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关系量子因果过程:精确模型、连续极限与涌现引力的边界

Relational Quantum Causal Processes: Exact Models, Continuum Limits, and the Boundary of Emergent Gravity

Yipeng Xu

arXiv 2607.26672首次发表:更新:

AI 中文总结

本研究构建关系量子因果过程的精确模型,证明其向洛伦兹度量测度空间的收敛性等结果,提出 RQCP-QG 框架以分离机制与开放假设,探索引力的量子起源。

AI 中文摘要

关系量子因果过程将有限操作语境表述为局部完全正映射上的正规正泛函,响应差异生成影响代数,其中心投影定义了联合可读取的布尔事件。我们从该起点出发构建一系列精确且可控的模型:新鲜环境幺正碰撞电路产生具有精确电荷中心固定代数、固定响应阶下均匀有限步极限及图控制亚稳态马尔可夫动力学的退相交换动力学;吸收态模型展现非阿贝尔量子存储器与布尔记录间的尖锐相变;反转协变缺陷动力学在受限图族上生成局部有限偏序,且无需假设李雅普诺夫时间。在经认证的序、正加性记录测度、紧性与可识别性的条件下,我们证明了向洛伦兹度量测度空间的子序列收敛、有限重构界及可容许光滑极限的唯一性;互补有限调节器为模块化到 boost 响应、零层析、同更新变分恒等式、诱导二次引力及兼容公共细化极限提供可控测试。这些结果在其所述模型内是精确或可控的,但尚未构成单一背景独立的微观定律,无法联合生成邻接性、时间、体积归一化、维度、符号、非线性爱因斯坦约束及量子物质。因此我们提出 RQCP-QG 作为定理索引框架,将已建立的机制、条件复合及开放假设相分离。

英文摘要

Relational quantum causal processes formulate finite operational contexts as normal positive functionals on local completely positive maps. Response differences generate an influence algebra, and its central projections define jointly readable Boolean events. We develop this starting point through a sequence of exact and controlled models. Fresh-environment unitary collision circuits produce dephasing-exchange kinetics with an exact charge-center fixed algebra, a uniform finite-step limit at fixed response order, and graph-controlled metastable Markov dynamics. An absorbing-state model exhibits a sharp transition between non-Abelian quantum memory and Boolean records. A reversal-covariant defect dynamics generates a locally finite partial order on a restricted graph family without assuming a Lyapunov time. Conditional on a certified order, a positive additive record measure, compactness, and identifiability, we prove subsequential convergence to a Lorentzian metric-measure space, finite reconstruction bounds, and uniqueness of admissible smooth limits. Complementary finite regulators provide controlled tests of modular-to-boost response, null tomography, same-update variational identities, induced quadratic gravity, and compatible common-refinement limits. These results are exact or controlled within their stated models, but they do not yet constitute a single background-independent microscopic law that jointly generates adjacency, time, volume normalization, dimension, signature, nonlinear Einstein constraints, and quantum matter. We therefore present RQCP-QG as a theorem-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.

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