[MST-EUT Theory Series #22] Deriving Planck's Law from New Relativistic Field Equations - MST-EUT從新相對論場方程推導黑體輻射 (v1.0-zh)

This document constitutes Series #22 of the MST–EUT Theory Series and presents a first-principles derivation of the blackbody radiation law from the new relativistic field equations of the Mass–Space–Time Entanglement Unified Theory (MST–EUT). The derivation does not assume Planck’s law, photon gas statistics, or quantized oscillators as axioms. Instead, the spectral form of blackbody radiation emerges from the intrinsic structure of vacuum field modes, relativistic invariant measures, and topologically quantized closed entropic flows. This work establishes blackbody radiation as a structural consequence of the MST–EUT vacuum dynamics rather than a phenomenological postulate. 本文為 MST–EUT 理論系列第 22 篇,從 MST-EUT 所提出之新相對論場方程出發,完成黑體輻射定律的第一性原理推導。推導過程不預設普朗克定律、光子氣體統計或量子振子模型,而是由真空場模態的內在結構、相對論不變測度,以及封閉熵流的拓撲量子化條件自然湧現出黑體輻射的譜形。本文確立黑體輻射為 MST-EUT 真空動力學的結構性結果,而非經驗性假設。