Eigenstate attractiveness

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If any superposition of quantum states is stable, why the preference for one of the eigenstates of the observable at the measurement? What is the attraction of such state?
 

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If any superposition of quantum states is stable, why the preference for one of the eigenstates of the observable at the measurement? What is the attraction of such state?
It's a postulate of quantum mechanics. As with any postulate (test this with Euclid's postulates), you aren't going to get very far asking why it works; the only answer is that that's how the universe we live in works.
 
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