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Multiple-event probability in general-relativistic quantum mechanics

Frank Hellmann·Mauricio Mondragon·Alejandro Perez·Carlo Rovelli
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Abstract

We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse" algorithm. We first point out certain difficulties of some natural definitions of multi-event probability, including the conditional probability widely considered in the literature. We then observe that multi-event probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum classical boundary, one can always trade a sequence of non-commuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the "wave function collapse" algorithm can nevertheless be recovered. The discussion bears also on the nature of the quantum collapse.

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Frank Hellmann, Mauricio Mondragon, Alejandro Perez, Carlo Rovelli. 2006-10-27. Multiple-event probability in general-relativistic quantum mechanics. https://doi.org/10.1103/physrevd.75.084033

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