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Autism and Quantum Mechanics
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Schrödinger's cat is indeed a terrible analogy, but so is the Christmas presents one. A cat is always either alive or dead, and the contents of a Christmas present are determined before opening it. But the state of a quantum particle is fundamentally ambiguous before measurement. This is demonstrated by experiments breaking the Bell inequality if you want to know more!
No, the state is not what's ambiguous, but rather a single, definitive value of the variable is what does not exist unless it's already in an eigenstate of said variable.
Yes, I am aware of what you meant, but your wording may be misleading.