  In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have
proposed a model unifying general relativity and quantum mechanics based on a
noncommutative geometry. This geometry was developed in terms of a
noncommutative algebra A defined on a transformation groupoid given by the
action of a group G on a space E. Owing to the fact that G was assumed to be
finite it was possible to compute the model in full details. In the present
paper we develop the model in the case when G is a noncompact group. It turns
out that also in this case the model works well. The case is important since to
obtain physical effects predicted by the model we should assume that G is a
Lorentz group or some of its representations. We show that the generalized
Einstein equation of the model has the form of the eigenvalue equation for the
generalized Ricci operator, and all relevant operators in the quantum sector of
the model are random operators; we study their dynamics. We also show that the
model correctly reproduces general relativity and the usual quantum mechanics.
It is interesting that the latter is recovered by performing the measurement of
any observable. In the act of such a measurement the model ``collapses'' to the
usual quantum mechanics.
