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Zed comments on Schroedinger's cat is always dead - Less Wrong Discussion
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I think that what you're saying is technically correct. However, simplifying the thought experiment by stating that the inside of the box can't interact with the outside world just makes the thought experiment easier to reason about and it has no bearing on the conclusions we can draw either way.
It's a distinction with a difference: the point is that a closed system means a factorizable wavefunction, not lack of interaction. (The latter is strictly impossible!)