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arXiv:1405.7907gr-qc

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

Sean M. Carroll, Charles T. Sebens

Abstract

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.

arXiv comments
15 pages. A version of this paper appears as a chapter in Quantum Theory: A Two-Time Success Story, Yakir Aharonov Festschrift (2013), D.C. Struppa, J.M. Tollaksen, eds. (Springer-Verlag), p. 157. This work is a summary of a more comprehensive paper at http://arxiv.org/abs/arXiv:1405.7577
Journal reference
DOI
doi:10.1007/978-88-470-5217-8_10
Subjects
gr-qcGeneral Relativity and Quantum Cosmology quant-phQuantum Physics

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Linked by 4 identifiable commenters in 4 comments across 4 threads, from Mar 2016 to Mar 2026.

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Discussed in comments4 threads

  1. Are the Mysteries of Quantum Mechanics Beginning to Dissolve? 1 comment

    • There’s papers that “derive” Born’s rule from the many worlds interpretations, e.g. https://arxiv.org/abs/1405.7907 I don’t claim to understand them though. I have tried.

      spot5010View on HNParent context

  2. Multicomputation as a General Paradigm for Theoretical Science 1 comment

    • > 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…

      taliesinbView on HNParent context

  3. Do electrons think? (1949) 1 comment
  4. The Neuroscientist Who Lost Her Mind 1 comment

    • 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…

      GolDDranksView on HNParent context

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