AI 中文总结
该研究挑战无绝对时间时量子系统必为哈密顿定态的观点，提出时间重参数化不变的量子演化定律，指出其全局态非定态，建议重新审视相关假设。
AI 中文摘要
我们挑战物理学中一种普遍观点：若不存在绝对时间参数，无需参考外部时钟描述的量子系统可被假定处于其哈密顿量的定态。我们提出一种时间重参数化不变的量子演化定律，该定律针对给定初始条件，会预测与薛定谔方程相同的态空间轨迹，仅对于非平凡轨迹，它不预测轨迹遍历的速度。该演化定律的所有解均为薛定谔方程解的时间重参数化版本。我们展示在该框架下如何相对于内部时钟恢复薛定谔方程的预测。与Page-Wootters形式论或狄拉克的哈密顿约束量子化不同，此处的全局态并非定态。我们讨论导致“态可被假定为定态”这一普遍结论的假设，并建议需对这些假设进行重新审视。
英文摘要
We challenge the common belief that if there is no absolute time parameter in physics, a quantum system described without reference to an external clock can be assumed to be in a stationary state of its Hamiltonian. We present a time-reparameterisation invariant quantum evolution law, which for a given initial condition predicts the same trajectory in state space as the Schrödinger equation, except that for nontrivial trajectories it does not predict the speed at which the trajectory is traversed. The solutions of this evolution law are all time-reparameterised solutions of the Schrödinger equation. We show how the predictions of the Schrödinger equation are recovered relative to an internal clock in this framework. In contrast to the Page-Wootters formalism or Dirac's quantisation of the Hamiltonian constraint, here the global sate is not stationary. We discuss the assumptions leading to the common conclusion that the state can be taken stationary and suggest that they need to be revisited.
Comments7 pages
