What exactly is the meaning of environment being slow? Maximillian Schlosshauer book Decoherence mentions this: "Let us now consider the situation in which the modes of the environment are "slow" in comparison with the evolution of the system. That is, we assume that the highest frequencies (i.e. energies) available in the environment are smaller than the separation between the energy eigenstates of the system. In this situation, the environment will be able to monitor only quantities which are constants of motion. In the case of nondegeneracy , this quantity will be the energy of the system, thus leading to the environment-induced superselection of the energy eigenstates for the system (i.e., eigenstates of the self-Hamiltonian of the system)." 1. If the energies in the environment is smaller than the separation between the energy eigenstates of the system, does it mean it is accepted or not (as quantum as I know only unit can be accepted in QM)? 2. Why did it mention "constants of motion".. it is talking about position? Or is momentum consider constants of motion, why? 3. What does "nondegeneracy" mean? 4. Can you give an example where the environment is "slow" and energy of the system is chosen? Help appreciated much.