Multiple-event probability in general-relativistic quantum mechanics Export

@misc{citeulike:934172, 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.}, archivePrefix = {arXiv}, author = {Hellmann, Frank and Mondragon, Mauricio and Perez, Alejandro and Rovelli, Carlo}, citeulike-article-id = {934172}, citeulike-linkout-0 = {http://arxiv.org/abs/gr-qc/0610140}, citeulike-linkout-1 = {http://arxiv.org/pdf/gr-qc/0610140}, day = {27}, eprint = {gr-qc/0610140}, keywords = {article, mechanics, physics, quantum, relattivity}, month = {Oct}, posted-at = {2009-03-04 19:45:48}, priority = {2}, title = {Multiple-event probability in general-relativistic quantum mechanics}, url = {http://arxiv.org/abs/gr-qc/0610140}, year = {2006} }

TY - ELEC ID - citeulike:934172 L3 - citeulike-article-id:934172 N2 - 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. TI - Multiple-event probability in general-relativistic quantum mechanics KW - article KW - mechanics KW - physics KW - quantum KW - relattivity AU - Hellmann, Frank AU - Mondragon, Mauricio AU - Perez, Alejandro AU - Rovelli, Carlo PY - 2006/Oct/27/ UR - http://arxiv.org/abs/gr-qc/0610140 ER -