Spin and Rotations in Galois Field Quantum Mechanics

Abstract

We discuss the properties of Galois Field Quantum Mechanics constructed on a vector space over the finite Galois field GF(q). In particular, we look at 2-level systems analogous to spin, and discuss how SO(3) rotations could be embodied in such a system. We also consider two-particle `spin' correlations and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless not violated in this model.

arXiv comment21 pages, 11 pdf figures, LaTeX. Uses iopart.cls. Revised introduction. Additional references

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• A General Theory of Quantum Relativity
• Time and M-theory
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• Galois Field Quantum Mechanics
• Bell's Inequalities, Superquantum Correlations, and String Theory
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• Some Mutant Forms of Quantum Mechanics
• Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element
• Interference and Oscillation in Nambu Quantum Mechanics
• Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
• A statistical model for quantum spin and photon number states
• Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
• Is Quantum Gravity a Super-Quantum Theory?