A Mechanical Classical Laboratory Situation With A Quantum Logic Structure

this paper we will make a similar attempt but now concentrating on the logical aspects of the example. 1. CLASSICAL ENTITIES AND QUANTUM ENTITIES. In the discipline quantum logic the basic structure of research was originally the structure of orthomodular lattice. Quantum-like entities had such a structure of orthomodular lattice for the set of their propositions, while classical entities had a structure of distributive orthomodular lattice (or Boolean algebra) for the set of their propositions. Meanwhile the classification classical entities versus quantum-like (or non-classical entities) has been studied much more in detail, relating the corresponding structures to real physical situations [2]. We have taken a very easy criterion from the results of this research on the possibility of distinguishing between the two kind of entities classical and non-classical. We shall consider an entity (classical or non-classical) to be described by a set M (denoted by m, n, ...) of measurements and a set ## # # ( denoted by p, q, ...) of states. In different approaches different names have been given to these two basis sets (measurements have been called yes-no experiments, questions, propositions, observables and operations, and states have also been called preparations), but mainly these differences will play no role in what we would like to show in this paper. The results can easily be translated in the proper approach. We must remark that when we use the concept 'state', then we mean 'pure state'. The more general situation of mixed states will not be considered here, since our example in any case does not contain mixed states. The following characterization of a classical entity shall be adopted (it is the characterization explicitly used in [3]) : Criterion for classical cha..