How to switch between relational quantum clocks
How to switch between relational quantum clocks
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DOI：
10.1088/1367-2630/abd1ac
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发表时间：
2020-12-01
影响因子：
3.3
通讯作者：
Vanrietvelde，Augustin
中科院分区：
文献类型：
--
作者：
Hohn，Philipp A.;Vanrietvelde，Augustin
每个时钟都是一个物理系统，因此最终是量子的。因此，一个自然出现的问题是如何描述相对于量子钟的时间演化，特别是相对于不同量子钟的动力学是如何相关的。这是一个特别紧迫的问题，因为量子引力中时间问题的多重选择方面，它假定在一般的广义相对论系统中没有内部时钟的独特选择，不同的选择导致不等价的量子理论。利用最近统一的方法来切换量子参考系统[Vanrietvelde et al 2020 Quantum 4 225; Vanrietvelde et al 2018 arXiv：1809.05093 [quant-ph]]，我们展示了一种在量子理论中不同时钟选择之间切换的系统方法。我们说明它的参数化粒子，它像重力一样，具有哈密顿约束。我们明确地在相对于非相对论时间变量的量子演化和相对于粒子位置的量子演化之间切换，这需要仔细地正则化所谓的到达时间可观测的零模式。虽然这个玩具模型很简单，但我们的方法是通用的，特别是直接适用于量子宇宙学。它通过时钟选择中性的狄拉克量子化理论，系统地将相对于不同时钟选择的约化量子理论联系起来，类似于流形上的坐标变化。这一方法提出了一个新的选择问题的观点，表明它是一个完整的关系量子理论的选择功能，作为狄拉克量子化和量子去参数化理论的结合。正是这种结合允许人们在不同的时间参考系统之间不断切换，这是广义协变性的量子概念的先决条件。最后，我们表明，量子不确定性一般会导致一个不连续的关系动态切换时钟时，在经典的情况下。
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is thus how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related. This is a particularly pressing issue in view of the multiple choice facet of the problem of time in quantum gravity, which posits that there is no distinguished choice of internal clock in generic general relativistic systems and that different choices lead to inequivalent quantum theories. Exploiting a recent unifying approach to switching quantum reference systems [Vanrietvelde et al 2020 Quantum 4 225; Vanrietvelde et al 2018 arXiv: 1809.05093 [quant-ph])], we exhibit a systematic method for switching between different clock choices in the quantum theory. We illustrate it by means of the parametrized particle, which, like gravity, features a Hamiltonian constraint. We explicitly switch between the quantum evolution relative to the non-relativistic time variable and that relative to the particle's position, which requires carefully regularizing the zero-modes in the so-called time-of-arrival observable. While this toy model is simple, our approach is general and, in particular, directly amenable to quantum cosmology. It proceeds by systematically linking the reduced quantum theories relative to different clock choices via the clock-choice-neutral Dirac quantized theory, in analogy to coordinate changes on a manifold. This method suggests a new perspective on the multiple choice problem, indicating that it is rather a multiple choice feature of the complete relational quantum theory, taken as the conjunction of Dirac quantized and quantum deparametrized theories. Precisely this conjunction permits one to consistently switch between different temporal reference systems, which is a prerequisite for a quantum notion of general covariance. Finally, we show that quantum uncertainties generically lead to a discontinuity in the relational dynamics when switching clocks, in contrast to the classical case.