"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 tau, required to measure the total energy with accuracy Delta E, is bo unded according to tau Delta E > (h) over bar. 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 p rinciple measurable within a closed system and what are the corresponding u ncertainty relations.