 
Summary: Published as: Aerts, D., Coecke, B., Durt, T. and Valckenborgh, F., 1997, "Quantum,
classical and intermediate I: a model on the PoincarŽe sphere", Tatra Mt. Math. Publ., 10,
225.
Quantum, Classical and Intermediate I : a Model on the PoincarŽe Sphere.
Diederik Aerts*, Bob Coecke
, Thomas Durt
and Frank Valckenborgh
TENA , Free University of Brussels,
Pleinlaan 2, B1050 Brussels, Belgium.
Abstract. Following an approach, that we have called the hiddenmeasurement ap
proach, where the probability structure of quantum mechanics is explained as being due
to the presence of fluctuations on the measurement situations, we introduce explicitly
a variation of these fluctuations, with the aim of defining a procedure for the classical
limit. We study a concrete physical entity and show that for maximal fluctuations the
entity is described by a quantum model, isomorphic to the model of the spin of a spin 1/2
quantum entity. For zero fluctuations we find a classical structure, and for intermediate
fluctuations we find a structure that is neither quantum nor classical, to which we shall
refer as the 'intermediate' situation.
1. Introduction.
Quantum theory is different from classical theories in many aspects. It entails a non
