Synthese

, Volume 50, Issue 2, pp 213–231

Spin and space

  • Robert Weingard
  • Gerrit Smith
Article

Abstract

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.

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Bibliography

  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
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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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