  The notion of time is given a different footing in Quantum Mechanics and
General Relativity, treated as a parameter in the former and being an observer
dependent property in the later. From a operational point of view time is
simply the correlation between a system and a clock, where an idealized clock
can be modelled as a two level systems. We investigate the dynamics of clocks
interacting gravitationally by treating the gravitational interaction as a
classical information channel. In particular, we focus on the decoherence rates
and temporal resolution of arrays of $N$ clocks showing how the minimum
dephasing rate scales with $N$, and the spatial configuration. Furthermore, we
consider the gravitational redshift between a clock and massive particle and
show that a classical channel model of gravity predicts a finite dephasing rate
from the non-local interaction. In our model we obtain a fundamental limitation
in time accuracy that is intrinsic to each clock.
