We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra A on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ. We show that every a ∈ 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 A which can be used to define a state dependent dynamics; i.e., the pair (A, ϕ), where ϕ is a state on A, is a "dynamic object". Only if certain additional conditions are satisfied, the Connes-Nikodym-Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (A, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ 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 * Vatican Observatory, V-00120 Vatican City State. 1 usual quantum mechanics.We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra A on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ. We show that every a ∈ 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 A which can be used to define a state dependent dynamics; i.e., the pair (A, ϕ), where ϕ is a state on A, is a "dynamic object". Only if certain additional conditions are satisfied, the Connes-Nikodym-Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (A, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ 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.