### A Priori Probability and Localized Observers

#### Foundations of Physics, Volume 22, pages 1111-1172 (1992).

** 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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#### Matthew J. Donald

#### The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great
Britain.

#### e-mail :
mjd1014@cam.ac.uk

#### home page:
http://people.bss.phy.cam.ac.uk/~mjd1014