  The Karolyhazy uncertainty relation is the statement that if a device is used
to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the
measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of
combining the principles of quantum mechanics and general relativity. In this
note we show how this relation arises in our approach to quantum gravity, in a
bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We
use this relation to define a space-time-matter foam at the Planck scale, and
to argue that our theory is holographic. By coarse graining over time scales
larger than Planck time, one obtains the laws of quantum gravity. Quantum
gravity is not a Planck scale phenomenon; rather it comes into play whenever no
classical space-time background is available to describe a quantum system.
Space-time and classical general relativity arise from spontaneous localisation
in a highly entangled quantum gravitational system. The Karolyhazy relation
continues to hold in the emergent theory. An experimental confirmation of this
relation will constitute a definitive test of the quantum nature of gravity.
