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Classical and nonclassical representations in physics II: quantum mechanics

The conceptual and formal structure of quantum mechanics is analysed from the point of view of the dynamics of distinctions, occcuring during the observation process. The Hilbert space formalism is simplified with the help of the concept of closure: closure of an eigenstate under an operator is generalized to the linear closure of a subset of states, and this is further simplified to orthogonal closure, meaning that a set of states can be distinguished by a single observation. Quantum states can be seen as (overlapping) subsets of unobservable infra-states, with the transition probability between two states proportional to the number of infra-states they have in common. This makes it possible to reconstruct the superposition principle. An analysis of the observation process leads to the interpretation of closed sets of infra-states as attractors of the dynamics induced by the interaction with the observation apparatus. This interaction is always partially indeterminate, because of the unobservable micro- state of the apparatus.