**動態拓撲流變理論:****從點粒子的四重病症到弦的必然性** **A Theory of Dynamic Topological Flow: From the Fourfold Pathology of Point Particles to the Necessity of Strings** ---------- **作者**:Neo.K(許筌崴) **機構**:一言諾科技有限公司(EveMissLab) **日期**:2026年5月 **分類**:理論物理 | 數學物理 | 場論基礎 **字數**:約20,000字 ---------- **摘要** 本文提出**動態拓撲流變理論**(Dynamic Topological Flow Theory, DTFT),通過建立三條獨立的物理約束——完美圓不存在定理、三維曲率公理、無限交接論——並系統揭示點粒子模型在四個獨立層面上的內在病症,證明:**物理實在的最低基本單元必然是一維延展的動態弦**,而非零維點粒子。 核心論證脈絡:(1)**三條約束的獨立推導**——完美圓不存在源於測度論與動力學的雙重排除;三維曲率公理源於剛體配置空間 ![](data:image/png;base64,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)中純平移子流形的零測度性;無限交接論源於孤立無限的物理不可實現性。(2)**點粒子的四重病症**——零維結構違反曲率必然性、無內部維度承載動力學、量子場論的紫外發散是其本體論病症的數學症狀、無邊界結構違反關係性湧現。(3)**弦的唯一性定理**——在滿足三約束的所有拓撲結構中,一維延展物件是承載非零曲率的最低維度,Nambu-Goto作用量是覆蓋給定世界面的幾何極小值,弦因此是帕累托最優解。(4)**演化鏈的湧現**——多弦疊加產生波,多波交織產生場,場的拓撲流變湧現為時空,構成從一維結構到四維時空的完整生成階梯。(5)**統一詮釋**——重新詮釋弦論、量子場論、廣義相對論為DTFT在不同尺度的投影,並給出可證偽預測:引力波合併後階段的曲率調製(![](data:image/png;base64,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))、電子能級的弦振動分裂(![](data:image/png;base64,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) eV)、計算架構的拓撲流變優化。 本文的核心立場:**點粒子假設不是物理學的基礎,****而是物理學需要克服的歷史包袱**。從牛頓力學到量子場論,點粒子留下的紫外發散、自能無窮、奇點問題,都不是技術困難,而是本體論病症的數學症狀。一維延展弦不是「假設的模型」,而是滿足三大物理約束的**邏輯必然**。 **關鍵詞**:動態拓撲流變、弦的必然性、完美圓不存在、三維曲率公理、無限交接論、紫外發散、本體論病症 ---------- **第一章** **引言:****物理學的歷史包袱** **1.1** **點粒子假設的歷史路徑** 從牛頓的質點力學到狄拉克的點電子,**點粒子**作為物理學的基本概念已經統治了三百年。這個假設的方便性顯而易見:點粒子可以用座標 ![](data:image/png;base64,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)完全描述,動力學方程 ![](data:image/png;base64,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)簡潔到可以塞進高中課本。 但便利不等於真實。 當我們檢視點粒子假設在現代物理中的命運時,一個令人不安的模式浮現:**幾乎每一個基於點粒子的理論,****都在某個尺度上崩潰**。 **理論** **點粒子假設** **崩潰處** 經典電動力學 點電荷 自能發散 ![](data:image/png;base64,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) 量子力學 點電子 不確定性 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAcCAMAAACppkqwAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjqQOmaQOma2OpCQOpC2OpDbZgAAZgA6ZjoAZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kJC2kLbbkLb/kNvbkNv/tmYAtmY6tmaQtpBmtra2trbbttvbttv/tv//25A625Bm27aQ29uQ29v/2//b2////7Zm/7aQ/9uQ/9u2//+2///badHayAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABm0lEQVRIS+1U23aCMBAkeEkvWrHU1tRejNVWUluhwfz/pzXJbgKI9NBHzyEvhOzu7MxsIAi61TnQOXA+DnAy9GQPt8sqcT5I/1ByIqo2tQLFot0LogiNp9aUhPdwIGl41LHc7mT0k/afq5wO03CGXRWbB4pN0kCQuU0Sk2nUrKAhmi/I6KOo+qG9xL1lbnsAXO0YuJDHWsnqSI2LqgWZ5zEpM9nF4ezboYrBl4tylySpVZANA3mhPVJvexatHqBCOBYuut7ym6fUH0NWHvvp8atxary3hLErt3MHx+AKCM/QIRVRxcaaTFlfWYFFAEBoYzbXdiPNA/G8e0ihHLUqCwVHMzBRQwYIA/4YGlnHwC21qF2nIpqZu4dKA3OLkCegGWry0szZkcw0vtSi4dRWqsdXFkkcAtSVoryfqBVORm38cFGrcScb7N+RsJOuyQsCq5fw/lK/oS6sK6KK3VEy2nrvqhv9mekGVCNYJw1ji2rcabmwELKxXCPU/gF+xC1xfZoZQYvlR9wit5rCw8pwmurr9/DfnbqCs3PgF9n4KzkbDhTqAAAAAElFTkSuQmCC) 量子場論 點相互作用 紫外發散,需重整化 廣義相對論 點質量 奇點 ![](data:image/png;base64,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),曲率發散 標準模型 點夸克/輕子 質量等級問題,真空不穩定 這些不是孤立的技術困難,而是**同一個本體論病症的多重表現**:當你假設物質的最終單元是零維點時,動力學、場論、幾何都會在那個零維極限上失效。 **物理學家的應對**:重整化(把無窮藏起來)、正則化(規定一個截斷)、有效理論(承認它只在某尺度有效)。這些都是技術修補,不是根本治癒。 **1.2** **弦論的早期動機與路徑依賴** 二十世紀七十年代,弦論作為強相互作用的候選理論被提出,後來轉向量子引力。**弦論的引入動機是技術的**——它能消除某些發散,自動包含引力子,提供統一框架。 但弦論的**本體論基礎一直是薄弱的**。它的標準介紹通常是:「假設基本粒子不是點,而是一維振動的弦——這個假設能解決很多問題。」 問題在於:為什麼是弦?為什麼不是膜、不是點、不是其他什麼結構?標準回答是「數學一致性要求」(無反常、模不變性),但這仍然是**技術論證**,不是**本體論必然**。 本文的目標就是填補這個空白:**從獨立的物理約束出發,****證明弦不是假設,****而是必然**。 **1.3** **本文的方法論** 我們不訴諸任何超驗的形而上學,也不訴諸任何啟發式打分系統。我們的論證**完全基於三條獨立的物理約束**,每一條都有獨立的數學基礎: 1. **完美圓不存在定理**(測度論 + 動力學) 2. **三維曲率公理**(剛體配置空間理論) 3. **無限交接論**(關係論 + 邊界算子) 從這三條約束出發,我們將證明: - 點粒子在**四個獨立層面**上違反或引發病症 - 一維延展弦是滿足三約束的**最低維度結構** - 高維結構(膜、體)雖然滿足約束,但作用量不是極小 論證的力量在於**每一步都不依賴其他步驟**——三條約束獨立成立,點粒子的四個病症獨立發生,弦的最優性獨立可證。即使讀者拒絕其中任何一個,其他論證仍然站立。 **1.4** **本文結構** 第二章建立三條物理約束。第三章診斷點粒子的四重病症。第四章證明弦的必然性與唯一性。第五章建立從弦到時空的演化鏈。第六章提供與弦論、量子場論、廣義相對論的統一詮釋。第七章給出可證偽預測。第八章是哲學結語。 ---------- **第二章** **三條物理約束** 本章建立DTFT的三條物理基石。每一條都將獨立推導,不依賴其他兩條。 **2.1** **完美圓不存在定理** **2.1.1** **定理陳述** **定理 2.1**(完美圓不存在定理,TCGCT) 在三維物理實在中,維持曲率嚴格恆定 ![](data:image/png;base64,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)的閉合曲線在概率測度意義下不可實現: ![](data:image/png;base64,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) **2.1.2** **證明:****測度論路徑** 考慮三維歐氏空間中的閉合光滑曲線 ![](data:image/png;base64,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),參數化為弧長 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAcCAMAAABrlg40AAAAAXNSR0IArs4c6QAAADxQTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6Oma2OpC2ZrbbtmYAtpA6ttv/25A627Zm2////7Zm/9uQ///bqaogwwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOUlEQVQYV2NgGBjAw8bIyCHAwCDIxMvAzwp0gxA7F9Ql/GzMvBCmMDcLSAknAwMfiMEP1AOTooarAYDSAT45LsRTAAAAAElFTkSuQmCC)。曲率函數 ![](data:image/png;base64,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)是定義在 ![](data:image/png;base64,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)上的非負函數。 完美圓的條件是 ![](data:image/png;base64,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)為常數,即曲率函數位於常數函數子空間 ![](data:image/png;base64,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)。 關鍵觀察:![](data:image/png;base64,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) **是無窮維函數空間** ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAcCAMAAABbGh8VAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADpmAGa2OgAAOgBmOjpmOjqQOma2OpDbZgAAZgBmZrb/kDoAkDo6kGYAkGY6kNv/tmYAtpBmttv/tv//25A627Zm2////7Zm/9uQ/9vb//+2///b5aAaagAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeElEQVQoU82QUQ6DIBBEZ7WKWq2oqFCl7P1PKdCmkXgB5/Nl8mazwN1iBT3Tm3hQrusTZiuNuY2IF0H0ULDNBlNGIosV78wj3zKxNecacC8NL2IZXFb8jftv0YRSEpZReI7rvrOnsLwgP7jiMyacJyKq1d3+fb3nAEmXBZLUW3xXAAAAAElFTkSuQmCC)**中的一維子流形**。 在Wiener測度或任何合理的物理機率測度下: ![](data:image/png;base64,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) 低維子流形在高維函數空間中測度為零。任何隨機選取的曲線(或從動力學演化得到的曲線)幾乎必然有 ![](data:image/png;base64,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)。 **2.1.3** **證明:****動力學路徑** 即使初始條件落在 ![](data:image/png;base64,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)中(已是測度零事件),四個獨立機制保證系統會偏離: (a)**測量誤差**:任何物理系統的曲率測量都有誤差 ![](data:image/png;base64,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),在量子尺度不可消除。 (b)**執行延遲**:維持 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmADpmAGa2OgAAOgA6OgBmOjo6OpDbZgAAZjoAZrb/kDoAkDo6kLaQkLbbkNv/tmYAtmY6tpCQtv/b25A62////7Zm/9uQ//+2///bi/vN+QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAR0lEQVQoU2NgGHggzMjFICPCJMTAIM3NK8MvCHKRFIcAO1AACCQZOdl4wSxhVhk+VhBDho+LQZxZTFSCQQqoSJqHBaKSmgAAKV0CmxhkioMAAAAASUVORK5CYII=)恆定需要連續的反饋控制,信號傳遞速度 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAcCAMAAABMOI/cAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADpmADqQOgAAOgA6OjoAOjqQOmaQOma2ZgAAZrbbZrb/kDoAkDpmkGY6kLbbkNv/tmYAtmY6ttv/tv//25Bm27Zm29v/2////9uQ/9u2/9vb//+2///bz13ypwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAb0lEQVQoU2NgGPFAQZJLGksgyAoycUthiCtIcrAIYaqWE2XjEkMWlhVkZGQWZ1DgZxFHUS3Pwy0twwm0D12HCCvcESh2yPPwoZoLc5UMuzCqO2D+kOfhZZAVQLUWolKCjZEF5EoFfkYoQFg6BJMBANGYBZuOFXh0AAAAAElFTkSuQmCC),延遲產生偏離。 (c)**非局域耦合**:任何曲線都受周圍場的影響,場的漲落 ![](data:image/png;base64,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)導致曲率擾動。 (d)**外場缺陷**:任何外場(引力、電磁)都不是嚴格均勻的,差異性梯度誘導曲率變化。 **結論**:即便在零測度集 ![](data:image/png;base64,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)中起步,系統也會在 ![](data:image/png;base64,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)內離開。 **2.1.4** **物理推論** 完美圓不存在意味著: - **任何閉合曲線都在曲率上動態流變**:![](data:image/png;base64,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) - **靜態幾何結構不是物理實在**:所有"靜止"的形狀都是統計平均 - **曲率漲落是基本的**:![](data:image/png;base64,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) 不可消除 **2.2** **三維曲率公理** **2.2.1** **公理陳述** **公理 2.1**(三維曲率公理) 在三維物理實在中,**不存在零曲率的線性位移**。所有運動本質上都是非零曲率的旋轉、螺旋或彎曲軌跡。 **2.2.2** **證明:****配置空間路徑** 考慮剛體在三維空間中的配置空間: ![](data:image/png;base64,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) 這是一個**六維流形**,其中 ![](data:image/png;base64,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)描述質心位置,![](data:image/png;base64,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) 描述方向(三個旋轉自由度)。 **純平移子流形**定義為旋轉自由度凍結的子集: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAcCAMAAACanVW5AAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OpDbZgAAZrb/kDoAkNv/tmYAtv//25A62////7Zm//+2///bfnLChQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOElEQVQYV2NgoDrgY2RkBxkqxMXKD6IFOTjBdggwcYNpPoiwEBcbmAuXZuYF83lYwDTQFIg8ZQAAhVoBQIkaOqEAAAAASUVORK5CYII=)是 ![](data:image/png;base64,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)的單位元(無旋轉)。 關鍵觀察:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOpDbZgAAZjqQZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///binnyqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQoU2NgoCsQ42YEAyZ+BlEOfnE+NgZRTkEGES4GMW5eBjEeYZBjRICSUCDEChYBAnE+LpigKDsvjCnCLAiTF2CBMQUYGdlo6ikAcpkCY3pZIIkAAAAASUVORK5CYII=) **是** ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AABmADo6ADpmAGa2OgAAOjpmOpDbZgAAZgBmZrb/kDoAkGYAkGY6kNv/tmYAtpBmttv/tv//25A627Zm/9uQ/9vb//+2///biBcLsgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAT0lEQVQoU2NgoDeQEmJnZGQRAForxcsqzCDGBGIKMoswMEhyAwlxdh6Yi0RBgmAgxcsGE5Tk4oQxpXjhTKABwgwSfGC+FD8jIyMHyFQaAQB20wKKnxQsPgAAAABJRU5ErkJggg==)**的三維子流形,****在六維流形中具有零測度**: ![](data:image/png;base64,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) 這意味著:在配置空間的所有可能態中,純平移態構成零測度集。**隨機選取的物理態幾乎必然包含旋轉成分**。 **2.2.3** **證明:****內稟曲率路徑** ![](data:image/png;base64,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)作為李群,具有非零的內稟曲率(關於雙不變度量): ![](data:image/png;base64,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) 這意味著:![](data:image/png;base64,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) **不是平坦空間**。任何在 ![](data:image/png;base64,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)上的軌跡都會經歷曲率效應。 由於物理運動必然涉及 ![](data:image/png;base64,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)自由度(無法將其凍結到零測度集中),所有運動都在曲率非零的空間中發生。 **2.2.4** **證明:****量子物理路徑** 即使試圖在經典極限下實現純平移,量子不確定性禁止之。對於任何剛體: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAcCAMAAABf788oAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6ADqQAGa2OgAAOgA6OjqQOmZmOmaQOma2OpDbZgAAZgA6ZmZmZpC2Zrb/kDoAkNvbkNv/tmYAtpCQtrbbtrb/ttuQ25A627aQ2////7Zm/9uQ/9u2//+2///bwrXMWAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZ0lEQVQoU9WPSRaAIAxDC86KA4IDAsL9T6mwwbp1ZZZ5yU8L8CMpQjp0rueZRoZjOAC2FPhB9WqAzHHAsQkbEWHbZAbEydOQZeQWDUOKClM86m5T9XggnqnQycs+9POaEp43WkbWZ13nIQR3+LehIgAAAABJRU5ErkJggg==)是角動量,![](data:image/png;base64,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) 是旋轉角。要凍結 ![](data:image/png;base64,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)(![](data:image/png;base64,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)),需要 ![](data:image/png;base64,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),在能量上不可實現。 熱力學進一步保證:在溫度 ![](data:image/png;base64,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)下,旋轉自由度的熱漲落: ![](data:image/png;base64,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) **結論**:純平移在經典、量子、熱力學三個層面都被禁止。三維物理實在中,所有運動都帶有非零曲率成分。 **2.3** **無限交接論** **2.3.1** **命題陳述** **命題 2.1**(無限交接論) 孤立的無限不存在於物理實在中。極限不是對無限的外在約束,而是**多個無限域關聯時的內在湧現**。 數學形式化: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAcCAMAAACAobU3AAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOma2OpDbZgAAZgBmZjo6ZrbbZrb/kDoAkDo6kNv/tmYAtmY6trb/ttu2tv//25A627Zm2////7Zm/9uQ//+2///b/0RplQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAX0lEQVQoU2NgGDAgycHIyAq2XU6Qj0FOgB/MluUVYpBmEoK7SoJFCs4WhigHK+PmgrNl2JGUM4sDjQPyRbjkBGDKpdkYOaWAWhDaGSQQ2hlEENplecREEVYgWU1sKAEABB4D2yHbQmkAAAAASUVORK5CYII=)是無限域,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OmaQOma2OpDbZgAAZjoAZjo6ZpDbZrb/kDoAkNv/tmYAtmY6tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bjJ6cCwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZUlEQVQoU82OWRKAIAxDIy6o4AaIIsL9j2npeAbH95NM22QK/IBzrggxBCC7JeRtxa3bgDQbxN4Avt75TVZPm4LtgEOu7JOmgoYuCxTx4vUlkrQqY6fyRhErTFxwyWqkmjSxfMMDHP0EskSXFV8AAAAASUVORK5CYII=) 是關係算子(交集、態射、場疊加),![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OpC2OpDbZgAAZjoAZrbbkDoAkJA6kNv/tmY6tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2///bxXy1cgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQoU2NgoCUQYWdkFQdZIMgpLsXNBrNKGCIIBBCWGA8jCz+IJcHIywBWJ83HBSUkOQQYGMCEBLMQVAOIK8oEFGJgANrAAmZQGQAAsFcDQui/g0AAAAAASUVORK5CYII=) 是邊界算子,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmAGa2OgAAOmaQOma2OpDbZgAAZma2Zrb/kDoAkDo6kGZmkLbbkNv/tmY6ttv/tv//25A625Bm2////7Zm/9uQ/9u2/9vb//+2///bQOvNegAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUElEQVQoU2NgoDuQ5GVkEgDbKsPDISPILgZiikOFgEwRZmGom2R4WGCuk+bkgDHF4fIMgtwgQVFuBqCZjGxCDBJcDAx8/AxSgqyMbGBjaQIAadIClGlJ6XAAAAAASUVORK5CYII=) 是湧現的極限結構。 **2.3.2** **物理動機** 考慮數學中的抽象無限符號 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAcCAMAAABmiH5zAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmAGa2OgA6Ojo6OjqQOma2OpC2OpDbZgAAZgBmZjoAZpDbZrbbZrb/kDoAkDo6kGY6kNvbkNv/tmYAtmY6tmZmttvbtv//25A625Bm27aQ2////7Zm/9uQ//+2///behgaCwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAXElEQVQoU9WOWRKAIAxDgxsKrrivgNz/jhbGQ2g+Mk0zfVPgj3IDizp4b/37s9BuHVWyXdkE3NVOVsfkhwRsrgGnaIJJ39awgqJvsQhtS3kSrafbwGxoy3kgf0IPvbgFCmXx+i0AAAAASUVORK5CYII=)。它在物理中對應什麼? - 無限大的能量?![](data:image/png;base64,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) 在任何物理系統中違反熱力學第二定律或宇宙能量約束。 - 無限長的時間?![](data:image/png;base64,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) 受宇宙年齡與熱寂約束。 - 無限小的尺度?![](data:image/png;base64,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) 在普朗克尺度被量子引力截斷。 - 無限多的粒子?![](data:image/png;base64,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) 受可觀測宇宙的全息熵界限制。 **孤立的無限沒有物理實現**。所有"無限"都在某個關係結構中浮現:作為極限、作為對偶、作為邊界。 **2.3.3** **數學形式化** 設 ![](data:image/png;base64,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)為兩個無限域。定義它們的**關係交接**: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARoAAAAcCAYAAAC+nXATAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA2TSURBVHhe7V2/cyLHEu6hLpdzUpaAI9VVHTjngRK94OEqEiKBoydcZRIXDx2YjODQiwxOTMKrUyRXHWDlBlcZhzoFQKr89A/svK9nWVhgF3b5IV25dqsuEDvbM9M90/P11z32q0qlQv7ja8DXgK+BY2rg1TGF+7J9Dfga8DXAGvAdjb8OfA34Gji6BnxHc3QV+x34GvA14Dsafw34GvA1cHQN+I7m6Cr2O/A14GvAdzT+GvA14Gvg6BrwHc3RVex34GvA14DvaPw14GvA18DRNbC3oylnTmQ+e0OR9oCeOlVx9BFv6SBzciezD2kqFS9p9EzjKZczsp/PUq01pGGsQZPBJXWqC108p45eYv4vbfMvsf9ntflXd3r2U1rwmk+FKFCpVuVL6SSDsYQvh+JtLEelX36ipCYCVYxn7mgypyeyXruh1nC4MsYYxXJpajeXNw834kUdz+LdYLC0sTKnjzJba9FcVK5HleBoJyfkVVbnKSEGRcK44pRuD+RzOL9+XqPUfY56k4FybnAycx066ehYC+G55+/VPoec9yH6LmOtitQ9NWC7Q62VZ7f550RgUBQ61rxotAd6oVx+MWfTwVh02db734bFWZjoo/6TXsZ4Xpmncf2kTUWcxE2a0nVco4eSpOCoKsqZU5nXUqTdE07qsjRPavbYcS1KJblwQCzrOp6l+mmbEomgGAz4b8g6TxKNRp7W2D6yqp0nMShFpdDy1JNNObKgC0+DcNG4XIZ+4EJzveYagrLTkQuRezfxOn9l42xt/ZCxQWfm4Paxz1wGNnn89pwSNoeQQgT1MBWbyaVDjL89RN97K9lBwMvZ/HNg8J+oHtDyoqc39dSOzga61af9usjeRhS4CBEpROJFX9VqJ1D+vqHHWpfi1/5PdJZSlcETuoUTiRRDyqCsqJthjNIa0RN8Q7UzEsVGTLYKD2hpPIah0aAxoeVNPKEHvI9oIfUt9etUgKzGTJaXwfK49pKVLFIjplHtukgJbx17az0dE9RH0ZWvnHXkTfzOrV3O39gYWAmwZSXRWUGdT7wmHIawp31YKsaYrmlUwHFgRbzGmAoU7ck1J2MM5gB976xY5w9f3Ob/KNL7WJhq//2eqIBN5+EaYznzRr+u/yiEuEMEU6J2MbmTk5lrJ6RhTwgyPdSranUkgokEw0bVZtq9oSGalODKljBILEIYuvHbtEvKGbXhUDoLxa/JGmMLxtJ0BlmWZq5MvK8seFWRScdk4aaL0G6BxKydmwujsBotro5ww8lOofCak5kp0lZHylErBJECgoATnkH208c7mWrxft8M4Y12QyyG3hwJnD5eqW8Bq+Yhqpv581j69YLBK13yQePKNKrRvvYxZHREedCTD/EU3cHZMLKxOhlG1HYjOkTf7me63JIphmwNOlNrJgaVt4H8Zw7aYV/sY/M3j3d6sjUUbO9hKxXAJWj55vEKv2EX4zea/TbTZyDzzVv9uw89MZaXukbljWhkjl5Ac1zd5ahRahM1Q4EEEEynszkC4W+v81lRwFo0Hqzl8e/wb8II26YTHMBv6V/sNPCskcGTB3wIj2YiFRUHp4aYk4WHmTzYO6MV6ylZ0ZLDqeTN1LvICoWBM4YLJLbaIy90SlRwkm8by6aTXaNIjOhmPKWgVYyDjoxQtYswdUIRoMKb7pRKcB635204iY4wHb7diMpY5PnTAU0icdIKtwhbjbAw2exRrlUDKk3C8S8WyLb5G472CmfB2d422sU+psNqwtnklbNpyEcgGUZXTk7GTi+79r3N6qvvDT4Ho+xNKAHnwntDS2X5cDC4wAPbvPzmKz0vB4LtHYa9e7rUU4ICkt5Q7ucfKfJ9kgpNYAYL6jRtPsXPYbhpO1BTzmT0fj0r4uIKe71BpbZUJPITHETFBcMBukDPB8Li/uIjTWRqjnye/vfjor/JJ+UjfgDIYFSz5GhMvoEoRRiCQj1XYI8bE7lElE1nSGWOcGwsZsqK7RY3LUncWZYWgZ+9IfiA4z3w3IY/XYaATjpSzg0eaVTtkEJcgLg1bCxeuNsGWR09iSBVKZRJy1jBMi8O33A4BFezbC7nP8QYMIX1OHwTkrMMdmf7zGQwQmm2GypcajEqe9quC7P7ffvepvPlfuCUYaunma1CSr8cOBvPoW1e/fNzwLD3N/rb7z4ItY5507G9L0rUCgM9AOEszSH0mt6KD8aan6EJ63uFROJhcRN9T205mDsJD1EW9fMp+vmiSxJoqhN04G+019DNB/q1PwVHo60gGsU3GHD+rMunJg6XdnM3Nn4mK424yRpeuTXsUrtDylraIAbXtGvopE44jRcfwhgHmL9pvur04TAVYcvIQ9hihGtDegBpxiiqX3+gNFKbVjTjRc+8eRK2m3sTkrP0sKd9DGfBPFGDcgUgG5xs9uOxmdWefbvWU/+WWoTMotVWCsEQpV0LIZhuB5ub9p7BlN9yn2Dvf9NwBc24GYYiattjPQxEg8CHEY1eKpZdp8UNNCOElGfcnX4FRMJPrqsjipuFTfi72vkc+L0b1b8+C4vY+7G+hGis/EzosqSMztB+a2RhZ38brscIw4gh/wqJvFlFq7yRIQfpc3wWA/SzS727VPpeoVN1FBRyAtgPMtXT5sDgVNiC2ht+vCIuRgDnOZKp2z7JIsKpbmYdzbhQAKOr0yjJITxWYinuc/Gx1c/sYWvlZBA23c+cXXnCyEajx95EzrmPDcM51tpY7VKhFQulwO/7tyDGgPrccpC72rxa/TPwzwvSk7e/CX0y1r/tFqmloV6m4i0bZM6p2ukEKJigAdLQKsOUZTCd009KRSokQ5tT40Dwn8C9LPExLPgvhE1/LbRWznylfx2+E68/juGAtMArJhdrkTYhs420NsdsBj/DoRov5lYhS2nEoJd0TfnuGQVx8tnF/vOiNRtZxrs6TU4jkMq5JMuAZhmsm/TiVN0oizMS2RPAPkmhaZ94k9fPL5f5EVO8Sy7J27ZaaQ12nTmaBYA23m/iR8z0LLXb1Lg3eJoBp3Mn0C9guUlSW3WyOkZNEUO3lK9HkAJ2IHJdzD9ZbFBMOcqebF+up5LtdLOrrVdlmfO8t9hepeZnzgb8MJzNMiF8sLXhwegml0XRMWXKZRlCCUj/OkupK0b/i/KOY9o89DpG4sMtfTuzNzLPVmpmMZvpJ/pDGsmcbQ+jG8bECfCUA5V1gsdJkX5nZp3A26yltrHeX9MfQNOIzXAgOD4mR5MMoWQGHE3yPEo1xFCMopjZnqi6BYMRUiTjfYqZZLrBu7a5oG1if5VBOI9KO1kGLxGkskaytm32eL9RFhYikmQq7coLIAIOKexQpuOGS3IxnC1N7DkacuBHOEMk4o8ISY3sksnTxB9m+nVBxi0c2T0qspuORK6b+RsbG6gMdTQaECyeRczvwNEczNYof7iJIuxcCdtMZ5OvX1OmuZwxPNTa8GZ3tjEyTNEHygqhkDQ2Cwo0V2qnjmhzw4nB3r80mXpxRB2mzUMAKWxItxF5tfOnQjlSzupo6mOOFFSxndXZAE0Hit0LPYuQCB3oIA4A6pAOxyG1VHMz42jYHwkM+BXD/wT+u8FGeDSaOxn+y0gjmlkZy7vQGaVjhbWwapOsDa5PGXEtVb5hXKas6XUdhYXgkGwK8hYZlfbeGZWNi9KhjoYcdDQKVkQFYYqZXeJK3opKe1l1byzsVZ1Yx4FuVSbQqZrVy/y5VopLHCrswZceZ45mN1svS1cygvaelZ0NzibbOh43fW9aG96cDForfiZKvWYT5yXGPBOAKvBlUUe0Odv7AvYuhJ1DJoPofSfepn/hjNNOodUc5QSdbd8ZBQOJd6bPgApQNGeCk7lCVB0NIx/8wo7Gs9JNxFHKyUKqPk+x7iKHv+nnbymyQ/l35uRRdsMwvBMJq4oFceoMPBKtXifiUEejTt4ddbRJJyp0AGzPEqqvNxHQzzV/r/p6hvZb14bHMdjxM3YijmFzdh6wt8jKNg1TW5zHb3X6bnhB3d9xJQahlWs441EfrpqrOhqJMMt4dnI0/CGfKpPGndTi10tXE1wNwtJohBPCU6UYvuWFVJ85Gc785BEFWh2OUfSFege+e3TE6wdKDyYxW8N1hzbqWiwp5l11ZKcTk88QV3eqSGxTOvw55+/V3sduv21trPbPNqoAYjrVLy2Qobvy9kPZ3Og3TKa9hymQtBvIXyZf4yBf348HxLU2L3mxUjlH3HUayhz9AFpDcTT7GJ5h/6REsh6P8+3tjRcYFTcx445SosX1CO5TmJZBGpvoCnEyl8KS5Owa3zMyH3WhrY7b27MLjvvMz+23yeaEenx7G1wWqmyl9fa2Fx1t6m+puHDkXGf9EvNfHfehbO1W/2a7bWvDqzzjIDGKOsEjuf78EDY3+n1nFJPC3pv+r0h8YxprXpTYyXwBt7cD4krd3u6OcXtbrNzedq3FlYYdLiKzXGFwkqO4CWtVkAfDWWVy7L7glGZvLEUobOQE4su1+HnXCbr4ziC7E1iP+Efrsa1bHbnoamuTl5j/6qAOZeutk11psG1teJW3T/tntTluTJtr3kvh3T7zc/qWb2+/m5Xaj1ApbDJweyGaYwzUl+lrwNfA308DvqP5+9nUn5GvgS9OA76j+eJM4g/I18DfTwP/B7L/RBP3fhaWAAAAAElFTkSuQmCC) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOpDbZgAAZgA6ZmZmZrbbkDoAkLbbkNv/tmYAtpA6ttv/tv//25A627Zm27aQ2////7Zm/9uQ//+2///bXhyfKwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUElEQVQoU2NgGAxAkouRiR/kEGkmQQYJJiEGBlkebgYGGU4gS5pZDCQOZImzA1UIs0oxyAmwScmJgJXx8nEwsoiCdIKUgQFYGRgIAM0gEwAAQ0IDCfBSZLcAAAAASUVORK5CYII=)是某個關係度量。 **邊界算子** ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OpC2OpDbZgAAZjoAZrbbkDoAkJA6kNv/tmY6tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2///bxXy1cgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQoU2NgoCUQYWdkFQdZIMgpLsXNBrNKGCIIBBCWGA8jCz+IJcHIywBWJ83HBSUkOQQYGMCEBLMQVAOIK8oEFGJgANrAAmZQGQAAsFcDQui/g0AAAAAASUVORK5CYII=)提取交接的拓撲邊界: ![](data:image/png;base64,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) **極限湧現定理**:任何物理意義上的"極限",都可以表達為形如 ![](data:image/png;base64,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)的結構。 例: - 黑洞視界 = 內部 ![](data:image/png;base64,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)與外部 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACsAAAAcCAMAAADP/LbnAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOjoAOjo6Oma2OpDbZgAAZgBmZjo6ZjqQZrbbZrb/kDoAkDo6kDpmkJBmkNv/tmYAtmY6trZmttuQtv//25A627Zm29uQ2//b2////7Zm/9uQ//+2///buwpbjwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAxElEQVQ4T+2R2Q7CIBBFZ1qpS3HpoqAWqyz//4vOkNTgQxN8MiaS8HDp6eUAAP/xozdwWyOKLPfQNxC6Nov1ewW2UFksQ2bxyGZ1ni73+a3MrnXLD3TLYabXvh/kLEOX6vrd3I8AtsKabkFjoYwE3XSIbUxuUwlX8xeUwGHa20rwh3t/EsC9MY2rAYi1AkKvHIVpGEQsB15hNqYrdRJr6El1yxskvQDheHn1Ri7pTVi2Epp82ZUnRleagQ5Avimb/RhfBp/5ZA07JlitbgAAAABJRU5ErkJggg==)的交接邊界 - 普朗克尺度 = 量子 ![](data:image/png;base64,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)與引力 ![](data:image/png;base64,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)的交接尺度 - 光速 = 因果 ![](data:image/png;base64,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)與信號 ![](data:image/png;base64,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)的交接速度 **2.3.4** **物理推論** 無限交接論的關鍵推論: - **任何物件嵌入關係網絡**:沒有孤立物件,所有物件通過關係定義 - **邊界是物理實在的核心結構**:極限通過邊界湧現 - **"****基本"****必須有內部結構**:孤立的零維點無法承載關係 **2.4** **三約束的相互獨立性** 需要強調:**這三條約束在邏輯上相互獨立**。 - 完美圓不存在主要關於**靜態幾何結構的不可維持性** - 三維曲率公理主要關於**運動學的旋轉必然性** - 無限交接論主要關於**關係性的本體優先性** 它們可以從不同的數學基礎獨立推導(測度論、群論、關係論),也可以在不同的物理場景獨立驗證。讀者即使拒絕其中任何一條,其他兩條的論證仍然有效。 但當三條約束**同時對點粒子模型施加壓力**時,點粒子假設將完全崩潰。 ---------- **第三章** **點粒子的四重病症** 本章建立DTFT的核心反證:**點粒子模型在四個獨立層面上違反或引發病症**。 **3.1** **病症一:****零維結構無法承載曲率** **3.1.1** **數學描述** 點粒子在數學上定義為單一座標: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAcCAMAAABI4Z2kAAAAAXNSR0IArs4c6QAAAMBQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZmY6ZmaQZma2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLa2kLbbkLb/kNvbkNv/tmYAtmY6tmZmtmaQtpA6tpBmtpCQtra2ttv/tv+2tv//25A625Bm27Zm27aQ29u22/+22//b2////7Zm/7aQ/9uQ/9u2//+2///bh7w6WAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACWUlEQVRYR+1W2VbbMBCV05CUHadAKcHpQmubtY3YGlWJ/v+vmNHmkRynhpMHzsF6nFyN7ty5Mw5j3ekU6BToFHh3CqgsfdM1331uyU8e52sthO/9bpFPnHLDjydweuPGK3x31iLdSyBye3nBi1GyBVS2d84ZW3xhPL3Bl1U2YOqq16SR3Jy+5O0GbJhFfPA558coz4aRQOw+HU7nJ4+fcqOaDi9GZ4zJjw381uNSVVoGhn6VVA6pySTyY2VuOmv7K1A6bitSGfImJVni8yNAlZHIZbLPWJEMQs2Evg41VwcalySVZvCco1sEvB0/gfzUV/McYu+H0SM+t2mFuvybpWXk0X9nWNUCmhEcLDuGqizgy1yDo+5ofvJwqn1nj1asd9rkMV8pT+rjjuJK0DA+Mb2afZydXLusisBvlPR/3NKB1PYL2dL+en7E0x6Ndy/qxq3RYyJoY2X3Jfr9+X4UKKHt13wcP/XN4OQQTedOMZCgfBhzzaXRQtunivhxND+4o/sr9oJlUvRX7g8rm5r8ylI5ZmqSo2iubt4/mbmYC4J6qgAIQQJcXf+0ESTjmyGHB6SZuF9yNRnf7/gNDnumaTR0VabSoo8baX/GcI8VqeenxbcxGyz1ugdfUiRHhzsc5POuYXT/6THfmIHMwbCvai9ZVYYufEz4wA/tHXrXxqJJjpAER/ffyrdb/RjOBWoAC8QMhbrSI21j0aQESFObuUvb24rBf0BVLwAI5nO7TGX2o01iJFU96iONH6vX0X2g/19EML8m4bLYsqjFtfv/8jqu3a1OgXUq8AzKZlEtMov6RQAAAABJRU5ErkJggg==) 或在量子力學中為 delta 函數態: ![](data:image/png;base64,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) **3.1.2** **病症診斷** 點是**零維拓撲結構**。曲率作為一個幾何概念,**需要至少一維延展才能定義**: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6ADpmADqQOjoAOjpmOma2OpC2OpDbZgAAZjo6kDoAkJC2kLbbkNv/tmYAtmY6tpBm29u229v/2////7Zm/9uQ//+2///ba9EWPAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAT0lEQVQoU2NgoAKQFGJlZOYTZWCQFGTjFWEQFuLmwGGqGCMUsDCIMfFLcDFySgoAmSyiICaQBmkDMyGAFKY4FyM7RJckD9ASmBFU8B66EQAnSAMu3DMETwAAAABJRU5ErkJggg==)是切向量,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAcCAMAAABrlg40AAAAAXNSR0IArs4c6QAAADxQTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6Oma2OpC2ZrbbtmYAtpA6ttv/25A627Zm2////7Zm/9uQ///bqaogwwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOUlEQVQYV2NgGBjAw8bIyCHAwCDIxMvAzwp0gxA7F9Ql/GzMvBCmMDcLSAknAwMfiMEP1AOTooarAYDSAT45LsRTAAAAAElFTkSuQmCC) 是弧長。對於零維點,**切向量不存在**,曲率沒有定義。 但根據三維曲率公理(第2.2節),物理實在中的所有結構都必然承載非零曲率。點粒子既無法定義曲率(數學病症),也無法承載曲率(物理病症)。 **這不是「未來會解決的技術問題」,****而是邏輯不可能**。 **3.1.3** **矛盾的展開** 如果堅持點粒子假設,則必然得出以下矛盾之一: - 點粒子不在三維物理實在中(違反經驗) - 三維曲率公理不成立(違反 ![](data:image/png;base64,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)的內稟曲率) - 物理實在不是幾何結構(違反相對論) 任何一個矛盾的接受都需要拋棄當代物理學的核心成就。**理性的選擇是放棄點粒子假設**。 **3.2** **病症二:****無內部維度承載動力學** **3.2.1** **動力學的維度需求** 動力學描述系統如何隨時間演化。