AI 中文总结
该研究在Page-Wootters量子力学框架下，揭示复合量子钟的相对论效应，发现内部能量对质心的反作用会引发时间非局域的薛定谔方程，还得到干涉可见度的二次方能量修正项，可通过差分测量分离。
AI 中文摘要
本研究在量子力学的Page-Wootters关系公式框架下，探究复合量子钟中相对论效应的显现机制。我们考虑一个同时包含内部自由度与质心自由度的系统，将内部系统视为内部钟，分析质心相对于该内部系统的条件演化。研究表明，内部部分会呈现出有效时间膨胀；在保留复合粒子完整质能结构的前提下，内部能量会通过一个算符值归一化因子对质心部分产生反作用。作为该反作用的直接结果，质心的条件动力学由一个在钟时间下非局域的薛定谔方程描述，其有效时间非局域性的量级为复合系统的康普顿时间。将该形式论应用于质心动量叠加态时，我们发现干涉可见度会出现一个与内部能量呈二次方关系的修正项，因此该修正项不仅依赖于控制标准时间膨胀退相的能量差，还取决于钟能量的绝对分布。尽管该修正项在参数上很小，但它是相对论性复合钟的普遍特征，原则上可通过差分可见度测量分离，该测量需比较跃迁频率相同但平均内部能量不同的钟。
英文摘要
In this work, we study the emergence of relativistic effects in a composite quantum clock within the Page-Wootters relational formulation of quantum mechanics. We consider a system with internal and center-of-mass degrees of freedom and analyze the conditioned evolution of the center-of-mass relative to the internal system treated as an internal clock. We show that the internal sector exhibits an effective time dilation. Retaining the full mass-energy structure of the composite particle, a back-reaction of the internal energy on the center-of-mass sector appears through an operator-valued normalization factor. As a direct consequence of the back-reaction, the conditioned center-of-mass dynamics is governed by a Schroodinger equation that is non-local in the clock time, with an effective temporal non-locality of the order of the Compton time of the composite system. Applying the formalism to a center-of-mass momentum superposition, we find that the interferometric visibility acquires a correction that is quadratic in the internal energy, and therefore depends on the absolute distribution of clock energies rather than only on the energy gaps that control the standard time-dilation dephasing. Although this correction is parametrically small, it is a generic feature of relativistic composite clocks and can, in principle, be isolated through a differential visibility measurement comparing clocks with equal transition frequency but different mean internal energies.
Comments12 pages
