### A Mathematical Characterization of the
Physical Structure of Observers.

#### Foundations of Physics, Volume 25, pages 529-571 (1995).

** Abstract ** It is proposed that the physical structure of an
observer in quantum mechanics is constituted by a pattern of elementary
localized switching events. A key preliminary step in giving mathematical
expression to this proposal is the introduction of an equivalence relation on
sequences of spacetime sets which relates a sequence to any other
sequence to which it can be deformed without change of causal
arrangement. This allows an individual observer to be associated with a
finite structure. The identification of suitable switching events in the
human brain is discussed. A definition is given for the sets of sequences of
quantum states which such an observer could occupy. Finally, by providing
an a priori probability for such sets, the definitions are incorporated into a
complete mathematical framework for a many-worlds interpretation. At a
less ambitious level, the paper can be read as an exploration of some of the
technical and conceptual difficulties involved in constructing such a
framework.

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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