Before Vectors, was it Components, and Quaternions?

  • #1

Main Question or Discussion Point

What did physicists use before the introduction of vectors by Gibbs & Heaviside, was it the exact same as we would use when denoting components with an x or y subscript or something completely crazy?

Also, I've read in quite a few places that quaternions are very useful for things like Special Relativity & in particle physics & I've definitely seen them being used quite a lot in Lie Algebra texts as I've browsed through. How hard are they, i.e. what makes them so crazy & what are the prerequisites?

The only bad thing I know about them is that it took Maxwell 20 Quaternion equations to convey what Hamilton was able to condense into 4, (or 8 in a sense...).
 
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  • #2
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I, too, am interested in knowing how physicist dealt with their concepts before the advent of vectors.
 
  • #3
SteamKing
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Not too well, IMO, which was why vectors were invented in the first place.

Quaternions were originally developed by Hamilton as a means of extending complex numbers into a three-dimensional space from the well-known complex plane.

http://en.wikipedia.org/wiki/Quaternion

Physicists were somewhat underwhelmed by using quaternions, and they fell into disuse for most tasks. More complex algebras than quaternions were needed for things like understanding special relativity. A simplified development of quaternions led to the familiar vector calculus of Gibbs. Vectors work well at describing what happens in two or three dimensions, but they cannot be generalized to higher dimensions.

http://en.wikipedia.org/wiki/Vector_calculus

This is how Maxwell's equations looked in their original form:

http://upload.wikimedia.org/wikiped...mical_Theory_of_the_Electromagnetic_Field.pdf

The modern differential forms of these same equations are much more compact:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html#c3
 

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