In shortinger's cat, the cat is put into a superposition of awake and asleep. By which what we're imagining is there is a physical configuration of the cat. When you talk about decoherence and the entanglement with the environment, what you mean is there are photons,. let's say, in the box with the cat, that will either interact with the cat or not - depending on whether it's awake or asleep. Just because it's our thought experiment doesn't mean we can set it up however we want.

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