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Many Worlds, the Born Rule, and Self-Locating Uncertainty

Sean M. Carroll, Charles T. Sebens

2014 · arXiv

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We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classical and quantum self-locating uncertainty, as in the cosmological multiverse.

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taliesinb
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> Aren't these multiway systems essentially what we see with ambiguous grammars... Yes. > One application of these might be to resolve the meaning of probabilities under the many-worlds interpretation... There's some ways to go before we Hilbert spaces, operator algebras, and the like, but yes, the idea would be that some path counting procedure would be used to derive the Born rule. It would be great to bridge with Carroll's self-locating uncertainty paper [0] > Under the section titled "Observers, Reference Frames and Emergent Laws" in this article, you can see some branches merging again in that first graph, so perhaps the probabilities of the Born rule are due to parallel computations that merge in this way... Right! [0]: https://arxiv.org/abs/1405.7907
GolDDranks
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That's not right. The combination of 1) local 2) realist 3) determinism has been disproven by Bell's theorem. But I it's still a "pick two" kind of choice. I, personally think that by Occam's razor, the Everett interpretation ("Many Worlds") makes the most sense, because it's simplest. And actually it retains all of the above three, but it introduces "self-locating uncertainty" (http://arxiv.org/abs/1405.7907), which effectively has the same kind of effect from our perspective.

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