Abstract

The main idea of quantum mechanics, whether formulated in terms of the Planck constant or the noncommutativity of certain observables, must be tied to the recognition of the relativity and nonuniversality of the abstract concept of set (manifold) in the description of quantum systems. This entails the necessarily probabilistic description of quantum systems: since a quantum system ultimately cannot be decomposed into elements or sets, we have to describe it in terms of probabilities of only a relative selection of certain elements or sets in its structure. This gives rise to the potential possibilities of quantum systems in an actual physical situation, and as a result the corresponding probabilities are ontologically real, like any other physically verifiable relationships. In this way, the quantum potential possibilities (and probabilities as their measure) are no less objectively real than the conventional reality which we identify with the physically directly verifiable elements, particles, etc. Indeed, the distribution of probabilities described by the nonfactorizable wave function is as objectively real and concrete as chairs, walls and all other physical things. In the pure quantum state the probabilities of selection of elements from the ultimately detailed state of the system are mutually coordinated and correlated by the phenomenon of wholeness of the system, and form an implicative logical structure governed by this phenomenon of wholeness. This idea of the implicative logical organization of the probabilistic structure of a quantum system in the so-called pure (non-detailable) state, and the governing role of the phenomenon of wholeness (in the redistribution of probabilities depending on the nature of the development of the real experiment), is in good agreement with the results of quantum correlation experiments (for example, the experiments of Alain Aspect, Nicolas Gisin and others).