Foundations of quantum physics: A general realistic and operational approach

We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it 'changes' under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1) the states of the entity, which describe the modes of being of the entity, (2) the experiments that can be performed on the entity, which describe how we act upon and collect knowledge about the entity, (3) the outcomes of our experiments, which describe how the entity and the experiments "are" and "behave" together, (4) the probabilities, which describe our repeated experiments and the statistics of these repeated experiments, and (5) the symmetries, which describe the interactions of the entity with the external world without being experimented upon. Starting from these basic notions we formulate the necessary derived notions: mixed states, mixed experiments and events, an eigenclosure structure describing the properties of the entity, an orthoclosure structure introducing an orthocomplementation, outcome determination, experiment determination, state determination, and atomicity giving rise to some of the topological separation axioms for the closures. We define the notion of subentity in a general way and identify the morphisms of our structure. We study specific examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity described by the standard quantum mechanical formalism. We present a possible solution to the problem of the description of subentities within the standard quantum mechanical procedure using the tensor product of the Hilbert spaces, by introducing a new completed quantum mechanics in Hilbert space, were new 'pure' states are introduced, not represented by rays of the Hilbert space.