NDLI: Planck’s Constant in the Light of Quantum Logic

Content Provider	Springer Nature Link
Author	Mittelstaedt, Peter
Copyright Year	2007
Abstract	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.
Starting Page	104
Ending Page	113
Page Count	10
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	47
Issue Number	1
e-ISSN	15729575
Language	English
Publisher	Springer US
Publisher Date	2007-05-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Planck’s constant Quantum logic Classical physics Mathematical and Computational Physics Elementary Particles, Quantum Field Theory Quantum Physics Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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