论文标题
永恒宇宙中的时间可观察
Time Observables in a Timeless Universe
论文作者
论文摘要
量子力学中的时间是特殊的：这是一个与Hermitian操作员无法关联的可观察的。结果，如果不调用外部古典时钟，就不可能在孤立的系统中解释动力学，这在量子重力的背景下变得尤其有问题。 1983年，Page and Wootters（PAW）率先提出了一种非常规的解决方案。PAW表明动态可能是静态宇宙两个子系统之间纠缠的新兴特性。在这项工作中，我们首先调查了在此框架中引入的可能性，一个遗传时间操作员补充了具有相同能量频谱的时钟汉密尔顿人。佩格（Pegg）于1998年提出了一个赫尔米尼亚操作员对这种汉密尔顿人的补充，后者将其命名为“年龄”。我们在这里表明，当在爪子上下文中引入时，可以将其解释为适当的Hermitian时间操作员与“良好”时钟汉密尔顿人的共轭。因此，我们表明，仍然遵循Pegg的形式主义，可以在爪子框架界的汉密尔顿河中引入，其汉密尔顿人的能量谱和理性能量比不等。在这种情况下，POVM描述了PEGG的POVM状态，即使它们不是正交的，也可以部分地可区分的系统，也可以提供对系统的一致动力学演变。
Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian time operator complement of a clock Hamiltonian having an equally-spaced energy spectrum. An Hermitian operator complement of such Hamiltonian was introduced by Pegg in 1998, who named it "Age". We show here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian. We therefore show that, still following Pegg's formalism, it is possible to introduce in the PaW framework bounded clock Hamiltonians with an unequally-spaced energy spectrum with rational energy ratios. In this case time is described by a POVM and we demonstrate that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially un-distinguishables.
