Incompleteness of measurement apparatuses
A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise. Each quantum observable is then an abstract representation of many measurement apparatuses, each incomplete in a different way. Moreover, a measured system must be prepared in a state that is orthogonal to the states of all particles of the same type in the environment. This is the main purpose of preparations. A system so prepared is said to have a "separation status". A new, more satisfactory definition of separation status than the spatial one proposed in previous papers then results. Conditions are specified under which the particles in the environment may be ignored as is usually done in the theory of measurement.