AI 中文总结
本文基于冯·诺依曼形式体系，提出量子-经典逻辑二分框架，从经典时钟的离散结构中推导出$\hbar$，并与't Hooft元胞自动机建立映射，为测量问题提供新逻辑进路。
AI 中文摘要
我们基于标准冯·诺依曼形式体系，对量子动力学提出一种基础性的重新诠释，主张在经典观测环境与量子被观测系统之间存在结构性的逻辑二分。与普适性框架相对，我们证明理论一致性要求不同的命题逻辑：布尔逻辑支配环境，而非布尔逻辑适用于被观测系统。在此框架内，理想经典时钟被表示为一个能量谱均匀离散化的开放系统。动力学遵循 Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) 主方程，并受哈密顿量保持可观测性的约束。尽管时钟的时间演化由与测量装置的耗散耦合驱动，但它允许一个稳定的、确定性的解，对应于信息保持的循环动力学。这一确定性区域作为逻辑吸引子涌现，并由测量相互作用固有的布尔结构所稳定。最终，$\hbar$ 作为基本标度参数从经典时钟的作用-角度对易关系中导出，揭示作用量子反映了经典时间性之下的离散逻辑结构。此外，该框架与 't Hooft 的元胞自动机形式体系建立了精确映射，提供了一种不需要隐变量和超决定论假设的替代本体论诠释。由此产生的量子动力学（作为潜在的重语境化）与经典动力学（作为时间的现实化）之间的区分，为测量问题提供了一种新颖的逻辑进路。
英文摘要
We present a foundational reinterpretation of quantum dynamics based on the standard von Neumann formalism, positing a structural logical bipartition between a classical observational environment and a quantum observed system. Against universalist frameworks, we show that theoretical consistency requires distinct propositional logics: Boolean logic governs the environment, while non-Boolean logic applies to the observed system. Within this framework, an ideal classical clock is represented as an open system whose energy spectrum is uniformly discretized. The dynamics follow from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation under the constraint that the Hamiltonian remains observable. Although the clock's temporal evolution is driven by dissipative coupling to the measurement apparatus, it admits a stable, deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime emerges as a logical attractor, stabilized by the Boolean structure inherent to the measurement interaction. Ultimately, $\hbar$ is derived as a fundamental scaling parameter from the classical clock's action-angle commutation relation, revealing that the quantum of action reflects the discrete logical structure underlying classical temporality. Furthermore, this framework establishes an exact mapping with 't Hooft's cellular automaton formalism, offering an alternative ontological interpretation that not require hidden variables and superdeterministic assumptions. The resulting distinction between quantum dynamics (as potential recontextualization) and classical dynamics (as temporal actualization) provides a novel logical approach to the measurement problem.
Comments22 pages
