关于动力学局域观察者时钟的（非）幺正性与爱因斯坦等效原理
On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle
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中文总结 AI 辅助
该研究探讨局域观察者时钟内禀时间的量子演化幺正性，发现固定弯曲背景下演化非幺正（违反量子等效原理），而微分同胚不变的动力学引力理论中演化幺正（保留等效原理），凸显微分同胚不变性的核心作用。
中文摘要 AI 辅助
我们研究相对于局域观察者时钟定义的内禀时间的量子演化幺正性。该观察者被建模为携带时钟和物质场探测器的相对论粒子，首先在固定弯曲背景下分析，随后在完全微分同胚不变的动力学引力理论中分析。在前一种情形下，我们发现相对于内禀时钟时间的演化通常是非幺正的，这意味着量子层面上爱因斯坦等效原理被违反。相反，在后一种情形下，微分同胚不变性使我们可以不失一般性地采用以观察者为中心的坐标。在由此产生的部分约化相空间上，一个微分同胚生成元线性依赖于时钟哈密顿量，生成与剩余微分同胚约束一致的关系演化。假设存在与微分同胚不变性一致的有效量子场论，这些特征确保相对于内禀时钟的演化是幺正的，从而即使在量子 regime 下也保留等效原理。我们的结果强调了微分同胚不变性在从局域观察者视角塑造关系幺正演化中的基础作用。
英文摘要
We investigate the unitarity of quantum evolution relative to an internal time defined by a local observer's clock. The observer is modeled as a relativistic particle carrying both a clock and a matter-field detector, analyzed first on a fixed curved background and subsequently within a fully diffeomorphism-invariant theory of dynamical gravity. In the former case, we find that evolution with respect to the internal clock time is generally nonunitary, implying a violation of the Einstein equivalence principle at the quantum level. In contrast, in the latter case, diffeomorphism invariance allows us to adopt observer-centric coordinates without loss of generality. On the resulting partially-reduced phase space, one of the diffeomorphism generators becomes linear in the clock Hamiltonian, generating a relational evolution that is consistent with the remaining diffeomorphism constraints. Assuming that an effective quantum field theory exists to be consistent with the diffeomorphism invariance, these features ensure unitary evolution relative to the internal clock, thereby preserving the equivalence principle even in the quantum regime. Our results highlight the fundamental role of diffeomorphism invariance in shaping relational unitary evolution from the perspective of a local observer.
