标题： 膨胀宇宙中的光学腔共振器 显示英文标题

标题： Optical cavity resonator in an expanding universe

摘要： 我们研究了放置在由罗伯逊-沃克度规描述的膨胀流形中的共振光学腔中驻立电磁（EM）波频率的演化。 构建了一个局部坐标系，在该坐标系中时空局域上是闵可夫斯基的。 然而，由于罗伯逊-沃克度规的共形性质，传统的转换到局域惯性坐标的操作引入了局域时间坐标的物理解释上的歧义。 因此，与常识预期相反，单独实施等效原理（EEP）并不能让我们判断原子钟的滴答速率是否与基于腔模的时钟相同。 为了解决这个歧义，我们利用麦克斯韦方程分析了在膨胀宇宙中腔体刚性和其EM模式的振荡。 我们发现，随着宇宙膨胀，腔体的尺寸和EM频率在共形坐标下都经历绝热漂移。 我们建立了EM模式的振荡方程，用WKB近似法求解，并将依赖于坐标的量归约为由使用原子钟计时的局域观察者所测量的对应量。 结果显示，通过变换到局域坐标，腔体频率的绝热漂移被完全抵消，基于腔模的时钟计时率与原子钟相同。 我们得出结论，与原子钟相比，驻立EM波在腔体谐振器中的频率不应有宇宙学漂移。 连续比较光学腔体谐振器的频率与原子钟的频率，可以强有力地测试宇宙中哈勃膨胀的局部各向同性和爱因斯坦等效原理。 显示英文摘要

摘要： We study evolution of frequency of a standing electromagnetic (EM) wave in a resonant optical cavity placed to the expanding manifold described by the Robertson-Walker metric. One builds a local coordinate system in which spacetime is locally Minkowskian. However, due to the conformal nature of the Robertson-Walker metric the conventional transformation to the local inertial coordinates introduces ambiguity in the physical interpretation of the local time coordinate. Therefore, contrary to a common-sense expectation, a straightforward implementation of EEP alone does not allow us to decide whether atomic clocks ticks at the same rate as the clocks based on EM modes of a cavity. To resolve the ambiguity we analyzed the cavity rigidity and the oscillation of its EM modes in an expanding universe by employing the Maxwell equations. We found out that both the size of the cavity and the EM frequency experience an adiabatic drift in conformal coordinates as the universe expands. We set up the oscillation equation for the EM modes, solve it by the WKB approximation, and reduce the coordinate-dependent quantities to their counterparts measured by a local observer who counts time with atomic clock. The solution shows that there is a perfect cancellation of the adiabatic drift of cavity's frequency by the transformation to local coordinates, and the time counted by the clocks based on EM modes of cavity has the same rate as that of atomic clocks. We conclude that there should be no cosmological drift of frequency of a standing EM wave oscillating in the cavity resonator as compared to the frequency of atomic clocks. Continuous comparison of the frequency of the optical cavity resonator against that of atomic clock yields a powerful null test of the local isotropy of the Hubble expansion and the Einstein equivalence principle in cosmology.