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The vector algebra war: A historical perspective | | James M. Chappell
; Azhar Iqbal
; John G. Hartnett
; Derek Abbott
; | | Date: |
29 Aug 2015 | | Abstract: | There are a wide variety of different vector formalisms currently utilized in
science. For example, Gibbs three-vectors, spacetime four-vectors, complex
spinors for quantum mechanics, quaternions used for rigid body rotations and
Clifford multivectors. With such a range of vector formalisms in use, it thus
appears that there is as yet no general agreement on a vector formalism
suitable for the whole of science. This surprising situation exists today,
despite the fact that one of the main goals of nineteenth century science was
to correctly describe vectors and the algebra of three-dimensional space. This
situation has also had the unfortunate consequence of fragmenting knowledge
across many disciplines and requiring a very significant amount of time and
effort in learning the different formalisms. We thus review historically the
development of our various vector systems and conclude that the Clifford
algebra multivector fulfills the goal of correctly describing vectorial
quantities in three dimensions. | | Source: | arXiv, 1509.0501 | | Services: | Forum | Review | PDF | Favorites | |
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