  The `problem of time' remains an unresolved issue in all known physical
descriptions of the Universe. One aspect of this problem is the conspicuous
absence of time in the Wheeler-Dewitt equation, which is the analogue of the
Schrodinger equation for the Universal wavefunction. Page and Wootters famously
addressed this problem by providing a mechanism for effectively introducing
time evolution into this timeless cosmological picture. Their method, which is
sometimes called the conditional probability interpretation (CPI), requires the
identification of an internal clock system that is meant to keep time for the
remainder of the Universe. Most investigations into this idea employ the
idealized limit of a non-interacting clock system, the so-called ideal clock.
However, by allowing for interactions, we have found the counter-intuitive
result that a non-interacting clock is not necessarily the optimal choice, even
if it is `ideal'. In particular, the uncertainty that is associated with the
physical measurement of an atomic clock is found to decrease monotonically as
the interactions grow stronger. This observation, which is reinforced by a
previous study using a semi-classical clock, paves the way to an independent
argument that is based on the energy conservation of any isolated system. Our
conclusion is that ideal clocks must be prohibited from the CPI when recovering
cosmological time evolution. Interactions are necessary for describing time
evolution as a strict matter of principle. Lastly, we also consider the
implications of this result for the experience of time in the evolution of the
Universe.
