  It is commonly accepted that the study of 2+1 dimensional quantum gravity
could teach us something about the 3+1 dimensional case. The non-perturbative
methods developed in this case share, as basic ingredient, a reformulation of
gravity as a gauge field theory. However, these methods suffer many problems.
Firstly, this perspective abandon the non-degeneracy of the metric and
causality as fundamental principles, hoping to recover them in a certain
low-energy limit. Then, it is not clear how these combinatorial techniques
could be used in the case where matter fields are added, which are however the
essential ingredients in order to produce non trivial observables in a
generally covariant approach. Endly, considering the status of the observer in
these approaches, it is not clear at all if they really could produce a
completely covariant description of quantum gravity. We propose to re-analyse
carefully these points. This study leads us to a really covariant description
of a set of self-gravitating point masses in a closed universe. This approach
is based on a set of observables associated to the measurements accessible to a
participant-observer, they manage to capture the whole dynamic in Chern-Simons
gravity as well as in true gravity. The Dirac algebra of these observables can
be explicitely computed, and exhibits interesting algebraic features related to
Poisson-Lie groupoids theory.
