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``Weighing'' a closed system and the time-energy uncertainty principle

Yakir Aharonov·Benni Reznik
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Abstract

A gedanken-experiment is proposed for `weighing'' the total mass of a closed system from within the system. We prove that for an internal observer the time $τ$, required to measure the total energy with accuracy $ΔE$, is bounded according to $τΔE >\hbar $. This time-energy uncertainty principle for a closed system follows from the measurement back-reaction on the system. We generally examine what other conserved observables are in principle measurable within a closed system and what are the corresponding uncertainty relations.

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Yakir Aharonov, Benni Reznik. 1999-06-09. ``Weighing'' a closed system and the time-energy uncertainty principle. https://doi.org/10.1103/physrevlett.84.1368

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