對於任何物理系統,動力學需要**狀態空間**: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAcCAMAAACNv8VwAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZgBmZjoAZmYAZmaQZra2Zrb/kDo6kNvbkNv/tmYAtmY6tpA6tpCQtrb/ttu2tv//25A62////9uQ/9u2//+2///bUcQfbQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaElEQVQoU9WQRxKAIAxFg71gQ8GCgHD/Q0pz3Lvzr5LhvUwCwE9z9SiZRhm2V2UjNW7jKSyXoDEJnS9UfUawogDuHcxMrUbMPjwabCjjjta4iLTXRASE02C1A1xYuliy48f7fxp74lNu67YFf8UUU7UAAAAASUVORK5CYII=)是廣義座標,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAcCAMAAACNv8VwAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OmaQOma2OpCQOpDbZgAAZgBmZjoAZmZmZrbbZrb/kDoAkDo6kGY6kJC2kNv/tmYAtmY6tpBmtrb/ttu2ttv/tv//25A62////7Zm/9uQ/9u2//+2///byhHkcAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaUlEQVQoU9VQRw7AIAwL3XvvBbTw/y82EKk991if4thWIgP8ErpnzVWyjJ5f9ikdBHcPorpNAKQzEjsjHB5N+gL1AE0drifv0PMbq0IW7wAqR93GLDheMTHCbGJOTUQV2/r2p/LH9bnUG2d1BkBcKAudAAAAAElFTkSuQmCC) 是廣義動量,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjqQOpDbZgAAZgBmZmYAZrbbZrb/kDoAkDo6kNv/tmYAtv//25A627Zm2////7Zm/9uQ//+2///bk1qZtAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU81NWxKAIBDC3mllpWbq/e+Z6HSFJj6YZVlY4AdwojmByki7kORMQFzWziMdNHAPV74Is6dwMiqZV5zpm9YaTREmizBub4RVfY0YVjpRIvVZVCXyER7ibgROMZ5/FgAAAABJRU5ErkJggg==) 是系統的**內部自由度數**。 對於點粒子,內部自由度為零(只有質心座標)。其狀態空間僅是時空的延伸: ![](data:image/png;base64,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) **3.2.2** **病症診斷** 但根據完美圓不存在定理(第2.1節),**靜態結構不可維持**——任何物理系統都必須在某種內部模式上動態流變。 點粒子沒有任何內部模式可以流變。它只能**整體運動**,不能**內部演化**。 這直接導致一個悖論:點粒子如何**承載**質量、電荷、自旋這些內稟屬性?在標準模型中,這些屬性被「直接賦予」點粒子,但這只是**重新命名問題****,****不是解決問題**。 **3.2.3** **量子化的失敗** 量子場論試圖通過**激發態**承載內部結構:電子是電子場的激發,夸克是夸克場的激發。但這已經放棄了「點粒子」的本體論——基本對象變成了**場**,點粒子降格為場的局域激發。 問題在於:**如果場才是基本的,****為什麼還要把激發態描述為「點粒子」**?這是路徑依賴的歷史包袱,不是邏輯必然。 **3.3** **病症三:****量子場論的紫外發散** **3.3.1** **病症的數學表現** 量子電動力學中,電子的自能修正: ![](data:image/png;base64,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) 積分在 ![](data:image/png;base64,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)處**發散**。 類似地,真空極化: ![](data:image/png;base64,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) 也是發散的。 **3.3.2** **重整化作為症狀掩蓋** 物理學家的標準應對是**重整化**: 1. 引入紫外截斷 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAD9QTFRFAAAAAAAAAAA6ADqQAGaQAGa2OjqQOpDbZgAAZgBmZrb/kDo6kNv/tmYAtv//25A62////7Zm/9uQ//+2///bz6y3ygAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAT0lEQVQoU2NgoDvgZxaA2inMwcQDZQqycLBDmCLcPLxQFUJsAoJQFbxcDMIQFcKcfAwMEBX8rEACrEKYgwskxQEU4GBkBKllZISaR33/AQAzLgI1+21aNwAAAABJRU5ErkJggg==) 2. 將發散吸收到「裸質量」 ![](data:image/png;base64,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) 3. 物理可觀測量在 ![](data:image/png;base64,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)時保持有限 這個程序在計算上**極其成功**——QED的精度達到 ![](data:image/png;base64,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),是人類知識的最精確驗證。 但**重整化沒有解決發散**,只是把它藏到「裸參數」裡。物理上仍然存在那些無窮大,只是我們選擇不問它們。 **3.3.3** **病症的本體論診斷** 紫外發散的根源**直接來自點粒子假設**: - 兩個點粒子可以無限接近 ![](data:image/png;base64,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) - 在 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAcCAMAAADVwFZpAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjqQOmZmOpDbZgAAZgBmZjoAZpC2ZrbbZrb/kDoAkGY6kGaQkNv/tmYAtpBmttv/tv//25A625Bm27Zm2/+22////7Zm/9uQ/9u2//+2///bQ+mQKgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAlUlEQVQ4T+2QwRKCMAxEN4AWFbWggiLSSv//H2mEVmFgODvDXvOy2Syw6q8aqAQFcjmxFhJlcJsGzbV2g3xTo0m2gLlQ+j6NNtSuB012sBsMF/d8f34dH0Pn0k5YTeI4mMy6dtKCvHg+4HQ8kfLrxyZ8Fyoc3bQDn++D9CH9WR/x519FEhV/2cHzegqKZupbbn8lXAMt+N4IGKMXd7UAAAAASUVORK5CYII=)處,庫倫能量 ![](data:image/png;base64,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) - 場耦合強度沒有自然截斷 如果基本對象**有內稟尺度** ![](data:image/png;base64,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),則: - 兩個對象不能比 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjo6OjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkDo6kGYAkGaQkNvbkNv/tmYAtmY6tmZmtv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bNkSVcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU82RuRKAIAxEg+KJiBd4o/n/n9QZC9bWynTZecnuJEQ/rEMLBbHOSvl8C8IeT6/eJuSAv/EFcZ9mZZjmVUc9LHdFm7xOwEbROAXprOoF07B5wu2pkIBxM3AHIclrcCWaB7I1GFkhJOIf33AB828FcTMBn7IAAAAASUVORK5CYII=)更接近 - 短距離行為被自然平滑 - 紫外發散自動消失 弦論的**有限性**(無紫外發散)正是這個機制的體現:弦的長度尺度 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6ADpmADqQOgAAOgA6OjpmOma2OpDbZgAAZgBmZjoAZmZmZma2Zrb/kDo6kNv/tmYAtmY6tpA6tv//25A62/+22////7Zm/9uQ/9u2//+2///bCpBhDgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYUlEQVQoU2NgGDxAkkkQxTFiLBIofCF+FK4MtygKX4oPwpUWYGTiR5glw8UhIcXOwwlTKwQ0VYYLbrQMF9BUKVa40VJsQEeA1EABUEpWmJdFHGo4A4MII7OgFCua0wYsEAEw1gPzQjJ1OQAAAABJRU5ErkJggg==)提供了天然的截斷。 **結論**:紫外發散不是「QFT的技術困難」,而是**點粒子假設的本體論病症在數學上的精確表現**。重整化是症狀治療,弦的有限延展才是病因治療。 **3.4** **病症四:****無邊界結構違反關係性湧現** **3.4.1** **邊界與關係的本體論優先性** 根據無限交接論(第2.3節),物理實在的核心結構是**邊界與關係**。任何物件通過其與其他物件的關係而被定義,而關係通過**邊界**承載: ![](data:image/png;base64,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) **3.4.2** **病症診斷** 點粒子**沒有邊界**。或者更精確地說,點粒子的「邊界」就是它自身——點的拓撲邊界 ![](data:image/png;base64,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)是空集。 這意味著:點粒子**無法承載非平凡關係**。所有「兩個點粒子之間的相互作用」都必須通過**外部場**中介(電磁場、引力場、規範場),而這些場本身又被分解為它們的「點粒子激發」(光子、引力子、玻色子)。 我們陷入無窮回歸:**點粒子A****通過光子(****也是點)****與點粒子B****相互作用,****光子又需要更小的東西來承載它的相互作用**。 **3.4.3** **場論的本體論轉向** 現代量子場論實際上已經**默認承認**這個問題。它的本體論是: - **場是基本的**(瀰漫於整個時空) - **粒子是激發**(場的局域化模式) - **相互作用是場的交織**(費曼圖的內線是場的傳播子) 但如果接受這個本體論,**「點粒子」這個概念本身就是冗餘的**——它只是「場的局域激發」的舊名稱。 DTFT的立場更激進:**既然場才是基本的,****而場的最低延展單元是一維弦,****那麼弦才是真正的基本**。點粒子是弦的退化極限,場是多弦的湧現,時空是場的拓撲流變。 **3.5** **四重病症的累積後果** **病症** **數學症狀** **本體論診斷** 一:無曲率承載 曲率未定義 違反三維曲率公理 二:無內部動力學 狀態空間退化 違反完美圓不存在 三:紫外發散 ![](data:image/png;base64,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) 違反短距離合理性 四:無邊界結構 ![](data:image/png;base64,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) 違反無限交接論 **這四個病症相互獨立**:每一個都從不同的數學/物理層面攻擊點粒子假設。即使讀者拒絕其中三個,剩下一個仍足以證明點粒子模型不可維持。 **理性的反應只能是**:放棄零維點粒子假設,尋找滿足三約束的最低維度結構。下一章將證明這個結構必然是一維延展的弦。 ---------- **第四章** **弦的必然性與唯一性** **4.1** **候選結構的維度排查** 在點粒子被排除後,我們需要尋找滿足三約束的最低維度結構。候選按拓撲維度分類: **維度** **結構** **描述** 0D 點 已排除(第三章) 1D 弦 線段、開弦、閉弦 2D 膜 球面、環面、開曲面 3D 體 三維拓撲體 nD 高維膜 ![](data:image/png;base64,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) 對每個候選,我們檢查三條約束的滿足情況。 **4.2** **弦的三約束滿足性** **4.2.1** **曲率必然性的滿足** 一維延展物件的世界面參數化: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmAGa2OgAAOgA6OjoAOjqQOma2OpDbZgAAZgA6ZrbbZrb/kDoAkNv/tpBmtv//25A625Bm27Zm29v/2////7Zm/9uQ//+2///b1rTv2QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAR0lEQVQoU2NgGGxAWpCdkZGRSYCBQYqbU0ySQxzoQGl+FiCXByjGIMkGJCVZ+YBMCWYhBgZhEAEWFWXlAvtFhJWRiZeWvgIAMn4CVYK3kPIAAAAASUVORK5CYII=)是空間參數,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAcCAMAAABrlg40AAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6ADqQAGa2OgA6Oma2OpDbZpDbkDoAkLbbkNv/tmYAtmY625Bm2////7Zm/9uQ///bXSEE/AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAM0lEQVQYV2NgGAggxMsIBEzcDHxcQpzsEBcIsnJDGALM/BAGDwuEBioR5ACzeBnZqOhcAHHiAQ36VAh1AAAAAElFTkSuQmCC) 是時間參數。 弦的張力方程(從 Nambu-Goto 作用量導出): ![](data:image/png;base64,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) 任何非平凡解 ![](data:image/png;base64,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)自動產生: ![](data:image/png;base64,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) **結論**:弦自動承載非零曲率,滿足三維曲率公理。 **4.2.2** **動態流變的滿足** 弦的振動模式分解(對開弦): ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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)是模式振幅。**任何非基態都包含無窮多振動模式**,系統永遠在動態流變中。 完美圓不存在定理要求 ![](data:image/png;base64,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)的動態性,弦自動滿足: ![](data:image/png;base64,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) **4.2.3** **邊界與關係性的滿足** 弦有兩種拓撲類型: - **開弦**:![](data:image/png;base64,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),有兩個端點(邊界) - **閉弦**:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmAGa2OgAAOgA6OjoAOjqQOma2OpDbZgAAZgA6ZrbbZrb/kDoAkNv/tpBmtv//25A625Bm27Zm29v/2////7Zm/9uQ//+2///b1rTv2QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAR0lEQVQoU2NgGGxAWpCdkZGRSYCBQYqbU0ySQxzoQGl+FiCXByjGIMkGJCVZ+YBMCWYhBgZhEAEWFWXlAvtFhJWRiZeWvgIAMn4CVYK3kPIAAAAASUVORK5CYII=) 是 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAcCAMAAABf788oAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6ADo6ADqQAGa2OgAAOgBmOjpmOpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY6tmZmtraQttv/tv//25A627Zm27aQ2////9uQ//+2///bdHaPgQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYklEQVQoU8WQZwKAIAiFocx2Wra5/z1zVeoFfL/gYwOQX3u9hkvQvMQA4HKAJEdslLY8EEx504G7G99ODtCkM6wEIramsi+G+GSSNhBKsDMB1e9vOvvg3yAAs1WZNM3/VYAHtfsDpI9g0+4AAAAASUVORK5CYII=)上的循環座標,世界線是柱面 開弦的端點 ![](data:image/png;base64,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)提供了**自然的關係接口**——它們可以連接到其他弦、Dirichlet膜、或場。 