  We present a mathematical structure which unifies mathematical structures of
general relativity and quantum mechanics. It consists of the noncommutative
algebra of compactly supported, complex valued functions ${\mathcal A}$, with
convolution as multiplication, on a groupoid $\Gamma $ the base of which is the
total space $E$ of the frame bundle over space-time $M$. A differential
geometry based on derivations of ${\mathcal A}$ suitably generalizes the
standard differential geometry of space-time, and the algebra ${\mathcal A}$,
when represented in a bundle of Hilbert spaces, defines a von Neumann algebra
${\mathcal M}$ of random operators that generalizes the usual quantum
mechanics. The main result of the present paper is that there exists a space
${\mathcal M_0}$, dense in ${\mathcal M}$, that is isomorphic with the algebra
${\mathcal A}$. This isomorphism allows us to transfer all differentially
geometric constructions, generalized Einstein's equations including, made with
the help of ${\mathcal A}$ (and its derivations) to the space ${\mathcal M_0}$.
In this way, we obtain a generalization of general relativity in terms of
random operators on a bundle of Hilbert spaces. However, this generalization
cannot be extended to the whole of ${\mathcal M}$, and this is the main
mathematical obstacle, at least in this approach, to fully unify theory of
gravity with physics of quanta.
