“Weighing” a Closed System and the Time-Energy Uncertainty Principle

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 backreaction 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.