On the Foundation of Quantum Theory

In the literature, quantum mechanics is founded by a very abstract set of postulates. For several reasons I propose that this set should be replaced by straightforward postulates based on the notion of conceptual variables, a notion generalizing the statisticians' parameters: In his mind, any observer/ actor in each given situation may have several conceptual variables. Some of these are accessible, can in some future be given numerical values by measurements or experiments. The notion of a maximal accessible conceptual variable is crucial. This can be motivated by an assumption to the effect that all physical variables in the actor's context have parallels in his mind. Examples are given. Under weak technical conditions, basic postulates of quantum mechanics can be shown to be implied by a postulate assuming that the actor in his mind has two related maximally accessible variables. Some specific symmetry conditions are needed. The notion of being related has a precise definition. A parallel development can be based on conceptual variables shared by a group of communicating observers.