Gao, Shan (2025) Can Self-Locating Uncertainty Ground the Born Rule? An Inconsistency Argument. [Preprint]
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Abstract
Vaidman's self-locating uncertainty (SLU) represents an innovative and influential approach to deriving Born rule probabilities in the Many-Worlds Interpretation (MWI) of quantum mechanics, offering a promising epistemic foundation for understanding probabilities in a deterministic multiverse. This paper examines a potential inconsistency in the SLU framework: while the concept relies on observer branching to generate multiple copies and thus enable uncertainty about branch location, such branching results in pure, deterministic local states for each copy, making the mixed reduced density matrix (RDM)—a key element in deriving amplitude-squared probabilities—unavailable. Conversely, if the mixed RDM is retained, the observer remains unentangled and spans all branches, eliminating the multiplicity essential to SLU. The derivations by McQueen and Vaidman appear to draw on both SLU (which presupposes branching) and the mixed RDM (which presupposes no branching), without fully addressing this tension. Our analysis suggests that the inconsistency poses a significant challenge to grounding the Born rule purely in SLU, independent of specific branching models. The results highlight unresolved questions in the foundations of Everettian probability and point toward the need for further refinement or supplementation of the SLU approach.
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| Item Type: | Preprint | ||||||
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| Keywords: | Many-Worlds Interpretation; Born rule; branching; self-locating uncertainty; probability; mixed reduced density matrix | ||||||
| Subjects: | Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Prof. Shan Gao | ||||||
| Date Deposited: | 26 Dec 2025 14:04 | ||||||
| Last Modified: | 26 Dec 2025 14:04 | ||||||
| Item ID: | 27624 | ||||||
| Subjects: | Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 25 December 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/27624 |
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