# Foundations of Quantum Physics: A General Realistic and Operational Approach

DOI: 10.1023/A:1026605829007

- Cite this article as:
- Aerts, D. International Journal of Theoretical Physics (1999) 38: 289. doi:10.1023/A:1026605829007

## Abstract

We present a general formalism with the aim ofdescribing the situation of an entity, how it is, how itreacts to experiments, how we can make statistics withit, and how it ‘changes’ under the influence of the rest of the universe. Therefore we baseour formalism on the following basic notions: (1) thestates of the entity, which describe the modes of beingof the entity, (2) the experiments that can be performed on the entity, which describe how weact upon and collect knowledge about the entity, (3) theoutcomes of our experiments, which describe how theentity and the experiments "are" and “behave” together, (4) theprobabilities, which describe our repeated experimentsand the statistics of these repeated experiments, and(5) the symmetries, which describe the interactions ofthe entity with the external world without beingexperimented upon. Starting from these basic notions weformulate the necessary derived notions: mixed states,mixed experiments and events, an eigenclosure structure describing the properties of theentity, an orthoclosure structure introducing anorthocomplementation, outcome determination, experimentdetermination, state determination, and atomicity giving rise to some of the topological separationaxioms for the closures. We define the notion ofsubentity in a general way and identify the morphisms ofour structure. We study specific examples in detail in the light of this formalism: a classicaldeterministic entity and a quantum entity described bythe standard quantum mechanical formalism. We present apossible solution to the problem of the description of subentities within the standard quantummechanical procedure using the tensor product of theHilbert spaces, by introducing a new completed quantummechanics in Hilbert space, were new ‘pure’states are introduced, not represented by rays of theHilbert space.