International Journal of Theoretical Physics

, Volume 47, Issue 2, pp 492–510

GR-Friendly Description of Quantum Systems

Article

Abstract

We present an axiomatic modification of quantum mechanics with a possible worlds semantics capable of predicting essential “nonquantum” features of an observable universe model—the topology and dimensionality of spacetime, the existence, the signature and a specific form of a metric on it, and a set of naturally preferred directions (vistas) in spacetime unrelated to its metric properties.

Keywords

Geometrical quantum mechanics Quaternion Principal metric Lorentzian Hyper-Kähler Birkhoff category Topos FLRW metric Boolean Measurement Propensity Cosmology 

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References

  1. 1.
    Aczel, P.: Lectures on semantics: the initial algebra and final coalgebra perspectives. In: Schwichtenberg, H. (ed.) Logic of Computation. Springer, Berlin (1997) Google Scholar
  2. 2.
    Adler, S.L.: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, Oxford (1995) MATHGoogle Scholar
  3. 3.
    Alfsen, E.M.: Math. Scand. 12, 106–116 (1963) MathSciNetGoogle Scholar
  4. 4.
    Balcar, B., Jech, T.: Bull. Symb. Logic 12(2), 241–266 (2006) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Block, N., Flanagan, O., Güzeldere, G.: The Nature of Consciousness: Philosophical Debates. MIT Press, Cambridge (1997) Google Scholar
  6. 6.
    Brody, D.C., Hughston, L.P.: J. Geom. Phys. 38, 19–53 (2001) MATHCrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Cartan, H.: C. R. Acad. Sci. Paris 211, 759–762 (1940) MATHMathSciNetGoogle Scholar
  8. 8.
    Chalmers, D.: The Conscious Mind. Oxford University Press, New York (1996) MATHGoogle Scholar
  9. 9.
    Chen, J., Li, J.: J. Diff. Geom. 55, 355–384 (2000) MATHGoogle Scholar
  10. 10.
    Fodor, J.A.: The Language of Thought. Harvard University Press, Cambridge (1975) Google Scholar
  11. 11.
    Gaeta, G., Morando, P.: J. Phys. A 35, 3925–3943 (2002) MATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Goldblatt, R.: Topoi. In: Studies in Logic and the Foundations of Mathematics, vol. 98, revised edition. North-Holland, New York (1984) Google Scholar
  13. 13.
    Hughes, J.: A study of categories of algebras and coalgebras. PhD thesis, Carnegie Mellon University (2001) Google Scholar
  14. 14.
    Kibble, T.W.B.: Commun. Math. Phys. 65, 189–201 (1979) MATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Kurosh, A.G.: Lekcii po obcshei algebre, Vtoroe izdanie. Nauka, Moskva (1973) Google Scholar
  16. 16.
    Massey, R., et al.: astro-ph/0701594 (2007) Google Scholar
  17. 17.
    Morando, P., Tarallo, M.: Mod. Phys. Lett. A 18(26), 1841–1847 (2003) MATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Schilling, T.A.: Geometry of quantum mechanics, PhD thesis, Pensylvania State University (1996) Google Scholar
  19. 19.
    Trifonov, V.: Europhys. Lett. 32(8), 621–626 (1995) CrossRefMathSciNetGoogle Scholar
  20. 20.
    Trifonov, V.: Int. J. Theor. Phys. 46(2), 251–257 (2007) MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Turi, D.: Functorial operational semantics. PhD thesis, Free University, Amsterdam Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.American Mathematical SocietyCumberlandUSA

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