The time-energy uncertainty relation for quantum events

• URL: http://arxiv.org/abs/2108.13974v1
• Date: Tue, 31 Aug 2021 16:57:12 GMT
• Title: The time-energy uncertainty relation for quantum events
• Authors: Matteo Fadel and Lorenzo Maccone
• Abstract summary: Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. 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. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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