Quantum, classical and intermediate I: a model on the Poincaré sphere

Following an approach, that we have called the hidden-measurement approach, 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.