Multiple-event probability in general-relativistic quantum mechanics
摘要
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.
引用
@article{arxiv.gr-qc/0610140,
title = {Multiple-event probability in general-relativistic quantum mechanics},
author = {Frank Hellmann and Mauricio Mondragon and Alejandro Perez and Carlo Rovelli},
journal= {arXiv preprint arXiv:gr-qc/0610140},
year = {2008}
}