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 $\tau$, required to measure the total energy with accuracy $\Delta E$, is bounded according to $\tau \Delta E>\mathrm{}ħ$. 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.

• Received 10 June 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.1368