论文标题
关系可观察物，参考帧和条件概率
Relational observables, reference frames, and conditional probabilities
论文作者
论文摘要
我们讨论了在时间反应不变的量子力学中的关系可观察物的构建，我们认为可以从条件概率方面理解它们的物理解释，这些概率是从量子限制方程的解决方案中定义的，这些方程在page-wootters形式主义的概括中。在这方面，我们展示了世界线张量场的条件期望值与适当定义的关系可观察物的量子平均值有关。我们还评论这些可观察物的动力学如何与量子参考框架的概念有关。在提出了一般形式主义之后，我们分析了一个回忆的宇宙学模型，为此我们构建了单位发展的量子关系可观察物。我们以一些关于这些结果在量子重力中构建和解释的构建和解释的相关性的评论。
We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions of the quantum constraint equation in a generalization of the Page-Wootters formalism. In this regard, we show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We also comment on how the dynamics of these observables can be related to a notion of quantum reference frames. After presenting the general formalism, we analyze a recollapsing cosmological model, for which we construct unitarily evolving quantum relational observables. We conclude with some remarks about the relevance of these results for the construction and interpretation of diffeomorphism-invariant operators in quantum gravity.
