A MATHEMATICAL CHARACTERIZATION OF THE PHYSICAL STRUCTURE OF OBSERVERS

It is proposed that the physical structure of an observer in quantum m echanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to t his proposal is the introduction of an equivalence relation on sequenc es of spacetime sets which related a sequence to any other sequence to which it can be deformed without change of causal arrangement. This a llows 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 i nto a complete mathematical framework for a many-worlds interpretation . At a less ambitious level, the paper can be read as an exploration o f some of the technical and conceptual difficulties involved in constr ucting such a framework.