I'm reading this Sebens and Carroll's paper on Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. Where they presented their derivations of the Born rule and compared them to Zurek’s Envariance-based Derivation and The Decision-theoretic Program by Deutsch and Wallace. My question is why is it important to reproduce Born's rule in Everettian quantum mechanics? Do different approaches provide different explanations of Everettian probability?
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1$\begingroup$ I don't understand how this question is not already answered by the introduction to the paper - you need something like the Born rule to explain why quantum measurements seem to have probabilistic results to individual observers. Can you be more specific what you don't understand here? $\endgroup$– ACuriousMind ♦Commented Nov 19, 2022 at 11:01
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The standard view of probability in quantum theory claims that for a quantum state $$|\psi\rangle=\sum\alpha_i|i\rangle$$ if you do a measurement of the observable with eigenstates $|i\rangle$, you will get one of the states $|i\rangle$ with probability $|\alpha_i|^2$: this is called the Born rule.
According to the Everett interpretation, what happens is that after the measurement there are multiple versions of you: one for each of the possible outcomes $|i\rangle$. So why should there be any probabilities at all? And why should those probabilities be given by $|\alpha_i|^2$? This is a problem because the Born rule seems to have passed many experiment tests, so if the Everett interpretation can't reproduce it, then it is false. For more explanation of probability and experimental testing of the Everett interpretation, see
https://arxiv.org/abs/1508.02048
Some other interpretations, such as the Copenhagen or statistical interpretations, assume that the Born rule is true. Some other interpretations, such as the pilot wave theory, claim they can explain the Born rule and predict deviations from it:
