Time as a statistical variable and intrinsic decoherence

We propose a novel approach to intrinsic decoherence without adding new assumptions to standard Quantum Mechanics. We generalize the Liouville equation just bl: requiring the dynamical semigroup property or time evolution and dropping the unitarity requirement. With no approximations and specific statistical assumptions we find a generalized Liouville equation which depends on two characteristic time tau(1) and tau(2) and reduces to the usual equation in the limit tau(1) = tau(2) --> 0. However, for tau(1) and tau(2) arbitrarily small but finite. our equation can be written as a finite difference equation which predicts state reduction to the diagonal form in the energy representation. The rate of decoherence becomes faster at the macroscopic limit as the energy scale of the system increases. In our approach the evolution time appears, a posteriori, as a statistical variable as if time evolution would take place randomly at average intervals tau(2), each evolution having a time width tau(1). A generalized Tam Mandelstam inequality is derived, The relation with previous wort; by Milburn is discussed.