Abstract
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born’s rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative procedure is proposed for constructing an averaged density matrix for a random small region of the universe and then calculating observational probabilities indirectly by Born’s rule as conditional probabilities, conditioned upon the existence of an observation.
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Many Worlds, the Born Rule, and Self-Locating Uncertainty.Sean M. Carroll & Charles T. Sebens - 2014 - In Daniele C. Struppa & Jeffrey M. Tollaksen (eds.), Quantum Theory: A Two-Time Success Story. Springer. pp. 157-169.

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