Planck’s Constant in the Light of Quantum Logic
The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology, a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However, this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation.
KeywordsPlanck’s constant Quantum logic Classical physics
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- 3.Dalla Chiara, M.L., Giuntini, R.: Quantum logics. arXiv:quant-ph/0101028 v2 (2001) Google Scholar
- 5.Foulis, D.J., Bennett, M.K.: Effect algebras and unsharp quantum logics. Found. Phys. 1331–1352 (1994) Google Scholar
- 6.Heinonen, T.: Imprecise Measurements in Quantum Mechanics. Turun Yliopisto, Turku (2005) Google Scholar
- 14.Varadarajan, V.S.: Geometry of Quantum Theory, vol. 1. Van. Nostrand, Princeton (1968) Google Scholar