SAE QM Paper 10 The Continuum Limit and the Path Integral- The Emergence of Classical Mechanics / 连续极限与路径积分——经典力学之浮现
Han Qin
Full bilingual text and framework available at self-as-an-end.net This paper concludes the SAE (Self-as-an-End) quantum-mechanics series. It does two things: it synthesizes into a single unified picture the ontology established across the nine preceding papers, and it settles the three matters left open by Movement III — the ontological status of the continuum limit, the ontological reading of the path integral, and the emergence of classical mechanics. As a concluding paper it offers no new prediction; its value lies precisely in the ontological synthesis. The picture is spined on one distinction: ρ-OR (pre-closure multi-occupancy) and ρ-AND (closure into single content). Movement I (P1–P5) treats the ontology, carrier, and phenomena of the pre-closure ρ-OR realm; Movement II (P6–P7) treats the closure event of ρ-OR→ρ-AND singularization; Movement III (P8–P10) treats the macroscopic and continuum emergence that follows closure. Every item of the standard quantum-mechanical furniture — the wavefunction, the complex amplitude, ℏ, Schrödinger evolution, tunneling, entanglement, the Born rule, measurement, decoherence, quantum field theory, the path integral, the classical limit — takes its place within this picture as a formal shadow of the ρ-OR/ρ-AND ontology. The path integral is read as a literal transcription, at the effective layer, of the ρ-OR realm (not an ontological identity, nor a derivation from SAE); the stationary-phase ridge is a closure-readable effective-layer face, not the settling of measurement; and Type-A (direct-empirical) novelty is shown to be structurally zero, the framework's contribution being a class of Occam-style ontological adjudication. 本文为 SAE(Self-as-an-End)量子力学系列之收束篇。其工作有二:一是把全系列九篇所立之本体一以贯之地综述为一张统一之图,二是收束乐章 III 所余之三事——连续极限之本体地位、路径积分之本体读法、经典力学之浮现。 作为收束篇,本文不提新预测,其价值正在本体之整合。统一之图以一条分判为脊:ρ-OR(前闭合多容)与 ρ-AND(闭合单内容)。乐章 I(P1–P5)述前闭合 ρ-OR realm 之本体、载体与现象;乐章 II(P6–P7)述 ρ-OR→ρ-AND 单一化之闭合事件;乐章 III(P8–P10)述闭合之后宏观与连续之涌现。标准量子力学之每一件家具——波函数、复振幅、ℏ、薛定谔演化、隧穿、纠缠、玻恩规则、测量、退相干、量子场论、路径积分、经典极限——皆于此图中各安其位,作 ρ-OR/ρ-AND 本体之形式化阴影。路径积分作 ρ-OR realm 在有效层之字面转写(非本体同一、非从 SAE 推导);驻相脊作 closure-readable 之有效层之脸,非测量之落定;甲型(直接经验型)之新意经证为结构性为零,本框架之贡献在一类奥卡姆式之本体论裁决。
•Jun 29, 2026•0 citations