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It is shown that a lack of knowledge about the measurements of a physical system gives rise to a nonclassical probability calculus for this physical system. It is also shown that the nonclassical probability calculus of quantum mechanics can be interpreted as being the result of a lack of knowledge about the measurements. Examples are given of macroscopic real systems that have a nonclassical probability calculus. A macroscopic real system that has a quantum probability calculus is also given, and more specifically a model for the spin of a spin- 1/2 particle is constructed. These results are analyzed in light of the old hidden variable problem.
Diederik Aerts (1986) studied this question.