International Journal of Theoretical Physics

, Volume 47, Issue 1, pp 104–113 | Cite as

Planck’s Constant in the Light of Quantum Logic

  • Peter MittelstaedtEmail author


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 . We argue, that 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/, where m is the mass of the particle and Planck’s constant. We show that has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation.


Planck’s constant Quantum logic Classical physics 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.University of CologneCologneGermany

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