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arXiv · 2108.13974

The time-energy uncertainty relation for quantum events

Matteo Fadel·Lorenzo Maccone
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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 $\Delta {t}\Delta E\gtrsim\hbar$, 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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Matteo Fadel, Lorenzo Maccone. 2021-08-31. The time-energy uncertainty relation for quantum events. https://doi.org/10.1103/physreva.104.l050204

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