WP_021 Ontological Topology of Indian Schools: Advaita Vedānta, Vaiśeṣika Atomism, and the Quantized Geometry of the Brahman Field / 印度學派之本體拓撲學:吠檀多不二論、勝論極微觀與「梵」場域之量子化幾何

This paper serves as Working Paper No. WP_021 in the Global Ontological Isomorphism Network series. It reconstructs the foundational physics of classical Indian ontology by establishing a rigorous isomorphic mapping between Advaita Vedānta (Non-duality), Vaiśeṣika natural philosophy, and modern quantum field theory on discrete spacetime lattices. By applying lattice gauge theory, topological phase-masking, and non-linear quantum measurement theory, this study demonstrates that:1. Shankara's *Nirguṇa Brahman* (Unattributed Absolute) corresponds to a non-local, unexcited quantum vacuum ground state (\(|0\rangle_{\text{Brahman}}\)) prior to field quantization.2. The *Paramāṇu* / *Aṇu* (ultimate discrete particles) of Vaiśeṣika represent quantized lattice grid nodes (\(\ell_P \sim 1.6 \times 10^{-35} \text{ m}\)) and topological solitons emerging from localized field excitations.3. *Diś* (Space) and *Kāla* (Time) in Vaiśeṣika serve as continuous, active background metric fields (\(g_{\mu\nu}\)) rather than passive Newtonian containers.4. *Māyā* / *Avidyā* is formalized as a topological phase-masking and localized phase decoherence mechanism that obscures global entanglement entropy through local thermal noise (\(\Delta S_{\text{noise}}\)).5. Contemplative techniques such as *Neti-Neti* ("Not this, Not this") and Yogic mind-cessation (*Nirodha*) function as a systematic decoherence suppression algorithm (\(\hat{\mathcal{P}}_{\text{Nirodha}}\)) that collapses local boundary conditions and restores global phase coherence ("Ātman-Brahman Identity"). This work integrates into Module II (Holographic Geometry & Spacetime Emergence) and Module I (Monism & Quantum Vacuum Dynamics) of the higher-education curriculum architecture for world philosophy and quantum metaphysics. 本文為「全球本體論同構網絡」系列之 Working Paper No. WP_021。本研究透過建立吠檀多不二論(Advaita Vedānta)、勝論(Vaiśeṣika)自然哲學與離散時空格點上現代量子場論之間的嚴密同構映射,重構了印度古典本體論的物理學基礎。 透過應用格點規範場論、拓撲位相遮蔽與非線性量子測量理論,本研究證成: 商羯羅之「無相梵」(Nirguṇa Brahman)精準對應於場量子化前非局域、未受激發的量子真空基態($|0\rangle_{\text{Brahman}}$)。 勝論中的「極微」(Paramāṇu / Aṇu)代表普朗克尺度下的量子化格點節點($\ell_P \sim 1.6 \times 10^{-35} \text{ m}$),以及由局域場激發所湧現的拓撲孤立子(Solitons)。 勝論中的「方」(空間)與「時」(時間)充當連續且動態的背景度規場($g_{\mu\nu}$),而非被動的牛頓式容器。 「瑪雅/無明」(Māyā / Avidyā)被形式化為拓撲位相遮蔽與局域位相退相干機制,透過局域熱雜訊($\Delta S_{\text{noise}}$)掩蓋全域糾纏熵。 沉思觀照法門「非此非彼」(Neti-Neti)與瑜伽心至寂滅(Nirodha)被形式化為系統性退相干抑制演算法($\hat{\mathcal{P}}_{\text{Nirodha}}$),能瓦解局域邊界條件並恢復全域相位相干性(親證「梵-我同一」)。