 
Summary: Quantum structures in macroscopical reality*
D. Aerts, T. Durt, A. A. Grib , B. Van Bogaert and R. R. Zapatrin,
Abstract : We want to show in this paper that it is possible to construct macroscopical entities that
entail a quantum logical structure. We do this by means of the introduction of a simple macroscopical
entity and study its structure in terms of lattices and graphs, and show that the lattice is nonBoolean.
1. Introduction.
The principle idea that we want to put forward in this paper is the following : some
of the most characteristic properties of quantum entities can be found as properties of
ordinary mechanistic macroscopical entities as well. Both groups of researchers (D. Aerts,
T. Durt and B. Van Bogaert in Brussels, and A. A. Grib and R. R. Zapatrin in St. Peters
burg) have been investigating this principle idea, and have approached it from different
directions. In this joint paper we want to investigate the connection between the results of
the two groups.
The mechanistic macroscopical entity that we will present in this section has been
presented in Aerts (1985, 1986, 1987) with the aim of giving a possible explanation for the
nonclassical character of the quantum probability model. In this earlier work it is shown
that the probability model connected to a situation with a lack of knowledge about the
about the experimental effect on the physical entity is nonclassical. And also that the non
classical probability calculus of quantum mechanics can be interpreted as being the result
of a lack of knowledge about the changes effected by the experiments. But an explicit
