Decoherence is the fact that macroscopic things are constantly interacting with their environment. If you're in a wake cat or in a sleep cat, different photons will hit you and be absorbed. So you become entangled with the environment very, very quickly. It's a well known fact that if you let decoherence happen and then you look just at the quantum state of the system, so you forget the environment,. okay, you ignore it. That's creating the constructing the density matrix which we talked about earlier.

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