A fundamental problem with decoherent histories

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Title: A fundamental problem with decoherent histories

Author: Ding Jia

Abstract: In ordinary quantum theory, probabilities are only assigned to measurement outcomes. The decoherent histories program is proposed as a generalization, which also assigns probabilities to histories unassociated with measurements. To qualify as a generalization, probabilities for measurement histories should be recovered in special cases. However, for pure initial states a set of histories is decoherent if and only if it forms generalized record, even though there are measurement histories which lose record. Therefore decoherent histories fail to generalize measurement histories. To accommodate such measurement histories, a “mock histories formalism” is devised. Like the decoherent histories formalism, it does not hold measurement as a fundamental concept. Unlike the decoherent histories formalism, it does not impose the decoherence condition. Although the mock histories formalism is as incapable as the decoherent histories formalism in providing unambiguous predictions or retrodictions, and in singling out quasiclassical realms, it does not do worse. Altogether, these considerations cast doubt on whether it is reasonable to impose the decoherence condition at all in studying quantum histories.

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• Original versions: Article v1.0