# A priori probability and localized observers by matthew j donald

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A Priori Probability and Localized Observers by Matthew J Donald ...

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 space-time physics, of

requiring instantaneous ”wave-packet collapse” across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, 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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