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A Priori Probability and Localized Observers by Matthew J Donald
Abstract. A physical and mathematical framework for the analysis of probabilities
in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and spacetime physics, of
requiring instantaneous ”wavepacket collapse” across the entire universe. The physical starting point is the idea of an observer as an entity, localized in spacetime, for
whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with his observations of the system at that
moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum ﬁeld theory. A function deﬁning the a priori probability
of mistaking one local state for another is analysed. This function is shown to possess
a broad range of appropriate properties and to be uniquely deﬁned by a selection of
them. Through a general model for observations, it is argued that the probabilities
deﬁned here are as compatible with experiment as the probabilities of conventional
interpretations of quantum mechanics but are more likely to be compatible, not only
with modern developments in mathematical physics, but also with a complete and
consistent theory of measurement.
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