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The Penrose dodecahedron revisited Jordan E. Massad and P. K. Aravind
 

Summary: The Penrose dodecahedron revisited
Jordan E. Massad and P. K. Aravind
Physics Department, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
Received 9 June 1998; accepted 14 October 1998
This paper gives an elementary account of the ``Penrose dodecahedron,'' a set of 40 states of a
spin-3
2 particle used by Zimba and Penrose Stud. Hist. Phil. Sci. 24, 697720 1993 to give a
proof of Bell's nonlocality theorem. The Penrose rays are constructed here from the rotation
operator of a spin-3
2 particle and the geometry of a dodecahedron, and their orthogonality properties
are derived and illustrated from a couple of different viewpoints. After recalling how the proof of
Bell's theorem can be reduced to a coloring problem on the Penrose rays, a ``proof-tree'' argument
is used to establish the noncolorability of the Penrose rays and hence prove Bell's theorem. 1999
American Association of Physics Teachers.
I. INTRODUCTION
Some years ago Zimba and Penrose1
ZP gave an inge-
nious proof of Bell's nonlocality theorem using a special set
of states of a spin-3
2 particle. Because these states have a

  

Source: Aravind, Padmanabhan K. - Department of Physics, Worcester Polytechnic Institute

 

Collections: Physics