Abstract
We developed in Brussels a heuristic model, the ∈-model, in which it is possible to simulate a continuous transition between a classical (deterministic) and a quantum (probabilistic) regime. The lattice of properties related to this model was intensively studied [3, 5 to 10] and it appears that it exhibits a continuous transition between the classical and the quantum lattices. These lattices are representative of classical situations at one side and of quantum situations at the other side. It is not presently known if a continuous transition between the classical, deterministic, and the quantum, fuzzy, regimes does occur in nature. Even if this would occur, no one exactly knows the border-line between the two regions. This is an aspect of the so-called problem of measurement which deals with the comprehension of the way in which the macroscopic, deterministic and sharp world to which observers and measuring apparata belong coexists with the microscopic, unsharp, quantum world. In our model, we assume that “hidden variables” are present at the level of the apparatus, which is a non-standard hypothesis. The reader may thus consider this paper as a good example of how speculative ideas can be implemented in the framework of quantum logics.
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Durt, T. (1999). Orthogonality Relations: From Classical to Quantum. In: Aerts, D., Pykacz, J. (eds) Quantum Structures and the Nature of Reality. Einstein Meets Magritte: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2834-8_7
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