WWCY said:does it make sense for one to think of the time-evolved state as some sort of time-keeping device?
no dynamical variable in a system with Hamiltonian bounded from below can act as a perfect clock in the sense that there is always a nonvanishing amplitude for any realistic dynamical variable to "run backwards".
The notion of a "clock" in Quantum Mechanics refers to the concept of time and how it is measured in the quantum world. In classical mechanics, time is considered to be an absolute and continuous quantity. However, in quantum mechanics, time is treated as an operator or parameter that is subject to uncertainty and can be influenced by the state of the system.
In Quantum Mechanics, time is measured using a quantum clock, which is a physical system that undergoes periodic changes and can be used to measure the duration of events in a quantum system. The concept of a quantum clock is based on the idea that time is an observable quantity that can be measured in discrete units called "ticks".
The notion of a "clock" is important in Quantum Mechanics because it allows us to describe and understand the behavior of quantum systems over time. It also helps us to make predictions about the outcomes of quantum experiments and to study the effects of time on quantum systems.
The notion of a "clock" is closely related to the uncertainty principle in Quantum Mechanics. This is because the measurement of time in a quantum system is subject to the same uncertainty as other observables, such as position and momentum. This means that the more precisely we measure the time, the less certain we are about other quantities, and vice versa.
Yes, the notion of a "clock" can be applied to all quantum systems, regardless of their size or complexity. This is because the concept of time is fundamental to the laws of quantum mechanics and is applicable to all physical systems, including atoms, molecules, and even the entire universe.