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Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables.
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Y. Aharonov, P. Bergmann, and J. Lebovitz, Time asymmetry in the quantum process of measurement
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M. Gell-Mann and J.B. Hartle, Equivalent Sets of Histories and Multiple Quasiclassical Domains
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