标题： 引力熵是观察者相关的 显示英文标题

标题： Gravitational entropy is observer-dependent

摘要： 在量子引力中，有人主张对观察者所起作用的正确计算，将给定时空子区域中的可观测算子的冯·诺依曼代数从III型提升到II型。 虽然这允许其熵的数学精确定义，但我们表明这个过程取决于所使用的观察者。 我们通过考虑存在许多可能观察者的设置来明确这一点；通过推广之前的方法，我们得出了相对于不同观察者（以及相对于任意观察者集合和任意全局物理状态）的子区域密度算符，并在半经典极限下计算了相关的熵，以及一些超出此极限的具体例子。 我们发现，不同观察者看到的熵可以有很大差异。 我们的工作广泛使用了量子参考系（QRF）的形式主义；事实上，正如我们指出的，这里以及之前工作中考虑的“观察者”只不过是QRF。 在此过程中，我们证明了Chandrasekaran等人[arXiv:2206.10780]所引用的物理状态和可观测量的描述等价于Page-Wootters形式主义，从而得出非正式的口号“PW=CLPW”。 我们希望本文能有助于促进QRF和量子引力社区之间长期期待的结合。 更多细节将在一篇配套论文中出现。 显示英文摘要

摘要： In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers and for arbitrary global physical states), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the `observers' considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [arXiv:2206.10780] is equivalent to the Page-Wootters formalism, leading to the informal slogan "PW=CLPW". It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.