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    PAPERS|September 01 2002

    Polar and axial vectors versus quaternions

    Cibelle Celestino Silva;
    Cibelle Celestino Silva
    Group of History and Theory of Science, DRCC, Instituto de Fı́sica “Gleb Wataghin,” P.O. Box 6165, UNICAMP, 13083-970 Campinas, SP, Brazil
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    Roberto de Andrade Martins
    Roberto de Andrade Martins
    Group of History and Theory of Science, DRCC, Instituto de Fı́sica “Gleb Wataghin,” P.O. Box 6165, UNICAMP, 13083-970 Campinas, SP, Brazil
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    Am. J. Phys. 70, 958–963 (2002)
    Article history
    Received:
    April 17 2001
    Accepted:
    March 06 2002
    Citation

    Cibelle Celestino Silva,Roberto de Andrade Martins; Polar and axial vectors versus quaternions.Am. J. Phys. 1 September 2002; 70 (9): 958–963.https://doi.org/10.1119/1.1475326

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      Vectors and quaternions are quite different mathematical quantities because they have different symmetry properties. Gibbs and Heaviside created their vector system starting from the quaternion system invented by Hamilton. They identified a pure quaternion as a vector and introduced some changes in the product of two vectors defined by Hamilton without realizing that the scalar product and vector product cannot be interpreted as the scalar part and vector part of the quaternion product. Toward the end of the 19th century some authors realized that there was an incompatibility between the vector and quaternion formalisms, but the central problem was not altogether clear. This paper will show that the main difficulty arose from Hamilton’s contradictory use ofi,j, andk both as versors and as vectors.

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