Gemsheim Sebastian, Rost Jan M
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany.
Phys Rev Lett. 2023 Oct 6;131(14):140202. doi: 10.1103/PhysRevLett.131.140202.
The nature of time as emergent for a system by separating it from its environment has been put forward by Page and Wootters [Phys. Rev. D 27, 2885 (1983)PRVDAQ0556-282110.1103/PhysRevD.27.2885] in a quantum mechanical setting neglecting interaction between system and environment. Here, we add strong support to the relational concept of time by deriving the time-dependent Schrödinger equation for a system from an energy eigenstate of the global Hamiltonian consisting of system, environment, and their interaction. Our results are consistent with concepts for the emergence of time where interaction has been taken into account at the expense of a semiclassical treatment of the environment. Including the coupling between system and environment without approximation adds a missing link to the relational time approach opening it to dynamical phenomena of interacting systems and entangled quantum states.
佩奇和伍特斯[《物理评论D》27, 2885 (1983年)PRVDAQ0556 - 282110.1103/PhysRevD.27.2885]在忽略系统与环境之间相互作用的量子力学设定中，提出了通过将系统与其环境分离，时间对于该系统而言是涌现出来的这一观点。在此，我们通过从由系统、环境及其相互作用构成的全局哈密顿量的能量本征态推导出系统的含时薛定谔方程，为时间的关系概念提供了有力支持。我们的结果与考虑了相互作用但以对环境进行半经典处理为代价的时间涌现概念相一致。精确包含系统与环境之间的耦合为关系时间方法增添了一个缺失的环节，使其能够适用于相互作用系统的动力学现象和纠缠量子态。
