Summary: Published as: Aerts, D., 1994, "Quantum structures, separated physical entities and probability",
Found. Phys., 24, 1227 - 1258.
Quantum structures, separated physical
entities and probability.
Department of Theoretical Physics,
Free University of Brussels, Pleinlaan 2,
B-1050 Brussels, Belgium.
Abstract. We prove that if the physical entity S consisting of two separated physical entities S1 and S2 satisfies
the axioms of orthodox quantum mechanics, then at least one of the two subentities is a classical physical entity.
This theorem implies that separated quantum entities cannot be described by quantum mechanics. We formulate
this theorem in an approach where physical entities are described by the set of their states, and the set of their
relevant experiments. We also show that the collection of eigenstate sets forms a closure structure on the set of
states, that we call the eigen-closure structure. We derive another closure structure on the set of states by means
of the orthogonality relation, and call it the ortho-closure structure, and show that the main axioms of quantum
mechanics can be introduced in a very general way by means of these two closure structures. We prove that for
a general physical entity, and hence also for a quantum entity, the probabilities can always be explained as being
due to the presence of a lack of knowledge about the interaction between the experimental apparatus and the