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

الأصل · EN

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 >ℏ. 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.