The Dissipative Static Graviton Model (DSGM): Formulating Gravity and Cosmological Observables via Grid Thermodynamics/耗散靜態重力子模型 (DSGM):透過網格熱力學建構重力與宇宙學可觀測量

[English Abstract]

The fundamental mathematical distinction between the continuous geometric manifold of General Relativity (GR) and the discrete, probabilistic formalism of Quantum Mechanics (QM) presents ongoing theoretical challenges in formulating a unified framework. Concurrently, the standard cosmological model (ΛCDM) relies on phenomenological components---Dark Matter and Dark Energy---to address observational discrepancies at galactic and cosmic scales. This paper investigates an alternative framework, the Dissipative Static Graviton Model (DSGM), which postulates an absolute, discrete, Euclidean-flat Planck-scale graviton matrix. By modeling mass as a dissipative quantum state that continuously consumes grid gravitons, gravity emerges kinematically as a localized topological absorption gradient. We construct the microscopic foundation using an adiabatic PT-symmetric non-Hermitian Lagrangian, demonstrating that local unitarity and Ward-Takahashi identities are rigorously preserved despite secular mass evolution. Through tensor contraction and effective optical metrics, we derive the Schwarzschild momentum-reversal limit without requiring geometric singularities. By applying an effective field theory (EFT) ansatz for the sub-critical viscoplastic behavior of the quantum vacuum, the model recovers flat galactic rotation curves. Furthermore, mass dissipation necessitates a secular Variable-Mass Clock effect, reproducing Type Ia supernova time dilation and Tolman surface brightness attenuation in a static spatial background. Finally, the time-reversal of mass dissipation points to a cold Dirac-limit Grid Condensation Phase Transition, providing a purely geometric derivation of the Cosmic Microwave Background (CMB) acoustic peaks consistent with Planck satellite observations.

[中文摘要]

廣義相對論 (GR) 的連續幾何流形與量子力學 (QM) 的離散機率形式之間存在根本的數學差異,這為建構大一統框架帶來了持續的理論挑戰。同時,標準宇宙學模型 (ΛCDM) 依賴暗物質與暗能量等唯象成分,以解決星系與宇宙尺度的觀測異常。本文探討了一個替代框架——耗散靜態重力子模型 (DSGM),該模型假設了一個絕對、離散且歐幾里得平坦的普朗克尺度重力子矩陣。透過將質量建模為一種持續消耗網格重力子的耗散量子態,重力在運動學上湧現為局部的拓樸吸收梯度。我們使用絕熱 PT 對稱非厄米拉格朗日量建構了微觀基礎,證明了儘管質量隨時間長期演化,局部么正性與沃德-高橋恆等式 (Ward-Takahashi identities) 仍受到嚴格保護。透過張量縮併與有效光學度規,我們推導出了史瓦西動量反轉極限,而無需引入幾何奇異點。藉由將有效場論 (EFT) 擬設應用於量子真空的次臨界黏塑性行為,本模型自然地恢復了平坦的星系自轉曲線。此外,質量耗散必然導致長期的「可變質量時鐘效應」,從而在靜態空間背景中重現了 Ia 型超新星的時間膨脹與托爾曼表面亮度衰減。最後,質量耗散的時間反演指向了一個極冷的狄拉克極限「網格冷凝相變」,為符合普朗克衛星觀測的宇宙微波背景 (CMB) 聲學峰提供了純幾何的推導。