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- Aerts, D. (1984). Construction of a structure which makes it possible to describe the joint system of a classical and a quantum system.
Reports in Mathematical Physics,20,pp. 421-428.

Abstract:We consider the joint system of a classical system and a quantum system. We require the same conditions on the two systems as those that give the description of two classical systems by means of the cartesian product of the phase spaces and the description of two quantum systems by means of the tensor product of the Hilbert spaces. We set up a structure that enables us to describe the joint system of a classical system and a quantum system.- Aerts, D. (1984). Construction of the tensor product for lattices of properties of physical entities.
Journal of Mathematical Physics,25,pp. 1434-1441.

Abstract:We construct the tensor product for the property lattices of two entities. We give a physical interpretation for this tensor product. We show that the tensor product is never an orthocomplemented lattice if both entities are nontrivial. It also never satisfies the covering law. This is the reason why this tensor product does not exist in quantum mechanics and does not exist in quantum logic. We analyze the relation of the tensor product with the usual description of two entities in quantum mechanics. At the end, we give a mathematical way of constructing this tensor product.- Aerts, D. (1984). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation.
Helvetica Physica Acta,57,pp. 421-428.

Abstract:We show that quantum mechanics is not a complete theory. We do not as in the case of Einstein Podolsky and Rosen derive this incompleteness by a logical reasoning ex absurdum, but indicate explicitly which are the missing elements of reality in the description by quantum mechanics of separated physical systems.- Aerts, D. (1984). How do we have to change quantum mechanics in order to describe separated systems. In S. Diner, D. Fargue, G. Lochak and F. Selerri (Eds.),
The Wave-Particle Dualism(pp. 419-431). Dordrecht: Kluwer Academic.

Abstract:Since we were able to show recently that quantum mechanics can not describe separated physical systems we analyse again the reasoning of Einstein-Podolsky-Rosen, and find that the most straight forward conclusion of this paradox is not correct. We indicate the missing elements of reality in the quantum mechanical description of separated physical systems. We show that Bell inequalities are satisfied iff the two physical systems are separated, whether the systems are quantum systems or classical systems is of no matter. We give an example of a classical macroscopical situation where Bell inequalities are violated.- Aerts, D. (1984). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation.
Annales de la Fondation Louis de Broglie,2,pp. 163-175.

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