On classical and quantum objectivity

We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful-or equivariant-realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that the classical notion is overdetermined.