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Summary: Published as: Aerts, D. and Durt, T., 1994, "Quantum, Classical and Intermediate, and
illustrative example", Found. Phys., 24, 1353-1369.
Quantum, Classical and Intermediate,
an illustrative example
Diederik Aerts* and Thomas Durt
Department of Theoretical Physics,
Free University of Brussels, Pleinlaan 2
B-1050 Brussels, Belgium.
Abstract. We present a model that allows to build structures that evolve continuously from classical
to quantum, and we study the intermediate situations, giving rise to structures that are neither classical
nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of
these intermediate situations, and demonstrate how the superposition principle disappears during the
transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics
for the intermediate situations.
1. Introduction.
We use the approach where the quantum structures arise as a consequence of the presence of
fluctuations on the measurement situations, and where the indeterminism of the measurement
process is due to the fact that an experiment e consists of different possible sub-experiments
e() that are not distinguished macroscopically. During an experimental process correspond-
ing to the experiment e, one of these hidden experiments e() actually occurs, and each one
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