# Macroscopic Observability of Spinorial Sign Changes under 2*π* Rotations

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## Abstract

The question of observability of sign changes under 2*π* 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 4*π* periodicity of rotations.

## Keywords

Manifold Tangent Space Geodesic Distance Classical Physic Torsion Tensor## Notes

### Acknowledgments

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.

## References

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