  When gauge field theory coherent states for loop quantum gravity (LQG) were
introduced, an optimized semiclassical proper length emerged, corresponding to
the edge length $\epsilon$ of a graph embedded in a given classical geometry.
Here $\epsilon$ is explored in more detail. $\epsilon$ at the Earth's surface
is found to lie between 100 $\mu $m and 0.7 m. The implied quantum fluctuating
space-time strain amplitude and noise spectrum are estimated to be $4\; 1/2$
orders smaller than the current experimental detectability. However, such a
macroscopic $\epsilon $ makes regularization of the semiclassical
electromagnetic Hamiltonian problematic for photon wavelengths shorter than
$\epsilon$. The origin of a large $\epsilon$ is traced to an edge-wise tensor
product of independent edge-based coherent states for the whole graph state.
This provides physical grounds for recently proposed collective coherent
states, where $\epsilon$ acquires the interpretation of a sliding scale. A new
proper distance $\xi$ emerges as the characteristic length of semiclassical
LQG. $\xi$ will affect the LQG photon vacuum dispersion relations, and is also
accessible to current measurements of space-time strain. Matter interactions
may also affect $\xi$.
