CLASSICAL AND NONCLASSICAL REPRESENTATIONS IN PHYSICS .2. QUANTUM-MECHANICS

The conceptual and formal structure of quantum mechanics is analyzed from the point of view of the dynamics of distinctions, occurring 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 slates, 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 infrastates, with the transition probability between two states proportional to the number of infrastates 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 infrastates as attractors of the dynamics induced by the interaction with the observation apparatus. This interaction is always partially undeterminate, because of the unobservable microstate of the apparatus. © 1990 Taylor & Francis Group, LLC.