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.