Sergio F. Martinez

The projection postulate is the source of a long standing controversy in the interpretation of the axiomatic foundations of quantum mechanics. In a sense which is made precise in chapter II the projection postulate is a mathematical theorem easily derivable within the mathematical framework of the theory. This theorem receives a clear and straightforward interpretation if Luders' rule is given only statistical significance. Under the assumption that an interpretation of quantum mechanics has to provide an account of the process of measurement as a change on the state of individual systems, however, additional interpretive assumptions are needed in order to arrive at a satisfactory interpretation of Luders' rule. ;I show in chapter III that there are serious problems with the usual interpretation by making explicit in a quantum logical framework the concept of individual state and minimal disturbance implicit in this view. In chapter IV I show that it is possible to formulate a natural interpretation of Luders' rule as a description of 'dispersion free' state transformations within a semantic framework that takes states of individual systems to be represented by Boolean ultrafilters , as opposed to the usual approach that takes individual states to be represented by lattice ultrafilters. This lay the ground for the clarification of several interpretive issues in the foundations of quantum mechanics. It is shown that Luders' rule can be justified as a description of individual state transformations without the need of imposing additional assumptions. The derivation of Luders' rule within the semantic framework of B-states shows an important connection between interpretation that take individual state to be 'relative' to experimental situations and the statistical structure of the theory