Fundamental principles of quantum theory

Abstract

After introducing general versions of three fundamental quantum postulates—the superposition principle, the uncertainty principle, and the complementarity principle—we discuss the question of whether the three principles are sufficiently strong to restrict the general Mackey description of quantum systems to the standard Hubert-space quantum theory. We construct an example which shows that the answer must be negative. We introduce also an abstract version of the projection postulate and demonstrate that it could serve as the missing physical link between the general Mackey description and the standard quantum theory.