  We continue our program of unifying general relativity and quantum mechanics
in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid
$\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle
over spacetime, and $G$ a suitable group acting on $\Gamma $. We show that
every $a \in {\cal A}$ defines a random operator, and we study the dynamics of
such operators. In the noncommutative regime, there is no usual time but, on
the strength of the Tomita-Takesaki theorem, there exists a one-parameter group
of automorphisms of the algebra ${\cal A}$ which can be used to define a state
dependent dynamics; i.e., the pair $({\cal A}, \phi)$, where $\phi $ is a state
on ${\cal A}$, is a ``dynamic object''. Only if certain additional conditions
are satisfied, the Connes-Nikodym-Radon theorem can be applied and the
dependence on $\phi $ disappears. In these cases, the usual unitary quantum
mechanical evolution is recovered. We also notice that the same pair $({\cal
A}, \phi)$ defines the so-called free probability calculus, as developed by
Voiculescu and others, with the state $\phi $ playing the role of the
noncommutative probability measure. This shows that in the noncommutative
regime dynamics and probability are unified. This also explains probabilistic
properties of the usual quantum mechanics.
