THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

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, which 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 a lack of knowledge about the interaction between the experimental apparatus and the entity. (shrink)

We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.