A coarse grained description of time evolution: irreversible state reduction and time-energy relation

Summary

We show that a proper coarse grained description of time evolution leads to a finite-difference equation (1) with step τ for the density operator. This implies state reduction to the diagonal form in the energy representation and a quasi-ergodic behaviour of quantum-mechanical ensemble averages. An intrinsic time-energy relation ℕ ΔE⩾ ħ/2 is proposed and its equivalence to a time quantization discussed.