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,
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, B-1050 Brussels, Belgium.
Abstract. Following an approach, that we have called the hidden-measurement 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.
Quantum theory is different from classical theories in many aspects. It entails a non-