will therefore correspond to an average over several intervals, and therefore its evolution cannot be unitary.

In a real experiment, there will be decoherence in the system under study due to interactions with the environment, that will be superposed on the effect we discuss. Such interactions might be reduced by cleverly setting up the experiment. The decoherence we are discussing here however, is completely determined by the quality of the clock used. It is clear that if one does experiments in quantum mechanics with poor clocks, pure states will evolve into mixed states very rapidly. The effect we are discussing can therefore be magnified arbitrarily simply by choosing a lousy clock. This effect has actually been observed experimentally in the Rabi oscillations describing the exchange of excitations between atoms and field [@Br].

Fundamental limits to realistic clocks
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We have established that when we study quantum mechanics with a physical clock (a clock that includes quantum fluctuations), unitarity is lost, conserved quantities are still preserved, and pure states evolve into mixed states. The effects are more pronounced the worse the clock is. Which raises the question: is there a fundamental limitation to how good a clock can be? This question 