, Volume 50, Issue 2, pp 213–231 | Cite as

Spin and space

  • Robert Weingard
  • Gerrit Smith


In this paper we will take a careful look at the well-known fact that a complete 2π rotation in three dimensional space, while leaving vectors, tensors and generally the integral representations of the rotation group unchanged, causes a sign change in the half-integral spinor representations of the rotation group. First, in a brief introduction, we review the origin of the sign change of spinors by a 2π rotation. Next, we analyze Aharonov and Susskind's (hereafter referred to as A. & S.) (1967) original proposal for detecting such a sign change and compare it with a later proposal1 for detecting the sign change using neutron beams that are coherently split and recombined. While the A. & S. experiment is, we think, conceptually more interesting, the neutron beam experiment has actually been carried out. And finally, we discuss the philosophical significance of the rotationally induced spinor sign change.


Dimensional Space Integral Representation Neutron Beam Spinor Representation Rotation Group 
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  1. Aharnov, Y. and Susskind, L.: 1967, ‘Observability of the Sign Change of Spinors under 2π Rotations,’ The Physical Review 158, 1237–1238.Google Scholar
  2. Greenberger, D. M. and Overhauser, A. W.: 1980, ‘The Role of Gravity in Quantum Theory,’ Scientific American (May) 242, 66–76.Google Scholar
  3. Hartung, R. W.: 1979, ‘Pauli Principle in Euclidean Geometry,’ American Journal of Physics 47, 900–910.Google Scholar
  4. Johnson, C. S. and Pedersen, L. G.: 1974, Problems and Solutions in Quantum Chemistry and Physics, Addison-Wesley, Reading, Massachusetts.Google Scholar
  5. Misner, C. W., Thorne, K. S., and Wheeler, J. A.: 1973, Gravitation, Freeman, San Francisco.Google Scholar
  6. Rose, M. E.: 1957, Elementary Theory of Angular Momentum, John Wiley and Sons, New York.Google Scholar
  7. Werner, S. A., Colella, R., Overhauser, A. W. and Eagen, C. F.: 1975, ‘Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field,’ Physical Review Letters 35, 1053–1055.Google Scholar

Copyright information

© D. Reidel Publishing Co 1982

Authors and Affiliations

  • Robert Weingard
    • 1
    • 2
  • Gerrit Smith
    • 1
    • 2
  1. 1.Department of PhilosophyRutgers CollegeNew BrunswickUSA
  2. 2.Department of PhysicsSyracuse UniversitySyracuseUSA

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