Spacetime Quantum Reference Frames and superpositions of proper times
Spacetime Quantum Reference Frames and superpositions of proper times
复制标题
时空量子参考系和固有时间的叠加
作者：
F. Giacomini
在广义相对论中，时空的描述依赖于理想化的杆和钟，它们确定了一个参考系。在任何具体的场景中，参考系都与物理系统相关联，这些物理系统最终都是量子性质的。因此，对物理定律的相对论性描述需要考虑这样的量子参照系（QRF），通过量子参照系，时空可以被赋予操作意义。在这里，我们引入时空量子参考系的概念，它与时空中的量子粒子相关联。这种表述的优点是，可以平等地对待空间和时间，并允许我们从另一个量子系统的角度来描述一组量子系统的动力学演化，其中其余物理系统演化的参数与被视为QRF的粒子的固有时间相一致。关键的是，两个不同的QRF中的真时并不通过标准变换联系起来，但它们可能是一个相对于另一个的量子叠加。具体地说，我们考虑了弱引力场中的N个相对论量子粒子系统，并引入了一个无时间的公式，其中N个粒子的全局态看起来是“冻结的”，但动力学演化是根据关系量恢复的。粒子的位置和动量希尔伯特空间用于通过到粒子的局部坐标系的变换来固定QRF，使得度量在QRF的原点处是局部惯性的。内部希尔伯特空间对应于时钟空间，它在粒子的局部框架中保持适当的时间。得益于这种完全关系的构建，我们从QRF的角度展示了剩余粒子如何在关系变量中动态演变。这里提出的结构包括Page-Wootters机制的非相互作用的时钟时，外部自由度被忽略。最后，我们发现在QRF中可以观察到引力红移的量子叠加和特殊相对论时间膨胀的量子叠加。
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.
影响因子：
3.3
作者：
Bartlett, Stephen D.;Rudolph, Terry;Turner, Peter S.
通讯作者：
Turner, Peter S.