General Observables

Stephen J. Gustafson, Israel Michael Sigal

Alfredo Luis

We examine basic properties of complementarity by using the most general description of quantum observables as positive-operator measures. We show that, in general, two observables can be complementary or not depending on the measure of fluctuations adopted and that complementarity is not a symmetric relation. This occurs because the states that determine the measured statistics do not necessarily coincide with the minimum uncertainty states for the same observable. We also show that there are observables without a complementary observable and that complementarity is not preserved by the Neumark extensions.

K. Kong Wan, R. G. McLean

The notion of observables localized with respect to a general spectral measure is introduced as a generalization of the localization with respect to the spectral measure of the position observable. The physical features of these observables are discussed and certain of their algebraic and lattice theoretic properties are presented.

Göte Nyman

The perception-related origins of physical measures and standards are considered within the framework of the general observer theory. The impact of observer characteristics on the development of observer-centric physics, physical concepts and metrics are analyzed. A preliminary theoretical approach is suggested for the construction of a general observer theory and formulation of its relationship to observer-centered physical concepts and theories. The approach makes it possible to construct a theory of the observer, intrinsic in any theory of physics.