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orthonormal comments on Schroedinger's cat is always dead - Less Wrong Discussion
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Clarification: the outside world does interact with the inside, but not in any way that depends on whether the cat is alive or dead. (If the contents of the box are positively charged electrically, they can continue to exert a force on objects outside. But if the cat is positively charged†, then the box needs to shield its influence on the electromagnetic field so that you can't tell from outside if it's moving or not.)
† That is, if it's a cation.
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!)