Notion of a "clock" in Quantum Mechanics

[WWCY]

TL;DR

Unitary evolution and "timekeeping"

Suppose the unitary operator $e^{-\frac{i}{\hbar}\hat{H}t}$ acts on $|\psi (0) \rangle$, does it make sense for one to think of the time-evolved state as some sort of time-keeping device? If not, why? If so, is such a notion useful?

Thanks in advance!

 

[HomogenousCow]

Well any observable phenomenon which behaves non-uniformly in time is a clock

 

[PeterDonis]

does it make sense for one to think of the time-evolved state as some sort of time-keeping device?

No, because that unitary operator is for time evolution in the absence of any measurement, and in order to use anything as a time keeping device, you have to be able to make measurements on it to see what its reading is.

It is possible, with some caveats, to find an observable (as distinct from a time-evolved quantum state) that can function as a "clock"; see John Baez' article here:

http://math.ucr.edu/home/baez/uncertainty.html

 

[Elias1960]

Unruh, W.G., Wald, R. (1989). Time and the interpretation of canonical quantum gravity, Physical Review D 40(8), 2598-2614 prove the following:

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".

 

[WWCY]

Thanks for the replies, cheers!