International Journal of Theoretical Physics

, Volume 54, Issue 6, pp 2042–2067 | Cite as

Macroscopic Observability of Spinorial Sign Changes under 2π Rotations



The question of observability of sign changes under 2π rotations is considered. It is shown that in certain circumstances there are observable consequences of such sign changes in classical physics. A macroscopic experiment is proposed which could in principle detect the 4π periodicity of rotations.


Manifold Tangent Space Geodesic Distance Classical Physic Torsion Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I am grateful to Martin Castell for his kind hospitality in the Materials Department of Oxford University where this work was completed, and to Manfried Faber and Christian Els for comments on the earlier versions of this paper. Christian Els also kindly carried out parts of the calculation in Appendix A especially the derivation of the curvature in (A.14). This work was funded by a grant from the Foundational Questions Institute (FQXi) Fund, a donor advised fund of the Silicon Valley Community Foundation on the basis of proposal FQXi-MGA-1215 to the Foundational Questions Institute. I thank Jurgen Theiss of Theiss Research for administering the grant on my behalf.


  1. 1.
    Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman and Company, New York (1973)Google Scholar
  2. 2.
    Penrose, R.: The Road to Reality: A Complete Guide to the Laws of the Universe. Jonathan Cape, London (2004)Google Scholar
  3. 3.
    Hartung, R.W.: Am. J. Phys. 47 (900) (1979). See also P.O. Brown and N.R. Cozzarelli, Science 206, 1081 (1979); and T.R. Strick, V. Croquette, and D. Bensimon, Nature London 404, 901 (2000)Google Scholar
  4. 4.
    Doran, C., Lasenby, A.: Geometric Algebra for Physicists. Cambridge University Press, Cambridge (2003)CrossRefMATHGoogle Scholar
  5. 5.
    Hestenes, D.: Am. J. Phys. 71, 104 (2003)CrossRefADSGoogle Scholar
  6. 6.
    Aharonov, Y., Susskind, L.: Phys. Rev. 158 (1237) (1967). see also H.J. Bernstein, Sci. Res 18 33 (1969)Google Scholar
  7. 7.
    Werner, S.A., Colella, R., Overhauser, A.W., Eagen, C.F.: Phys. Rev. Lett. 35, 1053 (1975)CrossRefADSGoogle Scholar
  8. 8.
    Weingard, R., Smith, G.: Synthese 50, 213 (1982)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Penrose, R., Rindler, W.: Spinors and Space-Time, vol. 1. Cambridge University Press, Cambridge (1987)Google Scholar
  10. 10.
    Koks, D.: Explorations in Mathematical Physics: The Concepts Behind an Elegant Language Springer (2006)Google Scholar
  11. 11.
    Choquet-Bruhat, Y., DeWitt-Morette, C., Dillard-Bleick, M.: Analysis, Manifolds and Physics: Parts I and II, Revised Edition, North Holland, Amsterdam (2000)Google Scholar
  12. 12.
    D’Inverno, R.: Introducing Einstein’s Relativity. Oxford University Press, Oxford (1992)MATHGoogle Scholar
  13. 13.
    Aldrovandi, R., Pereira, J.: Teleparallel Gravity: An Introduction (2013). T. Ortín, Gravity and Strings (Cambridge University Press, 2004); K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979)Google Scholar
  14. 14.
    Eisenhart, L.P.: Amer. Bull. Math. Soc. 39, 217 (1933)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Nakahara, M.: Geometry, Topology and Physics. Adam Hilger IOP Publishing Ltd, Bristol and New York (1990)CrossRefMATHGoogle Scholar
  16. 16.
    Ryder, L.H.: J. Phys. A 13, 437 (1980)CrossRefADSMATHMathSciNetGoogle Scholar
  17. 17.
    Eberlein, W.F.: Am. Math. Monthly 69, 587 (1962); See also Eberlein, W.F.: Am. Math. Monthly 70, 952 (1963)Google Scholar
  18. 18.
    Christian, J.: Disproof of Bell’s Theorem: Illuminating the Illusion of Entanglement, 2nd Edition. BrownWalker Press, Boca Raton, Florida (2014)Google Scholar
  19. 19.
    Abraham, R., Marsden, J.E.: Foundations of Mechanics (AMS Chelsea Publishing, Providence, RI (2008)Google Scholar
  20. 20.
    Du, Q.H.: J. Math. Imaging Vision 35, 155 (2009)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Kambe, T.: Geometrical Theory of Dynamical Systems and Fluid Flows, 2nd Revised Edition. World Scientific Publishing Company, Singapore (2010)MATHGoogle Scholar
  22. 22.
    Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer-Verlag, New York (1989)CrossRefGoogle Scholar
  23. 23.
    Peres, A.: Quantum Theory: Concepts and Methods, p. 161. Kluwer, Dordrecht (1993)Google Scholar
  24. 24.
    Milnor, J.W.: Topology from the Differentiable Viewpoint. Princeton University Press, Princeton, NJ (1965)MATHGoogle Scholar
  25. 25.
    Rodgers, J.L., Nicewander, W.A.: Am. Stat 42, 59 (1988)CrossRefGoogle Scholar
  26. 26.
    Frankel, T.: The Geometry of Physics: An Introduction, p. 501. Cambridge University Press (1997)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Wolfson CollegeUniversity of OxfordOxfordUK

Personalised recommendations