  Background independence is often emphasized as an important property of a
quantum theory of gravity that takes seriously the geometrical nature of
general relativity. In a background-independent formulation, quantum gravity
should determine not only the dynamics of space-time but also its geometry,
which may have equally important implications for claims of potential physical
observations. One of the leading candidates for background-independent quantum
gravity is loop quantum gravity. By combining and interpreting several recent
results, it is shown here how the canonical nature of this theory makes it
possible to perform a complete space-time analysis in various models that have
been proposed in this setting. In spite of the background-independent starting
point, all these models turn out to be non-geometrical and even inconsistent to
varying degrees, unless strong modifications of Riemannian geometry are taken
into account. This outcome leads to several implications for potential
observations as well as lessons for other background-independent approaches.
