Advertisement

International Journal of Theoretical Physics

, Volume 48, Issue 1, pp 261–281 | Cite as

Similarity-Projection Structures: The Logical Geometry of Quantum Physics

  • Daniel Lehmann
Article

Abstract

Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical Boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.

Keywords

Similarity-Projection structures Measurement algebras Quantum Logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lehmann, D.: A presentation of quantum logic based on an “and then” connective. J. Log. Comput. 18(1), 59–76 (2008). doi: 10.1093/logcom/exm054 MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Lehmann, D.: Quantic superpositions and the geometry of complex Hilbert spaces. Int. J. Theor. Phys. 47(5), 1333–1353 (2008). doi: 10.1007/s10773-007-9576-y MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Lehmann, D., Engesser, K., Gabbay, D.M.: Algebras of measurements: the logical structure of quantum mechanics. Int. J. Theor. Phys. 45(4), 698–723 (2006). doi: 10.1007/s10773-006-9062-y CrossRefMathSciNetGoogle Scholar
  4. 4.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1995) MATHGoogle Scholar
  5. 5.
    Whitney, H.: On the abstract properties of linear dependence. Am. J. Math. 57, 509–533 (1935) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Engineering and Center for the Study of RationalityHebrew UniversityJerusalemIsrael

Personalised recommendations