Time-energy uncertainty relation for quantum events

Textbook quantum mechanics treats time as a classical parameter and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as xe002;txe002;E > h over bar , the term xe002;t must be interpreted as a time interval and not as a time measurement uncertainty due to quantum noise. However, quantum clocks allow for a measurement of the time at which an event happens by conditioning the system's evolution on an additional quantum degree of freedom. Within this framework we derive here two uncertainty relations that relate the uncertainty in the quantum measurement of the time at which a quantum event happens on a system to its energy uncertainty.

Automated summary

Textbook quantum mechanics treats time as a classical parameter rather than a quantum observable, which fails to explain conventional time-energy uncertainty relations. However, with quantum clocks, it is possible to measure time and derive two uncertainty relations linking time quantum measurement uncertainty to energy uncertainty.