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"Weighing" a closed system and the time-energy uncertainty principle
1School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel and Department of Physics, University of South Carolina, Columbia, South Carolina 29208, USA.
Physical Review Letters
|October 4, 2000
Summary
This study proposes a thought experiment to weigh a closed system internally. It reveals a time-energy uncertainty principle for internal observers, linking measurement accuracy to time, crucial for understanding closed system dynamics.
Area of Science:
- Quantum Physics
- Thermodynamics
- Measurement Theory
Background:
- Understanding the limitations of measurement within isolated systems is crucial.
- Previous work has not fully addressed internal observers' constraints in closed systems.
Purpose of the Study:
- To propose a gedanken experiment for internally weighing a closed system.
- To derive the time-energy uncertainty principle for an internal observer within a closed system.
- To explore the measurability of other conserved observables and their uncertainty relations.
Main Methods:
- Theoretical analysis of a gedanken experiment.
- Derivation of uncertainty relations from measurement backreaction.
- General examination of conserved observables in closed systems.
Main Results:
- A lower bound for the time-energy uncertainty relation (tauDeltaE > h-bar/2) for internal observers was established.
- The measurement backreaction is identified as the source of this uncertainty principle.
- The framework for analyzing measurability of other conserved quantities was developed.
Conclusions:
- Internal measurement of total mass/energy in a closed system is fundamentally limited by a time-energy uncertainty principle.
- This principle arises from the unavoidable backreaction of measurement on the system.
- The study provides a foundation for exploring quantum measurement limits in isolated systems.