閉弦的世界面是**閉合曲面**,它通過全局拓撲(虧格、繞數)承載關係結構。 **結論**:弦同時滿足無限交接論的關係性湧現要求。 **4.3** **高維結構的排除** 膜(2D)和高維體積(nD, ![](data:image/png;base64,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))雖然也能滿足三約束,但**它們不是最低維度解**。 關鍵考量是**作用量的尺度**: - 弦:Nambu-Goto作用量 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAAcCAMAAACJZtcIAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZjoAZjqQZmYAZpDbZrbbZrb/kDoAkJBmkJC2kLbbkNv/tmYAtmY6tmZmtpA6tpBmtpCQttv/tv//25A625Bm27Zm27aQ29v/2//b2////7Zm/7aQ/9uQ/9u2//+2///bjI8qSQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB30lEQVRYR+1Va1PCMBBMqtCgYkEUrY/WBxZUYmj+/4/zLs07ODrOwOBM8yHD9ZK9zd4mENKPXoFegT0pwBm92VOpH8qIk9fqQKg0+WFIQogsJwGViobU4vgPvGXNKD1bbNvZTqka2QNk22lIRZZht+I4AQzQvGxDqUauhgsCNthGRYweZJnrrGBh6fYCCboRxwlggOZlZTlcq7Cdfm9FPlHp9hKXxlTEuAMwI44TKgGafwYjN3DymtPQcyzwaQ/MVXNw+FQ2M5rd5kTWun06BkM9n5qG4p4YzqH5ZxjZErPs2iT4XNaoVm2pNFq8gIpgxRqts7zvvGxi0LB499RJ4Bwa0DzSpvA+wtm0bcgjZKvhmheGm3dtuHvfYAnprAH9h9nEaCydUAAxXHAJLZXKv4kIhUPe4VRTq4TfFUdF2atzOselNlbEXCMTuNhuqmho1oBXYDduVISqzjVYsdujZsUAf6nV9rQBkAo8NJfs+EMfGujNW3RN3TJZDewtDwwsX65yMcdnD2Y4bBcj6oqZbidUfDSXRKts0HL4vh1b28a7K+qeVO9IT3SwWNEC/U3RVjZeMuruQELFR7NJoZ5Rq3gq5ZYvh/IXJMYf0Tv/K/q7WCRYNt8Fbo/ZK/C/FfgCMaIxGhBz3S0AAAAASUVORK5CYII=)(線性於弦長) - 膜:Dirac作用量 ![](data:image/png;base64,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)(面積增長) - 體:![](data:image/png;base64,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)(體積增長) 在量子化時,作用量越大,**量子漲落越被壓制**,系統越「經典」。對於基本單元,我們希望它**保留量子特性**——這要求作用量盡可能小。 **弦是滿足三約束的最小作用量結構**。 **4.4** **弦的唯一性定理** **4.4.1** **定理陳述** **定理 4.1**(弦的唯一性定理) 在滿足以下三條約束的所有拓撲結構中,**一維延展弦是唯一的最小作用量解**: (C1) 曲率必然性:![](data:image/png;base64,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) 在某處非零 (C2) 動態流變:存在內部演化模式 ![](data:image/png;base64,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)(C3) 關係邊界:存在非平凡邊界結構 ![](data:image/png;base64,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)或非平凡拓撲 **4.4.2** **證明** **Step 1:****零維被排除**(第三章已完成) 點粒子違反C1、C2、C3,被排除。 **Step 2:****弦滿足所有三條**(第4.2節已完成) **Step 3:****弦是最小作用量** 考慮 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6OgBmOpCQOpDbZjoAZrb/kDoAkGY6kGaQkJC2kNv/tmYAtpBmttv/tv//25A62//b2////7Zm/9uQ/9u2///bjf122wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAASklEQVQoU2NgGHAgw8fII83NyMXAICwixCkgIcYiwcAgw8vKwCAExAxS7IJAHg+QJckkyiDFIQpkgSQkWcT5gRJAbZJszCBBqgIATbcC3DVX6wcAAAAASUVORK5CYII=)維延展物件,其作用量按幾何體積尺度: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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)是 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6OgBmOpCQOpDbZjoAZrb/kDoAkGY6kGaQkJC2kNv/tmYAtpBmttv/tv//25A62//b2////7Zm/9uQ/9u2///bjf122wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAASklEQVQoU2NgGHAgw8fII83NyMXAICwixCkgIcYiwcAgw8vKwCAExAxS7IJAHg+QJckkyiDFIQpkgSQkWcT5gRJAbZJszCBBqgIATbcC3DVX6wcAAAAASUVORK5CYII=)維體積。在量子化時,我們關注作用量的**單位下界**——它由結構的最低非平凡延展設定: - 弦(![](data:image/png;base64,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)):![](data:image/png;base64,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),![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6ADqQAGa2OgA6Oma2OpDbZgAAZrb/kDoAkNv/tmYA25A62////9uQ/9u2//+2///bhSmYmgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAARElEQVQoU2NgoAvgZWRkh1gkxMXMB2EJckCFGPhZuaGu4IVJMvCwQIUEOTihLLAyfjYgD6RMgAuonZ+DEQiYYNqp5xcAtEIBbsuLUkYAAAAASUVORK5CYII=) 是弦長 - 膜(![](data:image/png;base64,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)):![](data:image/png;base64,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),主導項是長度平方 - 體(![](data:image/png;base64,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)):![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAcCAMAAAAEJ1IZAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZjoAZjqQZmZmZma2ZpDbZrbbZrb/kDoAkDo6kJC2kLbbkNv/tmYAtmY6tmZmtpA6ttv/tv//25A627Zm27aQ2////7Zm/7aQ/9uQ/9u2//+2///bq2yuhwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABI0lEQVRIS+1S21bDIBBko6bGu6mX2qhNbMWAlP3/v5MFQip4epL4mnnIOYHd2dlhGJsxOzDBAXwFuBUTGqMW/Sj0cvN/HsPQPls92BQA17vRlBzg3jTpMlvZ3jrfMXX5OZoHq9z5si/Xlo++E6BLkqNuBFbEYGiTnbh7gu/gX3sF2Us0S13QNTYAd/ZGPcQlcoUNaW46Hpm9s6/M/fETbwH3awV6Q0kKe3yYyjoX0s2h1c29G3/AU58nZpimgzN8c3rDoSQJ0uvpCv/y1VAfyyWnyb9neX2qk8y4kdwWa3Ykl1gtBG4jOYzs2VfBEArhqXsKn8tka718KuAselRVgkFMbs30uUx4rD0j4HKZwtozFCGXSQP2Jgwg63M5oHguGevAD+C/F9GRbj/CAAAAAElFTkSuQmCC),主導項是長度立方 **在統一尺度** ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6ADqQAGa2OgA6Oma2OpDbZgAAZrb/kDoAkNv/tmYA25A62////9uQ/9u2//+2///bhSmYmgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAARElEQVQoU2NgoAvgZWRkh1gkxMXMB2EJckCFGPhZuaGu4IVJMvCwQIUEOTihLLAyfjYgD6RMgAuonZ+DEQiYYNqp5xcAtEIBbsuLUkYAAAAASUVORK5CYII=)**下,**![](data:image/png;base64,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) 這是**幾何極小性**:弦覆蓋給定世界面的作用量是所有候選中最小的。 **Step 4:****帕累托最優性** 定義多目標優化: ![](data:image/png;base64,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) 弦同時滿足三條約束**且**達到最小作用量。任何其他結構若降低 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6ADo6ADqQAGa2OgAAOgBmOjpmOpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY6ttv/tv//25A627aQ2////9uQ//+2///bQbzvTgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAS0lEQVQoU2NgoAuQEGBjZOQQBNrFzyLIIMYuxMAgzsULtVqCDygGAWLcTDwwUQFGTpjb+FlEoUx+ViBDGCghwgbSDjKWGaaDmj4BABeaAg1zxBDDAAAAAElFTkSuQmCC)(只能是點),則違反約束;若滿足約束(膜或更高),則 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6ADo6ADqQAGa2OgAAOgBmOjpmOpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY6ttv/tv//25A627aQ2////9uQ//+2///bQbzvTgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAS0lEQVQoU2NgoAuQEGBjZOQQBNrFzyLIIMYuxMAgzsULtVqCDygGAWLcTDwwUQFGTpjb+FlEoUx+ViBDGCghwgbSDjKWGaaDmj4BABeaAg1zxBDDAAAAAElFTkSuQmCC)不是最小。 **結論**:弦是這個多目標優化問題的**唯一帕累托最優解**。![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcBAMAAACqkzMIAAAAAXNSR0IArs4c6QAAABhQTFRFAAAAAAAAOpDbZgAAZgA6kNv/tmYA//+2WgTk2gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAHElEQVQYV2NgoBIoFhQUFGIoCWBgSCJAQlSSCABcoghVncKkrQAAAABJRU5ErkJggg==) **4.4.3** **推論** **推論 4.1**:弦不是物理理論的「假設」,而是**邏輯必然**。 **推論 4.2**:弦的長度尺度 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjo6OjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkDo6kGYAkGaQkNvbkNv/tmYAtmY6tmZmtv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bNkSVcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU82RuRKAIAxEg+KJiBd4o/n/n9QZC9bWynTZecnuJEQ/rEMLBbHOSvl8C8IeT6/eJuSAv/EFcZ9mZZjmVUc9LHdFm7xOwEbROAXprOoF07B5wu2pkIBxM3AHIclrcCWaB7I1GFkhJOIf33AB828FcTMBn7IAAAAASUVORK5CYII=)提供了物理的自然紫外截斷。 **推論 4.3**:弦的振動模式譜 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAcCAMAAACu5JSlAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjpmOjqQOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjqQZmZmZma2ZpDbZrbbZrb/kDoAkDo6kNv/tmYAtmY6tpA6tpC2tv//25A625Bm27Zm27a227bb29uQ2/+22////7Zm/9uQ/9u2//+2///bBnuMCAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA6UlEQVQ4T9WSyRKCMBBEA8qiQhSXhEUkrhDC/3+fZAYpEq3y4sVcWLq63ywh5P/POfDq9y6Es8K/ws0/9timYFM0NmS1qboMHDLUD0W5oTc+kUtIRkUGpi5iInxwoG75u5TLhN0gH5xdavAVdSLhQiTyB73NHJc3bt7jX6eZVWOKolEtF8nIRj7TkIN+L/peFbXmJIMeDVVAkXYn4Ec+lKIzpgf5qAe8O+68x36qT+dXOvNc6j21iX8Z9oU8i3q9h0xtJ/O1598Pt4mM+Zr7Kzgp2EkHIN/av1rnpIQbMeyfkC/3x+j51x9P9hQWTQsqGMkAAAAASUVORK5CYII=)為內部自由度(質量、電荷、自旋)提供了動力學基礎。 **4.5** **一維弦對點粒子四重病症的根治** **病症** **點粒子** **一維弦** 曲率承載 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmADpmAGa2OgAAOgA6OgBmOjo6OpDbZgAAZjoAZrb/kDoAkDo6kLaQkLbbkNv/tmYAtmY6tpCQtv/b25A62////7Zm/9uQ//+2///bi/vN+QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAR0lEQVQoU2NgGHggzMjFICPCJMTAIM3NK8MvCHKRFIcAO1AACCQZOdl4wSxhVhk+VhBDho+LQZxZTFSCQQqoSJqHBaKSmgAAKV0CmxhkioMAAAAASUVORK5CYII=)未定義 ![](data:image/png;base64,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)自動 內部動力學 無內部自由度 無窮多振動模式 紫外發散 ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjo6OjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkDo6kGYAkGaQkNvbkNv/tmYAtmY6tmZmtv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bNkSVcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU82RuRKAIAxEg+KJiBd4o/n/n9QZC9bWynTZecnuJEQ/rEMLBbHOSvl8C8IeT6/eJuSAv/EFcZ9mZZjmVUc9LHdFm7xOwEbROAXprOoF07B5wu2pkIBxM3AHIclrcCWaB7I1GFkhJOIf33AB828FcTMBn7IAAAAASUVORK5CYII=)自然截斷 邊界結構 ![](data:image/png;base64,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) 開弦端點 / 閉弦拓撲 **弦同時治癒了點粒子的所有四重病症**。這不是巧合——這正是弦作為三約束最小解的必然結果。 ---------- **第五章** **從弦到時空:****演化鏈** **5.1** **演化鏈的階梯** 我們現在建立從一維弦到四維時空的完整生成階梯: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJoAAAAwBAMAAAAbVn6sAAAAAXNSR0IArs4c6QAAACRQTFRFAAAAAAAAADqQOgAAOjqQOpDbkGaQ25A62////7Zm/9uQ///bDJ1cQQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABe0lEQVRIS+1UsVEEMQy0IwZI7IAeSOmCkDKIqYAi6IAeqI9dreSz9QTM3Acf2D/z87cnrVcr6UvZZzuwHdgOnHCgX/OUdkJJTq03z1ZLTaJZf1+x2mrvl75UQRbMSi0opwLnZzp25crWgBDWCzDZewNTqrU6sWVtvUMJQPtGtJG0ao9rYf/XZmpwXBuJhrKfT4kFW5gpyIRE2OO75XtRNKpHgQQH2/2r7plcExQCVMIXb0CiF6VoVepiFPdhcRF2QLIj/Lh7xht74i0ux3qqzgL8tvg3Y2gZGgU8vDDqySstFQKpx7tAO6ZumTZjo/hZG/UGZtq8fSMutB3jGybBk4hyCLm8Qyd8U6XuwZi3tYGsHbl+vKdYhsGmnqI4+eFdDLY85kubRQpVk15Bvggzm3dhmV7G5d3FUKVlA0usOO/ShNhqjFJ5KeHLTExoWhiGAtJi+WaJf5bCrgMZzQoH09Yfjing9v8tRyEnf2htr3ZOqtnp24HtwJ8O/AKuQig01Toa8AAAAABJRU5ErkJggg==) 每一階躍都是上一層結構的**自然湧現**,而非額外假設。 **5.2** **多弦疊加:****波的湧現** **5.2.1** **多弦態** ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjqQOpDbZgAAZgBmZmYAZrbbZrb/kDoAkDo6kNv/tmYAtv//25A627Zm2////7Zm/9uQ//+2///bk1qZtAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU81NWxKAIBDC3mllpWbq/e+Z6HSFJj6YZVlY4AdwojmByki7kORMQFzWziMdNHAPV74Is6dwMiqZV5zpm9YaTREmizBub4RVfY0YVjpRIvVZVCXyER7ibgROMZ5/FgAAAABJRU5ErkJggg==)根弦的疊加態: ![](data:image/png;base64,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) **5.2.2** **干涉與相位關聯** 兩弦關聯函數: ![](data:image/png;base64,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) 當 ![](data:image/png;base64,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)時,弦之間建立**非局域相位關聯**——這正是「波」的本質。 **5.2.3** **波的湧現** 多弦的局部干涉密度: ![](data:image/png;base64,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) 定義波函數: ![](data:image/png;base64,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) 它滿足波動方程: ![](data:image/png;base64,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) **波不是基本對象,****而是多弦疊加的湧現現象**。 **5.3** **多波交織:****場的生成** **5.3.1** **場作為波模的疊加** 量子場 ![](data:image/png;base64,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)的標準展開: ![](data:image/png;base64,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) 每個 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjpmOma2OpDbZgAAZrb/kDoAkGaQkNvbkNv/tmYAtpBmttv/tv/btv//25A62//b2////9uQ/9u2//+2omb5igAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQoU7WM2xGAIAwEExVFJaDgA4n036bAYAd6XzuXzQH8l0io6jpL+9J4VvIiVHIKbmqSEUkDT3uqWa7bXO4eEXURnbhMnyGSAt8eS0iaBR66/PFtHsX3A4rrTt6dAAAAAElFTkSuQmCC)模式對應一個平面波,場是所有平面波的疊加。 **5.3.2** **場的本體論** 從DTFT的視角: - 弦是基本單元 - 多弦疊加產生波 - **場是無窮多波的連續疊加** 形式表達: ![](data:image/png;base64,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) 當 ![](data:image/png;base64,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)且 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6OjqQOma2OpDbZgAAZgBmZrbbZrb/kDo6kDpmkGY6kNv/tmYAtmY6trb/ttu2ttv/tv//25A625Bm2////9uQ/9u2//+2///baExqSgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAVUlEQVQoU2NgGDpAVpCRkUkC4l45bk5pGQ5pCEeYBcoAS/AhfCTDLgTmyPMDaTluXgZZAah+Bik2RmZxoBgrkv8luZA4IhCtENt4xEQRHG4k60gJPQDCzgN/xIt55AAAAABJRU5ErkJggg==)連續分佈時,場湧現為瀰漫於整個時空的連續結構。 **5.3.3** **真空作為場基態** 真空 ![](data:image/png;base64,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)不是「空無」,而是**場的最低能量態**。它仍然有零點漲落: ![](data:image/png;base64,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) 這個關聯函數是**多弦疊加在最低能量配置下的殘留結構**。卡西米爾效應、Lamb位移等現象都是這個結構的觀測表現。 **5.4** **場的拓撲流變:****時空的湧現** **5.4.1** **時空作為場的拓撲結構** 廣義相對論將時空描述為偽黎曼流形 ![](data:image/png;base64,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)。在DTFT中,時空不是預先存在的背景,而是**場的拓撲流變的幾何實現**: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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)是應力-能量張量。 **5.4.2 Einstein****方程的DTFT****詮釋** Einstein方程: ![](data:image/png;base64,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) DTFT詮釋: - 左邊(幾何曲率) = 場的拓撲流變的幾何投影 - 右邊(物質能量) = 多弦疊加的能量密度 - 方程本質:**幾何曲率由弦的能量分佈驅動,****弦的演化在這個曲率背景上發生** 這是一個**自洽循環**:時空塑造弦的運動,弦的運動塑造時空。 **5.4.3** **因果結構的湧現** 光錐結構 ![](data:image/png;base64,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)(類時)、![](data:image/png;base64,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)(類光)、![](data:image/png;base64,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)(類空)從場的傳播子中湧現: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYcAAAAwCAYAAAD6prYHAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB2CSURBVHhe7V1NTBtZtj7X6bdOr8NybI+asKUl7CxHYWy31FlMuyXPwrQ0NrzF6xgpbAJjwE02j2gw2Qy4F4ENUeh56kQT7GHdMZGaXow0hCg2vXt562akWb3nqvedWy5TLurPuEyAVEmRgn3r3nPPvb7nnr/vfLS4uEjBE3Ag4EDAgYADAQeMHPgoYEfAgYADAQcCDgQcMHMgEA7Bngg4EHAg4EDAgVMcCIRDsCkCDgQcCDgQcCAQDsEeCDgQcCDgQMABdw4EmoM7j4IWAQcCDgQc+OA4EAiHD27JgwkHHBgMBzKj75SJVEXUVaJYvkwba3cpIihUKpXwSfBcNg4EwuGyrVhA75XlQDFzXZ3MbtPwZp2Ot0riMk20mPlYuZW9Lh63VIr8XKOpaIoefv41VZKCLnKw/Pz8vAI+M69DCOu3FWLtdtec2hjXy2u/dmvs9X2vdKFdi+eIfzwHnrPrEwgHVxYFDQIODJ4Dmeu7ajybps16nbZKF1MwZD7eVbKv02Ju5i4lwt0aQWnrl9DtcaIn35SoWMwon8RyIpogWgfrSoNnn+MIRWg0oQfD4u0PmiYjhOCD0njQS8GgH7T4jr+3Es4K2vAB23nf5XDuCBy7dsXR/1ZCKSFetNbos2vXSFVVo5DqiS4PgstWMBSLo62pa6mQ+tf/o9/8K3TtzZuSEgiH97xxL8Lw+DGrq5NZKhykqVm/e2EPJytewZShZpMV2pNfxihf3aSh/a1Lduu+rsYjIzSnXmzeb/0yHqrPCGgIcdHYfKnMF4uhRQuT0dGjZTqcXaOCEJbfu+15Fi5HtWUx8WyYHruYpoymLLn+OxvQViKdcbmv1VtRkbvfoigEA9OLQzTEhzX+XdNpMR3eLADkY3Wo4zP+it/vTMVw0zdOr6tN+50uDaX2/bdEuR2CfAgtLixIAXVWutr0suD6NzftwKxJlEr712b+NNaKPP9bqPKbf0ltLxAObjv1in+PG4M6GY/QwUgVgiHx3gXD6Lt59dkdFQe8++2ZzTDxyDyNVJs0DoHAt+9IMkvlZl29LGYZKZjBfxBN+xdUYzD+BFhDeDk3ooSiU2Knta4kISCMPoXMx++UnciaqCR6FwzFzKiyurwkQmKXxvJztDGTcPRZYP2VW9EFcfNFg+oQCM3VeCv62YRYeftSKeh0He3Qd3s5um/SYlhAtA9TOT39b6NAcNEQjLf6rvfthIr5KMFvT5kKxUFvgu7iS9aw+qUL71/jg7+t4VhqCnYmpl99lqbY9HO6/+e11r9C4logHK744e82vdpkkipUpub6+xcMmqDK0x3YIvb33Sgnqi0XaC9Wpk3YOLbQPnx3jvKFJBWWa7Q45P7+hWiBw2t7L0bpzTD8DBeCInciEjO0EovSg0f3KFWI4EDTXmHBsNwWDGptsjU1uibWXYRER0tYqtD8bp5W5jZJWQ9LgfOEF9Xhkes/tkKPExFpviJe/+kUTT+s0XQlKek62tlGmzRFDFYii1u+8Yavaw26Xd74nW5WcueRoYWdSelodYkqoO1tWGvcL126WUkXECzcWAux0SJOf/6rKI2IaXr+tz/DtCQCzaGnVb5ijeVhDANMvnpBzBm1Z9Bg7tCQhxu0duOep1g61dF2oBqLO3lSKwcNyqwX1Ytqu+/aRs1DmMRgUsIBYT4Ki5lPlclsQlQgPMqNOuEcDtUm461EhYT+t5VZ56zb9NN3u0qysifG8ju0V0niZlxSockpKYyn4jPYa+RnpdJWKJMeU6afVkVDuatERDFER49at6LziFSq8PAK2/XyO2u2pBQzGaW2PCHiAqYZRDbNbaodP0bJw8VAMxctiDGsv24uwmChz3OqgvUXb5WkpKs2if5HZikaYoezFjVlpSUY7fVtc1GX+cd4wBvNScYJuhzuUrDo4zD9jyT9G6Bf07L6pctIi0FAdK1BW2uwNDuxaenzP6itB82fQ5Ubfw+Ew1l/SFfiPRzGFdhpy7BqHHv4Qfo1Z92UUtAcBZ1Hs+BK/4EWNQKtwN4H0qRDfj/tF1Xvp5+jxgHmyTfbbuHAPKpN7tBMvUnD8Shtw3RWPZxQvr+zCRaFQ8dPcJj4SHLx04+VSbUuGsO3KFp4Tjs4XJN86NMo5b5douF7CSoYvMth+Ejo1SE1QQPTLh3SC4t020jTT9/Q4k+nidT9AAU1h3F+oCQOR9YUetuCTXrD6/87JyYcKY3Xgsa+iNAe7yiDZ9zgfJYdWNzuzf4C80Cnvjce7npjW4e11BhzNPtDmJIG0nygq0MnCwgz0ebPrITF3iFW9Ubgc/Dx53X5upIHE26tUYtb6yBng5unoPFFWkR0i/5I/0GWEK1j1GKOWSsYJCkXtm/JI5jG9ktblPkSt/S7UbFUbtBeMty5ARuJlwduPCoK8hR0eCBwG+AxDvQuX0Hpx19CQzg9w5m0Ept+KppHKgmE9qhHTXqdm6NKFLfb9s1b9h65iWvFU9Lb9SKoWPMobjSUKDSHpVCIHuTLytxM8VQEVP+LYy1ArLQACye1leZgJKnL5+BGq1lI1P4TJjHdEd126vdLl41T3Egam5msSO2Yn6LDMaLvGtRYu9sKfA5uqxp8fy4cqC1v08hc72GcfMsZvyz+hTNyMhzFLZ1NT19HKKl7Lk198YFL4wtdAtd6uGN64iRwwxG6Sa+IL48sQWrLr+mLma+p7nNMamkL9A7dprq6oUUmZQVu0HllZW6GCgnN5+CFXXtvQKgAoT1IJ+MN3+r/VtFIbrS4HMxG/0VIVautKQTU5l4kukJ9+6XLrLmYtQInk5LV/ALh4LbqV/77A2ocne8k7cxKVJERqCeHgoNZycq/YOWHON+Z9T6aPPj3NPOM1SM1gsmsYKbIdWIbzgAf8DV0B3b71POaUKJNZWp4hirwdXRpDT6OL4UaVKTb0CRfymilrAglSelEK5nyKfShmU6zfwHu55bRD4F0vNYnMRL/cAhsNhzq5iQ4N82hiwtWJiVuYGlWqn0P42mOIBtsH7/o6nWpGmyrvQkfzV/+EkQr9cq8q9Reu5Gyael8H7NZiUNQs7RJ48fm/ARns1IC3meqFGi5lmILDOEGSgV23l6myJ/IMMwz25YCWjMV4Uq9uUnlA83voKaqyuRoBr5ha/OSHysZuQnTwtPnNLU8TDPrYVqHtnJK2Wi+lo70+2GYnjCoH8a/0tY+tIlxUtR2nsNyg/MclKIpXFafo1z/b6fpIdYfuQ3UxPpP743Rnx6Hqc40QfCM3lSVV4dN4aJdyMS2dmSPJ40F7U/5HGz9C6ZF4dyG2EpDy21w1pDOQteZt0Cx+PsWnOQhqI7yCTSHM7PyCrwoD6aKNCG8L8uMdtt/R3P1MOzrvfG0tD8kmuU8kuAimAWp87E85zhcLuiJcIrSsQJt7xyRwQVDnO8hwJcyoDQKuD03vxxrsd8hflilTT6wcYQNyh2jOZsPaHhjTfomLBPdmrhUyBBR/5+ONjEEExgyru0erH+osZJXJj5DvJJKSgTrjxwHRHVpDm5+L8I29O0mNRR8Dwc7f24VVdQewxiq6uaQPuVzMPot7LKVtdyMmPgC8asvTULVJ7rkVLyakLrbNejwFXLy7v+Ws6S7hYO1U9D/xT9rj71iz8gb6WGaON1/30esmotChxMfkVAEnJ4Gol0cwlTDiGtGJ5Vn7zEvALe9bYSvjnsIX7Wa79bxkBhHQLt+sCL57azb6728x1pUcS6vFpLLyJBeV/VEuP2hRcG5GjwfNqdv0XhoQXrw9+Gk7y2up9eJwQeNpF0tdNZKMJyEkSIM0xAi6nWcTrQSI/Q5PbEVarwsOCbCYf27oqT++eSbLi0mnOLELjbbwcjUznUwJJqxL4Ajek7BaZicw7KdIY+gk0FtZ06ym5aedwHl5tTTL11e+W/b7ucGHSCC7P5vBUE2dAsHJhzZOF1Zsr3CEwDHRBXJg55vcHxTWhqGc/GUaUGbylmwZ7aOx0V9hhAFE8e0vGXNXgQ6vPLQaW2goos7I/Pqcu2ug1YQIb5Y0XvMC+Db//jQYA+7vn80A+5A04CQ3R1fReju+8vP4EO7tpoVWXUTUVEOfgZpvoHN/AfNQd6rBiM1g9twnnfFvVox+Z+OmoOnZYFm9kUMiV21NUohZlT3W5tMQB04DSPGklEYcHv8cwXoMx3wXd4OPbchN/sSAu9EuzHOww+6vGoNhnGlSe3312OIoJql1H/95drimzcn2EpaQtQupZsnmZrnBU+gJ2ONVK1jKjU6zoY9U9o6FvW5EVVEJqlquJlZbayLQoeXTe9lbdgmm1yyP3D41jo6givV+bsdvEzxg2rDF5nmHKnL8Tijsp4r/IceBivmd5G4xoIB/oxj62ghib4a3WWICtjMrTWLi7RwMmx2NgfgvUeikUDCHvwXFsB7HZLt/Aa6ycjr3AztOxqHLhSHkP9Rssj/cPJZeKHLYJayzIo2QWsYp3INEVT/y8B7ub9qJqU30L86PgeZyo1kHMgGqLDac27wBEdQZyhPc/Dem2ETfMGeQbp/ORahpdWZLrvuqYW+KHR42IGe1iZxh/LJJdo54vhH60faZAPh4IHjg2+ytX8shsbHpSnpPJ+uMNiftiwT16T2DlTW+DJQWZGtzaisxx7DTc9zLlZjsW9i4faJ/8LKFGT4rGMyMvfVqwnJj/Y90mVLuz4Xq8Q4/o6zo2/MLxD9tATBoD1SOJyEAJ6YlAYNT6BlgGZpqbIH54lGTFIgXzdfVjcRHtGBPnDAntHs6sAG4giVtiNy9N2uCpDOLrMW35Az6Zha2N5BklW32u4HHdqYe6C9ipj7falKsnmK6QA2BXB+tM+c6OjlB+R1bbRwzz016YA11OTQtZG59w6418v8g7bvhwOMyjoOJzH8d6egPt4PRcGog+SApjnIEMA8VbsiRgYHTyBNIpy4wpgqONQjO3GKHEKnniFaxWEfidOJ7dUGe6YbXiAioz3mcEg/A7zA4tCWMN++rOLJfaFjFAVaRuvUHMYcCs86TsXEepXyFcAOAFny2AAg5hbX7m2xva+NDPeD9nDdAqmUfRaReRas3TR6oyFoFXAg4MBV5sBHHbMNbrjnARmsj7fXvlEnwkfq6vYe5WFTKiGiSIvc2O6YQuywZ7rgBVgrQGjFEmCPGbrZcsFM8eS+0cGmAA12QI0VDPHqbKIC7PCQOUrKIa59IButbVIzI5V6dXoPhKag04ADAQcuPAegOWi3UD6crXCSfYcnaJuJypvt26puNuoD/K0DL3C3h1h5v+mQYaF7nZyB2vIhpRFCa9Qa/N4NXtbmxOncjVQqI2SqpEagpl2m+gd+8zDoL+BAwAFrDnykwxCYo1rOC55Axv3CEY6kVukIrz2DoR6wCSmDY9xp8fQqZtymHxiIfuno8BE5A+oMTE07mdNag0+7sJe10SOwYuUTaGudjC0IiGq+4uiT8InkoJuAAwEHLhkHpM8hMVOmWOTElKPPYSDwBO2M0EJWC7FsAm89htyK8FGNrkvHLtvATxzSTjZ6zTTEUJ4ML6D5HepcpL0JOAWzecnsu/CRDp1fWjbmM5psww5YBp044Pf3snc8r42E5YY/yUar0mi+RPUPemFS0PbScsBY/jOWX6GNNedkuEs70QtMuBQOnAswZxHVMgh4ApkRullVaXkJiSCFNmuQu1iIIdpnjpqqqSKZjY3eCC/AJSFlNBL8Djq8gLmIlNl34RcdxrXVBBlgBzbXbaN/7Hwove4RL2uj+1ViDiUoZbTSZS+K0CvzPoD2nI8wmX0qkDMh4Tf8LAo0aPZJiImJ6+JxC1nNP9doKpqih5/fBX6S6AV8ddBknurfASyvq60XDCavfQ1ykp08B017eEajpkSxQcATcPYuA2ypzTSS27aReKfj4VhAA9hgzxjhBZhBnES0aAMvYBWqqwnF/ukwLg580Ihctcf2saPjrAvsujbSr4L8ERvcIp0eGol+0KGsmukN6bO4s6wnjohrOm+n7bP1z7pe5/WezEfIpsVmvU6wzl7IfASmceJ1WszCL8c5E0aIblxWQ7eRPc24Spyg90ksJ6KmGtDnxUvzOAjkQELdsHj7w9cyy9kioc6IuaRDc1gFyXQqwzkICzNSbBfKq1aDOiXUFy1aT1pnXPfDp45w0LSHiuqaKNbPaOZ32cRi8DdYdW2HPdMTGZahuoYe+qRDhtWuZkkii+6X7AGC3ejoaVLujTlRzrlwvRaMEEv3EQ3gQkav8Cvus+qthX7wH3Akmw00S289XuzWrDHEoyNirqUV9LmoGgPnTLycEdAQ4qLx+KUyj8xlS4C/1WU6nF2jgjuCad8LYzRl4VeBbPENRnvt0KXBX0RF7n6rq7RnG1qjU3XNDIGhE+aiMVgB/dmB/7UBAhdD91bGlCjg1StJ1MzumwPdHXShsrL2sJTdoUwf+C5s7lgEYpiXLE/pfB6put5a+8Ge0WAmdmVSnF2o7lnpCJN2y5SwA1UWDDZhtOC5Fzr0pemFh3b7QUsQLEsET9uEW5kRjiUYUCk4LxAfPu/nD7o7HQYD0KSUPAMg3nkzj0uLvpwdUUK/nhI7rTUlaYLmzlx/p+xE18R6QoRQV9wWpU/Oe2pCHH7+mO4lIqeq3HmZl4aWuiBuvmhQHQKhuRpvRT+bYJgQpaDT1S7ted+kxRjwlORQVrWg8XEH3M9GSJzSEqzoNr+rAQs+p/triVP88zJvpzZdwoG1B2Tvn1tpRmka8phreRbsGQnWtwxUVhYMDqisfdBBx+OYgwTL1EFHTrPbKx39LqbxfTaZwXLnvJbSOR6jXhUHLUJsh1LGTHYL4j1BfPg5aYu+OLJrCKitQ8f26zNgEs6v+6Mqbb8ao/QGaibbVIw7P2I8joQ8nJVYlB48ukcp+AyxVPJhwbAMwVCBYLhbm2z9z6gmJKy0C4mfdG9DqaHs6FfJOqn5FWX2XpGA5O65opzcq2Mr9Bg2Li56R3fnKD+doumHNZqu4FYOunREVSNMuRXMNj7TJ6/DWRgrwenf6fDgXYiwZl+D8W+jgOlwV4bQa8CCUB58fS5VPYdesWdYoOjp/n5y7aLQ0e+czlpDWpr67rxT40ARNcOR6DR5hfgwzkF3oB/OVZHVDVgUfJmXfoAasU+A/5aPoULcyTtNGl6KINNfb6KZkfTvjT4E3dSk9/duFOPZPBIG5aCMyLqTCDoW9pFt4JA5waH3uzhnef/oNb1SAVBpAQddzHwKB3VCSKgZYCMxHHdtMt5KVEjof/tpggKkjJKq7Imx/A7tVZKykhx4ic9IqPgM9hr5GR/smTRqZD+tioYCYDzUXKCj1Rbf4uuqXCGF7bT5nTVHjuhlR28D6jUzKpSHX4VESh1T8rMbdA9Swlwz27TvlJMKch0BZKg0l5B01RBZSSOokhY6qadtpSUYazm0BYVVVTkdkM8KD8muKt2ptrIi3h9U5UHzSAjM0k/T0qUSDmf5vQTvDIYDbPraTG8DZtoAddI1lHeIDzOFFcB9lJsqLXLGfAIZ9HHAkOh/t53H2dVUF4giVwJjQbIIn49mzorQu6oKU0R3DVRdWFTaGfr63wU+gCxYpYUMn4R5+x1U4Ofq6JFwKM7WVZ1NQnFP7oiZOgRoXKsoVz2cUL4H1AxVwqHjJyXVz0OlOPqxMjVaF43hWxQtPKcdBSYPPvRplPLfLtEn9xJUMNSk1ooLndRckA7phQXqQvQGkumiBZKpFf9weQvdACS4ymVHH34lfp1SaSw/q2xAm8C2sNAmmvSGLxW/c1qNI6X5WtDYF9DKTKXvdFOP/raF2citcJB81UsUkx2FnBDrdw3ZQDj4+eu8ZH3pZULNyYPa4Qo122U+mvK8R+aDul82xMqbnWpuWklRaR+T3eoJgGYgWQ7XHWoHA2jBFaQmkZC4Dht012PKjJdaUL2qHnK0ktXThh/pVGpzAILsd96Del+irqJw0H5pizJf4paOinJL5YYGzY3bu3lcacOH47XgWoynjGI8cHwDursr2mj/l9ANDVJGiU0/FU3IZ4ZSU1FF6CA3R+vRk5u3HDtyE8bNp8Tt/CwtJ8uO3rgty46yT+LXE016+9K+7Kgz/9uXHZMAMRUFkl0YK8K1+7StR20yS53yOxj6Mge6dNrKsq7fNaihJpS/F4vX3pRKuhmrry0VCIe+2HfJX7YpEyp9T4bqanaz1M0rm0iws3N6e4H4cOOihgPVMSrJ5rAs9fGMkFcfvBlJ92g17hph1wdhA3+1AzXztVaox6r4s/diPM5lPCkcgT38lYSU4UO/tvyavpj5D6obtIZBThhBGdAcHiDedJc1B3q7AVBPkyAzjr/3BoSyFOtBjTKalaz+3zYr2WoOXmC9vbQZBB8D4TAIrl6SPo03bC5J2cvDB3Z8yd7u3gvEh9O4esQTm4x0zUBW63N46SR/w67RQU9QK2F2ThaStIxC9sMSJLLuGmHXCy/9aqujCRxBF0BV5VNnnNQIJrOCVQWpLQ6iALRhMtIenlOVFEItlWhT+ffhGVpHfWcrbcUvHnA/mdHrysMH00LsjhH7HN6uOfscdDorBw3xFiYw6fego9ajWwtiLJ2SYatIx2sBTED8wz5QXTcLWVWLs9Uc9HlbOLbtWHJKu2i+ho5/E74Qn8N9A+Hg5668hH1JaHGYVHZx+m6um7LTbeajRyttujhkPUN8uPItRsPtVAxNWOCFcvdLe4UsJ1NqFdRkPgkcrwB3NPscSIdNade46Pgg0NLK58CjdHCz4NfgVlVrjErXWQy8QfgmjYmnlge/FuaaFRrUjOZ3UFNVZXI0A9+wtXnJD3qlyePpc5piSJm1MK1ZlRVtvoZxcoTuWzjSvdJQzMCvgmilB5U69vIKzT5WCDJBmrueePBVyL367TQ9xAWA/VdNuYfG6E8o9lyXe2ArNHpTVV4dNoWLdsFOY1l20+iYdpuHWTvw6n/Qci8WBN10G6H37wPh0DvPrtQbfPCtq02EpmZRR6PhqYaxDpeOgkyOvPAC8eHGTNZuNsuMHiuvbOr8bpmq5RiZNYdYOU2HaAPjk8q+ENY0pKBA2K1xDKOPAe1UVvvzOCjLiHQ6dCBGE3ToPX/nXKDt3fhi+X04Semxgjz4ORxJVx0+RZSQiL8T5TaURvPLsRb7HXSomXVwqNc60F7p05zNgJTZWJMmHctEtyY8SGNpKDIO13KHATt5Dnce0+P1Ey3Bg0zo9MrV4horeWXiM+hcKimRWB7pIi/BxpPMYw2HrEkNRZXaBQseq1DWdqd6qCr/6ckh7ZWn3e00X0gOyRd+W+sC4XC2FblSb2mH/TiKJB37nuPiCvFh4KTmfF7kENQu/p5Ao/DHqER2PI5IJXPeAsAWF4+RN9N+9nUH9uk+9dyHk7ZbnK/CZisq7eN9CxpI+meQE2Iq3nSRNoKM9/9jTplOPBRVZV1GCPFh/OPQYojNhpyYynPeovHQgg3UjN/zgQ+acjvaIWslGDTnN5tvNhAiCuFh4SB3o0n6SOB4Htp/Qk94/c74YK8iSmqxEyX1zyeo9WzoS0s446iqE4ucIQGOncA6XIZRawiZnNayXS9ahXE6pzQKmciaI07M8/sJhIPfHA36u5IcMEO6X9RJln7EDXh1V4neWhWNOvIGTFnH50W3DJ9dnRBZ9TGiohz8DDDfTO/l6MUPYekgH5QG48u8pUlSSzhLIbhNv1yY4TJ0OA0WAObD3BR9JE1Q+GenMjnCZ3D/cl/mZinls7+B+RUIB192TdDJVebARc5tsOI74xY1/iiU5XicUVltcYsGsWZ6GKyElAE20R5jEx1bQ18wDtSt6C5DVAzkcPN7flIzm80BeO+RaCS+loLXAnivM6yd30AXENywn0gkDXhvQeRe+G9SCoSD37sn6O/cOWBnivKTkPMYw096ua+tH38JDSE/RDcl+d2/XX9dYbA/PbFNXGNU1lvLQGVFtjajsh47YCedF+1exmHfxMJtDuH9Rja3OtwNn1llP9u+52V8YxuOsrqBZEFCgmCpFweLx4ECzcEjo4JmAQcCDvjHAdZubsPHBcwzj+hq/o0d9OSNA4Fw8ManoFXAgYADAQc+KA4EwuGDWu5gsgEHAg4EHPDGgf8H2K/f1LLjMn8AAAAASUVORK5CYII=) **因果性不是時空的內在屬性,****而是場關聯的湧現特徵**。 **5.5** **演化鏈的完整圖景** **層級** **結構** **數學描述** **湧現機制** L1 弦 ![](data:image/png;base64,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) 滿足三約束的最低結構(第四章) L2 波 ![](data:image/png;base64,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) 多弦疊加 L3 場 ![](data:image/png;base64,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) 多波連續疊加 L4 時空 ![](data:image/png;base64,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) 場的拓撲流變 **整個物理世界從一維弦生成**。每一階躍都是自然的數學湧現,不需要額外假設。 ---------- **第六章** **統一詮釋** **6.1** **弦論的DTFT****基礎** 傳統弦論的標準介紹:「假設基本粒子是一維振動的弦——這個假設能解決紫外發散、自動包含引力子、提供統一框架。」 DTFT的反轉:**弦不是假設,****是必然**。傳統弦論的所有技術成功都是這個必然性的後果: - 紫外有限性 = 點粒子病症三的根治 - 引力子的自動包含 = 弦振動模式中包含張量場 - 規範對稱的湧現 = 弦端點的U(N)結構 DTFT為弦論提供了**它一直缺乏的本體論基礎**——回答「為什麼是弦?」這個根本問題。 **6.2** **量子場論的DTFT****詮釋** QFT的核心概念在DTFT中獲得清晰的本體論定位: **QFT****概念** **DTFT****詮釋** 場 ![](data:image/png;base64,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) 多弦疊加的連續極限 粒子(場激發) 弦振動模式的局域化 真空 $ 0\rangle$ 重整化 對點粒子假設的補丁,弦中不需要 紫外截斷 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAD9QTFRFAAAAAAAAAAA6ADqQAGaQAGa2OjqQOpDbZgAAZgBmZrb/kDo6kNv/tmYAtv//25A62////7Zm/9uQ//+2///bz6y3ygAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAT0lEQVQoU2NgoDvgZxaA2inMwcQDZQqycLBDmCLcPLxQFUJsAoJQFbxcDMIQFcKcfAwMEBX8rEACrEKYgwskxQEU4GBkBKllZISaR33/AQAzLgI1+21aNwAAAABJRU5ErkJggg==) 弦的長度尺度 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjo6OjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkDo6kGYAkGaQkNvbkNv/tmYAtmY6tmZmtv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bNkSVcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU82RuRKAIAxEg+KJiBd4o/n/n9QZC9bWynTZecnuJEQ/rEMLBbHOSvl8C8IeT6/eJuSAv/EFcZ9mZZjmVUc9LHdFm7xOwEbROAXprOoF07B5wu2pkIBxM3AHIclrcCWaB7I1GFkhJOIf33AB828FcTMBn7IAAAAASUVORK5CYII=)的反映 規範場 弦的內部對稱模式 **QFT****是DTFT****在點粒子近似下的有效理論**。在能量遠低於弦尺度(![](data:image/png;base64,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))時,弦表現得像點粒子,QFT是準確的。在接近弦尺度時,QFT失效(紫外發散),需要弦的完整描述。 **6.3** **廣義相對論的DTFT****詮釋** GR的核心方程 Einstein方程 ![](data:image/png;base64,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)在DTFT中獲得本體論解釋: - 時空 ![](data:image/png;base64,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)不是基本對象,而是場的拓撲流變的幾何投影 - 物質 ![](data:image/png;base64,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)是多弦的能量密度 - 引力是時空曲率,曲率是場流變的幾何表現 - 引力子是閉弦的特定振動模式(自旋-2、無質量) **GR****是DTFT****在大尺度經典極限下的有效理論**。 **6.4** **統一框架的全景** DTFT提供以下統一: ![](data:image/png;base64,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) 從這個基礎,以下都可以推出: - 量子力學(單弦的振動量子化) - 量子場論(多弦疊加的有效理論) - 廣義相對論(場流變的幾何投影) - 弦論(本框架的數學技術版本) 這不是「再一個統一理論候選」,而是**對既有理論的本體論清理**。DTFT不否認任何已驗證的物理,只是揭示它們共同的更深基礎。 ---------- **第七章** **可證偽預測** 理論的科學價值在於可證偽性。DTFT給出三類可證偽預測: **7.1** **引力波的曲率調製** **預測 7.1**:引力波不是純正弦,而是攜帶源的曲率流變信息。 合併後階段(ringdown)的應變: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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)是合併系統的曲率演化,![](data:image/png;base64,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)。 **檢驗方法**:分析LIGO/Virgo合併事件的後段數據,尋找: ![](data:image/png;base64,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) 偏離量級 ![](data:image/png;base64,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)。 **時間表**:LIGO O5運行(2027),靈敏度提升10倍後可達。 **7.2** **電子能級的弦振動分裂** **預測 7.2**:如果電子是弦,其能級應有微小分裂: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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),![](data:image/png;base64,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) m。 預測分裂量級: ![](data:image/png;base64,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) **檢驗方法**:超高精度光譜學測量氫原子 ![](data:image/png;base64,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)躍遷,尋找約 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAcCAMAAABBJv+bAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGa2OgAAOpDbZgAAZjo6ZpC2ZpDbZrbbZrb/kDoAkGY6kNv/tmYA25A625Bm27Zm2/+22////7Zm/9uQ//+2///b2ADczwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAf0lEQVQ4T+2QSRKAIAwEEzdExX0D//9PgaCIJ8ujJacuJpNMAvC/VxeYGEbCOT1vbW3/JBMwRN2NdR3JfbqA4lnIYzlzK29N7mpCViQr7uWQn8lmrAlgOl3ZR6MAVOXYzYYVBUx6Mcnyk20ncsPIMNFrG/lgkAUixtWrM3/BtANxvwiYSFZesAAAAABJRU5ErkJggg==)eV 級別的額外譜線。 **現狀**:當前精度約 ![](data:image/png;base64,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)eV,需提升 ![](data:image/png;base64,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)倍。在精密光梳技術發展下可期。 **7.3** **高能散射截面的弦修正** **預測 7.3**:在能量接近 ![](data:image/png;base64,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)的散射過程中,弦結構導致截面修正。對於 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAcCAMAAAAkyw3kAAAAAXNSR0IArs4c6QAAAEVQTFRFAAAAAAAAAAA6ADqQAGa2OgAAOjqQOma2OpC2OpDbZgAAZpDbZrb/kDoAkGaQtmYAtpBm25A62////7Zm/9uQ//+2///bHHByuQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAe0lEQVQ4T+2SSw6AIAxEQUX8a6Fy/6OqJJaWhLhlYXfkDTNTglL/1PoC4TC6mYvtCId1cAr0UlBm+JxGIQyb4+eE0WSOvufKhPcuT4aWKQnDex+NpkllCIMVjaI5cyTsbx1amc06EsYnF4pbEw5rbCWFyf4D1/qL6u11AeR7BUXFQ5cnAAAAAElFTkSuQmCC)散射: ![](data:image/png;base64,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) 其中 ![](data:image/png;base64,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)是依賴於弦類型的可計算參數。 **檢驗方法**:LHC高能對撞數據在 ![](data:image/png;base64,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)TeV 處的精密分析,尋找與QFT預測的偏離。 **時間表**:HL-LHC升級後(2029-)。 **7.4** **預測的累積邏輯** 如果**任何一個**預測得到驗證,DTFT獲得實證支持。如果**所有預測**都失敗,DTFT被證偽。 這正是科學理論應有的姿態:**做出可被反駁的預測**,而不是構造永遠正確的形而上學。 ---------- **第八章** **哲學結語** 物理學的歷史是一部**逐漸放棄錯誤本體論假設**的歷史。 牛頓放棄了亞里士多德的「自然位置」;Einstein放棄了絕對時空;量子力學放棄了確定性軌跡。每一次放棄都伴隨著陣痛,但帶來了更深的理解。 點粒子是物理學最後一個未被清理的形而上學遺產——一個從亞里士多德的「不可分原子」延續至今的兩千年舊習。它的便利性掩蓋了它的不一致性:從電子自能發散到量子場論的紫外問題,從黑洞奇點到大爆炸初始條件,點粒子在每一個理論的邊界處都製造麻煩。 本文的論證很簡單:**三個獨立的物理約束,****點粒子的四個獨立病症,****弦的唯一最優性**。每一步都不訴諸超驗的形而上學,每一步都有獨立的數學基礎,每一步都可被批判和檢驗。 但簡單不等於膚淺。當這個論證被完整接受時,它推翻的不僅是「點粒子是基本的」這個命題,而是**整個現代物理學基於零維對象建構的世界圖景**。 從弦看世界,一切都流變。沒有靜止的點,沒有完美的圓,沒有孤立的無限。有的只是**動態的拓撲流變**——弦在振動,波在干涉,場在演化,時空在曲率中起伏。 這不是對現有物理的修補,這是對「存在意味著什麼」的重新定義。 ---------- 從點到弦 從靜態到流變 從假設到必然 這不是又一個理論 這是物理學從歷史包袱中解脫的開始 ---------- (歪臉笑) ---------- 完稿於2026年5月 ---------- **附錄A:****符號表** **符號** **含義** ![](data:image/png;base64,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) 弦的世界面參數化 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmADpmAGa2OgAAOgA6OgBmOjo6OpDbZgAAZjoAZrb/kDoAkDo6kLaQkLbbkNv/tmYAtmY6tpCQtv/b25A62////7Zm/9uQ//+2///bi/vN+QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAR0lEQVQoU2NgGHggzMjFICPCJMTAIM3NK8MvCHKRFIcAO1AACCQZOdl4wSxhVhk+VhBDho+LQZxZTFSCQQqoSJqHBaKSmgAAKV0CmxhkioMAAAAASUVORK5CYII=) 曲率 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjo6OjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkDo6kGYAkGaQkNvbkNv/tmYAtmY6tmZmtv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bNkSVcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU82RuRKAIAxEg+KJiBd4o/n/n9QZC9bWynTZecnuJEQ/rEMLBbHOSvl8C8IeT6/eJuSAv/EFcZ9mZZjmVUc9LHdFm7xOwEbROAXprOoF07B5wu2pkIBxM3AHIclrcCWaB7I1GFkhJOIf33AB828FcTMBn7IAAAAASUVORK5CYII=) 弦的長度尺度 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOpDbZgAAZjqQZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///binnyqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQoU2NgoCsQ42YEAyZ+BlEOfnE+NgZRTkEGES4GMW5eBjEeYZBjRICSUCDEChYBAnE+LpigKDsvjCnCLAiTF2CBMQUYGdlo6ikAcpkCY3pZIIkAAAAASUVORK5CYII=) 弦的張力 ![](data:image/png;base64,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) 弦振動模式的振幅 ![](data:image/png;base64,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) 量子場 ![](data:image/png;base64,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) 時空度規 ![](data:image/png;base64,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) 應力-能量張量 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmAGa2OgAAOmaQOma2OpDbZgAAZma2Zrb/kDoAkDo6kGZmkLbbkNv/tmY6ttv/tv//25A625Bm2////7Zm/9uQ/9u2/9vb//+2///bQOvNegAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUElEQVQoU2NgoDuQ5GVkEgDbKsPDISPILgZiikOFgEwRZmGom2R4WGCuk+bkgDHF4fIMgtwgQVFuBqCZjGxCDBJcDAx8/AxSgqyMbGBjaQIAadIClGlJ6XAAAAAASUVORK5CYII=) 極限結構(無限交接論) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OmaQOma2OpDbZgAAZjoAZjo6ZpDbZrb/kDoAkNv/tmYAtmY6tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bjJ6cCwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZUlEQVQoU82OWRKAIAxDIy6o4AaIIsL9j2npeAbH95NM22QK/IBzrggxBCC7JeRtxa3bgDQbxN4Avt75TVZPm4LtgEOu7JOmgoYuCxTx4vUlkrQqY6fyRhErTFxwyWqkmjSxfMMDHP0EskSXFV8AAAAASUVORK5CYII=) 關係算子 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAcCAMAAACEVGUKAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OpC2OpDbZgAAZjoAZrbbkDoAkJA6kNv/tmY6tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2///bxXy1cgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQoU2NgoCUQYWdkFQdZIMgpLsXNBrNKGCIIBBCWGA8jCz+IJcHIywBWJ83HBSUkOQQYGMCEBLMQVAOIK8oEFGJgANrAAmZQGQAAsFcDQui/g0AAAAAASUVORK5CYII=) 邊界算子 **附錄B:****四理論對應關係(****內部備忘)** (此附錄不公開,僅記於作者私房。) **本論文約束** **形而上學底層** 完美圓不存在 Cl-1自洽性 + Cl-2對偶性的物理投影 三維曲率公理 Cl-4生成性的運動學投影 無限交接論 Cl-3守恆性的關係性投影 (姊妹篇〈Closure公理與物理約束的本體論統一〉將正式展開此映射。) ---------- 字數:約20,500字