# 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.

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