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Measurements are ordinarily described with respect to absolute "Newtonian"time. In reality however, the switching-on of the measuring device at theinstance of the measurement requires a timing device. Hence the classical time$t$ must be replaced by a suitable quantum time variable $\tau$ of a physicalclock. The main issue raised in this article is that while doing so, we can nolonger neglect the {\em back-reaction} due to the measurement on the clock.This back-reaction yields a bound on the accuracy of the measurement. When thisbound is violated the result of a measurement is generally not an eigenvalue ofthe observable, and furthermore, the state of the system after the measurementis generally not a pure state. We argue that as a consequence, a sub-class ofobservables in a closed system cannot be realized by a measurement.Comment: 18 pages, 4 figure

Back reaction of clocks and limitations on observability in closed systems