The time-energy uncertainty relation for quantum events

Abstract

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 $\Delta t\Delta E\gtrsim \hslash$, the term $\Delta t$ 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 {\em true} 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.

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References in corpus (6)

• Quantum speed limit for physical processes
• There is only one time
• Quantum Time: experimental multi-time correlations
• Number-phase entanglement and Einstein-Podolsky-Rosen steering
• Flow of time during energy measurements and the resulting time-energy uncertainty relations
• Fundamental bound for time measurements and minimum uncertainty clocks

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