下区分FQ流体模型与现有主流理论。本文完善FQ统一场论动力学分支,与压差‑度规等效性证明、磁散射机制、原生轨道解等前置工作形成完整闭环。